While our primary definition of risk is the variability in the historical return series, we can tailor our risk measures to the investor situation.
There are three main classes of historical risk statistics: absolute risk mea- sures, downside risk measures, and benchmark relative risk measures.
Absolute Risk
Absolute riskis defined as the total variability in returns. By total vari- ability we mean two things. First, it is the total dispersion of returns that we are interested in measuring. The primary measure of absolute risk is the standard deviation of periodic short-term returns. Second, when we measure the risk of a fund by using standard deviation, we include both the variability inherent in the underlying asset class, as rep- resented by the benchmark, as well as any extra-benchmark volatility introduced by an active manager.
Downside Risk
There are investment strategies specifically designed to reduce the risk of extreme losses as well as strategies with a higher than average risk of extreme losses. An example of a strategy with a risk of extreme losses would be one that employs leverage by borrowing money to invest. Sev- eral risk measures exist to isolate this downside risk. Downside risk measures also provide a better indication of risk when the assumptions underlying the use of standard deviation do not hold.
Relative Risk
Absolute returns to an actively managed portfolio include two compo- nents: the return delivered by the capital markets over the period and the value added over the benchmark earned by the manager. We isolate the value added over the benchmark in order to assist in judging the efforts of the manager. We make the same distinction in risk measurement. The total variability in returns, or absolute risk, includes both the volatility inherent in the markets over the period and the volatility introduced or tempered by the manager. We are interested in isolating the degree of this relative risk in order to put the benchmark relative return into perspec-
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tive. We can measure the degree of association between the fund and benchmark return variability using regression analysis and other tools.
FORWARD- VERSUS BACKWARD-LOOKING RISK
The relative volatility of different investments is a major factor in our investing decisions. Past volatility is used as a proxy for absolute risk in several ways. We use measures of historical volatility to estimate future volatility. For example, based on the historical returns, we can see that we might not be too confident in earning around 17% in any one year in small company stocks, even though that is our long-term average return.
We would be progressively more confident in achieving the average return to other asset classes. This confidence comes in exchange for a lower long-term average return. Historical volatility also informs our estimate of the probability of experiencing a short-term loss. We have a higher probability of losing money in any one year in an asset class with a wider dispersion of returns than one with a smaller dispersion.
Past volatility helps us estimate future volatility, but the same caveat about past returns not necessarily providing a good indication as to future return applies to risk measurement as well. So while past volatility helps us to estimate future volatility, performance measurementis strictly concerned with measurement of past volatility rather than the estimation and management of future volatility. Forward-looking risk estimation (ex-ante risk) is the process of forecasting the expected risk of the current portfolio. As part of the portfolio management process, we evaluate the risk of making changes to the current portfolio versus the expected gains.
Backward-looking (ex-post risk) risk is the measurement of the his- torical risk experienced by the investor in the portfolio or the benchmark relative risk produced by the manager. Historical risk statistics become less relevant to the forecasting of future risk as fund composition, man- ager style, capital markets relationships, and other factors change. As an extreme example, take the case of a fund that was invested in Treasury bills in the past but currently holds stocks. We would agree that anysta- tistics representing the past risks of investing in this fund are now irrele- vant. Another example would be a balanced fund with a low historical risk of large capital losses resulting from an initial asset allocation to bonds. This fund is more at risk of sustaining a capital loss after an extended bull market in stocks. This is because of the increase in the rela- tive weight to equities as stocks rose in value, assuming there is no rebal- ancing back to the initial asset allocation by selling stocks and buying bonds. In addition, risk postures may change as the manager’s strategy evolves, for example, by raising or lowering the cash allocation in a fund.
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The estimation of the anticipated risks implied by the current com- position of the portfolio is a different discipline than the measurement of historical risk. To estimate current and predict future risks, we would focus mainly on the measurement of the risk implied by the currentfund holdings. Even here we usually assume that the current composition of the fund will remain stable over the term predicted. In addition to past volatility, there are additional techniques for estimating risk that depend on the type of portfolio. For example, if we had a bond fund, we would calculate the fund’s average duration, credit quality, and other risk fac- tors specific to fixed income securities. These would give us an indica- tion as to the risk of loss due to unexpected interest rate changes or quality downgrades. For an equity portfolio, we look at the average P/E, market capitalization, country exposure, industry exposure, and other equity risk factors to gauge future volatility. A concentrated investment in technology stocks is expected to be more volatile than a more diversi- fied portfolio. In addition to looking at the current characteristics of the portfolio, Value at Risk (VaR) is another technique used to quantify an estimate of forward-looking risk. VaR uses the current fund holdings, together with the volatility and correlation of returns among these hold- ings, to derive estimates of expected future risk. Because of their for- ward-looking nature, characteristics analysis, VaR, and other tools are more the provenance of risk management than risk measurement.
While backward-looking risk informs the estimation of forward- looking risk, and forward-looking risk is an important investment con- sideration, it is the former that we are concerned with in this book.
When we are measuring performance, we are interested in quantifying the past history of an investment, and this includes the risk and risk- adjusted return track record of the fund or manager. Backward-looking risk measures represent the actual volatility experienced by an investor in the fund during the period measured.
While return volatility is a good proxy for risk in many situations, there are definitions of risk that are not as well captured by the return volatility. For example, to an investor relying on the income produced by an investment to fund current spending, potential for the investment not to provide the required periodic income would be the relevant defi- nition of risk. So, it is important to distinguish between volatility as a measureof risk versus a definition of risk. But periodic return volatility is the usual proxy for the risks experienced while investing.2
2For a history of the development of the concept, measurement, and management of risk see Peter Bernstein, Against The Gods, The Remarkable Story of Risk (New York: John Wiley & Sons, 1996).
CHAPTER 9
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Absolute Risk
e invest via diversified portfolios to maximize the return we expect to earn given a particular tolerance for risk. We measure the level of risk taken by way of summary statistics that describe the variability of periodic returns, or return volatility, around the average return enjoyed. The pri- mary measure of volatility used in the investments industry to represent risk is the standard deviation of return around the mean return. The mean, standard deviation, and other descriptive statistics are used to depict the total, or absolute risk inherent in a pattern of historical returns. We differ- entiate absolute risk from the measurement of risk concerned with devia- tions from target or benchmark returns, which are the subjects of Chapters 10 and 11. In this chapter, we first examine the calculation and use of sta- tistics that describe the historical time series of returns and then measure the average, or middle return, about which the periodic returns have var- ied, and then look at statistics that measure the degree of variability around the average. For standard deviation to accurately describe the vari- ability in a return series the distribution must be approximately normally distributed. The chapter closes with a discussion of the properties of the normal distribution and statistics that indicate a departure from normality.