Should I Buy Stocks Now?

Should I Buy Stocks Now?

Many, if not most, financial advisers recommend accumulating wealth from a diversified set of investments including stocks.  An investor can add stocks to her/his portfolio by purchasing stocks from an individual company or from buying mutual funds.  With the stock market down double digits since the beginning of 2020, some experts say stocks are “on sale” and now is a good time to buy, but just over half of Americans report they own stocks. This is down from 62% prior to the 2007/8 recession and it includes ownership of stocks that are contained within retirement funds and mutual funds, as well as individual stocks.  Common reasons to not buy stocks/mutual funds are (1) stocks are complicated and I don’t know how to get started, and (2) stocks are too risky.  Let’s review both of these drawbacks.

Stocks are Complicated

All too often, some of my friends and family are reluctant to purchase stocks because they do not understand the stock market.   Even some of my most intelligent friends shy away from financial conversations that involve the stock market because they do not want to appear ignorant.

If you did not learn about investing in school or from your parents, how can you figure this out?  How do you convert your dollars into stocks?  How do you learn which stocks are worthwhile?  Should you purchase individual stocks or mutual funds and, by the way, what exactly are mutual funds?

Investment Clubs Help You Buy Stocks

You can learn about many of these topics in a fun way by forming an investment club with like-minded friends and/or family.  Since 2004, I have been a member of Take Stock, a ladies’ investment club.  Our club is one of the 4,000 investment clubs of the National Association of Investors Corp. (NAIC).  The NAIC was formed in 1951 as a 501(c)(3) nonprofit organization with the aim of teaching individuals how to become successful long-term investors.  Originally, the NAIC’s focus was investing in common stocks, but, with the popularity of 401(k)s and other retirement plans, the NAIC has added education about stock and bond mutual funds.

The NAIC (also more recently known as Better Investing) stresses four principles for successful, long-term investing:

  1. Invest regularly, regardless of market conditions;
  2. Reinvest all earnings;
  3. Invest in growth companies (and growth mutual funds); and
  4. Diversify to reduce risk.

What Information Can I Get from NAIC/BI?

NAIC/Better Investing (NAIC/BI) provides many tools and resources to help individuals as well as investment clubs learn about investing.  There is a stock selection guide (SSG) that organizes companies’ performance information to allow you to determine for yourself whether a particular company is a stock you want to purchase and the price is reasonable.  Some of the free resources offered by NAIC/BI include:

  • Over 100 free stock investing videos;
  • An introduction to stock investing that explains the SSG;
  • How to start your own investment club;
  • Investor education articles;
  • Stories from members; and
  • 90-day free membership.

How My Club Works

My club was formed in 1999. It is comprised of nine women who meet monthly in each other’s homes.  Of the nine members, the one with the longest tenure is a charter member and the most recent arrival has been in our club for just over one year.   During our meetings, we review our club’s portfolio (currently stocks of twelve companies), discuss stocks to research for possible future purchase, and vote on any companies that we have already researched. It is not required that you meet in members’ homes—you could choose to meet at your local library, a restaurant, etc.  We typically meet in the evening on the second Tuesday of each month and the hostess for that month provides a light meal.  Every July, we meet at a local park for a summer concert and we bring our families/friends.

Monthly “dues” are used to invest in stocks and your ownership is based upon what percentage of the total portfolio you have invested through your paid dues.  The monthly dues are in multiples of $25 (i.e., $25, $50, $75 etc.) and there is a monthly minimum of $25.

I highly recommend forming or joining an investment club.  You’ll have the opportunity to learn more about the stock market, to learn more about individual companies that you and your club research, and you’ll get to know your friends and acquaintances better.  The best part is you’ll have fun while investing in your financial well-being and you will all become richer by enhancing your friendship.

One Final Caveat

If you are new to investing you will probably want to invest the portion of your money that you will not need in the near term, such as a down payment on a home you wish to  purchase three or more years from now, your children’s education fund, or your retirement fund.  Your rainy-day fund should be kept in more liquid investments that can be accessed quickly.

So now that you know you can have fun and learn about the stock market, you may still be reluctant to buy stocks due to the risk involved.  Let’s review this objection to increasing your wealth. . .

Stocks Are Too Risky

One of the primary concerns about owning stocks is the risk inherent in these investments.  What if I invest my money in the stock market and the stock market crashes as we have seen since Covid-19 or like we saw in 2008/2009?  While it is true that declines of 15+% in your investment portfolio are not desirable, it is also true that in every case where the stock market has had a large decrease, the stock market more than made up for the declines in the months and years following the drop.

As of this writing (April 30, 2020), since the beginning of 2020, the Dow Jones Industrial Average (Dow) is down about 18% and the S&P 500 is down about 11%.   While not good news, if you were invested in the market during 2019, you would still be ahead because the Dow rose more in 2019 than the current 2020 drop. (Dow added 22% and the S&P 500 added 28% during 2019).

We have likely heard the old adage:  risk is reward. That is, the more reward that is sought, the more risk that must be taken.  If you are desirous of the smallest risk possible, then you would probably choose to park your money in (for example) savings bonds or certificates of deposit which will guarantee you a reward albeit a small one.  If you prefer more reward, then you will likely choose to invest some of your portfolio into the stock market.  Let’s look at an example of how a specific risk tolerance manifests into investment growth.

Risk-Reward Comparison

Five years ago, assume you invested $1,000 with (1) small risk (investing in a certificate of deposit), (2) medium risk (investing in an S&P 500 mutual fund) or (3) high risk (investing in only one individual stock).  Here are the results:

 

CD:  “low” riskS&P 500: “medium” riskAmerican: “high” riskApple:   “high” risk

5/1/15

 $1,000 $1,000 $1,000

 $1,000

12/31/19 $ 1,073 $1,531 $633

 $2,376

4/30/20

 $1,077 $1,395 $298

 $2,209

5-year return

7.7%39.5%-70.2%

120.9%

4.75-year return (through 12/31/19, 0pre-Covid)

7.3%

53.1%-36.7%

137.6%

 

Takeaways from this Exercise

Here are the key takeaways from this table.

  • The lowest-risk investment provides a 7.7% return over five years. This is based on investing $1,000 over a period of five years at current CD rates of 1.5% per year.  Note that while the original investment of $1,000 grows over the five years, it is growing less than the rate of inflation over the five years so you have “lost ground” by investing in a CD.    Over this same five-year period, the Consumer Price Index rose by 8.9%, higher than the 7.7% earned in the CD; thus, your buying power is less since the cost of goods has risen by 8.9% while your investment grew at 7.7%.
  • The medium-risk investment provides a much better return than low risk. You would have earned nearly 40% over the five-year period.
  • The high-risk investment was defined as investing in only one single stock. As you can see, if you chose American Airlines for your one stock, you would have lost 70% of your investment.  However, if you had chosen Apple as your one stock, you would have more than doubled your money and earned a 121% return over five years.

Keep in mind that the results above include the effects of the drop in the stock market from COVID-19.  If we look instead at year end 2019 — before the effects of COVID-19 — we see returns of 7.3% (CD), 53% (S&P 500), -37% (AAL), and 138% (AAPL).

Your Risk Appetite

If your risk appetite is miniscule, then you would probably want to avoid the stock market altogether and put your money into certificates of deposit.   This will not bring wealth to you but it will give you peace of mind.  If you have more tolerance for risk, then investing in the stock market by diversifying your stocks is a much better way to accumulate wealth.   As shown in the example above, it is possible to earn more from investing in high-growth stocks, but it is also virtually impossible to pick which individual stocks will generate above average future growth.  The medium-risk option will usually provide much better returns over the long terms than will the low risk-option.

How I Built My Wealth

Stocks—primarily mutual funds with a variety of individual stocks—have contributed to my personal wealth accumulation.  I recommend including stocks in your assets and joining or forming an investment club with friends and family can be a fun way to further your wealth.  Good luck!

 

Kay Rahardjo, FCAS, MAAA is an actuary and risk management professional. She retired from The Hartford in 2014 from her role as Senior Vice President and Chief Operational Risk Officer. She developed and taught an operational risk management course at Columbia University.

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.  I explain different ways you can diversify your investments and provide illustrations of its benefits in this post.

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 flipSecond flip
HeadsHeads
HeadsTails
TailsHeads
TailsTails

 

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 this 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. Buy a new Xbox and some games for $500.
  3. Spend $700 on clothes.
  4. Get the latest iPhone for $1,000.
  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:

OptionCostEnjoyment Ranking
Ski weekend$1,0003
Xbox5004
Clothes7002
iPhone1,0005
Nothing01

 

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.

Financial Risk & Reward 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.

InsurerDeductiblePremiumAverage Net CostTotal Cost if You have a Large Claim
1$500$1,475$-590$-1,975
11,0001,325-530-2,325
15,000850-340-5,850
25001,500-615-2,000
21,0001,200-455-2,250
25,000900-390-5,900

 

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.

Financial Risk & Reward 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.  Here are links to more information 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.  For more information about stocks, check out this post.
  • 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.

 

Financial Risk: An Introduction

Understanding financial risk is key to making sound 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 financial 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 financial risk, identify some ways to measure it and provide different types of graphs to illustrate it.  In this post, I provide insights on how to make financial decisions in the context of risk and reward.

Financial 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.