Tag: Stocks

The Case for a Few Good Stock Runners

The Case for a Few Good Stock Runners

Many investors limit the amount of their investments in individual companies to manage the riskThe possibility that something bad will happen. More in their portfolios.  Others advocate holding on to stocks whose prices increase faster than the rest of your portfolioA group of financial instruments. 

Why I Chose Patience over Re-balancing

Why I Chose Patience over Re-balancing

Many financial advisors recommend re-balancing your portfolioA group of financial instruments. More no less often than annually to ensure the asset allocation is consistent with your risk tolerancePersonal preference indicating how much risk you are willing to take to achieve a higher return. More, as 

Diversification: Don’t Get Misled by these Charts

Diversification: Don’t Get Misled by these Charts

Diversification is an important component of any investing plan.  It assists you in limiting your risk either to a single asset class or a single security within an asset class.  However, I have seen a couple of graphs from which you could form the wrong conclusions about diversification.  In this post, I show you the charts, identify the wrong conclusion that could be drawn from them, and explain and illustrate the correct conclusion.

Diversification Fallacy #1: A Combination of Stocks and Bonds Provides a Higher Return than just Stocks

I first saw a chart[1] in a post on Schwab’s website a couple of years ago.  It is the first graph on this page.  It was prepared in 2018 and compares the cumulative return on the S&P 500 and a portfolio that is 60% stocks (as measured by the S&P 500), 35% bonds and 5% cash from 2000 to 2017.  I’m not sure why Schwab chose to use an 18-year period for this chart, other than the beginning of the time period corresponds to the turn of the century.  The portfolio is re-balanced annually.  In that chart, the total return on the re-balanced portfolio is slightly higher than the S&P 500 (167% versus 158% or 5.6% vs 5.4% per year).

My Version of Chart

Because I can’t include the Schwab chart here, I created a chart (shown below) that shows a similar result for the same time period.  It compares the cumulative returns on the S&P 500 with those of a portfolio of 60% stocks and 40% 20-year US Treasuries (using an approximation I derived for older years).  The mixed portfolio is re-balanced annually, similar to the calculations in the Schwab chart.

Cumulative returns on S&P 500 and mixed portfolio
Cumulative Returns

In this graph, the ratio of the value of the S&P 500 at each year end to its value on December 31, 1999 is shown in purple.  The blue line shows the corresponding ratios for the portfolio of 60% stocks and 40% bonds.  The S&P 500 never makes up the losses it experienced in the first few years of this 18-year time period.

Incorrect Inference about Diversification

At first glance, these charts appear to imply that you can earn more if you hold a 60%/35%/5% mix of stocks, bonds and cash (or 60% stocks/40% bonds) than if you invest in just the S&P 500.  That conclusion confused me, as bonds tend to have total returns that are lower than stocks over the long run and cash has close to no return.   If you re-balance your portfolio annually, as assumed in the graph, your total return in each year will be 60% times the return on stocks plus 35% times the return on bonds plus 5% times the return on cash.  Since the returns on bonds and cash are less than the return on stocks, I was sure that the weighted average of the returns would have to be less than the return on stocks alone.

The Reality

It wasn’t until recently that I figured out why the chart looks the way it does.  The analysis was performed in 2018, so it used the most recent complete 18-year period available.

Historical Perspective

It turns out that period was a rarity in recent history – it was one of only three 18-year periods in which bonds had a higher total return than stocks when considering all such periods from the one starting in 1975 to the one starting in 2002!  If we go back all the way to 1962, the mixed portfolio had higher returns in about a third of the 18-year periods.  The chart below illustrates this point.

18-Year Cumulative Returns for period starting in 1963

Each pair of bars corresponds to an 18-year period (the time period in the Schwab chart) starting in the year shown.  The bar on the left in each pair shows the estimated cumulative 18-year return on a portfolio of 60% stocks[2] and 40% bonds[3] that is re-balanced annually.  The bar on the right shows the corresponding return on the S&P 500 during each period.  As you can see, in most recent years, the right bar (100% stocks) has a higher return than the left bar (60% stocks and 40% bonds).  In older years, the left bar tends to be higher.

How to Use this Information

If your investment goal is to maximize your return without regard to risk, a portfolio with 100% stocks will better meet that objective more than two-thirds of the time when considering 18-year periods and an even higher percentage of the time if you consider only more recent experience.  If interest rates increase substantially at some point in the future, you might look at the longer time period for deciding whether to add bonds to your portfolio, as interest rates were higher and rose in many of the years from 1962 to 1980.  But you’ll want to wait until interest rates are a fair amount higher than their current levels before those years are relevant to your decision-making.

If, however, you want to reduce volatility, adding bonds (or other asset classes) to your portfolio can help.  My post on diversification for investments provides several illustrations about how the addition of bonds to your portfolio reduces risk, but also reduces your total return.  As you consider using other asset classes to reduce volatility, you will need to consider your time horizon for your investments.  As indicated in the chart above, there have been no 18-year periods in the time covered by the analysis in which the S&P 500 had less than a 3% annualized return or 59% compounded return.

Fallacy #2: Diversification in Rank Order Matters

When I first saw this chart from Callan[4], I thought it was very impressed with how it illustrated the benefits of diversification.

Callan Periodic Table of Investment Returns

The font is small so your probably can’t read the words and numbers, but the visual impact is terrific.  Each column is a calendar year.  Each color corresponds to a different index.  The rows correspond to the order of the returns on each index in each calendar year, with the top row showing the index with the highest return; the bottom, the lowest return.

The indices by color (in the order they appear in the first column) are:

  • Rust: S&P 500 Growth
  • Olive green: S&P 500
  • Grey: MSCI (Morgan Stanley Capital International Index) World ex US
  • Dark blue: S&P 500 Value
  • Light green: Bloomberg Barclays Aggregate US Bond Index
  • Medium blue: Bloomberg Barclays High Yield Bond Index
  • Mustard: Russel 2000 Growth
  • Brown: Russell 2000
  • Light blue: Russell 2000 Value
  • Orange: MSCI Emerging Markets

Incorrect Inference about Diversification

At first glance, it appears that there is a lot of diversification among these asset classes, as the colored boxes move up and down on the chart from year to year.

The Reality

It wasn’t until I plotted the returns (using roughly the same colors) on a line chart that the true lack of diversification became apparent.

Annual returns from 1997 to 2017 for funds in Callan chart

Even though the order of the indices changes, as shown in the Callan chart, most of them actually move substantially in sync.  For example, the MSCI Emerging Markets Index moves all over the Callan chart not because it adds diversification but because its returns are much more volatile.  In 14 of the 20 years in the Callan chart, the MSCI Emerging Markets Index is either at the top or the bottom.  It moves in the same direction as most of the other indices, it just makes bigger moves.

Correlations

The goal of adding new asset classes to your portfolio is to increase diversificationAsset classes are diversifying when they have negative or even small positive correlation.  I provide a detailed explanation of correlation and diversification in this post.  The chart below shows the correlations between each pair of indices in the Callan chart.

Correlations between funds in Callan chart

High positive correlations are highlighted in red (as that means they aren’t diversifying).  Medium positive correlations are shown in yellow and small positive and negative correlations (the ones we are seeking) are in green.

It becomes quickly apparent that the only asset class that is diversifying over this time period is US bonds (Bloomberg Barclays (BB) Aggregate US Bond Index).  If you look at the line graph above, I have made the line for the Bloomberg Barclays Aggregate US Bond Index a bit thicker than the others to help you see its lack of correlation with the other investment classes.

Different Insights

While I found the diversification message misleading in this chart, I still found value in the data itself.

Investment-Grade Bonds add Diversification

First, as discussed above, the diversification benefit of investment-grade bonds relative to all of the stock indices is quite evident.  Interestingly, high-yield bonds are highly correlated with stocks, so don’t add diversification.

Asset Classes Show Risk-Reward Balance

Second, I calculated the average annual return and the standard deviations of those returns.  As shown in the chart below, the different indices are spread widely along the spectrum that balances risk and reward.

Average and standard deviations of returns on funds in Callan chart

Specifically, the Bloomberg Barclay Aggregate US Bond Index is in the lower left corner indicating it has a lower average return than all of the other asset classes over this time period but also has the lowest risk as measured by the standard deviation of the annual returns.  By comparison, the MSCI Emerging Markets Index has both the highest annual average return and the highest risk, as it is in the upper right corner of the chart.  All of the other indices fall in the middle on both average return and risk.

Selecting Asset Classes for Your Portfolio

As you are choosing the asset classes in which you want to invest, you need to consider all three of average annual return, risk and diversification benefits.  For example, if you have a very long time horizon and can tolerate the ups and downs of the returns, the historical data indicates that investing primarily in the Emerging Markets index would maximize your return.

If you have a shorter time horizon or are less able to watch the value of your investments go up and down, you might want to invest in something with a lower return, such as one of the stock indices.  If you have even lower risk tolerance or a shorter time horizon, you might want to add something like the Aggregate US Bond Index to your portfolio.  It is important to recognize, though, that adding the less volatile asset classes to your portfolio, even if they are diversifying, will lower the expected annual return on your portfolio at the same time it is lowering your risk.

Caution about Using Past Findings in the Future

In closing, I caution you that the time period covered by the Callan charts corresponds to a time period during which interest rates were relatively low and generally decreasing.  During the time period from 1997 to 2017, the highest yield on the 10-year US Treasury on a year-ending date was 6.7% at the end of 1999.    It decreased to 1.7% at the end of 2014 and increased very slightly to 2.7% by the end of 2017.  By comparison, it hit a high of 12.7% at the end of 1981 and is currently (August 2020) below 1%.  Neither extreme is covered by this time period.

The relatively stable returns on the Bloomberg Barclay Aggregate US Bond Fund Index may be more representative of the time period included in the analysis and may understate the overall volatility of that index over a longer period of time.  Similarly, the other indices may behave differently in other interest rate environments.

I suggest using the information in this post to enhance your understanding of the returns, volatility and diversification benefit of the different asset classes.  You’ll want to supplement this information with your views on future economic environments before making any investment decisions.

[1] I am not able to include the chart directly in this post as I am not willing to accept the conditions that would be required by Schwab to get its permission.

[2] As measured by the S&P 500.

[3] As measured by the iShares 20+ Year Treasury Bond Fund ETF starting in 2002 and my approximation of those returns for prior years.  I note that the Schwab chart uses the Bloomberg Barclays U.S. Aggregate Bond Index for bonds and the FTSE Treasury Bill 3 Month Index for cash.  I don’t not have access to that information.  Because I used a government bond index that tends to provide lower returns than a corporate bond index, I used 40% weight to bonds and ignored the cash component.

[4] Used with permission.  https://www.callan.com/?s=2017+Periodic+Table.  August 8, 2020.

7 Must-Know Stock Market Sell Signals

7 Must-Know Stock Market Sell Signals

Before we talk about the specific indicators that would signify stock market sell signals, we must understand why we bought each stock in the first place. The simple theory of ‘buy low, sell high’ seems practically very easy, but the reality of the situation is 

Why I Don’t Hold the All Seasons Portfolio

Why I Don’t Hold the All Seasons Portfolio

The All Seasons PortfolioA group of financial instruments. More reports amazing statistics about its returns.  I’d never heard of the All Seasons PortfolioA group of financial instruments. More, so had to check it out.  As I’ll discuss in more detail, it is an asset allocation 

Selecting Stocks with a Score

Selecting Stocks with a Score

A friend of mine really likes selecting stocks with a score, the Piotroski score in particular.  Briefly, Professor Piotroski created a set of nine financial ratios that contribute to the score. If a company meets a certain criterion and has favorable results on 8 or 9 of the ratios, his analysis indicates that the company’s stock is likely to do well. My friend is primarily a value investor. The appeal of the Piotroski score to him is that it focuses on value stocks and, while it relies heavily on statistical analysis, it isn’t a black box.

In this post, I’ll identify the group of stocks to which the Piotroski score applies. I’ll then briefly explain the financial ratios that determine the score. I’ll close with a specific example of a stock I bought solely using the Piotroski score and provide some general guidance on applying the results of the score.

Book-to-Market Ratio

What is It?

The book-to-market (BM) ratio is a financial ratio. The numerator is the book value of the company. This value is shown on the balance sheet in the company’s financial statements and is usually reported as “Shareholders’ Equity.”

The denominator of the ratio is the total market value of the company on the evaluation date as the financial statements. The total market value is the stock price multiplied by the number of shares outstanding and is also called the market capitalization.

In mathematical terms,

BM Ratio = Book Value divided by Market Capitalization

Piotroski waits for the financial statements to be published for a particular year end to get the book value. He then looks up the market capitalization on the evaluation date of the financial statements for use in the ratio.

Piotroski’s Criterion

In his paper, Piotroski identifies value stocks as companies that have BM Ratios in the highest quintile (highest 20%) of traded stocks. These stocks have high book values relative to their market capitalization. Looked at from the other perspective, these stocks have low market capitalizations (and therefore low stock prices) relative to their book value.

Recall that the book value is the company’s assets minus its liabilities. In theory, if the company were liquidated on the evaluation date of the financials, shareholders would get their portion of the Shareholders’ Equity, based on the proportion of shares owned. Therefore, a BM ratio of 1.00 means that the market capitalization of the stock is equal to the Shareholders’ Equity.

By comparison, the cut-off for the highest quintile of BM ratios[1] across all stocks reported in the ValueLine Analyzer Plus on May 29, 2020 is 1.47. The book values per share of these companies are almost 50% higher than their stock prices!   You can see why Piotroski might consider these stocks to be potentially good values at their current prices.

Why Might It Be High?

There are at least two reasons that the BM ratio might be high.

First, the market may perceive that either assets are overvalued or liabilities are undervalued. Both of these situations would cause the reported book value to be higher than its true amount.

For example, some companies have not fully funded their pension plans. That means that the estimated present value of the future pension benefits is more than the liability on the balance sheet. Companies disclose these differences in the Notes to Financial Statements. If the liability for pension benefits is understated, it will cause the company’s book value to be overstated.

Second, financial theory tells us that the market value of a company’s stock is equal to its book value plus the present value of future profits. If the market perceives that the company is unlikely to make money in the future, the market capitalization will be less than the book value.

The Piotroski score focuses on companies in the second category. That is, it attempts to identify companies that will be profitable in the future from among all of the companies that the market thinks will have negative future profits.

Piotroski Score

The Piotroski score is calculated as the sum of a set of 9 values of 1 or 0. There are 9 criteria in the calculation, in addition to the BM ratio being in the highest quintile. The process assigns a 1 if a company’s financial statement values meet each criterion and a 0 if it does not. As such, companies that meet 8 or 9 of the criteria are considered more likely to have above market average performance.

The 9 criteria are listed below:

  1. Return on assets (ROA) = Net income / Total assets at beginning of year > 0
  2. ROA this year > ROA last year
  3. Cash flow from operations > 0
  4. Cash flow from operations > net income
  5. Long-term debt / Total assets this year < Long-term debt / Total assets last year
  6. Current ratio this year > current ratio last year
  7. Shares outstanding this year <= shares outstanding last year
  8. Gross margin this year > gross margin last year
  9. Total sales / Total assets this year > Total sales / Total assets last year

Piotroski performed his analysis using data from companies’ financial statements from 1976 to 1996. The average of the one-year returns for the companies with scores of 8 or 9 was 7.5 percentage points higher than the average for all companies with high BM ratios and 13.5 percentage points higher than the average for the market as a whole.

How to Calculate It

If you are familiar with reading financial statements, you can calculate the Piotroski score yourself using the formulas above. Or, you could extract the key ratios from a source, such as ValueLine, Tiingo or Bloomberg, all three of which require subscriptions. I use the latter approach as I have a subscription to ValueLine that I use for a variety of purposes.

An easier option is to use a Piotroski calculator or screener.   I’ve never used any of these tools, but I used Google to find a couple free options you might try.

  • Old School Value – This Excel spreadsheet will calculate and show you how a company does on each of the 9 tests and the total score.
  • ChartMill – This screener lets you identify stocks based on their Piotroski score. As such, it helps you find stocks with scores of 8 or 9, but does not show you the details of the underlying calculation.

I suggest being careful to check the documentation of any of these tools to make sure that the descriptions of the 9 tests are the same as I’ve included above (which I took directly from Piotroski’s paper). In poking around on-line, I found more than one site that did not correctly specify the nine tests.

My Experience Selecting Stocks with a Score

Although I’ve looked at stocks using the Piotroski score several times, I’ve made only one purchase using it as my primary buying criterion. I purchased FUJIFILMS (FUJIY) in March 2012. At the time, FUJIY had a BM Ratio of about 1.40, as compared to a market average BM ratio of about 0.5. It had a Piotroski score of 8, having failed the test for an increase in gross margin.

For many, many years, FUJIY’s biggest product was film for cameras. With the advent of the digital camera, its market shrank rapidly. In the year before I purchased the stock, its price decreased by 32%. As I was looking at the company, it was transitioning its business from camera film to other types of related products, including medical imaging and, more recently, office products with its purchase of Xerox. With a good story and a high Piotroski score, I decided to buy the stock.

It turns out I was a little early in buying the stock. In the 12 months after I bought the stock, it decreased by 19% while the S&P 500 increased by 13%. However, if I had bought it a year later, my total return would have been much better over both the short and long term, as shown in the table below.

Total Return starting in March 2013
1 Year2 YearsUntil June 2020
FUJIFILMS+51%+84%+171%
S&P 500+22%+36%+110%

 

So, even though my returns were lower than the market average because I bought the stock too early in the company’s turnaround, I correctly decided to keep it after its first year of poor performance. That is, if I had sold the stock one year after I purchased it and bought an S&P 500 index fund, I would have been worse off.

Caution

As with any investing strategy, it is important that you understand the assumptions underlying the Piotroski score. I also recommend that you understand the story behind the company you are considering for investment, as described in my post on buying stocks based on their financial fundamentals. There are companies that may have a Piotroski score of 8 or 9 that don’t have a good turn-around story, such as the one I described for FUJIY. In those cases, you may not want to rely solely on the Piotroski score.

 

[1] Calculated in this case as Book Value Per Share at most recent fiscal year end divided by Price on May 29, 2020, so not exactly equal to the ratio as calculated by Piotroski.

Picking Stocks Using Pictures

Picking Stocks Using Pictures

Technical analysts select companies for their portfolioA group of financial instruments. More based on patterns in stock prices.  That is, it allows them to enhance their process of picking stocks by using pictures. This approach is very different from some of the others I’ve discussed, 

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 portfolioA group of financial instruments. More by purchasing stocks from an individual company or from buying mutual funds.  With the stock 

At What Price Should I Buy a Stock?

At What Price Should I Buy a Stock?

Deciding at what price to buy a stock or other security is almost as hard as deciding whether to buy the security at all.  There are many different approaches for deciding at what price to buy a stock.  One of the ones I’ve seen discussed most often is dollar-cost averaging.  Other strategies include (1) buying the position on whatever day you decide to buy it and (2) setting a target price that is below the current trading price, among many others.  In this post, I’ll explain and compare these three strategies.

Dollar-Cost Averaging

Dollar cost-averaging is a strategy for buying stocks that is intended to reduce the risk that you will “buy high.”

How it Works

Here are the key steps for implementing this strategy:

  • Identify the security you want to buy.
  • Determine how much money you have to invest in that security.
  • Divide that amount into equal increments. In the examples below, I have split the amount into four increments.
  • Decide over what time period you want to make your purchases. In the examples below, I have illustrated a purchasing time period of four weeks.
  • Invest one increment at points in time evenly spaced over your selected time period. For example, let’s say you want to invest over four weeks.  You might buy the selected security every Wednesday in four equal pieces.  If you have $1,000 to invest, you would buy $250 of the selected security each Wednesday for four weeks.

The underlying premise of this approach is that you buy more shares of the selected security than if you happened to have bought the security on a day that the price is high.  Specifically, because you are buying the security in equal dollar amounts, you will buy more shares when the price is low and fewer shares when the price is high.  As such, your average purchase price will be low.

Simple Example

Here’s a simple example in which you invest a total of $4,800 in increments of $1,200 a week for four weeks.

WeekStock PriceShares Purchased
1$10.00120
28.00150
312.00100
49.25130

In this example, you buy a total of 500 shares.  If you had bought all of your shares on at $10 (the first week price), you would have 480 shares ($4,800 / $10).  In this scenario, you will have 4% more shares ([500 – 480]/480 – 1) if you use dollar-cost averaging than if you bought all of your shares at the first week’s price.  4% more shares corresponds to 4% more money when you sell the security.  Although 4% may not sound like a large difference, it can add up over time as you buy and sell stocks.

To be clear, though, dollar-cost averaging isn’t always better.  If you had bought all of your shares at the Week 3 price of $8, you would have 600 shares or 20% more than if you used dollar-cost averaging.

Investing Strategies

Here are the three strategies for determining when to buy a security that I’ll use for illustration.

Strategy 1 – Invest Immediately

Invest all of your available money on the day you decide to make the purchase.

Strategy 2 – Dollar-Cost Averaging

Use dollar-cost averaging by buying ¼ of your money available on Wednesday of four consecutive weeks[1]. This strategy is similar to what happens when you buy securities in your employer-sponsored retirement account if you are paid weekly.  Every week, you employer takes some of your wages and invests it in the security you have selected.

Strategy 3 – Wait for Price Drop

Invest all of your available money after the stock price has dropped by 5%. Hold your money in cash while waiting for the price to decrease.

More Examples

I’ve created a few more simple examples to compare the strategies for deciding when to buy a security.  These examples are intentionally simple and therefore unrealistic.  Nonetheless, they are helpful in understanding the different strategies because of their simplicity.  In all of the examples, you have $1,000 to invest.

Smooth Increase

In the first scenario, the stock’s price goes up smoothly by 10% every year.  A graph of its price over two years would look like this.

Line graph with straight line going from $10 stock price on day zero to $12 stock price on day 700

The chart below focuses on the first month of the above chart and includes the purchases for Strategies 1 and 2 as dots.

Graph showing prices when you buy under Strategies 1 and 2

Under Strategy 1 (big red dot), you buy all of your stock on the first day at $10 a share, so you are able to purchase 100 shares.

Under Strategy 2 (smaller green dots), you would buy $250 of stock on each of the first, eighth, fifteenth and twenty-second days.  The table below shows the prices on those days and the number of shares you buy.

DayPriceShares Bought
1$10.0025.00
810.0224.95
1510.0424.90
2210.0524.88

The total number of shares you buy is 99.73.

Under Strategy 3, you never buy the stock because the price never decreases by 5%.

The table below compares the numbers of share bought under each strategy

StrategyNameNumber Shares BoughtValue in Two Years
1Invest Immediately100.00$1,210
2Dollar-Cost Averaging99.731,203
3Wait for Price DropN/A1,000

In this scenario, there is very little difference between the first two strategies, though you will buy more shares if you invest immediately. Any time you delay your purchases in this scenario, you are certain to pay a higher price which reduces the number of shares you can buy.  Under Strategy 3, because the price never decreases, you never buy the stock, so end up with the same amount of money with which you started.

Smooth Check Mark

The second illustration is stock whose price goes down smoothly for six months and then increases for the next 18 months.  A graph of its price would look like this.

Line graph with line that looks like a check mark.

The chart below focuses on the first six months of the above chart and includes the purchases for all three strategies as dots.

Graph showning prices you pay under 3 strategies if price graph is checkmark

Under Strategy 1 (big red dot), you buy all of your stock on the first day at $10 a share, so you are able to purchase 100 shares.

Under Strategy 2 (smaller green dots), you buy $250 of stock on each of the first, eighth, fifteenth and twenty-second days.  The table below shows the prices on those days and the number of shares you buy.

DayPriceShares Bought
1$10.0025.00
89.9825.05
159.9625.10
229.9425.15

The total number of shares you buy is 100.30.

Under Strategy 3, you buy 105.2 shares at $9.50 (5% below the initial price of $10) on day 177.

The table below compares the numbers of share bought under each strategy and the amount of money you will have at the end of two years.

StrategyNameNumber Shares BoughtValue in Two Years
1Invest Immediately100.0$1,097
2Dollar-Cost Averaging100.31,100
3Wait for Price Drop105.21,154

In this scenario, the best strategy is to wait until the price drops by 5% which happens to be the minimum price over the two-year period.  The results of the other two strategies are very similar, though investing all of your money on the first day is the worst choice, as you buy stock during the period in which the price has fallen under the other two strategies.

Bumpy Increase 1

Next, we will look at two illustrations of what a stock price might actually look like.  Here is a graph of the first illustration.

Prices when they increase on a bumpy path

The chart below focuses on the first month of the above chart and includes the purchases for Strategies 1 and 2 as dots.

Prices at which you buy under strategies 1 and 2

Under Strategy 1 (big red dot), you buy all of your stock on the first day at $10 a share, so you are able to purchase 100 shares.

Under Strategy 2 (smaller green dots), you would buy $250 of stock on each of the first, eighth, fifteenth and twenty-second days.  The table below shows the prices on those days and the number of shares you buy.

DayPriceShares Bought
1$10.0025.00
89.8325.43
159.8825.30
229.8025.51

The total number of shares you buy is 101.24.

Under Strategy 3, you don’t buy any shares because the price never falls by 5%.

The table below compares the numbers of share bought under each strategy

StrategyNameNumber Shares BoughtValue in Two Years
1Invest Immediately100.00$1,144
2Dollar-Cost Averaging101.241,158
3Wait for Price Drop0.001,000

In this scenario, the best strategy is to buy your stock using Dollar-Cost Averaging (Strategy 2), but only by a small amount compared to using the Invest Immediately strategy.  You will have 1% more money than if in you invest it all on the first day and 13% more money than if you wait for the price to drop.

Bumpy Increase 2

The second realistic illustration is exactly the same as the first one with the exception that, in the first month, the price bounces around a bit above the initial $10 price rather than just below it.  The chart below focuses on the first month for this illustration and includes the purchases for Strategies 1 and 2 as dots.

Prices at which you buy under strategies 1 and 2

Under Strategy 1 (big red dot), you buy all of your stock on the first day at $10 a share, so you are able to purchase 100 shares.

Under Strategy 2 (smaller green dots), you would buy $250 of stock on each of the first, eighth, fifteenth and twenty-second days.  The table below shows the prices on those days and the number of shares you buy.

DayPriceShares Bought
1$10.0025.00
810.2124.49
159.8825.30
2210.3124.25

The total number of shares you buy is 99.04.

Under Strategy 3, you don’t buy any shares because the price never falls by 5%.

The table below compares the numbers of share bought under each strategy

StrategyNameNumber Shares BoughtValue in Two Years
1Invest Immediately100.01,144
2Dollar-Cost Averaging99.041,133
3Wait for Price Drop01,000

In this scenario, the best strategy is to use the Invest Immediately strategy (Strategy 1), but only by a small amount compared to Dollar-Cost Averaging.  You will have 1% more money than if in you use Dollar-Cost Averaging and 14% more money than if you wait for the price to drop.

More Realistic Examples

Now that you have a better understanding of the three different strategies, I’ll turn to even more realistic scenarios.

  • The first of these scenarios will use the actual returns on the S&P 500 from 1928 through early 2020. This scenario is likely to be relevant when you are considering an investment in an index fund.
  • The second scenario is intended to be similar to an investment in an individual stock. To create the example, I took the S&P 500 times series and doubled the volatility.[2]

The daily stock prices are illustrated in the graph below.

S&P 500 prices from 1928 to 2020

Investment Horizons

To illustrate the impact of the different strategies, I looked at three different time periods over which you might hold the stocks – one year, five years and ten years.  If you are young and hold a stock until you retire, such as I have with some of the stocks I own, you might own the stock for 30 or 40 years.  I didn’t feel there was enough data available in the above time series to look at the impact on owning securities for more than ten years.  So, if you think you will be a very long-term investor, you will want to focus on the ten-year results.  Also, these analyses are not helpful to people who plan to own stocks over very short periods of time, such as some traders who might buy and sell a security in the same day.

Comparison of Realistic Results

The table below compares how much money you would have, on average across all possible starting dates for which data were available, at the end of each of the three time periods if you used each of the three strategies to buy $1,000 of an S&P 500 index fund.

StrategyOne YearFive YearsTen Years
Invest Immediately1,0741,3721,873
Dollar-Cost Averaging1,0741,3731,877
Wait for Price Drop1,0221,1811,485

 

The table below compares how much money you would have, on average, at the end of each of the three time periods if you used each of the three strategies to buy $1,000 of the illustrative stock.

StrategyOne YearFive YearsTen Years
Invest Immediately1,0871,3761,875
Dollar-Cost Averaging1,0871,3791,880
Wait for Price Drop1,0771,3301,772

 

Dollar-Cost Averaging vs. Invest Immediately

For both the S&P 500 and the illustrative stock, there are only very small differences (less than 0.3% for the one-year investment horizon and less than 1.3% for the longer investment horizons) in the average amount of money at the end of each of one, five and ten year between the Dollar-Cost Averaging and Invest Immediately strategies.

Wait for Price Drop

On the other hand, there is a larger difference between the average amount of money at the end of the three time periods if you use the Wait for Price Drop strategy and the average amount using either of the other two strategies.  For the S&P 500, you will have between 5% and 20% less money, on average, if you use the Wait for Price Drop strategy than if you use the Invest Immediately strategy, depending on your investment horizon.

For the more volatile illustrative stock, you will have between 1% and 5% less money, on average, if you use the Wait for Price strategy than if you use the Invest Immediately strategy.  With the higher volatility of the illustrative stock, it is more likely to have a 5% price drop.  There are therefore fewer scenarios in which you don’t get any investment return than there are using the S&P 500 prices.  As such, there is a smaller difference between the results of the Wait for Price Drop strategy and the other strategies for a more volatile security than for a more stable one.

Key Takeaways

As can be seen, the best strategy depends on the pattern and volatility of the security’s price.  Briefly:

  • For securities that have fairly smooth trends, there isn’t a lot of difference between the Invest Immediately and Dollar-Cost Averaging strategies.
  • For securities with more volatile prices, such as the two Bumpy Increase scenarios, the choice between the Dollar-Cost Averaging and Invest Immediately strategies can be a bit larger. However, there isn’t one that is better in all situations – Dollar-Cost Averaging was better in Bumpy Increase 1 while Invest Immediately was better in Bumpy Increase 2.  Because you can’t know whether your security’s price will follow a pattern closer to Bumpy Increase 1 or Bumpy Increase 2, neither strategy is preferred.
  • If you think that the price of the stock might trend down somewhat significantly or has a lot of volatility allowing the price to be significantly lower than the current price, waiting for a 5% (or other value you select) price decrease (Strategy 3) could be the best strategy. The drawback of this strategy is that there are a lot of scenarios in which you will never buy the security and then will get no return.

What Do I Do?

With all this information, you might wonder what I do.  I first need to provide a little background about my current investing situation, as it is likely to be different from yours.

I am retired, so am starting to spend my investments.  As such, I have a shorter investment horizon than I did when I was younger and in the saving mode.  I have a number of stocks and a few mutual funds that I have owned for many, many years and do very little trading of those positions.

Another portion of my money is in sector funds (index funds that focus on one segment of the economy, such as industrial companies, healthcare or technology) and a few large companies.  I tend to hold those securities for six months to two years.  The securities I am trading are closer in nature to the S&P 500 time series than even the hypothetical company with twice the volatility as the S&P 500.  As such, the Wait for Price Drop strategy doesn’t work for me.

With the very small differences between the Dollar-Cost Averaging and Invest Immediately strategies, I choose the Invest Immediately strategy because it is easier.  I have to place only one buy order instead of several orders.

Limit and Market Orders

As discussed in my post on stocks, there are different types of orders you can place when you want to buy a stock.  I always place limit orders.  A limit order allows me to buy a stock from the first person who wants to sell it to me at the price I have stated in the order.

The other type of order is a market order.  If you place a market order, you don’t get to set the price.  You buy the stock at whatever price it is trading at the moment you place the order.

There are risks to both types of orders.  If you place a market order and the price jumps up, you will buy the stock at the higher price.  If you place a limit order for a price below the current market price, you might never buy it similar to the Wait for Price Drop strategy.

A Compromise

To avoid the risk that I might buy a stock at a significantly higher price than I intend, I place a limit order with a limit that is about half way between the closing price and the low price from the previous day.  (I almost always place my orders over the weekend, so don’t have “up-to-the-minute” prices.)  This difference is often between 0.5% and 1% of the price.  By taking this strategy, I get a very small boost to my return by setting my limit below the market price but with very little risk that I won’t buy the stock because I have chosen the limit amount to be within a single day’s trading range.  The additional 0.5% to 1% doesn’t sound like a lot, but if I am able to increase my total return by that amount every year or two, it compounds quickly.

Footnotes

[1] There is nothing special about once a week for four weeks.  I did some testing of once a day for five days and found that there wasn’t a lot of difference in the number of shares bought, on average across a wide range of scenarios, from what the number using once a week for four weeks.  I also did some testing of what happens when you buy shares once a month for a year.  Across a wide range of realistic scenarios, you own fewer shares on average if you spread your purchases over a year as you purchase securities that you think will increase in price.  If the price of the security increases over the year, you will buy some of your shares at the higher price and own fewer shares.

 

 

[2] This note explains the nitty gritty details of how I adjusted the S&P 500 time series to create the second scenario.  I calculated the 200-day moving average of the daily closing prices of the S&P 500 from 1928 to early 2020.  The deviation is the actual closing price minus the moving average.  I doubled this deviation and added it back to the moving average to simulate prices for the hypothetical stock.

Mutual Funds and ETFs

Mutual Funds and ETFs

Mutual fund and ETFs (exchange-traded funds) allow you to invest in securities without having to select individual positions. Instead, the fund manager makes the decisions as to when to buy and sell each security. As such, a fund is an easy way for new or