run, this impact on expected return is not an important consideration in preventing losses. Thus, investors who focus on the short run tend to be relatively more risk averse. If the investor does, in fact, have a short time before the investment must be cashed in, then this is appropriate. However, in the long run, the increased expected return from careful risk taking clearly has a positive effect and must be taken into account in determining the amount of risk to take and thus in centering the distribution of outcomes. As mentioned in the previous chapter, investors benefit from the fact that returns accumulate more quickly over time than does risk. Other considerations also become more important in the long run. For example, as we will discuss in Chapter 29, over longer periods of time inflation creates considerable uncertainty in the real purchasing power of nominal investments. The benefit of tax deferment of capital gains is another consideration that grows with longer horizons. Thus, time horizon has a major impact on how investors should evaluate the risk and return trade-offs of different portfolio decisions. Probably the simplest and most important risk management exercise for an investor is the stress test. The stress test is a very simple exercise. A particular dimension of risk is identified and one asks what happens if there is a shock, that is, a major event along this dimension. The change in portfolio value is measured. For example, a stress test might answer the question, "Suppose the stock market were to decline by 10 percent; what would be the impact on my portfolio?" The basis for this measurement is a set of assumptions about how a stock market decline would affect the value of each security in the portfolio. We start by identifying "the stock market" with a particular benchmark. In the United States, we might use the S&P 500 stock index. If one of the investments in the portfolio were an S&P 500 index fund, then the impact on this investment would be simply a 10 percent decline. If there were an investment in a portfolio managed with a small amount of active risk relative to an S&P 500 benchmark, then one would expect the impact to be close to the 10 percent decline. A common statistical measure of equity portfolio risk is the beta, the expected change in value of a stock or portfolio relative to the change in value of the market. If a portfolio has a beta of 1, then its decline is expected to match that of the market, while a portfolio with a beta of .9 would be expected to decline only 9 percent if the market were to decline 10 percent. There are no set rules for how to measure the beta of a security. One common approach is to look at historical data and use it to statistically estimate a coefficient that measures the degree to which historically the security has, on average, moved when the market has changed. Such an approach is subject to all the usual statistical measurement issues such as how much data to use and whether to look at daily, weekly, monthly, or some other frequency of returns. In this, as in many risk management contexts, however, it is important not to lose sight of the forest for the trees. Accuracy is often not the primary issue. Just getting a reasonably accurate measure of exposure is often close enough to answer the most important questions. More generally, we want to measure the exposures of a portfolio to a set of common dimensions of risk. In addition to equity market changes, we might like to measure sensitivity to interest rate changes, currency changes, energy prices, credit spreads, foreign market changes, and so on. The particular measures one focuses on will depend on the portfolio characteristics.