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Computerized Investing > First Quarter 2014

Risk-Adjusted Return

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by CI Staff

A basic premise of sound investing is that investors are naturally risk-adverse. Investors seek the lowest level of risk for a given level of return and, alternatively, will not take on additional risk unless there is a higher chance of greater return. Though this is common knowledge, many individual investors neglect to take the time to actually look at an investment’s risk, or volatility, before purchasing. This issue’s Fundamental Focus provides some figures that are easy to calculate and can be used to serve as a gauge for the risk (volatility) of an investment.

Performance

Performance is the main factor that investors use to gauge “reward.” Looking at three of the largest and most well-known technology companies—Apple Inc. (AAPL), Microsoft Corp. (MSFT) and Google Inc. (GOOG) —reveals that each of these firms has strengths and weaknesses. They also have provided investors with different returns over the past three-year period. During the three years ending October 31, 2013, Apple managed a price change performance of 73.7%, while Microsoft gained 32.8% and Google shares were up by 67.9%. The annualized returns for the three companies are 20.2%, 9.9% and 18.9%, respectively. In comparison, the market as measured by the Vanguard Total Stock Market Index fund (VTSMX) was able to achieve an annualized rate of 14.6% during this time frame. On the basis of these numbers, investors would conclude that Apple performed the best of the three during the period, Google was a close second and Microsoft brought up the rear. While this statement is accurate, taking risk into consideration may paint a slightly different picture.

Standard Deviation

Risk is often measured by the volatility of a stock. One of the most commonly used measures of stock volatility is the standard deviation of an investment’s price change over a period of time. This measures the volatility of the investment’s returns. You can use an equation to calculate standard deviation but it is much easier to simply use the STDEV function available in Excel. The following three-year monthly price change standard deviations for Apple, Microsoft, Google and the Vanguard Total Stock Market Index fund were calculated using the Excel STDEV function. To annualize the figures calculated in Excel, you need to multiply the figures by the square root of 12.

Apple 26.13%
Microsoft 20.22%
Google 25.13%
VTSMX 13.07%

These figures show Apple as having the most price volatility of the three stocks, while Microsoft has had the least. All three have had more price volatility over the last three years as measured by standard deviation than the total stock market comparison fund.

  3-Year Annualized Return (%) 3-Year Standard Deviation (%) Risk Index (X) Risk-Adjusted Return (%)
Vanguard 500 Index Fund (VFINX) 16.39 12.47 0.95 17.18
Dreyfus MidCap Index Fund (PESPX) 16.95 15.49 1.19 14.30
Vanguard Small-Cap Index Fund (NAESX) 18.50 16.69 1.28 14.49
Vanguard Emerging Markets Fund (VEIEX) –0.58 20.13 1.54 –0.38
Vanguard Intermediate-Term Bond Fund (VFITX) 2.42 3.82 0.29 8.28
Source: Morningstar, Inc. Data as of October 31, 2013.

Risk Index

AAII tracks over 60 stock screens based on different investment methodologies. In addition to reporting performance, we also provide a risk index figure for each strategy, calculated as a measure of volatility compared to the overall marketplace. For our stock screens online, risk index is calculated by dividing a screen’s annual price change standard deviation since inception by the annual price change standard deviation of the S&P 500 index since inception.

However, you can create a custom “risk index” using any index as the comparison. For Apple, Microsoft and Google, we again use the Vanguard Total Stock Market Index fund for comparison. These calculated figures offer a quick and easy way to visualize the magnitude of volatility of a stock compared to a benchmark. The calculated risk indexes are as follows:

Apple 2.00
Microsoft 1.55
Google: 1.92
VTSMX 1.00

The risk index tells us that Apple and Google shares have been about twice as volatile in price as the Vanguard Total Stock Market Index fund, while Microsoft has been about 1.5 times as volatile in price. These figures can help put these companies’ stock performances into perspective.

Risk-Adjusted Return

Previous Fundamental Focus articles have discussed risk-adjusted performance measures such as the Sharpe ratio (Fourth Quarter 2012 issue of Computerized Investing) and Treynor ratio (First Quarter 2013 issue). Another ratio that you can easily calculate is three-year historical performance divided by three-year risk index. The benefit of using this particular figure is that the risk index component of the ratio standardizes a stock’s volatility to an benchmark, allowing you to gauge the volatility of a stock in terms of a benchmark of your choosing.

Using our sample tech companies and mutual fund benchmark, a risk-adjusted return is calculated using three-year historical performance divided by three-year risk index. The resulting figures for Apple, Microsoft, Google and VTSMX are 10.1%, 6.4%, 9.8% and 14.6%, respectively. Investing in the index mutual fund provided the best return given the level of risk taken. Apple would have to double the performance of the Vanguard Total Stock Market Fund to appropriately compensate investors for its additional risk.

Market Capitalization and Asset Classes

Most investors are aware that stocks with different market capitalizations produce different long-term returns, as do investments in different asset classes. However, investors may not take the time to look at their differences in terms of risk profile. Table 1 shows the three-year return, the three-year standard deviation, risk index and three-year risk-adjusted return for large-cap, mid-cap- and small-cap stocks, as well as emerging market stocks and intermediate-term bonds. As you can see from the table, large-cap stocks, represented by the Vanguard 500 Index fund (VFINX), have had the best three-year risk-adjusted return. The emerging markets asset class has done the worst, by far, whereas intermediate-term bonds are somewhere in the middle.

 

  5-Year Annualized Return (%) 5-Year Standard Deviation (%) Risk Index (X) Risk-Adjusted Return (%)
Vanguard 500 Index Fund (VFINX) 15.05 15.25 0.96 15.63
Dreyfus MidCap Index Fund (PESPX) 19.10 18.10 1.14 16.71
Vanguard Small-Cap Index Fund (NAESX) 19.49 20.87 1.32 14.80
Vanguard Emerging Markets Fund (VEIEX) 14.47 23.06 1.46 9.94
Vanguard Intermediate-Term Bond Fund (VFITX) 5.10 4.22 0.27 19.15
Source: Morningstar, Inc. Data as of October 31, 2013.

The time frame used plays a significant role. If we expand the time frame to five years, there is a considerable difference in risk-adjusted returns. Table 2 depicts the same figures on a five-year basis. Intermediate-term bonds produced the best risk-adjusted return over five years. Their low returns of recent years have a smaller impact in a calculation that includes five years of returns.

Conclusion

Individual investors have numerous easy options when researching the attractiveness of investment holdings. Performance may not be the most important factor to consider, especially for those at or near retirement. It is prudent to take into account the price volatility of shares, especially as you approach the time when investment funds may be needed for living expenses.

Depending on the time frame used in these calculations, intermediate-term bonds may have better risk-adjusted returns than even small-cap and emerging markets equities.

Incorporating standard deviation and the risk index into your research should help you make better choices when selecting investments, providing a risk-adjusted basis on which to make comparisons.


Discussion

R. Thomas from Washington posted 10 months ago:

Working through the examples for Apple, MS and Google, I arrive at the same risk-adjusted return as presented. However, when working though Table 1 and Table 2 I arrive at different risk-adjusted returns from what are presented. For example, using VFINX in Table 1, 16.39/0.95=17.25 rather than 17.18 as presented. What understanding am I missing?


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