Risk is a fundamental concept in any investment program. Beta and standard deviation are two common risk measures.

But many investors prefer to view risk differently, at least mathematically. Others do not understand how a complex formula for deriving individual betas and standard deviations can be used practically in a real investment program.

This workshop is devoted to those problems. It discusses risk from a variety of viewpoints and suggests some simple estimates of risk that range from calculating your own beta by graphing to viewing risk as a maximum likely loss of value.

## Another Look at Beta

Beta is a measure of the volatility of a stock’s return relative to the market. The beta of the market is always equal to 1.00. The beta of a stock indicates how much its return will vary vis-a-vis the market. For instance, let’s assume a stock has a beta of 0.75. If the market moves up 10%, the stock will move up on average by 7.5%; conversely, if the market drops by 10%, the stock will drop on average by only 7.5%. Rarely is a common stock beta near zero, and even more rarely is the beta negative, which implies that the movement is the opposite of the overall market. The beta, however, reﬂects only those factors that affect all stocks to some degree—interest rates and tax changes for example. Beta does not capture factors unique to a firm or its industry. Most investors should be diversiﬁed, which eliminates the risk not measured by beta, and thus beta is a relevant number for investors to consider.

Now let’s take a look at the betas for the stocks that make up the Dow Jones industrial average (DJIA). The DJIA is not indicative of the whole market—it is made up of only 30 industrial stocks—but we use it as an example of how to construct a risk profile for your own portfolio. The beta values for each stock come from *Stock Investor Pro*, AAII’s fundamental stock screening and research database as of August 25, 2017.

The betas range from a low of 0.31 for Wal-Mart Stores Inc. (WMT) to a high of 1.74 for Du Pont & Co. (DD). Du Pont’s beta is almost 75% higher than the market beta of 1.00 and is therefore 75% more volatile.

If you were to invest an equal dollar amount in all the 30 stocks of the Dow, the beta of a portfolio made up of these stocks is 1.01: It is simply the average of all the betas. (If you have different dollar amounts invested in stocks, you must determine the percentage of the total portfolio invested in each individual stock and multiply that by the beta. This will give you a dollar-weighted beta for the individual stock, and you can then add these weighted betas to determine your overall portfolio beta.)

Once you have determined your portfolio’s beta, you can determine an expected return. A return should provide the risk-free return plus a premium for taking on extra risk. Therefore, the formula for expected return is:

Riskless return + beta(market return – riskless return)

For instance, if common stocks, in general, are expected to earn a total return of 10%, and a riskless asset—a zero beta—such as a money market fund is expected to yield 2%, then the expected return on the equally weighted Dow 30 stocks would be 10.1%:

0.02 + 1.01(0.10 – 0.02) = 0.1008 = 10.1%.

Using beta in this fashion also gives you an indication of what you can expect your portfolio to return relative to the market. In this instance, the Dow’s 10.1% expected return is slightly more than the overall market’s expected return—an investor in the Dow would be receiving 0.1% in return for taking on more risk. A higher beta means more risk but results in a higher expected return. Let’s take one other example, however, where the market declines, say 30%. Your return experienced is likely to be near –30.3%:

0.02 + 1.01(–0.30 – 0.02) = –0.3032 = –30.3%

Once you have determined your portfolio’s expected return based on its level of risk, you can determine if the risk is worth the extra return. You can also compare it to your portfolio’s actual return. A portfolio that consistently returns less than its expected return is not providing enough return to justify the risk. A portfolio’s beta can also be used to produce a risk-adjusted rate of return. The risk-adjusted return is the portfolio return divided by the portfolio beta, and it reﬂects the return experienced relative to the level of risk experienced. The risk-adjusted return allows you to compare your portfolio’s return with the returns of other portfolios with different risk characteristics.

## A Non-Statistical Approach

Here is a simple, non-statistical (and old school) way for you to estimate beta. The tools required are graph paper (not semi-log or log scale), a straightedge and a pencil. From a website such as Yahoo Finance or Google Finance, once a week, determine the price change of your stock and the change in the value of a broad market index such as the S&P 500 index. Calculate the percentage change in stock price and the percentage change in the index value. **Table 2** gives an example.

This example only uses four periods and does not consider dividends. Some estimates use dividends, and others do not, but normally the beta is estimated over a three- to five-year period in order to include the average duration of the business cycle. Plotting the above points results in the graph in **Figure 1**.

The line was drawn by sight and made to intersect whole units. This line should be the best ﬁt for the data, minimizing the dispersion of points from the line. Of course, in practice, you would use more data points, but the idea is to generalize the relationship between the return on the security and the return on the market. If every point fell exactly on the line—which is virtually impossible—all variation would be explained by the market’s movement. The more the distance between the various points and the line, the more of the total risk that can be explained by risk unique to the firm or industry and the less confidence we would have in our beta estimate.

Once you have drawn the line, you can determine the beta by measuring the degree of change on each axis—the formula is on the graph. In our example, the beta was approximately 1.00, meaning that this security is about as volatile as the overall market.

## One Other Risk “Measure”

One final look at risk that has great appeal to investors is maximum likely loss. This is difficult to estimate for individual securities and is easier to discuss in terms of general security classifications. Like beta, it relies on historical information that may not be repeated.

Looking at the returns for common stocks and small stocks during the postwar period can provide some idea. **Table 3** lists those years in which either had a loss, and it provides the total return during that year.

Since 1946, common stocks, as represented by the S&P 500 have seen 15 down years, compared to 20 down years for small stocks. The biggest annual loss for the S&P 500, between 1945 and 2016, is 37.0% in 2008. For small stocks, 2008 was also their worst year as they fell 36.7%.

Remember that longer holding periods—say, over five years—provide strong diversification for these loss years.

*This article was written by John Markese for the March 1985 issue of the *AAII Journal*. At the time, Markese was director of research at the American Association of Individual Investors. Markese is also a former president of AAII and currently serves as chairman.*

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