Should Chris Pay off his Mortgage?

Chris @Money$tir asked other financial literacy and financial independence (FI) bloggers, in a post on March 9, 2019, whether he should pre-pay his mortgage or invest the money. He provided his thought process and calculations. In this post, I will review his calculations and then show that his decision will be easier if he narrows his question and analysis. I will also provide my findings and analysis to help inform his decision.

Background

Chris’s post provides all of the background. You might want to read his post quickly to understand his calculations and other considerations before you read the rest of this post.

Briefly, he will have just under $310,000 left on his mortgage on July 1, 2019. His payments are $1,525 and he will have an additional $4,000 a month available to either pre-pay his mortgage or invest.

I followed up with Chris and learned that he expects to take the standard deduction on his tax return, so he will have no tax benefit from his mortgage interest. His marginal tax rate on ordinary income is 22%; on capital gains and dividends, 15%. I also confirmed that Chris does not have any pre-payment penalties associated with his mortgage.

Three Re-Payment Options

Chris suggested three options in his article, two of which involve making pre-payments. The three options are:

1. Make $1,525 a month in mortgage payments until his mortgage is fully re-paid in July 2045, while investing the remaining $4,000 at 8% per year.

2. Take a middle-of-the road option and make mortgage payments of $3,525 each month and invest the remaining $2,000. Under this option, his mortgage will be re-paid in 2027.

3. Pay $5,525 each month – $1,525 in scheduled payments and $4,000 in pre-payments – until his mortgage is fully re-paid in 2024.

Chris calculated his pre-tax savings using an 8% return through July 2045. The values he calculated are:

• Option 1 – $4,145,000
• Option 2 – $3,772,000
• Option 3 – $3,594,000

In his post, Chris indicated he is leaning towards Option 3 – pre-pay his mortgage as quickly as possible.

Chris’s Math

One of Chris’s questions is whether his calculations are correct. I re-created Chris’s calculations. While I did not get his ending balances exactly, my results were within a couple of percentage points, so I suspect we made slightly different assumptions regarding either the timing of the interest charges (beginning or end of month) and/or his exact mortgage balance. I’m quite comfortable that the calculations he performed are what he intended.

I also confirmed that increasing his payments by $2,000 or $4,000 a month shortens the time until his mortgage is fully re-paid as he indicated in his post.

Re-framing the Question

Many of Chris’s considerations relate to additional flexibility he will have after his mortgage is fully re-paid. I believe that Chris has not correctly separated the mortgage re-payment question from his other decisions – renting out his house and buying a new one, not having a mortgage if he decides to downsize, freeing up money for other purchases and so on. That is, as discussed below, he can use his first five years of savings in Options 1 and 2 to make the rest of his mortgage payments. By understanding that, he can independently decide to do with the $5,525 a month after five years doesn’t depend on his choice of payment option.

If Chris changes his calculations consistent with the re-framed question (i.e., looking at only the $5,525 a month for the first five years), he can eliminate all of the noise of these other questions as they will become independent of his mortgage decision. In his calculations, Chris has set aside $5,525 every month until his mortgage would be fully re-paid in 2045 if he made the minimum payments. Instead, I propose that he set aside $5,525 a month only until 2024 (and not after) – that is, only until his mortgage would be fully paid under Option 3. Except in certain situations discussed below, Chris will make his mortgage payments starting in August 2024 from the savings that accumulates from the money he saved up until then and not from his future income or other savings. That stream of payments, if invested in a hypothetical risk-free, tax-free financial instrument at 3.625% would exactly pay off his mortgage regardless of which of his three re-payment options he chooses.

By focusing on this shorter stream of payments until 2024, he can do whatever he wants with the $5,525 a month after his mortgage is paid off under all three re-payment options. As a result, his decision-making process can focus solely on the risks and rewards of his three re-payment options without any consideration of other, unrelated financial decisions.

My re-framed question does not eliminate one of his considerations – his peace-of-mind from not having a mortgage. Chris will need to include this subjective consideration in his decision-making process, along with the considerations regarding risk and rewards presented below.

My Math

There are four changes I made to Chris’s calculations:

1. I assumed that Chris set aside $5,525 a month from July 2019 through August 2024, rather than until 2045. In addition, except as noted below, after July 2024, he will make his remaining mortgage payments from the savings he has accumulated and not from his income. Therefore, starting in August 2024, he can use the $5,525 a month however he wants as I excluded it from my analysis.

2. I introduced the impact of income taxes. Chris will pay taxes on his investment returns which will make the first two options look less attractive than is shown in his analysis.

3. I quantified the risk Chris will assume by investing in the first two re-payment options.

4. I focused on Chris’s financial position not only in 26 years (when his mortgage would be paid off making the minimum payments), but also in 10 years (when he might want to down-size).

Three Investment Strategies

Chris’s first and second options assume he will invest in an S&P 500-like ETF returning 8%. His calculations do not quantify the riskiness of the S&P 500, though he does mention the risk in his subjective considerations. I will provide explicit insights on the risk. In addition, because Chris is concerned with the riskiness of the S&P 500, I also looked at two other options, for a total of three investment strategies:

1. Invest in 100% in stocks, such as an S&P 500 ETF.

2. Invest in 100% bonds, such as a bond fund. I used the Fidelity Investment Grade Bond Index (FBNDX), as a proxy.

3. Invest 50% in each of stocks (an S&P 500 ETF) and bonds (the Fidelity bond index).

Under all three strategies, I assumed the Chris would re-invest all interest, dividends and capital gains, after tax, and would not withdraw it except to make his mortgage payments.

In my analysis, I calculated Chris’s financial position as if stocks and bonds had the monthly returns observed historically for the 10-year periods starting on the first of each month from January, 1980 through October, 2008 (10 years before my time series ended). There are 345 overlapping 10-year periods. For the 26-year time frame, there are only 153 overlapping periods covered by the Fidelity bond index data. I therefore looked at only the S&P 500 investment option when doing the calculations of Chris’s financial position in 2045.

Timeline

The infographic below clarifies the key dates under all three options and provides a teaser of the results.

Option 1

Under Option 1, Chris will make payments of $1,525 a month to his lender from July 2019 to August 2024 from his income. He will also save $4,000 a month over the same time period. This time period is represented in green. From August 2024 until July 2045, he will withdraw $1,525 from the savings he accumulated in the first five years to pay his mortgage. This period of time is shown in orange.

Option 2

Under Option 2, Chris will make payments of $3,525 a month to his lender from July 2019 to August 2024 (the green segment) from his income. He will also save $2,000 a month over the same time period. From August 2024 until December 2027 (the orange segment), he will withdraw $3,525 a month from his accumulated savings to pay his mortgage. He will have fully re-paid his mortgage by December 2027, so any leftover savings will remain invested until July 2045. This time period is represented in yellow.

Option 3

Under Option 3, Chris will make payments of $5,525 a month to his lender from July 2019 to August 2024 (the green segment) at which point his mortgage will be fully re-paid. Because he hasn’t put any money in savings, he will have no savings so nothing will happen related to the money from the green time period during the yellow time period.

Check-In Dates

The infographic also calls out July 2029 and July 2045. These are the two dates that Chris mentions in his post as being possible decision dates. In ten years (July 2029), he might want to sell his house and downsize. In July 2045, his mortgage will be fully paid if he makes his minimum payments and it offers another point at which to consider selling the house.

The infographic shows the balance of his mortgage and the average amount of his after-tax savings if he invests 100% in stocks. As will be discussed below, there is a lot of risk around this average and it is calculated using historical returns, so there is also uncertainty around it.

Summary of Findings

Here are the key findings of my analysis. They will be discussed in detail below.

● Chris’s time horizon is important in making his decision.

o If he plans to keep his house until 2045, the historical data indicate he is better off in three-quarters of the scenarios making his minimum payments and investing in stocks. The average values of his after-tax savings are shown in the infographic above and show that he will have more savings on average with lower monthly mortgage payments.

o If he plans to sell his house or use the money he has saved to fully re-pay his mortgage 10 years from now, the decision is not as clear cut and will need to consider his risk tolerance. Because Chris plans to continue to work for many years, he may be able to tolerate more risk than someone who plans to retire before their mortgage is fully re-paid.

● Chris’s investment mix is important in making his decision.

o If he plans to keep his house until 2045, the historical data indicate that he is better off investing 100% in stocks.

o If he plans to sell his house or use the money he has saved to fully re-pay his mortgage 10 years from now, the mix of investments will depend on his risk tolerance.

● The historical data indicate Chris’s downside risk is not significantly changed by the stock market possibly being near its peak.

Discussion

I will start by providing insights on Chris’s financial position on average across all of the time series of historical investment returns – first for the 10-year period and then for the full 26-year period. I will then discuss the riskiness of the options. The last part of this discussion will focus on how I evaluated his results if the stock market were at a peak.

Average Results – 10 Years

The table below summarizes Chris’s average financial position, based on the historical investment returns, in 10 years on July 1, 2029, the time frame he referenced as possibly wanting to downsize. The invested asset row shows the balance of his investments if he sells all of his positions on that date and pays the related taxes. The “net worth” row shows the average amount Chris will have left if he pays off the balance of his mortgage with his after-tax investments.

Payment Option 3 2 2 2 1 1 1
Mortgage Payment $5,525 $3,525 $3,525 $3,525 $1,525 $1,525 $1,525
Investment Option All 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks
Invested Assets $0 $10,620 $25,515 $34,396 $248,941 $285,615 $324,269
Mortgage Balance 0 0 0 0 221,928 221,928 221,928
“Net Worth” 0 10,620 25,515 34,396 27,033 64,687 102,341

I use “net worth” in quotes because it includes only the assets emanating from the $5,525 per month for the next five years and only his mortgage balance as a liability. In addition, Chris will have his house, all of his other taxable savings, his retirement accounts, and so on and so forth. Because all of these other assets are the same regardless of which option he chooses for his mortgage re-payment, I have excluded them from the comparison.

The positive “net worth” numbers mean Chris will get to keep the entire proceeds of his house if he sells it in 10 years plus the positive “net worth.” If there were negative “net worth” numbers (which there are in the graphs below), Chris would need to use that portion of the proceeds from his house to contribute to the settlement of his remaining mortgage balance.

The farthest left column – paying off his mortgage as quickly as possible – is the option Chris indicated is his initial preference. Under this strategy, he will have saved no invested assets from the $5,525 a month for five years and have no mortgage balance, so would get exactly the proceeds of his house if he were to sell it then. The remaining columns show that, on average using the historical returns, Chris will have more savings than his mortgage balance if he makes his lower mortgage payments and invests the rest of his $5,525 per month than if he pre-pays his mortgage as quickly as possible.

The smaller his mortgage payment, the higher his “net worth” or the more he will have available in excess of his mortgage balance in 10 years. For example, Chris will have a “net worth” of $34,396 at the end of 10 years, on average using historical returns, if he pays $3,525 a month towards his mortgage and invests the rest in 100% stocks as compared to $102,341 if he pays $1,525 a month towards his mortgage and invests the rest in 100% stocks. Because the average historical after-tax returns on his investments are higher than Chris’s pre-tax mortgage interest rate, he will accumulate savings above the balance of his mortgage.

In addition, at the average, Chris is better off if he invests more heavily in stocks. For example, if Chris makes his minimum mortgage payments and sells his house in 10 years, he will have $27,033 in after-tax savings if he invests 100% in bonds as compared to $102,341 in after-tax savings if he invests 100% in stocks.

I also calculated the averages for the 100% stocks investment strategy using the longer time period (back to 1950). While the results are slightly less favorable, they show generally the same results as are shown in the 100% stocks columns in the table above.

Average Results – 26 Years

The table below summarizes Chris’s average financial position on July 1, 2045, based on the historical investment returns. As discussed above, I don’t believe there is enough historical data regarding bond returns to include those investment strategies in this analysis. This table therefore shows results only based on the 100% stocks investment strategy and is based on stock returns going back to 1950.

Mortgage Payment Option 3 2 1
Mortgage Payment $5,525 $3,525 $1,525
Investment Option 100% Stocks 100% Stocks 100% Stocks
Invested Assets $0 $84,534 $373,269
Mortgage Balance 0 0 0
“Net Worth” 0 84,534 373,269

This table shows that the smaller mortgage payments Chris makes, the higher his savings will be 26 years from now on average using the historical returns.

Risky Results – 10 Years

So far, I have focused on Chris’s average returns. I mentioned in my introduction that one of the aspects of his decision that Chris does not quantify is risk. By looking at his “net worth” under 345 different historical scenarios (i.e., the number of complete 10-year time periods in my historical data) regarding bond and stock returns, we can get a sense for the riskiness of Chris’s choices.

Box & Whiskers – 10 Years

The graph below is called a box and whisker plot. My post on risk provides additional information about these graphs. The boxes represent the 25th to 75th percentiles of Chris’s “net worth” at 10 years. That is, I put the 345 “net worth” results in order from smallest to largest. The 25th percentile is the 86 th one on the list; the 75th percentile, the 259th. The whiskers (lines sticking out from the ends of the boxes) represent the 5th percentile to the 95th percentile and correspond to the 17th and 328th in order from smallest to largest.

Taller boxes and wider spreads between the top and bottom of the whiskers represent more risk. The placement of the boxes up and down on the graph show the overall level of the results. That is, boxes that are higher on the graph have higher returns than boxes that are lower.

This graph shows Chris’s “net worth” after 10 years under each of the investment and re-payment strategies.

Chris’s Re-payment Option 3 – pay off his mortgage as fast as possible – is shown on the far left. Because he makes no investments under this option, there is no risk and he always has no savings at the end of 10 years. As either the percentage of investments in stock increases or the amount of savings increases (moving to the right on the graph), both the risk and level increase. That is, with more savings, the boxes are higher on the graph and taller (e.g., compare the $1,525/0% Stocks box with the $3,525/0% Stocks box). The same comparison can be seen as the percentage of stock increases, by looking at the $1,525/0% Stocks relative to the $1,525/50% Stocks and $1,525/100% Stocks.

The tops of the boxes, tops of the whiskers and average values (shown in the table above) are all clearly higher with lower mortgage payments and a higher investment in stocks. The bottoms of the boxes and bottoms of the whiskers are all lower, though, so those options have more risk.

Efficient Frontier – 10 Years

Making a decision from the box & whisker plot can be challenging. If Chris is willing to view his risk-reward trade-off as being between his average “net worth” and his worst “net worth,” he can narrow down his choices. The drawback of this approach is it considers only one point in the range of possible results for measuring risk.

The graph below is a scatter plot showing the different options. My post on financial decision-making provides more insights on this type of graph. The x-axis (the horizontal one) shows Chris’s average “net worth” in 10 years. The y-axis (the vertical one) shows the worst “net worth” result observed based on the historical returns. Points on this chart that are up (worst results aren’t as bad) and to the right (higher average result) are better than points that are lower or to the left.

I have drawn a dashed line, called the efficient frontier, that connects those strategies (dots) that are optimal in that there are no other dots that have a higher average with the same worst result or have a higher worst result with the same average. Using the worst result as the sole measure of risk would allow Chris to narrow his choices down to the four on the efficient frontier, depending on how much risk he is willing to take.

You’ll see that there are two orange dots on this graph. They represent the points using the S&P 500 returns going back to 1950, whereas the blue points all use data starting in 1980. What I found most interesting is that the worst results are the same for both time series, though the average results are somewhat lower using the longer time series. The worst results occurred using the time series starting in February 1999.

Risky Results – 26 Years

The graph below shows the box & whisker plot of Chris’s “net worth” in July 2045, using the historical returns.

The 25th percentile of Chris’s “net worth” under all three options is about $0. As such, in 75% of the historical scenarios, Chris will be somewhat to significantly better off making smaller mortgage payments than making larger payments.

The much clearer results shown in this chart as compared to the one at 10 years results from the benefits of diversification over time. That is, the longer time period over which Chris is invested, the less risk there is in his financial results. Diversification is one way a portfolio can be diversified. Investing in both stocks and bonds is another. My post on how diversification reduces investment risk discusses these concepts in more detail.

The scatter plot below shows that in the worst scenario, Chris ends up losing about $120,000 over 26 years if he is 100% invested in stocks. The trade-off is that in 75% of the historical scenarios, he will have at least some savings and more than $370,000 in savings on average.

Current Market Cycle

Another concern that Chris and others on Twitter expressed is that the stock market has been going up for many years and is at risk of going down significantly in the near future.

Selection of Prior Peaks

To address that concern, I have reviewed the historical stock market returns to find points that would correspond to the market being at a peak. The two graphs below show the cumulative returns on the S&P 500 since 1950. (I had to create two charts so that the ups and downs from older periods could be seen. Even then the first peak on the second chart is a little tough to see even though it includes the largest single monthly decline in the entire time period.)

The eight green circles correspond to important peaks in the market, similar to Chris’s concern about today’s market.

“Net Worth” After Prior Peaks

I looked at Chris’s “net worth” ten years after each of those peaks, as shown in the table below. Recall that the bond index data are available starting only in 1980, so we can’t look at any strategies that include bonds for the earlier peaks.

Mortgage Payment $5,525 $3,525 $3,525 $3,525 $1,525 $1,525 $1,525
Investment Option All 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks
1/1/1962 $0 $4,528 $184
11/1/1965 0 -5,103 -62,533
11/1/1968 0 -36,596 -76,978
1/1/1973 0 -1,543 27,375
12/1/1980 0 44,331 61,920 79,509 99,120 138,282 177,444
8/1/1987 0 27,585 40,490 53,394 57,535 151,014 244,493
3/1/2000 0 -5,747 1,033 2,198 -13,435 -33,178 -52,922
6/1/2007 0 2,848 25,314 47,780 -8,634 62,814 134,263
Average – Last 4 0 17,254 32,189 45,720 33,646 79,733 125,819
Average – All 8 0 18,021 48,916
All Scenarios 0 10,620 25,515 34,396 27,033 64,687 102,341

In some of the time periods, particularly the ones starting on November 1, 1965 and November 1, 1968, Chris would have been better off pre-paying his mortgage as quickly as possible rather than investing. In others though, he would have been much better off making his minimum mortgage payments.

The average result for the most recent 4 “bad” time periods (third-to-bottom row) is slightly better than the average result across all possible time periods (bottom row). If all eight periods are included, Chris is better off making minimum payments, but not by as much as was observed in all scenarios.

Dollar Cost Averaging

In several of the “bad” periods (e.g., the ones starting on 12/1/1980, 8/1/1987 and 6/1/2007), Chris ends up with a very high “net worth” if he invests 100% in stocks. Although Chris buys some stocks at the peak of the market, he will also buy stocks as the prices go down (generally taking a year or two). The graphs above show that the market often re-bounds fairly rapidly after it has fallen. In these situations, Chris will achieve a high return on the stocks bought at or near the bottom of the market, thereby boosting his overall return.

Dollar cost averaging is the process of making regular investments regardless of the market cycle. It is a common investing approach and, although it may not be intentional, it is exactly what you do when you contribute to a 401(k) through payroll deductions. Dollar cost averaging lets you buy stocks at all levels, without timing the market, which can produce better total returns than trying to time the market and make your investment on a single day or just a few days a year. If Chris invests monthly, he is implementing a dollar cost average strategy.

Assumptions

The findings presented here depend on a large number of assumptions.

Investment Returns

I used historical monthly returns on the S&P 500 and the Fidelity Investment Grade Bond Index (FBNCX) downloaded from Yahoo Finance. I assumed that any dividends and distributions, reduced by any related income taxes, were immediately reinvested.

Yahoo Finance provides a Closing Price and an Adjusted Closing Price. I used the percentage changes in the Adjusted Closing Price to calculate the total return for each financial instrument. For the S&P 500, the Closing Prices and Adjusted Closing Prices were identical. For the Bond Index, they were not. I assumed that the difference in the percentage changes between the Adjusted Closing Price and the Closing Price were interest payments.

I assumed that Chris would fund any shortfalls from current income or other after-tax savings and that there would be no borrowing costs or additional taxes.

Income Taxes

I made several key assumptions about income taxes:

● All investments will be held in taxable accounts. Chris is already contributing the maximum amounts to his tax-sheltered retirement plans. In addition, he might encounter penalties if the withdrawals needed to make his mortgage payments did not meet the guidelines of the specific tax-sheltered account to which he made contributions. See my post on retirement plans for more details on such withdrawals.

● The interest payments from the Bond Index will be taxed at Chris’s marginal rate on ordinary income of 22%.

● Chris will pay tax at his marginal capital tax rate of 15% capital gains and losses when he sells his investments, either to make mortgage payments or withdraws the money at the end of 10 years or 26 years.

● Chris’s marginal tax rates won’t change over the time horizon of the analysis.

● There were no tax implications of borrowing.

Fine Print

Having been a consultant for over 20 years, I feel it necessary to touch on the many limitations on the findings of the analysis.

Variability

Most importantly, actual results will vary from those presented herein. I have used historical data as a proxy for what might happen in the future. However, it is unlikely that future results will exactly replicate any results previously seen. If any of the assumptions discussed above or otherwise made do not turn out to be appropriate to Chris’s situation, the findings may similarly be relevant to his decision-making process.

Economic Environment Differences

An important component of these differences is the interest rate environment. As shown in the chart below, interest rates (as measured by the 10-year Treasury in this chart) declined or were flat during almost the entire period from 1980 to the present – the time period for which data were available for the Bond Index.

It is more likely than not that interest rates will increase during the time horizon of this analysis. When interest rates increase, bond prices tend to decrease. If that were to happen, the findings based on historical bond returns likely overstate the results that might be observed in the future.

Data Used in My Analysis

I downloaded S&P 500 and the Fidelity bond index monthly returns from Yahoo Finance. Data were available for the S&P 500 going back to 1950, but only to 1980 for the Fidelity bond index. To the extent that these data are incorrect, the findings herein might also be incorrect (i.e., garbage in, garbage out).

Intended Use

The purpose of this analysis was to provide insights to help Chris make a more informed decision. It should not be interpreted as making a recommendation for any financial decision. The only information I have about Chris’s financial situation is what is outlined above and in his post. As such, there may be other aspects of his financial situation that cause this analysis to not apply correctly to his specific situation.

Lastly, the analysis may not be applicable to anyone else’s specific situation.

Investing in Bonds

Bonds are a common investment for people targeting a low-risk investment portfolio. One of the pieces of advice I gave my kids (see others in this post) is to never buy anything you don’t understand. In this post, I’ll tell you what you need to know so you can decide whether investing in bonds is appropriate for you.

What is a Bond?

A bond is a loan you are giving the issuer.  The parties to the transaction are exactly opposite of you taking out a loan. You’ll see the parallels if you compare the information in this post with that provided in my post on loans!  When you buy a bond, you are the lender.  The issuer of the bond is the borrower.

How Do Bonds Work?

The issuer of a bond sells the bonds to investors (i.e., lenders).  Every bond has a face amount.  Common face amounts are $100 and $1,000.  The face value of the bond is called the par value.  It is equivalent to the principal on a loan.  When the issuer first sells the bonds, it receives the face amount for each bond.

The re-payment plan for a bond is different than for a loan.  When you take out a loan, you make payments that include interest and a portion of your principal.  Over the life of your loan, all of your payments are the same (unless the interest rate is adjustable).   By comparison, a bond issuer’s payments include only the interest until the maturity date when it pays the final interest payment and returns the principal in full.

Before selling bonds, the issuer sets the coupon rate and the maturity date of the bond.  The coupon rate is equivalent to the interest rate on a loan.  The maturity date is the date on which the issuer will pay the par value to the owner of the bond.  It can vary from something very short, like a year, all the way to 30 years.  In Europe, there are even bonds with maturity dates in 99 years.  In the meantime, the issuer will pay coupons (interest) equal to the product of the coupon rate and the par value, divided by the number of coupons issued per year. Coupons are often issued quarterly. For example, if you owned a bond with a $1,000 par value, a 4% coupon rate and quarterly payments, you would get 1% of $1,000 or $10 a quarter in addition to the return of the par value on the maturity date.

What Price Will I Pay

You can buy bonds when they are first issued from the issuer or at a later date from other people who already own them.  You can also sell bonds you own if you want the return of your initial investment before the bond matures.  If you buy and sell bonds, the sale prices will be the market price of the bonds.

Present Value

Before explaining how the market value is calculated, I need to introduce the concept of a present value. A present value is the value today of a stated amount of money you receive in the future.  It is calculated by dividing the stated amount of money by 1 + the interest rate adjusted for the length of time between the date the calculation is done and the date the payment will be received.  Specifically, the present value at an interest rate of i of $X received in t years is:

The denominator of (1+i) is raised to the power of t to adjust for the time element.

Market Price = Present Value of Cash Flows

The market price of a bond is the present value of the future coupon payments and principal repayment at the interest rate at the time of the calculation is performed.

Interest Rate = Coupon Rate When Issued

The interest rate when the bond is issued is the coupon rate!  Because the issuer sells the bonds at par value (the face amount of the bond), the par value has to equal the market value.  For the math to work, the coupon rate must equal the interest rate at the time the bond is initially sold.

Interest Rates after Issuance

If interest rates change (more on that in a minute) after a bond is issued, the market value will change and become different from the par value because the “i” in the formula above will change.  When the interest rate increases, the price of the bonds goes down and vice versa.

Also, as the bond gets closer to its maturity date, the exponent “t” in the formula will get smaller so it will have less impact on the present value, making the present value bigger. As such, all other things being equal, a bond that has a shorter time to maturity will have a higher market price than a bond that has a longer time to maturity.  Remember that the par value is all paid at the end, so the market price formula is highly influenced by the present value of the repayment of the par value.

How is the Interest Rate Determined

There are two factors specific to an individual bond that influence the interest rate that underlies its price – the bond’s time to maturity and the issuer’s credit rating. In addition, there are broad market factors that influence the interest rates for all bonds.  These factors influence the overall level of interest rates as well as the shape of the yield curve.

What is a Yield Curve

The interest rate on a bond depends on the time until it matures.  If I look at the interest rates on US government bonds today (March 7, 2019) at this site, I see the following:

The line on this graph is called a yield curve.  It represents the pattern of yields by maturity.  In this case, there is some variation in yields up to 5 years and then the line goes up.

A “normal” yield curve would go up continuously all the way from the left to the right of the graph.  Up to five years, the chart above would be considered essentially “flat” and, above five years, would be considered normal.  If the entire yield curve went down, similar to what we see in the very short segment from one year to two years in this graph, it would be considered inverted.

Time to Maturity

The yield curve along with the maturity date of a bond influencethe interest rate and therefore its market price.  Looking at US Government bonds, the interest rates for bonds with maturities between 0 and 7 years are all around 2.5%.

The price of a 30-year bond will reflect interest rate of about 3%.  If the yield curve didn’t change at all, the same 30-year bond would be priced using a 2.5% interest rate in 23 years (when it has 7 years until maturity).  With the lower interest rate, the market value of the bond will increase (in addition to the increase in market value because the maturity date is closer).

Credit Rating

The other important factor that affects the price of a bond is its credit rating.  Credit ratings work in the same manner as your credit score does.  If you have a low credit score (see my post on credit scores for more information), you pay a higher interest rate when you take out a loan.  The same thing happens to a bond issuer – it pays a higher interest rate if it has a low credit rating.

Instead of having a numeric credit score, bonds are assigned letters as credit ratings.  There are several companies that rate bonds, with Standard and Poors (S&P), Moodys and Fitch being the biggest three.    When you buy a bond (more on that later), the credit rating for the bond will be quite clearly stated.

The graph below summarizes information I found on the website of the St. Louis Federal Reserve Bank (FRED).

It shows the interest rates on corporate bonds with different credit ratings on February 28, 2019. As you can see, there is very little difference in the interest rates of bonds rated AAA, AA and A, with a slightly higher interest rate for bonds rated BBB.  Bonds with BBB ratings and higher are considered investment grade.

Bonds with ratings lower than BBB are called less-than-investment grade, high yield or junk. You can see that the interest rates on bonds with less-than-investment grade ratings increase very rapidly, with C-rated bonds having interest rates close to 12%.

What are the Risks

There are two risks – default and market – that are inherent in bonds themselves and a third – inflation – related to using them as an investment.

Defaults

Default risk is the chance that the issuer will default or not make all of its coupon payments or not return the full par value when it is due.  When an issuer defaults on a bond, it may pay the bond owner a portion of what is owed or it could pay nothing.  The percentage of the amount owed that is not repaid is called the “loss given default.”  If the loss given default is 100%, you lose the full amount of your investment in the bond, other than coupon payments you received before the default.  At the other extreme, if the loss given default is only 10%, you would receive 90% of what is owed to you.

Issuers of bonds with low credit ratings are considered riskier, meaning they are expected to have a higher chance that they will default than issuers with high credit ratings. I always find this chart from S&P helpful in understanding default risk.

It shows two things – the probability of an issuer defaulting increases as the credit rating gets lower (e.g., the B line is higher than the A line) and the probability of default increases the longer the time until maturity.

These increases in the probability of default correspond to increases in risk.  Recall from the previous section that interest rates increase as there is a longer time to maturity when the yield curve is normal and as the credit rating gets lower. The higher interest rates are compensation to the owner of the bond for the higher risk of default.

When you read the previous section and saw you could earn between just under 12% on a C-rated bond, you might have gotten interested.  However, it has almost a 50% chance of defaulting in 7 years!  The trade-off is that you’d have to be willing to take the risk that the issuer would have a 26% chance of defaulting in the first year and a 50% chance by the seventh year!  It makes the 12% coupon rate look much less attractive.

Changes in Market Value

As I mentioned above, you can buy and sell bonds in the open market as an alternative to holding them to maturity.  In either case, you will receive the coupon payments while you own the bond, as long as the issuer hasn’t defaulted on them.  If you buy a bond with the intention of selling it before it matures, you have the risk that the market value will decrease between the time you purchase it and the time you sell it.  Decreases in market values correspond to increases in interest rates. These increases can emanate from changes in the overall market for bonds or because the credit rating of the bond has deteriorated.

If you hold a bond to maturity and it doesn’t default, the amount you will get when it matures is always the principal.  So, you can eliminate market risk if you hold a bond to maturity.

Interest Doesn’t Keep Up with Inflation

The third risk – inflation risk – is the risk that inflation rates will be higher than the total return on the bond.  Let’s say you buy a bond with a $100 par value for $90, it matures in 5 years and the coupons are paid at 2%.  Using the formulas above, I can determine that your total return (the 2% coupons plus the appreciation on the bond from $90 to $100 over 5 years) is 4.3%.  You might have purchased this bond as part of your savings for a large purchase.  If inflation caused the price of your large purchase to go up at 5% per year, you wouldn’t have enough money saved because your bond returned only 4.3%.  Inflation risk exists for almost every type of invested asset you purchase if your purpose for investing is to accumulate enough money for a future purchase.

How are They Taxed

There are two components to the return you earn on a bond – the coupons and appreciation (the difference between what you paid for it and what you get when you sell it or it matures).

Tax on Coupons and Capital Gains

The coupons are considered as interest in the US tax calculation.  Interest is included with your wages and many other sources of income in determining your taxes which have tax rates currently ranging from 10% to 37% depending on your income.

The difference between your purchase price and your sale price or the par value upon maturity is considered a capital gain.  In the US, capital gains are taxed in a different manner from other income, with a lower rate applying for most people (0%, 15% or 20% depending on your total income and amount of capital gains).

States that have income taxes usually follow the same treatment with lower tax rates than the Federal government, but not always.

Some Bonds are Taxed Differently

Within this framework, though, not all bonds are treated the same.  The description above applies to corporate bonds.  Bonds issued by the US government are taxed by the Federal government but the returns are tax-free in most states.

Some bonds are issued by a state, municipality or related entity.  The interest on these bonds is not taxed by the Federal government and is usually not taxed if you pay taxes in the same state that the issuer is located.  Capital gains on these bonds are taxed in the same manner as corporate bonds.

Included in this category of bonds are revenue bonds. Revenue bonds are issued by the same types of entities, but are for a specific project.  They have higher credit risk than a bond issued by a state or municipality because they are backed by only the revenues from the project and not the issuer itself.

The manner in which a bond is taxed is important to your buying decision as it affects how much money you will keep for yourself after buying the bond.  You should consult your broker or your tax advisor if you have any questions specific to your situation.

Do They Have Other Features

If you decide to buy bonds, there are some features you’ll want to understand or, at a minimum, avoid. Some of the types of bonds with these distinctive features are:

Treasury Inflation-Protected Securities or TIPS

TIPS are similar to US Government bonds except that the par value isn’t constant.  The impact of inflation as measured by the Consumer Price Index is determined between the issue date and the maturity date.  If inflation over the life of the bond has been positive, the owner of the bond will be paid the original par value adjusted for the impact of inflation.  If it has been negative, the owner receives the original par value.  In this way, the owner’s inflation risk is reduced.  It is completely eliminated if the owner purchased the bond to buy something whose value increases exactly with the Consumer Price Index.

Savings or EE Bonds

Savings bonds are a form of US Government bond.  You can buy them with par values of as little as $25.  They can be purchased for terms up to 30 years.  Currently, savings bonds pay interest a 0.1% a year.  The interest is compounded semi-annually and paid to the owner with the par value when the bond matures.   With the currently very low interest rates, these bonds are very unattractive.

Zero-Coupon Bonds

The issuer of a zero-coupon bond does not make interest payments.  Rather, when it issues the bond, the price is less than the par value. In fact, the price is the present value of just the principal payment.  So, instead of paying the par value for a newly issued bond and getting coupon payments, the buyer pays a much lower price and gets the par value when the bond matures.

I don’t know all the details, but believe that, in the US, the owner needs to pay taxes on the appreciation in the value of the bond every year as if it were interest and not as a capital gain on sale.  As such, it is better to own a zero-coupon bond in a tax-deferred or tax-free account, such as an IRA, a 401(k) or health savings account.  I’ve owned one zero-coupon bond – it was my first investment in an IRA.  If you want to buy a zero-coupon bond, I suggest talking to your broker or tax advisor to make sure you understand the tax ramifications.

Callable Bonds

A call is a financial instrument that gives one party the option to do something.  In this case, the issuer of the bond is given the option to give you the par value earlier than the maturity date.  When the issuer decides to exercise this option, the bond is said to be “called.”  The bond contract includes information about when the bond is callable and under what terms. If you purchase a callable bond, you’ll want to understand those terms.

Issuers are more likely to call a bond when interest rates have decreased. When interest rates go down, the issuer can sell new bonds at the lower interest rate and use the proceeds to re-pay the callable bond, thereby lowering its cost of debt.

In a low-interest rate environment, such as exists today, a callable bond isn’t much different from a non-callable bond as it isn’t likely to get called.  If interest rates were higher, a non-callable bond with the same or similar credit quality and coupon rate is a better choice than a callable bond. If the callable bond gets called, you will have cash that you now need to re-invest at a time when interest rates are lower than when you initially bought the bond.  (Remember that the reason that callable bonds get called is that interest rates have gone down.)

Convertible Bonds

Convertible bonds allow the issuer to convert the bond to some form of stock.  As will be explained below, stocks are riskier investments than bonds.  If you buy a convertible bond, you’ll want to understand when and how the issuer can convert the bond and consider whether you are willing to own stock in the company instead of a bond.

How Does Investing in Bonds Differ from Other Investments

There are two other types of financial instruments that people consider buying as common alternatives to bonds – bond mutual funds and stocks.  I’ll briefly explain the differences between owning a bond and each of these alternatives.

Bond Funds

There are two significant differences between owning a bond fund and own a bond.

A Bond Fund with the Same Quality Bonds Has Less Default Risk

If you own a bond fund, you are usually buying an ownership share in a pool containing a relatively large number of bonds.  Owning more bonds increases your diversification (see this post for more on that topic).  With bonds, the biggest benefit from diversification is that it reduces the impact of a single issuer defaulting on its payments.  If you own one bond, the issuer defaults and the loss given default is 50%, you’ve lost 50% of your investment.  If you own 100 bonds and one of them defaults with a 50% loss given default, you lose 0.5% of your investment.

A Bond Fund Has Higher Market Risk than Owning a Bond to Maturity

Recall that you eliminate market risk if you hold a bond until it matures.  Almost all bond funds buy and sell bonds on a regular basis, so the value of the bond fund is always the market price of the bonds.  Because the market price of bonds can fluctuate, owners of bond funds are subject to market risk.

Stocks

When you buy stock in a company, you have an ownership interest in the company.  When you own a bond, you are a lender but have no ownership rights. To put these differences in perspective, owning a stock is like owning a share in vacation home along with other members of your extended family.  By comparison, owning a bond is like being the bank that holds the mortgage on that vacation home.

Stocks Have More Market Risk

The market risk for stocks is much greater than for bonds.  Ignoring defaults for the moment, the issuer has promised to re-pay you the par value of the bond plus the coupons, both of which are known and fixed amounts.  With a stock, you are essentially buying a share of the future profits, whose amounts are very uncertain.

Stocks Have More Default Risk

The default risk for stocks is also greater than for bonds.  When a company gets in financial difficulties, there is a fixed order in which people are paid what they are owed.  Employees and vendors get highest priority, so get paid first.  If there is money left over after paying all of the employees and vendors, then bondholders are re-paid.  After all bondholders have been re-paid, any remaining funds are distributed among stockholders.  Because stockholders take lower priority than bondholders, they are more likely to lose some or all of their investment if the company experiences severe financial difficulties or goes bankrupt.

Companies often issue bonds on a somewhat regular basis.  When a bond is issued, it is assigned a certain seniority.  This feature refers to the order in which the company will re-pay the bonds if it encounters financial difficulties.  If you decide to invest in bonds of individual companies, especially less-than-investment grades bonds, you’ll want to understand the seniority of the particular bond you are buying because it will affect the level of default risk.  Lower seniority bonds have lower credit ratings, so the credit rating will give you some insight regarding the seniority.

When is Investing in Bonds Right for Me

There isn’t a right or a wrong time to buy a bond, just as is the case with any other financial instrument.  The most important thing about buying a bond is making sure you understand exactly what you are buying, how it fits in your investment strategy and its risks.

Low-Risk Investment Portfolio

If you are interested in a low risk investment portfolio, US Government and high-quality corporate bonds might be a good investment for you.  As you think about this type of purchase, you’ll also want to think about the following considerations.

How Long until You Need the Money

If you are saving for a specific purchase, you could consider buying small positions in bonds of several different companies or US government bonds with maturities corresponding to when you need the money.  If you’ll need the money in less than a year or two, you might be better off buying a certificate of deposit or putting the money in a money market or high yield savings account.  If it is a long time until you’ll need the money and you think interest rates might go up, you’ll want to consider whether you can buy something with a maturity sooner than your target date without sacrificing too much yield so you can buy another bond in the future at a higher interest rate.

How Much Default Risk are You Willing to Take

If you aren’t willing to take any default risk, you’ll want to invest in US government bonds.  If you are willing to take a little default risk, you can buy high-quality (e.g., AAA or AA) corporate bonds.  You’ll want to buy small positions is a fairly large number of companies, though, to make sure you are diversified.

How Much Market Risk are You Willing to Take

If you are willing to take some market risk, you can more easily attain a diversified portfolio by investing in a bond mutual fund.  As mentioned above, you’ll want to consider whether you think interest rates will go up or down during your investment horizon.  If you think that are going to go up, there is a higher risk of market values going down than if you think they will be flat.  In this situation, a bond fund becomes somewhat riskier than buying bonds to hold them to maturity.  If you think interest rates are going to go down, there is more possible appreciation than if you think they will be flat.

High-Risk Investment Portfolio

If you want to make higher return and are willing to take more default risk, you can consider buying bonds of lower quality.  As shown in the chart above, non-investment grade bonds pay coupons at very high interest rates.  However, you need to recognize that you are taking on significantly more default risk. One approach for dabbling in high-yield bonds is to invest in a mutual fund that specializes in those securities. In that way, you are relying on the fund manager to decide which high-yield bonds have less default risk. You’ll also get much more diversification than you can get on your own unless you have a lot of time and money to invest in the bonds of a large number of companies.

Where Do I Buy Bonds and Bond Funds

You can buy individual bonds and bond mutual funds at any brokerage firm.  Many banks, particularly large ones, have brokerage divisions, so you can often buy bonds at a bank.  This article by Invested Wallet provides details on how to open an account at a brokerage firm.

All US Government bonds, including Savings Bonds and TIPS can be purchased at Treasury Direct, a service of the US Treasury department.  You’ll need to enter your or, if the bond is a gift, the recipient’s social security number and both you and, if applicable, the recipient need to have accounts with Treasury Direct.  US Savings Bonds can be bought only through Treasury Direct.  You can buy all other types of government bonds at any brokerage firm, as well.

Diversification 2 – Using Diversification to Reduce your Investment Risk

Diversification is an important tool that many investors used to reduce risk. Last week, I explained diversification and how it is related to correlation.   In this post, I’ll illustrate different ways investment portfolios can be diversified and provide illustrations of the benefits.

Key Take-Aways

Here are some key take-aways about diversification.

  • Diversification reduces risk, but does not change the average return of a portfolio. The average return will always be the weighted average of the returns on the financial instruments in the portfolio, where the weights are the relative amounts of each instrument owned.
  • The smaller the correlation among financial instruments (all the way down to -100%), the greater the benefit of diversification. Check out last week’s post for more about this point.
  • Diversification can be accomplished by investing in more than one asset class, more than one company within an asset class or for long periods of time. One of the easiest ways to become diversified across companies is to purchase a mutual fund or exchange traded fund.  Funds that focus on one industry will be less diversified than funds that includes companies from more than one industry.
  • Diversification reduces risk, but doesn’t prevent losses. If all of the financial instruments in a portfolio go down in value, the total portfolio value will decrease.  Also, if one financial instrument loses a lot of value, the loss may more than offset any gains in other instruments in the portfolio.
  • A diversification strategy can be very risky if you purchase something without the necessary expertise to select it or without understanding all of the costs of ownership.

I’ll explain these points in more detail in the rest of the post.

Diversification and Returns

The purpose of diversification is to reduce riskIt has no impact on return.  The total return of any combination of financial instruments will always be the weighted average of the returns on the individual financial instruments, where the weights are the amounts of each instrument you own.  For example, if you own $3,000 of a financial instrument with a return of 5% and $7,000 of a different financial instrument with a return of 15%, your total return will be 12% (={$3,000 x 5% + $7,000 x 15%}/{$3,000+$7,000} = {$150 + $1,050}/$10,000 = $1,200/$10,000).  Similarly, two instruments that both return 10% will have a combined return of 10% regardless of how correlated they are, even -100% correlation.

Diversification among Asset Classes

When investing, many people diversify their portfolios by investing in different asset classes. The most common of these approaches is to allocate part of their portfolio to stocks or equity mutual funds and part to bonds or bond mutual funds.

Correlation between Stocks and Bonds

Two very common asset classes for personal investment are bonds and stocks. Click here to learn more about bonds, including a comparison between stocks and bonds.

The Theory

The prices of stocks and bonds sometimes move in the same direction and sometimes move in opposite directions.  In good economies, companies make a lot of money and interest rates are often low.  When companies make money, their stock prices tend to increase.  When interest rates are low, bond prices are high.[1]  So, in good economies, we often see stock and bond prices move in the same direction.

However, from 1977 through 1981, bond prices went down while stocks went up.  At the time, the economy was coming out of a recession (which means stock prices started out low and then rose), but inflation increased. When inflation increases, interest rates tend to also increase and bond prices go down. [2]

Correlation of S&P 500 and Interest Rates

Over the past 40 years, interest rates have generally decreased (meaning bond prices went up) and stock markets increased in more years than not, as shown in the graph below.

The blue line shows the amount of money you would have each year if you invested $100 in the S&P 500 in 1980.  The green line shows the interest rate on the 10-year US treasury note, with the scale being on the right side of the graph.  Because bond prices go up when interest rates go down, we anticipate that there will be positive correlation between stock and bond prices over this period. If we looked at a longer time period, the correlation would still be positive, but not quite as high because, as mentioned above, there were periods when bond prices went down and stock prices increased.

Historical Correlation of Stocks and Bonds

I will use annual returns on the S&P 500 and the Fidelity Investment Grade Bond Fund to illustrate the correlation between stocks and bonds.  The graph below is a scatter plot of the annual returns on these two financial instruments from 1980 through 2018.  The returns on the bond fund are shown on the x axis; the returns on the S&P 500, the y axis.  Over this time period, the correlation between the returns on these two financial instruments is 43%.  This correlation is close to the +50% correlation illustrated in one of the scatter plots in last week’s post.  Not surprisingly, this graph looks somewhat similar to the +50% correlation graph in that post.

Diversification Benefit from Stocks and Bonds

Recall that diversification is the reduction of risk, in this case, by owning both stocks and bonds.  The table below sets the baseline from which I will measure the diversification benefit.  It summarizes the average returns and standard deviations of the annual returns on the S&P 500 (a measure of stock returns) and a bond fund (an approximation of bond returns) from 1980 to 2018.  The bond fund has a lower return and less volatility, as shown by the lower average and standard deviation, than the S&P 500.

Bond Fund S&P 500
Average 0.6% 0.8%
Standard Deviation 1.6% 4.3%

 

The graph below is a box & whisker plot showing the volatility of each of these financial instruments separately (the boxes on the far left and far right) and portfolios containing different combinations of them.  (See my post on risk for an explanation of how to read this chart.)

In this graph, the boxes represent the 25th to the 75th percentiles.  The whiskers correspond to the 5th to 95th percentiles.  As the portfolios have increasing amounts of stocks, the total return and volatility increase.

These results can also be shown on a scatter plot, as shown in the graph below.  In this case, the x or horizontal axis shows the average return for each portfolio.  The y or vertical axis shows the percentage of the time that the return was negative. (See my post on making financial decisions for an explanation of optimal choices.)

There are three pairs of portfolios that have the same percentage of years with a negative return, but the one with more stocks in each pair has a higher return.  For example, about 24% of the time the portfolios with 30% and 50% invested in bonds had negative returns.  The 30% bond portfolio returned 8.9% on average, whereas the 50% bond portfolio returned 8.5% on average.   Therefore, the portfolio with 30% bonds is preferred over the one with 50% bonds using these metrics because it has the same probability of a negative return but a higher average return.

The choice of mix between stocks and bonds depends on how much return you need to earn to meet your financial goals and how much volatility you are willing to tolerate.  A goal of maximizing return without regard to risk is consistent with one of the portfolios with no bonds or only a very small percentage of them.  At the other extreme, a portfolio with a high percentage (possibly as much as 100%) of bonds is consistent with a goal of minimizing the chance of losing money in any one year.  The options in the middle are consistent with objectives that combine attaining a higher return and reducing risk.

Other Asset Classes

There are many other asset classes that can be used for diversification.  Some people prefer tangible assets, such as gold, real estate, mineral rights (including oil and gas) or fine art, while others use a wider variety of financial instruments, such as options or futures.  When considering tangible assets, it is important to consider not only the possible appreciation in value but also the costs of owning them which can significantly reduce your total return.  Examples of costs of ownership include storage for gold and maintenance, insurance and property taxes for real estate.  All of the alternate investments I’ve mentioned, other than gold, also require expertise to increase the likelihood of getting appreciation from your investment.  Not everyone can identify the next Picasso!

Diversification across Companies within an Asset Class

One of the most common applications of diversification is to invest in more than one company’s stock. It is even better if the companies are spread across different industries.  The greatest benefit from diversification is gained by investing in companies with low or negative correlation.  Common factors often drive the stock price changes for companies within a single industry, so they tend to show fairly high positive correlation.

Diversification across industries is so important that Jim Cramer has a segment on his show, Mad Money, called “Am I Diversified?”  In it, callers tell him the five companies in which they own the most stock and he tells them whether they are diversified based on the industries in which the companies fall.

To illustrate the benefits of diversification across companies, I have chosen five companies that are part of the Dow Jones Industrial Average (an index commonly used to measure stock market performance composed of 30 very large companies). These companies and their industries are:

American Express (AXP) Financial Services
Apple (AAPL) Technology
Boeing (BA) Industrial
Disney (DIS) Consumer Discretionary
Home Depot (HD) Consumer Staples

 

The graph below shows the correlations in the annual prices changes across these companies.

The highest correlations are between American Express and each of Boeing and Disney (both between 50% and 55%).  The lowest correlation is between Apple and Boeing (about 10%).

The graph below shows a box & whisker plot of the annual returns of these companies’ stocks.

All of the companies have about a 25% chance (the bottom of the box) of having a negative return in one year.  That is, if you owned any one of these stocks for one calendar year between 1983 and 2018, you had a 25% chance that you would have lost money on your investment.

The graph below shows a box & whisker chart showing how your volatility and risk would have been reduced if you had owned just Apple and then added equal amounts of the other stocks successively until, in the far-right box, you owned all five stocks.

The distance between the tops and bottoms of the whiskers get smaller as each stock is added to the mix. If you had owned equal amounts of all five stocks for any one calendar year in this time period, you would have lost money in 19% of the years instead of 25%.  The 25th percentile (bottom of the box) increases from between -5% and 0% for each stock individually to +14% if you owned all five stocks.  That is, 75% of the time, your return would have been greater than +14% if you had owned all 5 stocks.

As always, I remind you that past returns are not necessarily indicative of future returns. I used these five companies’ stocks for illustration and do not intend to imply that I recommend buying them (or not).

Diversification Doesn’t Prevent Losses

The above illustration makes investing look great!  Wouldn’t it be nice if 75% of the time you could earn a return of at least 14% just by purchasing five stocks in different industries?  That result was lucky on my part.  I looked at the list of companies in the Dow Jones Industrial Average and picked the first five in alphabetical order that I thought were well known and in different industries.  It turns out that, over the time period from 1983 through 2018, all of those stocks did very well.  Their average annual returns ranged from 19% (Disney) to 40% (Apple).  The Dow Jones Industrial Average, by comparison, had an average return of 10%.  That means that most of the other stocks in the Average had a much lower return.

Being diversified won’t prevent losses, but it reduces them when one company experiences significant financial trouble or goes bankrupt.  Here’s a current example.  Pacific Gas and Electric (PG&E) is a California utility that conservative investors have bought for many, many years.  I’ve added it to the box & whisker plot of the companies above in the graph below.

PG&E’s average return (10%) is lower than the other five stocks and about equal to the Dow Jones Industrial Average.  Its volatility is similar to Boeing and Disney as shown by the height of its box and spread of it whiskers being similar to those of the other two stocks.

However, on the day I am writing this post, PG&E declared bankruptcy.  PG&E has been accused of starting a number of large wildfires in California as the result of allegedly poor maintenance of its power lines and insufficient trimming of trees near them.  Here is a plot of its daily stock price over the past 12 months.

In the year ending January 26, 2019, PG&E’s stock price decreased by 72%.  From its high in early November 2018 to its low in January 2019, it dropped by 87%.

Although diversification can’t completely protect you from such large losses, it can reduce their impact especially if you are invested in companies in different industries.   If the only company in which you owned stock was PG&E, you would have lost 72% of your savings in one year.  If, on the other hand, you had owned an equal amount of a  second stock that performed the same as the Dow Jones Industrial Average over the same time period (-6%), you would have lost 39%.  The graph below shows how much you would have lost for different numbers of other companies in your portfolio.

This graph shows how quickly the adverse impact of one stock can be offset by including other companies in a portfolio.  In a portfolio of five stocks (PG&E and four others that performed the same as the Dow), the 72% loss is reduced to about a 20% loss.  With 20 stocks, the loss is reduced to 10% (not much worse than the -6% for the Dow Jones Industrial Average).

Diversification Over Time

Another way to benefit from diversification is to own financial instruments for a long time. In all of the examples above, I illustrated the risk of holding financial instruments for one year at a time. Many financial instruments have ups and downs, but tend to generally follow an upward trend.  The volatility and risk of the average annual return of these instruments will decrease the longer they are held.

For illustration of the diversification benefit of time, I have used returns on the S&P 500. The graph below shows the volatility of the average annual return on the S&P 500 for various time periods ranging from one to twenty years.

To create the “20 Years” box and whiskers in this graph, I started by identifying all 20-year periods starting from 1950 through the one starting in 1997.  I calculated the average annual return for each 20-year period.  I then determined the percentiles needed to create this graph.  The values for the shorter time periods were calculated in the same manner.

The average return over all years is about 8.8%.  Because we are using data from 1950 to 2018 for all of these calculations, the average doesn’t change.

The benefits of long-term investing are clear from this graph.  There were no 20-year periods that had a negative return, whereas the one-year return was negative 25% of the time.

My post about whether Chris should pay off his mortgage provides a bit more complicated application of the same concepts. In that case, Chris puts money into the account for five years and then withdraws it for either the next five years or the next 21 years. The longer he invests, the more likely he is to be better off investing instead of paying off his mortgage.

As a reminder, it is important to remember that this concept applies well to financial measures such as mutual funds, exchange-traded funds and indexes.  It also applies to the financial instruments of many companies, but not all.  If a company starts a downward trend, especially if it is on the way to bankruptcy, it will show a negative return no matter how long you own it.  If you choose to own stocks of individual companies, you will want to monitor their underlying financial performance (a topic for a future post) and news about them to minimize the chance that you continue to own them through a permanent downward trend.


[1]The price of a bond is the present value of the future interest and principal payments using the interest rate on the date the calculation is performed.  That is, each payment is divided by (1+today’s interest rate)(time until payment is made). Because the denominator gets bigger as the interest rate goes up, the present value of each payment goes down.    I’ll talk more about this in a future post on bonds.

[2]An explanation of the link between inflation and interest rates is quite complicated.  I’ll write about it at some point in the future.  For now, I’ll just observe that they tend to increase at the same time.

Diversification Part 1 – What is Diversification and How Does it Work?

One of the key concepts used by many successful investors is diversification.  In this post, I’ll define diversification and explain how it works conceptually.  Next week I’ll explain different ways you can diversify your investments and provide illustrations of its benefits.

What is Diversification?

Diversification is the reduction of risk (defined in my post a couple of weeks ago) through investing in a larger number of financial instruments.  It is based on the concept of the Law of Large Numbers in statistics. That “Law” says that the more times you observe the outcome of a random process, the closer the results are likely to exhibit their true properties.  For example, if you flip a fair coin twice, there are four sets of possible results:

 

First flip Second flip
Heads Heads
Heads Tails
Tails Heads
Tails Tails

 

The true probability of getting heads is 50%.  In two rows (i.e., two possible results), there is one heads and one tails.  These two results correspond to the true probability of a 50% chance of getting heads.  The other two possible results show that heads appears either 0% or 100% of the time.  If you repeatedly flip the coin 100 times, you will see heads between 40% and 60% of the time in 96% of the sets of 100 flips.  Increasing the number of flips to 1,000 times per set, you will see heads between 46.8% and 53.2% of the time in 96% of the sets.  Because the range from 40% to 60% with 100 flips is wider than the range of 46.8% to 53.2% with 1,000 flips, you can see that the range around the 50% true probability gets smaller as the number of flips increases.  This narrowing of the range is the result of the Law of Large Numbers.

Following this example, the observed result from only one flip of the coin would not be diversified. That is, our estimate of the possible results from a coin flip would be dependent on only one observation – equivalent to having all of our eggs in one basket.  By flipping the coin many times, we are adding diversification to our observations and narrowing the difference between the observed percentage of times we see heads as compared to the true probability (50%).   Next week, I’ll apply this concept to investing where, instead of narrowing the range around the true probability, we will narrow the volatility of our portfolio by investing in more than one financial instrument.

What is Correlation?

As discussed below, the diversification benefit depends on how much correlation there is between the random variables (or financial instruments). Before I get to that, I’ll give you an introduction to correlation.

Correlation is a measure of the extent to which two variables move proportionally in the same direction. In the coin toss example above, each flip was independent of every other flip.

0% Correlation

When variables are independent, we say they are uncorrelated or have 0% correlation. The graph below shows two variables that have 0% correlation.

In this graph, there is no pattern that relates the value on the x-axis (the horizontal one) with the value on the y-axis (the vertical one) that holds true across all the points.

100% Correlation

If two random variables always move proportionally and in the same direction, they are said to have +100% correlation.  For example, two variables that are 100% correlated are the amount of interest you will earn in a savings account and the account balance.  If they move proportionally but in the opposite direction, they have -100% correlation.  Two variables that have -100% correlation are how much you spend at the mall and how much money you have left for savings or other purchases.

The two charts below show variables that have 100% and -100% correlation.

In these graphs, the points fall on a line because the y values are all proportional to the x values. With 100% correlation, the line goes up, whereas the line goes down with -100% correlation.  In the 100% correlation graph, the x and y values are equal; in the -100% graph, the y values equal one minus the x values. 100% correlation exists with any constant proportion.  For example, if all of the y values were all one half or twice the x values, there would still be 100% correlation.

50% Correlation

The graphs below give you a sense for what 50% and -50% correlation look like.

The points in these graphs don’t align as clearly as the points in the 100% and -100% graphs, but aren’t as randomly scattered as in the 0% graph.  In the 50% correlation graph, the points generally fall in an upward band with no points in the lower right and upper left corners.  Similarly, in the -50% correlation graph, the pattern of the points is generally downward, with no points in the upper right or lower left corners.

How Correlation Impacts Diversification

The amount of correlation between two random variables determines the amount of diversification benefit.  The table below shows 20 possible outcomes of a random variable.  All outcomes are equally likely.

The average of these observation is 55 and the standard deviation is 27.  This standard deviation is measures the volatility with no diversification and will be used as a benchmark when this variable is combined with other variables.

+100% Correlation

If I have two random variables with the same properties and they are 100% correlation, the outcomes would be:

Remember that 100% correlation means that the variables move proportionally in the same direction.  If I take the average of the outcomes for Variable 1 and Variable 2 for each observation, I would get results that are the same as the original variable.  As a result, the process defined by the average of Variable 1 and Variable 2 is the same as the original variable’s process.  There is no reduction in the standard deviation (our measure of risk), so there is no diversification when variables have +100% correlation.

-100% Correlation

If I have a third random variable with the same properties but the correlation with Variable 1 is -100%, the outcomes and averages by observation would be:

The average of the averages is 0 and so is the standard deviation!  By taking two variables that have ‑100% correlation, all volatility has been eliminated.

0% Correlation

If I have a fourth random variable with the same properties but it is uncorrelated with Variable 1, the outcomes and averages by observation would be:

The average of the averages is 54 and the standard deviation is 17.  By taking two variables that are uncorrelated, the standard deviation has been reduced from 27 to 17.

Other Correlations

The standard deviation of the average of the two variables increases as the correlation increases.  When the variables have between -100% and 0% correlation, the standard deviation will be between 0 and 17. If the correlation is between 0% and +100%, the standard deviation will be between 17 and 27.  This relationship isn’t quite linear, but is close.  The graph below shows how the standard deviation changes with correlation using random variables with these characteristics.

Key Take-Aways

Here are the key take-aways from this post.

  • Correlation measures the extent to which two random processes move proportionally and in the same direction. Positive values of correlation indicate that the processes move in the same direction; negative values, the opposite direction.
  • The lower the correlation between two variables, the greater the reduction in volatility and risk. At 100% correlation, there is no reduction in risk.  At -100% correlation, all risk is eliminated.
  • Diversification is the reduction in volatility and risk generated by combining two or more variables that have less than 100% correlation.

Financial Decisions – Risk and Reward

Almost every financial decision is a trade-off between reward and risk.  In this post, I’ll use three examples to illustrate how financial decisions can be made in a risk-reward framework.  The examples are:

  1. Deciding what to buy with some extra money.
  2. Selecting a deductible for your homeowners insurance.
  3. Choosing to invest in a bond fund, an S&P 500 index fund or the stock of a single company. I’ll use Apple as the example for the single company.

Trade-offs in General

Almost all financial decisions involve some sort of a trade-off.  In last week’s post, I used statistical metrics (e.g., standard deviation, probabilities and percentiles) to define risk.  Many financially savvy people use those types of metrics.  To get you more comfortable with the idea of this type of trade-off, I’ll use a subjective measure for the first example – deciding what to buy with some extra money.  I’ll then use statistical measures for the other two examples.

Trade-off – Purchase Example

Let’s assume your grandparents or parents gave you $1,000 for some special occasion, such as a graduation, birthday, or marriage.  You have decided to spend the money in one of the following ways.

  1. Spend $1,000 on a ski weekend.
  2. Spend $500 on a new Xbox and some games.
  3. Spend $700 on clothes.
  4. Spend $1,000 on the latest iPhone.
  5. Don’t spend any of it.

You plan to put any money you don’t spend in your Roth Individual Retirement Account (IRA) or Tax-Free Savings Account (TFSA).

In this example, I’ll define the trade-off as being between how much you enjoy your new purchase and its cost. You rank each option on a scale from 0 to 5 based on how much you will enjoy it.  You’ll want to consider the great feeling you’ll get from putting money in your IRA or TFSA, knowing that it will lead to an enjoyable retirement, as part of how much you will enjoy the options that include a contribution.

The table below might reflect your rankings:

Option Cost Enjoyment Ranking
Ski weekend $1,000 3
Xbox 500 4
Clothes 700 2
iPhone 1,000 5
Nothing 0 1

 

Your first inclination might be to select the iPhone because it will give you the most enjoyment. However, that doesn’t take into account the fact that it costs more than the Xbox and clothes.  Clearly, though, you prefer the iPhone to the ski weekend because you get more enjoyment for the same cost.

I always find it much easier to understand data in a graph than in a table.  The graph below shows the data above.

The x-axis (the horizontal one) represents the reduction in how much money you have after buying each item. That is, it is the negative of the cost of each purchase.  The y-axis (the vertical one) shows how much you like each item.   In this graph, you prefer things that are either up (higher ranking) or to the right (less cost).

Efficient Frontier Chart

The graph above is called a scatter plot.  In theory, there are dozens of things that you could buy, such as is shown in the graph below.

The blue dots in this graph represent the cost and your level of enjoyment of all of the options. The green line is called the “efficient frontier.”  It connects all of the points the meet the following criteria:

  • There are no other purchases with the same cost that you enjoy more.
  • There are no other purchases with the same level of enjoyment that cost less.

Making Your Choice

The “best” choices are those that fall along the efficient frontier.  You can reject any choices that aren’t on the efficient frontier as being less than optimal.

Going back to the first example, I added an approximation of the location of the efficient frontier based on the five points on the graph.

From this graph, we can see that any of buying the iPhone, buying the Xbox and some games or buying nothing are “optimal” decisions because they are on the efficient frontier.  That is, while the ski weekend has the same cost as the iPhone, you rated it as providing less enjoyment so the ski weekend is not optimal.  The clothes option is both more expensive and provides less enjoyment than the Xbox option, so it is also not optimal.

In this example, I have used the change in your financial position as the measure of “risk” and your level of enjoyment as the measure of “reward.”  Your own evaluation of the trade-off between risk and reward will determine which of the options you choose from the ones on the efficient frontier.

This example was intentionally simplistic to introduce the concepts.  I will now apply these concepts to two more traditional financial decisions – the choice of deductible on your homeowners (or condo-owners or renters) insurance policy and your first investment choice. My post about whether Chris should pay off his mortgage provides an even more complicated example.

Trade-Offs – Insurance Deductible Example

In this example, you are deciding which insurer and what deductible to select on your homeowners insurance.  For this illustration, I have assumed that your house is insured for $250,000 and you have a $500,000 limit of liability.  You have gotten quotes from two insurers for deductibles of $500, $1,000 and $5,000.  As discussed in my post on Homeowners insurance, the deductible applies to only the property damage coverage and not liability.

For reward, I will use the average net cost of your coverage.  That is, I will take the average amount of losses paid by the insurer and subtract the premium.  Because the insurer has expenses and a profit margin, this quantity will be a negative number.  Larger values (i.e., those that are less negative) are better (less cost to you).

For risk, I will use the total cost to you if your home has a loss of more than $5,000.  Your total cost is zero minus the sum of your deductible and your premium.  This number is negative (because outflows reduce your financial position) and larger (less negative) values are better.

The table below summarizes the six options and shows the premium, reward (average net cost) and risk (total cost if you have a large claim) metrics for each one.

Insurer Deductible Premium Average Net Cost Total Cost if You have a Large Claim
1 $500 $1,475 $-590 $-1,975
1 1,000 1,325 -530 -2,325
1 5,000 850 -340 -5,850
2 500 1,500 -615 -2,000
2 1,000 1,200 -455 -2,250
2 5,000 900 -390 -5,900

 

For each insurer, the premium and absolute value of your net cost decrease as the deductible increases.  The total cost if you have a large claim, though, increases as the deductible increases. When converted to financial outflows, the total cost values get larger (less negative) as the deductible goes up.

Efficient Frontier Chart

For the $500 and $5,000 deductibles, Insurer 1 has a better price.  For the $1,000 deductible, Insurer 2 has a better price.  These relationships can also be seen in the scatter plot below.

As with the scatter plot for the first example, points that are up and to the right are better than those that are down and to the left.  In this case, the efficient frontier connects the $500 and $5,000 deductible options for Insurer 1 and the $1,000 deductible option for Insurer 2.

Making Your Choice

Your choice among the three points on the efficient frontier is one of personal risk preference and your financial situation.  The $5,000 deductible option is clearly the least expensive on average, but you would need to be willing and able to spend an extra $4,000 if you had a large claim, as compared to the $1,000 deductible policy.  If you don’t have $5,000 in savings available to cover your deductible, that choice is not an option for you.

When I look at this chart, I notice that there is a fairly large reduction in the net cost from Insurer 1’s $500 deductible quote to Insurer 2’s $1,000 deductible quote.  If I have the extra $500 in savings to cover a loss if I have a claim, that looks like a good choice.  But, again, it is up to you to consider your finances and risk tolerance.

Trade-Offs – Investment Example

The same type of analysis can be used to evaluate different investment options.  As long as you are looking at publicly traded stocks, ETFs, mutual funds or one of several other financial instruments, you can get lots of data about historical returns from Yahoo Finance.  It is important to remember to let the historical data INFORM your decision, as the past is not always a good predictor of the future when looking at financial returns.

How to Get Data

Here is how I use Yahoo Finance to get data.

  • Go to finance.yahoo.com.
  • Find the Quote Lookup box. When I go to that site, it is usually on the right side of the screen below the scroller with the returns on various indices.
  • Type the symbol for the financial instrument for which I’m seeking data. Every publicly traded financial instrument has a symbol. For example, Apple is AAPL and the S&P 500 is ^GSPC.  I can also enter the name of the company or instrument, though it isn’t always the best at finding the one I want.  If the lookup doesn’t work very well, I use Google for the symbol of the company or financial instrument.
  • Click on the Historical Data button just above the graph with the stock price.
  • Select the time period over which you want the data in the pull-down box on the left. I usually want the full time series, so select Max.
  • Select the frequency on the right. I tend to be a long-term investor, so I always select Monthly.
  • Hit the Apply button just to the right of the frequency selection.
  • Hit Download Data just below the Apply button. It will ask you the format in which you want the data.  I always select Excel.  You’ll get a spreadsheet with one tab with your data on it.

There will be several columns in the spreadsheet that downloads from Yahoo Finance.  I usually use the Date and Adjusted Close columns.  Stocks can split (meaning you get more shares but they are worth less) and companies can issues dividends (which mean you get cash).  If I just look at the closing price at the end of each month, it won’t reflect splits. Since I’m interested in total return, I want my data to reflect the benefit of dividends.  The Adjusted Close column adjusts the closing stock price for both splits and dividends.

Investment Choices

In this example, we will assume that you have $10,000 you want to invest.  To keep the analysis somewhat simple, we will also assume that you are going to buy only one financial instrument.  In my next two post, I’ll talk about diversification and the benefits of buying more than one financial instrument.  The choices you consider are:

  • An S&P 500 index fund – an exchange-traded fund or mutual fund that is intended to produce returns similar to the S&P 500. Symbol on Yahoo Finance is ^GSPC
  • A Nasdaq composite index fund – an exchange-traded fund or mutual fund that is intended to produce returns similar to the Nasdaq composite. Symbol on Yahoo Finance is ^IXIC.
  • Fidelity investment grade bond fund – a Fidelity-managed mutual fund that invests in a basket of high-quality corporate bonds. Symbol on Yahoo Finance is FBNDX.
  • Tweedy Browne Global Value Fund – a mutual fund that focuses on international stocks.Symbol is TBGVX.
  • Boeing – A manufacturer of commercial and military aircraft. Boeing’s stock symbol is BA.
  • Apple – No need to explain this one! Its stock symbol is AAPL.
  • Neogen – A small company that develops and sells tests of food for pathogens. Stock symbol is NEOG.

Riskiness of Choices

Here is a box and whisker plot of the risk of these seven options.  See my previous post for a discussion of risk and box and whisker plots.

In addition to showing the 5th, 25th, 75thand 95thpercentiles, I added a blue horizontal line showing the average return over the 15-year time period for each investment.

Risk Metric – Standard Deviation

For most financial decisions, I look at the average result (e.g., average cost, average return, etc.) as my measure of reward.  As illustrated in the first example, you can use any measure you want, including a subjective one like how much you will enjoy something.  There are many, many risk metrics from which to choose.  If you are interested in overall volatility (deviations both up and down from the average), standard deviation is a good metric.

The chart below show the scatter plot of these investments using the average return as the reward metric and standard deviation as the risk metric.

In this plot, points to the right are better because they represent higher reward.  Points that are LOWER are also better, because they correspond to less risk.  I’ve drawn the efficient frontier for these points as being the ones that are furthest to the right and lowest on the chart.  Using these two metrics, the bond fund, Tweedy Browne (the international mutual fund), Boeing and Apple are on the efficient frontier.  If these metrics are right for you, the other investments are less than optimal.  The choice among the investments on the efficient frontier will be based on your willingness to tolerate extra volatility to achieve a higher average return.

Metrics – Probability of Negative Return

If your investment objective is capital preservation and you have a very short time horizon (one month in this example), you might want to look at the probability that the return will be less than zero in any one month as your risk metric.  (If the return is less than zero, your investment will be worth less at the end of the month than the beginning of the month.)

The scatter plot below shows how the location of the points changes if we replace standard deviation in the chart above with the probability that the return will be less than zero in any one month.

Using the probability the return is less than zero causes the S&P 500 to be even worse relative to the efficient frontier than it was when we used standard deviation.  The change in metric also causes Neogen to move down onto the efficient frontier and Boeing to move just slightly above it. These two charts show how our evaluation of the various options can change if we select different metrics.

On a side note, I want to alert you to the importance of looking at the scale of a graph.  The scatter plot below is identical to the one above except I have changed the scale on the y-axis.  Instead of starting at 30%, it starts at 0%

By changing the scale, I have made the differences in risk look much smaller in the second chart than in the first chart.  In my mind, the 31% probability that the monthly return will fall below 0% of the Bond Fund is significantly less than the 42% probability for Apple.  The second chart makes it look almost trivial. As you are looking at graphs in any context, you’ll want to be alert for that type of nuance.

Closing Thoughts

The goal of this post was to help improve financial decision-making process by providing insights into a helpful framework.  While you may not create graphs such as the ones in this post, you will be better able to think about risk, what features of risk are important to you and how to balance it with reward.  These new tools will help you make better financial decisions.

 

Introduction to Risk

Understanding risk is key to making sound financial decisions.  Many people don’t have a good grasp on what risk means, particularly in a financial context, so I will focus this post on risk.  While I don’t provide any specific practical suggestions in this post, I believe that understanding risk is fundamental to financial literacy. So, in this post, I define risk, identify some ways to measure it and provide different types of graphs to illustrate it.  In my next post, I’ll provide insights on how to make financial decisions in the context of risk and reward.

What is Risk?

Risk is the possibility that something bad will happen.  Examples of bad things that have financial implications include:

  • Fire destroys your home.
  • You are injured in a car accident and can’t work.
  • The value of an investment goes down.
  • You spend too much or make a poor financial decision so don’t have enough money to meet your financial goals or commitments.

By comparison, volatility refers the possibility that something will deviate from its expected or average value, including both good and bad results.  For example, if you own an S&P 500 index fund, risk would focus on how often and by how much the value of the fund goes down.  Volatility focuses on how often and by how much the value of the fund goes both up and down.

Measures of Risk and Volatility

Most measures of risk have some element of probability associated with them.  A probability is a percentage or the equivalent fraction that falls between 0% and 100% (i.e., between 0 and 1).  It represents the ratio of the number of times that the outcome meets some criteria to the number of possible outcomes.

Probability – Simple Example

Let’s start with some simple, non-financial probabilities.  A coin has two possible outcomes – heads and tails.  When flipping a fair coin, it is equally likely that the result will be heads or tails.

  • The probability of getting heads on one flip is 50%, derived as one result being heads divided by two possible choices.
  • The probability of getting two heads both times on two flips is 25%. There are four possible results, as follows:

First flip

Second flip

Heads

Heads

Heads

Tails

Tails

Heads

Tails

Tails

 

There is one result (the first row) in which there are two heads.  The probability of getting two heads is therefore one result meeting our criterion divided by four possible results or 25%.

  • The probability of getting one heads and one tails on two flips is 50%. There are two rows in the table that have one heads and one tails.  Dividing the count of two results meeting our criterion by the four possible results gives us a 50% probability.

Probability – Applied to S&P 500 Returns

We can now extend this concept to a financial measure.  I downloaded the month-ending values of the S&P 500 from Yahoo Finance from 1951 through 2018.  I calculated the annual change in the index in each year to derive 68 years of returns.  Although the past is seldom a perfect predictor of the future, we can use it as a model of what might happen.  So, when I say there is a certain probability that the S&P 500 return will meet some criteria, I am using short hand for saying that it happened that percentage of the time in the period from 1951 through 2018.

The bar chart below shows the number of years in which the S&P 500 return fell into certain ranges.

We can use this information to calculate the probabilities of certain results, as follows:

  • There are 28 years in which the return was less than the average of the returns over that time period (8.4%). We can therefore calculate that there is a 43% probability that the S&P 500 will return less than 8.4% in any one year by taking the 28 years in which it fell below its average and dividing by the total number of years for which we have data (68).
  • There are 18 years in which the return was negative over that time period (2 of which fell in the -1.6% to +8.4% range). We can therefore calculate that there is a 29% probability that an investor in the S&P 500 will lose money in any one year by taking 18 years in which the return was negative and dividing by the total number of years for which we have data (68).

More Complicated Metric

Sometimes people are not only interested in how often a bad result happens but also how bad it will be when it is worse than that.  For example, you might want to know the average amount you will lose in a year in which there is a loss.  Using the information above about the S&P 500, we would select only the 18 years in which return on the S&P 500 was negative and take the average of those returns. In this case, the average is -11%. With this metric, you now know that there is a 29% probability that an investment in the S&P 500 will lose money in a year and that, in those years, you will lose 11% on average. This metric is a richer metric than probability, but is also much harder to grasp so I won’t spend a lot of time on it.

Standard Deviation

Another metric commonly associated with risk is the standard deviation.   While standard deviation is a very common metric, it doesn’t actually measures risk. It measure volatility because the calculation of standard deviation includes both good and bad results, not just bad ones.  For processes that have symmetric results (more on that in a minute), such as the S&P 500 returns graphed above, you can learn a bit about the distribution just based on the standard deviation.

  • Roughly 2/3 of the possible results will fall in the range defined by the average minus one standard deviation up to the average plus one standard deviation
  • Roughly 96% of the possible results will fall in the range defined by the average minus two standard deviations to the average plus to standard deviations.

As such, something with a higher standard deviation has a higher probability of being below a fixed threshold than one with a lower standard deviation.  For example, we might be looking at two investments both with average returns of 5%.  One might have a standard deviation of 2.5% and the other a standard deviation of 5%. The second one has about a 16% probability of having a negative return as compared to only a 2% probability for the first one.

Pictures of Risk

There are many ways to illustrate risk graphically.  The bar chart of the S&P 500 shown above is one example.

Line Graphs

The data can also be presented in a line graph.  A line graph is essentially the same as a bar chart except there is a point on the line rather than a bar corresponding to ranges of possible results. The line graph below shows the annual returns for the S&P 500.  The ranges I used in this chart are narrower than the ones I used in creating the bar chart, so the graph is bumpier.

In this graph, I also changed the counts of the outcomes on the y-axis (the vertical one) to percentages or probabilities. A graph of the probabilities of possible results is called a probability density function or pdf. (Just in case you were curious.)

Symmetric and Skewed Distributions on a Line Graph

I mentioned earlier that some processes have symmetric results.  If both sides of the line chart are identical, then it is symmetric. The S&P 500 graph above isn’t quite symmetric, but it is close.  Relative to the mean of 8.4%, the possible results extend further to the left (in the downward direction) than to the right (in the upward direction).  That is, the worst observed result was -40% or 48 percentage points worse than the average.  The best observed result was +45% or 37 percentage points better than the average.

Processes that are not symmetrical are called skewed.  In extreme cases, one side of the graph is very tall and doesn’t go very far.  The other side of the graph has a long skinny “tail.” Examples of processes that are skewed are (1) winning the lottery and (2) damage to your house.

The green line in the graph above represents a symmetric distribution with an average of 0.  You can see that it is the same on both the right and left sides of the y-axis.

The blue line represents the change in your financial position if you play the lottery.  There is a very high probability you won’t win anything ($0 change to your financial position after you’ve already bought your ticket).  The probability you will win a small amount is small and the probability you will win a lot is tiny.  This distribution is skewed and the long tail goes to the right.

The red line illustrates the change in your financial position due to possible damage to your home before considering insurance.  There is a high chance you won’t have any damage ($0 change to your financial position). The probability you will have a small loss is small and the probability you will have a large loss (but less than the value of your $100,000 home) is tiny.  Interestingly, there is a larger probability of having a total loss than of have a large loss because, at some point, the damage because so expensive to repair that it is cheaper to replace the whole house.  This distribution is skewed and the long tail goes to the left.

For processes that have skewed results, the rules of thumb about standard deviations don’t apply, so looking at probabilities and average losses below a threshold are more informative.

Comparing Risk

I’ve downloaded monthly returns from Yahoo Finance for four possible equity investments:

  • S&P 500
  • NASDAQ composite
  • Boeing
  • Apple

Because Apple went public in early 1981, I used returns from 1981 through 2018.  I’ll use these monthly returns to demonstrate several ways of illustrating and comparing the risk of different investment options.

Tables

Some people prefer to look at the numbers.  The chart below shows five statistics that measure the volatility or risk of the five equity investments.

 

S&P 500

Nasdaq

Boeing

Apple

Standard Deviation

3.3% 4.6% 6.4% 18.8%

25th percentile

-1.8% -2.6% -4.5% -5.1%

Interquartile range

5.3% 7.0% 12.0% 15.3%

Average loss when negative

-3.0% -4.7% -6.7% -8.6%

 

As indicated above, standard deviation is a measure of volatility.  The least volatile investment is the S&P 500 index.  The S&P 500 index is the weighted average of the prices of 500 large companies.  Larger companies tend to have less volatility.  Also, the large number of companies in the index adds diversification which also reduces volatility.  I’ll have a post about diversification in a few weeks.

The Nasdaq composite is the weighted average of the prices of all of the companies that trade on the Nasdaq exchange.  Although the companies that trade on the Nasdaq tend to be smaller and more volatile, there are over 3,300 of them so the index is fairly diversified. Nonetheless, the Nasdaq has a higher standard deviation than the S&P 500.

Boeing is a fairly large company, but looking at its stock alone offers no diversification (because you need two things, in this case companies, to create diversification). Therefore, its stock price has a higher standard deviation than either of the indices.  Apple, though a large company, has been a fast growing company so has had even more volatility in its stock price than Boeing.  It has the highest standard deviation of the four investments in the table.

The 25thpercentile (below which 25% of the monthly returns fall) is a measure of risk. We can see that this risk measure shows that these investments fall in the same order looking at this risk metric as when measuring volatility using standard deviation.

I’ve also shown the interquartile range.  It is calculated as the difference between the 75thand 25thpercentiles.  That is, the 75thpercentile is the value above which 25% of the monthly returns fall.  Therefore, the middle 50% (half) of the observations fall in the interquartile range. It is also a measure of volatility that tracks fairly closely with the standard deviation for processes that aren’t highly skewed.

The last two metrics are the probability that the return is less than 0% and the average return when it falls below zero.  Interestingly, Boeing stock has a lower probability of have a negative return in a month than the Nasdaq!  It turns out that Boeing’s average monthly return is enough higher than the Nasdaq’s (6.4% versus 4.6%) to offset the higher volatility (as measured by both the standard deviation and interquartile range).

Line Graphs

The figure below illustrates the monthly returns for the four investment options using a line graph.

Consistent with the information in the tables above, we can see the following:

  • The S&P 500 (red line) has the least risk. The peak in the middle of the chart is the highest and the plot is narrower than that of any of the other options.
  • The Nasdaq composite (purple line) has the next lowest risk. Its peak is only slightly lower than that of the S&P 500.  The tails are a little wider than the S&P 500.
  • Boeing (blue line) is next in order. The general shape of the Boeing plot is similar to those of the S&P 500 and Nasdaq composite, but is lower in the middle and wider in the tails.
  • Apple (green line) is the most risky. It barely has a peak in its plot and has some points that are far from the middle of the graph.

Box & Whisker Plots

A box & whisker plot has less information than a line graph, but is less busy than a line graph so many people find it easier to interpret quickly.  The box & whisker plot of the monthly stock returns is shown below.

The green rectangles are the “boxes” and the lines extending above and below the boxes are the “whiskers.” In this box & whisker plot, 5% of the monthly returns for each option fall below the bottom of each whisker and 5% fall above the top of the upper whisker.  Alternately, 95% of the returns were below the top of the upper whisker. As such, 90% of the monthly returns fell in the range defined by the whiskers.

Similarly, 25% of the monthly returns for each investment fell below the bottom of each box.  75% of the monthly returns are less than the top of each box.  Alternately, 25% of the returns were above the top of the box.  As such, 50% of the monthly returns fell in the range defined by the boxes.  The boxes correspond to the interquartile range I mentioned above.

The risk of each option can be seen by comparing the height of the boxes and whiskers.  We see the same characteristics as were described for the line chart.

Spectral Plots

A spectral plot focuses solely on risk, not volatility.  A spectral plot of the monthly returns on the four investments is shown below.

The legend shows whole numbers.  These numbers represent how frequently or seldom something will happen in months. In this case, the yellow-green boxes (corresponding to 5 in the legend) show the loss you would have every five months. Every five months corresponds to 20% of the time, so I took the 20th percentile values and plotted the negative of them (since the chart shows the percentage you will lose).  The bright red boxes (corresponding to 100 in the legend) show the percentage loss you would have every 100 months or at the 1st percentile.

It is clear that the S&P 500 has the least risk and Apple has the most risk of the four investments.  Boeing and the Nasdaq have very similar risk, with Boeing very slightly riskier.

Closing Thoughts

To be clear, I don’t anticipate that many of you will be able to create charts that look like these. I hope that by providing these examples, you’ll be able to understand any articles or graphics you read that address risk.

It is also important, in mmking financial decisions, to understand of the nature of the volatility involved.  Is it skewed like that of damage to your house?  Or, is it somewhat symmetric and short-tailed like the S&P 500?  Or somewhere in between?  If you have a good understanding of the nature of the risk involved, you’ll make a better decision.   I’ll talk more about risk and making financial decisions in my next post.

 

5 Steps to Begin Your Investing Journey

Riley is a senior financial analyst at a Fortune 500 company with a CPA and M.S. in Applied Economics who aspires to help young professionals navigate the sometimes-murky waters of finance.  He is also the author of the blog, Young and The Invested, which is dedicated to growing an online community for young professionals looking to improve their financial literacy and develop strategies to reach financial independence. In this guest post, he will provide 5 steps to help you begin your investing journey.

The oldest rule in investing is also the simplest: “Buy low, sell high.”  While it seems blindingly obvious and begs the question of why anyone would want to do anything else when investing, you might be surprised how hard it is to put into practice.

Investing is a discipline which plays not only on astute analysis and remarkable luck but also on people’s behavioral responses.  Holding onto your stocks during periods of intense market volatility takes a lot of courage and isn’t what the human brain is wired to withstand.

But how do you approach investing if you don’t have a background in it? Without much prior experience, it’s tough to say. There’s an ocean of information out there and sorting through it requires deliberate, thoughtful reflection when piecing together what you’ve read.

When it comes to growing your wealth and working toward financial independence, investing is an important tool.  Through investing, you can buy assets which, hopefully, grow in value, whether it is a home, a retirement account, stocks, or bonds.

Let’s walk through some simple steps on how you can begin your investing journey.

First, Invest in Yourself

This past summer, I attended a wedding with my wife and her family where my brother-in-law approached me with a conversation about investing.  He wanted to know how he could replicate the performance seen by the world’s greatest investors.  

Essentially, he wanted to turn a small sum of money into an account balance with two commas in quick fashion.

If only I knew the sure-fire way to make that path my own reality.  If I did, we wouldn’t have driven to the wedding in a rented subcompact.

I cautioned him those investors are truly gifted and the exception to the norm.  But what I then told him is the common trait these legendary financiers share: following a systematic and disciplined approach to investing.

I told him regardless of investing style, timeframe, or philosophy, they all have discipline, transact based on logical, informed thinking and do not let emotions drive their decisionsThese are the most important elements required for investing success.  But don’t just take my word for it, many folks seem to agree[1],[2],[3],[4].

The aforementioned investing strategies are merely a means to an end and come later.  Any investor starting out should develop these core principles and learn to stick to them during times of good and bad.

Develop Your Investing Approach

As I explained this to my brother-in-law, I could see his disappointment in my not knowing any shortcuts to overnight investing success.  However, we launched into a discussion around how he could develop his own disciplined investing approach by first becoming a student of markets.

Knowing that this discussion could become overly cumbersome in just one conversation, I decided to share only introductory steps.

Investing isn’t easy but, at the same time, it shouldn’t be seen as a frightening endeavor. If done wisely and consistently, investing can separate retiring comfortably at a reasonable age from working into your golden years out of necessity.

So, with that thinking, I will do the same here.  Short of a formal education in finance, my five high-level steps for gaining familiarity with investing in the market are as follows:

1 – Read a Lot About the Market

Sounds logical, right?  You’d be surprised by how many people I’ve heard say they got into a stock simply because so-and-so recommended it.

This person winds up not doing a lick of due diligence before investing.  This person didn’t know what was happening in the market, nor anything about the company beyond it being a hot stock tip.

To counteract this, I suggest first beginning by reading reputable sources that discuss markets (e.g., MarketWatch, the Financial Times, the Wall Street Journal, Reuters, Yahoo Finance, among others). As you read more, I suggest approaching every article with a heavy dose of skepticism.

This will make you more likely to piece together content from multiple sources and form your own thinking about markets and the companies in them.

As an exercise, take a moment to read this article about the earnings estimates for public companies.  After you’ve read it, what were the main, salient points that stood out to you?  I found the following to be most important:

  • Many investors seem to think lackluster stock market movement during this quarter’s earnings announcements indicates peaking corporate profits. When companies announce record earnings and markets barely move, it must mean expectations were high and future earnings don’t look to get any better.
  • Analysts, or those people who follow stocks and publish opinions on them, disagree, and are increasing their profit projections at the highest rate in 6 years. This is where the skepticism should come into play.  This conflict means someone is wrong, but who?  Perhaps both are right and yet both are wrong.  The truth likely lies somewhere in between.
  • A growing economy and corporate tax reform have benefited companies but trade war activity makes for an uncertain outlook. To illustrate uncertainty, reporting companies have seen the most volatile trading in two years immediately after announcing earnings results. However, it appears this trading reaction could be the result of poor understanding of the effects of the recent tax reform legislation and clouds the visibility for accurately forecasting future earnings.  Therefore, the volatility merely highlights poor forecasting abilities, not necessarily anything indicative of market direction.
  • A lot of positive developments exist to push markets higher but looming risks serve to temper optimism usually present with such strong earnings growth. Bottom line: there doesn’t appear to be a strong case for a plummeting market but neither for a sustained rally.

As you read more pieces like this, reflect after each one and begin to piece together content from what you’ve read.  Building this understanding won’t happen overnight.

2 – Start Looking into Individual Companies

Naturally, you will come across individual companies.  You should identify companies consistently performing well or making strides to improve.  I recommend starting your journey by researching five companies you admire and understand (preferably in different industries) and cultivating ideas about the strategies of each firm, their competitive advantages, and the core value they provide.

If you don’t believe any of these items to be durable over time, I would suggest moving on.  Recognize what sets these companies apart from their peers, the prospects for the markets in which they operate (e.g., growing market vs. declining market), and how the market values them. 

Cast aside companies if you uncover something you don’t like. Don’t let sunk costs guide your thinking.  Even if you are wrong in not liking the company, there are many other companies out there about which you don’t uncover anything you don’t like.  Investments in these companies will be less risky.

Ultimately, a stock represents a piece of a company, so sustainable profitability is an important factor.  You really want to assess how profitable these companies can be, because before you decide how much to pay for a stock, you need to understand how much money that company makes. 

If the company makes a lot of money consistently, you will likely have to pay more to acquire the stock.

3 – Take Action

At this point, if you’ve gotten a decent handle on the overall market’s activity and analyzed a set of attractively-valued companies you think stand out from the rest, it’s your time to pull the trigger. 

There are a number of retail brokers you may use to invest in individual stocks (e.g., Interactive Brokers, TD Ameritrade, Charles Schwab).

4 – Continue Following the Companies and Markets

By doing your due diligence, you will be able to follow these companies and see if they continue to perform as you expect. If a company makes a decision you don’t agree with or think will adversely impact its value going forward or the environment in which that company operates changes in a way that is adverse to the company, you might consider cutting your losses short and moving on.

5 – Keep It Simple, Invest in ETFs

Investing is hard.  It’s more art than exact science.  By writing this step-by-step guide, my goal is not to simplify the act of investing.  In fact, what I want to convey as clearly as possible is just how difficult it is to invest in individual stocks.

Investing is so much more than following some rules of thumb.  Getting an edge is difficult so you shouldn’t develop irrational self-confidence and think you have an investing edge when you really don’t.

Usually, being humble and saying to yourself that you don’t really know can be great to steady your decision-making.

If you don’t have confidence in selecting individual companies to outperform the market, another strategy is to use exchange traded funds (ETFs) to invest.  You can consider investing in low-cost ETFs through brokerages (e.g., Vanguard) or robo-advisors (e.g., Betterment).

Personally, I use both of those services to hold my ETFs.  I prefer Betterment because it automates my ETF holdings based on scientific research matched to my stated financial goals.

For example, I have a Roth IRA account with the stated financial goal of growing money through retirement in about 30 years.  Because of this goal, Betterment chooses to hold a diverse portfolio of 90% ETFs ranging from small cap value to globally diversified ETFs.

I recommend that you start your investing journey with ETFs, especially when you can hold these investments for long periods of time.  This allows the last real-edge in investing to work its magic: time in quality investments.

When Investing, Doing Less is More

I think about smart investing in a way that minimizes mistakes instead of pursuing maximum gains.  I don’t like taking on uncompensated risk

A portfolio requires a healthy balance of risk and reward as well as exposure to many different investments.  I keep the following items in mind when investing:

  • Steer clear of all avoidable risks. Don’t take on unnecessary risk when the probability of a better investment outcome doesn’t exist
  • Be cautious and highly skeptical of your conclusions and whether you feel you possess some edge. It is much more likely you don’t have one when compared to the deep pockets spending endless time and money seeking the next edge
  • Minimize the number of times you touch your portfolio. High portfolio turnover in search of better investments often leads to negative consequences for your returns
  • Avoid big mistakes. You stand to gain a lot more by doing nothing than thinking you have some edge (when you really don’t) and acting upon it

When investing, doing less is more.  Therefore, I recommend investing through low-cost ETFs.

Investing well can produce very rewarding experiences you share with those you love.  For me, it allowed me to buy my first home and now to grow the assets necessary to purchase my next one together with my wife to start our family.

In general, developing your own disciplined investing approach based on rational, informed decision-making can lead to financial independence.

Learning how to invest wisely at a young age will have you maximize your youth by allowing compounding to work to your benefit.  Do yourself a favor and invest in yourself by following these five steps to begin investing.


A big thanks to Riley for writing this post. He makes many important points to consider as you get started with investing. I invited to write a guest post on investing, as I haven’t written much on that topic yet. I greatly appreciate his rounding out the breadth of topics covered on our blog.

 

Retirement Savings/Saving for Large Purchases

In my previous post, I presented the first part of a case study that introduced Mary and her questions about what to do with her savings. In this post, I will continue the case study focusing on retirement savings and saving for large purchases. 

Case Study

To help set the stage, I created a fictitious person, Mary, whose finances I use for illustration.

  • Mary is single with no dependents.
  • She lives alone in an apartment she rents.
  • She makes $62,000 per year.
  • Mary has $25,000 in a savings account at her bank and $10,000 in her Roth 401(k).
  • Her annual budget shows:
    • Basic living expenses of $40,000
    • $5,000 for fun and discretionary items
    • $10,000 for social security, Federal and state income taxes
    • $4,000 for 401(k) contributions
    • $3,000 for non-retirement savings
  • Mary has $15,000 in student loans which have a 5% interest rate.
  • She owns her seven-year-old car outright. She plans to replace her car with a used vehicle in three years and would like to have $10,000 in cash to pay for it.
  • She has no plans to buy a house in the near future.
Mary's-Savings-Infographic

Her questions are:

  • Should I start investing the $25,000 in my savings account?
  • Should I have a separate account to save the $10,000 for the car?  
  • What choices do I have for my first investments for any money I don’t set aside for my car?
  • Should I pay off some or all of the principal on my student loans?

I talked about a framework for thinking about her savings and setting aside money for expenses she doesn’t pay monthly and emergency savings here.  In this post, I’ll focus on the rest of her savings.  I answer her questions about student loans here

Designated Savings

Designated savings is the portion of your investable asset portfolio that you set aside for a specific purchase, such as a car or home. Mary would like to buy a car for $10,000 in three years.  She needs to designate a portion of her savings for her car.

As part of her savings framework, Mary

  • Will set aside $13,000 for emergency savings.
  • Has $12,000 in her savings account after setting aside the $13,000 for emergency savings.
  • Included $3,000 a year for non-retirement savings in her budget, some of which she can use for her car.

Mary has decided she will use $5,500 as the start of her designated savings to replace her car. After reading this post, she has decided to pay cash for a car, rather than borrow or lease,  She will add half of her $3,000 of non-retirement savings each year to bring the total available balance to $10,000 in three years.  If Mary’s car becomes unrepairable sooner, she can use some of the money in her emergency savings, but will want to replenish that account as soon as she can.

Considerations for Investment Choices

When I’m saving money for a large purchase, such as a car or a down payment on a house, I’m willing to invest in something less liquid than a savings account or a money market account. That is, I don’t have to be able to access the money on a moment’s notice.  

I do, however, want a similar level of security.  It is very important to me that the market value of my investment not go down as I don’t want to risk my principal.  Because I tend to have time frames that are less than one year for these types of purchases, I tend to put my designated savings in certificates of deposit. 

Certificates of Deposit and Treasury Bills

In Mary’s case, she has three years.  She might consider longer-term certificates of deposit (CDs) or short-term government bonds. (Click here to learn more about bonds.) A CD is a savings certificate, usually issued by a commercial bank, with a stated maturity and a fixed interest rate.  

A treasury note is a form of a bond issued by the US government with a fixed interest rate and a maturity of one to 10 years.  A treasury bill is the same as a treasury note, except the maturity is less than one year.  When the government issues notes, bills and bonds (which have maturities of more than 10 years), it is borrowing money from the person or entity that buys them.  The table below shows the current interest rates on CDs and treasury bills and notes with different maturities.

Maturity CD[1] Treasury[2]
1-3 Months 2.32% 2.3%
4-6 Months 2.42% 2.5%
7-9 Months 2.56% N/A
10-18 Months 2.8% 2.7%
1.5–2.5 Years 3.4% 2.8%
3 Years N/A 2.85%
5 Years N/A 2.9%

When thinking about whether to buy CDs or Treasury bonds, Mary will want to consider not only the differences in returns, but also the differences in risk.  

Risks of Owning a Bond

Bonds have two key inherent risks – default risk and market risk

  • Default risk is the chance that the issuer will default on its obligations (i.e., not pay you some or all of your interest or principal).  Treasury notes, bills and bond issued by the US are considered some of the safest bonds from a default perspective.  I’m not aware that the US government (or Canadian government for that matter) has ever not paid the interest or repaid the principal on any of its debt. 
  • Market risk emanates from changes in interest rates that cause changes in the market values of bonds.  As interest rates go up, the market values of bonds go down.  All bonds come with a maturity date that is almost always stated in the name of the bond.[3]   If you buy a bonddon’t sell it until it matures and the issuer doesn’t default, you will get the face amount (i.e., the principal) of the bond no matter how interest rates change.  Thus, if you hold a bond to maturity, you eliminate the market risk

In summary, using certificates of deposit or Treasuries held to maturity can increase your investment return relative to a savings account without significantly increasing the risk that you’ll lose the money you’ve saved.  

Mary’s Decision

Because she can buy them easily at her bank or brokerage firm and they are currently yielding more the Treasuries with the same maturity, Mary has decided to buy 2.5-year CDs, earning 3.4%, with the $5,500 she has set aside to buy her car.

Long-term Savings – What to Buy

Mary has $6,500 in her savings account that isn’t needed for her emergency savings or her replacement car. She wants to start investing it or use it to pay down some of her student loans.  I’ll talk about her student loans next week.

Mary doesn’t want to spend a lot of time doing research, so is not going to invest in individual securities.[4]  Instead, she is looking at mutual funds and exchange-traded funds (ETFs).  A benefit of these funds over individual securities is that they own positions in a lot of companies so it is easier for Mary to diversify[5]her portfolio than if she bought positions in individual companies.

Mutual Fund and ETF Considerations

Briefly, here are some of the features to consider in selecting a mutual fund or an ETF.  I note that you may not have answers to a lot of these questions, but they should help you get started in your thinking[6].

  • The types of positions it holds and whether they are consistent with your investment objectives. Is the fund concentrated in a few industries or is the fund intended to produce the same returns as the overall market (such as the S&P 500 or Dow Jones Industrial Average)?  Does it invest in larger or smaller companies?  Does the fund focus on growth or dividend-yielding positions?  Is it an index fund or actively-traded?
  • The expense load.  All mutual fund and ETF managers take a portion of the money in their funds to cover their expenses.  The managers make their money from these fees.  Funds are required to report their expenses, as these reduce your overall return on investment.  There are two types of expense load – front-end loads and annual expenses.  If you buy a fund with a front-end load, it will reduce your investment by the percentage corresponding to the front-end load when you buy it.  Almost all funds have annual expenses which reduce the value of your holdings every year.  Although funds with lower expense loads generally have better performance than those with higher loads, there may be some funds that outperform even after consideration of a higher expense load.
  • Historical performance.  Although historical performance is never a predictor of future performance, a fund that has a good track record might be preferred to one that has a poor track record or is new.  As you review returns, look not only at average returns but also volatility (such as the standard deviation).  A fund with higher volatility should have a higher return.

Mutual Funds and ETFs – How to Buy

You can buy mutual funds directly from the fund management company.  You can also buy mutual funds and ETFs through a brokerage company.  If you buy them through a brokerage company, you will pay a small transaction fee but it is often easier to buy and sell the funds, if needed.  Holding these assets in a brokerage account also lets you see more of your investments in one place.

Mary’s Decision

Mary decides to invest in an S&P 500 index fund (a form of exchanged-traded fund that is intended to track S&P 500 returns fairly closely).  Since 1950, the total return on the S&P 500 corresponds to 8.9% compounded annually.  It is important to understand that the returns are very volatile from month-to-month and even year-to-year, so she might not earn as much as 8.9% return over any specific time period.[7]

Retirement Savings – What Type of Account?

As Mary thinks about her long-term savings, she not only wants to decide how to invest it, but also in what type of account to put it – a tax-sheltered retirement savings account or a taxable account she can access at any time[8].  

Retirement Account Contribution Limits

In the US for 2018, she is allowed to contribute $18,500 ($24,500 after age 50) to a 401(k) plus $5,500 ($6,500 after age 50) to an Individual Retirement Account.  

In Canada, the 2018 maximum contribution to group and individual Registered Retirement Savings Plans (RRSPs) combined is the lesser of 18% of earned income or $26,230.  The 2018 maximum contribution to group and individual Tax-Free Savings Accounts (TFSAs) is $5,500.  If you didn’t make contributions up to the limit last year, you can carry over the unused portion to increase your maximum contribution for this year.

In Canada, there are no penalties for early withdrawal from a RRSP or TFSA as long as the withdrawal is not made in the year you make the contribution, so it is easy to take advantage of the tax savings.  If you make the withdrawal from an RRSP, you need to pay taxes on the withdrawal.  In the US, there is a 10% penalty for withdrawing money from a 401(k) or IRA before the year in which you turn 59.5. As such, the choice of putting your money in a 401(k) or IRA needs to consider the likelihood that you’ll want to spend your long-term savings before then.

Returns: Taxable Account vs. Roth IRA/TFSA

Mary has decided she won’t need the money for a long time.  She will decide how much to put in her retirement account and taxable accounts after she looks at her student loans.  Mary’s savings is considered after-tax money.  As such, she can put it in a Roth IRA or TFSA.  She will not pay taxes on the money when she withdraws it.  If she didn’t put the money in a Roth IRA or TFSA, she would have to pay income taxes on the investment returns.[9]  If she puts it in a Traditional IRA or RRSP, the amount of her contribution will reduce her taxable income but she will pay taxes on the money when she withdraws it. This graph compares how Mary’s money will grow[10]over the next 30 years if she invests it in a Roth IRA or TFSA as compared to a taxable account.  

Savings comparison, Roth vs Taxable savings

As you can see, $4,000 grows to just over $30,000 over 30 years in a taxable account and just over $50,000 in a Roth account assuming a constant 8.9% return and a 20% tax rate.

Key Points

The key takeaways from this case study are:

  • You may need to save for large purchases over several years.  The amount you need to set aside today as designated savings for those purchases depends on how much they will cost, when you need to buy them and how much of your future budget you can add to those savings.
  • Certificates of deposit are very low-risk investment instruments that can be used for designated savings.  
  • Treasuries with maturity dates that line up with your target purchase date can also be used for designated savings.  By holding bonds to maturity, you eliminate the market risk.
  • Mutual funds and ETFs require less research and more diversification than owning individual companies (unless you own positions in a very large number of companies).  These instruments are an easy way to get started with investing.

Your Next Steps

This post talks about Mary’s situation.  Here are some questions you can be asking yourself and things you can do to apply these concepts to your situation.

  1. Identify the large purchases you want to make.  These purchases can include a car, an extravagant vacation or a house, among other things.  For each purchase, estimate when you will want to spend the money and how much they will cost. 
  2. Determine how much of your savings you can set aside for these large purchases.  Look at your budget to make sure you can set aside enough money to cover the rest of the cost.  If you can’t, you’ll need to either make changes to your aspirations or your budget.  In my budgeting series starting in a few weeks, I’ll dedicate an entire post to what to do when your expenses are more than your income.  
  3. Decide whether to start a relationship with a brokerage firm.  Last week, I provided a list of questions to help you get started if you do.
  4. Look into options for your designated savings.
    • What are the returns offered by your bank or, if you have one, brokerage firm, on certificates of deposit with terms corresponding to when you need your designated savings? 
    • How do Treasury returns compare to certificates of deposit?
  5. Decide how much of your long-term savings you want to put into retirement accounts and how much will be left for other savings.  I put as much as I could into retirement accounts, but always made sure I had enough other savings for large purchases that I hadn’t identified in enough detail to include in designated savings.  If you want to retire before the year you turn 59.5, you’ll also want to keep enough long-term savings out of your retirement accounts to cover all of your expenses until that year. 
  6. Decide whether you want to start investing your long-term savings in mutual or exchange traded funds or in individual stocks.  If mutual or exchange traded funds, take a look at the list of questions above.

[1]https://www.schwab.com/public/schwab/investing/accounts_products/investment/bonds/certificates_of_deposit, November 17, 2018.

[2]www.treasury.gov, November 17, 2018.

[3]Some bonds have features that allow the issuer to re-pay the principal before the maturity date.  For this discussion, we will focus on bonds that do not give the issuer that option.  These bonds are referred to as “non-callable.”  Bonds that can be re-paid before the maturity date are referred to as callable bonds.

[4]For those of you interested in investing in individual equities, a guest blogger, Riley of Young and The Invested (www.youngandtheinvested.com), will write about how to get started with looking at individual companies right after the first of the year.

[5]Portfolio diversification is an important concept in investing.  I’ll have a few posts on this topic in the coming months.

[6]If you are interested in more information on selecting mutual funds, I found a nice article at https://www.kiplinger.com/article/investing/T041-C007-S001-my-9-rules-for-picking-mutual-funds.html

[7]This volatility is often referred to as the risk of a financial instrument and is another important concept in investing. Look for insights into the trade-off between risk and reward coming soon.

[8]I’ll cover retirement savings more in a future post.

[9]Income taxes on investments are somewhat complicated.  For the illustrations here, I’ll assume that Mary’s combined Federal and state tax rate applicable to investment returns is 20% and that all returns are taxable in the year she earns them.  There are some types of assets for which that isn’t the case, but identifying them is beyond the scope of this post.

[10]For illustration, this graph shows a constant 8.9% return.  Over long periods of time, the S&P 500 has returned very roughly 8.9% per year on average.  The returns vary widely from year-to-year, but for making long-term comparisons a constant annual return is informative even though it isn’t accurate. 

Savings Framework and Emergency Savings

You may be thinking you’d like to get started with investing.  Before doing that, you’ll want to look at how much savings you have and how much you can invest.  In this three-part post, I’ll illustrate a framework to guide savings and investing decisions.   The post will focus on a very high-level structure for your investable asset portfolio and, specifically, emergency savings.  The next post present a case study addressing saving for large purchases and retirement.  The third post will continue with the case study, focusing on when to accelerate your debt payments.

Case Study

To help set the stage, I’ll create a fictitious person, Mary, whose finances I’ll use for illustration.

Mary’s Situation

  • Mary is single with no dependents.
  • She lives alone in an apartment she rents.
  • She makes $62,000 per year.
  • Mary has $25,000 in a savings account at her bank and $10,000 in her Roth 401(k).
  • Her annual budget shows:
    • Basic living expenses of $40,000
    • $5,000 for fun and discretionary items
    • $10,000 for social security, Federal and state income taxes
    • $4,000 for 401(k) contributions
    • $3,000 for non-retirement savings
  • Mary has $15,000 in student loans which have a 5% interest rate.
  • She owns her seven-year-old car outright. She plans to replace her car with a used vehicle in three years and would like to have $10,000 in cash to pay for it.
  • She has no plans to buy a house in the near future.

Mary's-Savings-Infographic

Mary’s Questions

Mary’s questions are:

  • Should I start investing the $25,000 in my savings account?
  • Should I have a separate account to save the $10,000 for the car?
  • What choices do I have for my first investments for any money I don’t set aside for my car?
  • Should I pay off some or all of the principal on my student loans?

Investable Asset Portfolio

Investable asset portfolio? Isn’t that something for companies and for the rich?  Actually, no. I think about any savings and other invested assets as a portfolio.  My husband and I own many other assets, such as our home, our cars and our household goods.  Because those are not assets that we can invest, we include them when we are evaluating our net worth but don’t consider them part of our investable asset portfolio.   Mary’s investable asset portfolio consists of her savings account and her Roth 401(k).

Within my portfolio, I strive to keep a target amount in very liquid (i.e., easily converted to cash), low risk assets for emergency savings.  If I have a large purchase that I want to make soon, such as when we sold our house but knew we were going to buy a new one, I invest that money in slightly less liquid, slightly more risky assets with slightly higher returns.  I’ll call these designated savings and talk about the investment I chose in the next post in this series.  I then look at the rest of my portfolio in terms of how long until I will need the money, how much return do I want and how much risk I can tolerate, as well as how much time I’m willing to spend researching and monitoring it.

Expenses Paid Less than Monthly

There are some expenses that you pay less often than once a month.  Examples include presents (most of us have a relatively large expenditure in December, but also don’t forget birthdays), property taxes if you own a house and insurance.  In the months that you don’t have these expenses, you’ll want to set aside enough money so you make these payments when they are due.

Mary has made a list of these expenses from her budget.  Specifically, she has budgeted $400 for presents, $1,000 for a vacation and $1,000 for car and renters insurance which she pays once a year.   She puts $200 a month into her bank savings account to cover these expenses. When she pays for her insurance or vacation, she transfers the money back to checking.

Emergency Savings

How Much?

Three to six months of basic expenses is considered a good target for emergency savings.  To help me estimate how much I need in emergency savings, I imagine what would happen if I couldn’t work for that time period. There are many expenses that will be eliminated, such as income taxes, commute expenses and some others. However, there are also additional expenses, possibly including the full cost of health insurance.[1]

In addition to not being able to work, other uses of emergency savings include unexpected medical expenses, serious illness or death in your close family that requires travel and major repairs to your car or house.  It is important to recognize what is an emergency and what is not.  For example, a funeral is an emergency, while a wedding is a luxury.  Your furnace needing replacement is an emergency.  Routine maintenance and even medium-sized repairs to your car or house are not emergencies as they are budget items.  An important component of using emergency savings is to modify your budget immediately to start re-building it.

Mary has decided to start with a target of four months of expenses for her emergency savings and plans to build it up using $1,500 a year from her non-retirement savings budget until it reaches six months of expenses.  As a first approximation of how much emergency savings Mary needs, she could take a third (four months divided by twelve months in a year) of her salary or just over $20,000.  Because Mary has a budget, she can identify those expenses that absolutely necessary. Her budget shows $40,000 of basic living expenses so a third of that would be $13,333.  She will use $13,000 as her target for her emergency savings, leaving her with $12,000 for designated and long-term savings.

Where to Invest?

Mary considers only a few choices for her emergency savings – including her bank savings accounts, a high-yield checking or savings account at a brokerage firm and a money market account.

A Bit about Money Market Accounts

Money market accounts tend to return a slightly higher yield than savings accounts.  They are like other securities in that you have to buy and sell them, but you can often have access to your money in 24 hours (as compared to instantly for a savings account).

Money market accounts also have slightly more risk than savings accounts. Many money market funds buy very safe securities, such as certificates of deposit and US government bonds so have very little risk.  Others take more risk by investing in commercial paper which is essentially a short-term loan for a company.  In 2008, the value of a few money market funds backed by commercial paper fell below $1.00.  When the value of a money market fund falls below $1.00, it is called “breaking the dollar,” For emergency savings, you’ll want to focus on funds backed by US government debt securities.

Money market accounts from a bank are insured by the Federal Deposit Insurance Corporation, while those at brokerage firms are not.  Money market funds at brokerage houses are insured by the US Treasury if the brokerage firm fails but not if the fund breaks the dollar.  If the value of the investments purchased by the money market fund fall in value, the value of your principal might decrease.  I am not aware of any money market funds that have lost value.  There are some money market funds that invest in higher risk instruments.  For emergency savings, Mary will consider only money market funds that buy low-risk instruments.

You might be thinking I’m kidding.  Keep some money in a savings account!  You might be excited to participate in the seemingly glamourous world of trading stocks and other financial instruments.  Unfortunately, those financial instruments are risky.  That is, you might lose some of the money you invest in those instruments if their value goes down.  (I have a lot to say about risk and reward and will dedicate at least one future post to the topic.)

Back to Mary’s Emergency Savings

Because emergency savings are meant to be available on a moment’s notice at their full value, Mary will keep hers in those two very boring places – a savings account and a money market account.

At one brokerage firm, high-yield checking and savings accounts are earning 0.35% to 0.45% as I write this post.  US government-backed money market accounts are earning as much as 1.9%[2]or about 1.5 percentage points higher than the checking and savings accounts.  (The money market rate at one bank is 1.87%[3]or essentially the same as the brokerage firm.) Mary decides to put half of her emergency savings in a high-yield checking account so she is sure to have instant access to it and half in a money market account.  This decision gives her an average return of 1.275%, as compared to the 0.06%[4]she was earning on her bank’s savings account. So, while the savings account and a money market account are not as exciting as buying stocks, she can improve her return as compared to her bank’s savings account.

In the next post in this series, I’ll talk about how Mary plans to invest her designated savings and long-term savings.  I promise – the choices get a bit less boring.

Key Points

The key takeaways from this case study are:

  • There are different purposes for savings – expenses you don’t pay every month, emergencies, large future purchases and long-term.
  • Expenses paid less than monthly can be budgeted and set aside in a very safe, easily accessed place, such as a savings account, until needed.
  • Emergency savings of three to six months of basic living expenses is a good target.If you have lots of back-up options – financially supportive parents or relatives, another place nearby you could live for a few months in an emergency or the like, your target can be at the low end of the range.   On the other hand, if you are like one friend of mine whose family lives in Europe while he lives in the US so an emergency trip home would be very expensive or you don’t have many back-up options, you might want to set the high end of the range as your ultimate target.
  • It is important to replace emergency savings as quickly as possible after using them.
  • A portion of emergency savings (the greater of one month’s expenses or travel expenses to immediate family) should be available at any time; while a portion can be invested in something that takes a day or two to access.

Your Next Steps

This post talks about Mary’s situation.  Here are some questions you can be asking yourself and things you can do to apply these concepts to your situation.

  • Make a budget. A budget will help you understand your financial situations. For help with budgeting, check out my series of posts with a step-by-step plan for building a budget, starting with this one.
  • Identify the expenses in your budget that you pay less than once a month. Determine how much you need to set aside each month to cover them.  In each month, you will increase this component of your savings by 1/12thof the total amount of less-than-monthly expense.  You will also reduce it by any of these expenses that need to be paid in the month.
  • Do you want to start a relationship with a brokerage firm? If so, here are some questions to consider:
    • What types of accounts does it offer?
    • What are the fees and limitations associated with those accounts?
    • What are the returns it is offering on those accounts?
    • Can you access those accounts using an ATM card, electronic banking or checks? What are the fees associated with them?  My brokerage firm waives all ATM card fees which is great in an emergency because I can get cash anywhere in the world.
    • Do you want to be able to meet with someone in person? This question was critical for me.  While I probably use e-mail more than I should, I need to be able to go into the office for big transactions and, to a lesser extent, advice.  If you are like me in that regard, particularly if you are looking for advice, you’ll want a brokerage firm with a conveniently-located office and a team you can trust.
  • Set an emergency savings target.
  • Look into options for your emergency savings.
    • Does your bank or, if you have one, brokerage firm, offer high-yield checking or savings accounts? What are the fees and limitations on those accounts? An account with a large minimum balance isn’t attractive for emergency savings because you might need to empty it on short notice.
    • Do you want to consider a money market account for some of your emergency savings? If so, what options are offered by your bank and brokerage firm? What returns are being offered? How long will it take to access your money? How easy is it to access the money, such as by transferring it to your checking account? In an emergency, you probably won’t want to feel overwhelmed by the process of accessing your emergency funds.

  • [1]For a longer discussion of emergency savings, check out http://brokewallet.com/emergency-fund/.

    [2]https://www.schwab.com/public/schwab/investing/accounts_products/investment/money_markets_funds/purchased_money_funds#government_treasury, December 2, 2018.

    [3]https://www.wellsfargo.com/investing/cash-sweep/rates-and-yields/, November 29, 2018.

    [4]https://www.wellsfargo.com/savings-cds/rates, November 17, 2018.

    Employee Stock Ownership: ESOPs and ESPPs

    I have seen three types of employer offerings related to employee stock ownership. I talked about the first in this post – allowing employees to purchase company stock in their defined contribution plans.  The second is and ESOP or Employee Stock Ownership Plan. The third, an ESPP or Employee Stock Purchase Plan let you buy company stock, often at a discount.

    Employee Stock Ownership Plan (ESOP)

    The first is an Employee Stock Ownership Plan (ESOP) which an employer can set up as a component of its defined contribution plan.  (For more information about defined contribution plans, see my post on that topic.) Under an ESOP, an employer contributes company stock to an employee’s defined contribution account.  The employee cannot sell the stock until he or she resigns or retires from the company, though there are exceptions.

    If you want to diversify your company stock holdings, you’ll need to talk to your human resources representative to understand your options, if any.  ESOP contributions are usually subject to vesting (increased ownership by the employee as his or her tenure with the company increases). When the employee retires or resigns, he or she will either receive a lump sum or periodic payments, depending on the terms of the plan.

    Employee Stock Purchase Plan

    The second is an Employee Stock Purchase Plan (ESPP).  An ESPP allows employees to purchase company stock through payroll deductions.  Many employers offer their company stock at a price lower than is available if purchased on a stock exchange.  The ability to purchase the stock at a discount can be a real benefit, as long as the stock price doesn’t go any lower than your purchase price before you sell it.  

    ESPPs have varying rules as to how long you have to hold the stock before you can sell it. Also, the tax treatment may be different based on how long you hold the stock.  As I discussed in last week’s post about owning company stock in my 401(k), I preferred to not have much of my investments in my employer’s stock. Therefore, I generally purchased stock through the ESPP, but sold it as soon as was allowed to lock in the benefit of the discounted purchase price.