Custom Search

ASSET VERSUS PORTFOLIO RISK

The history of returns on different asset classes provides compelling evidence of a risk return trade-off and suggests that the variability of the rates of return on each asset class is a useful measure of risk. However, volatility of returns can be a misleading measure of risk for an individual asset held as part of a portfolio. To see why, consider the following example.

Suppose there are three equally likely outcomes, or scenarios, for the economy: a recession, normal growth, and a boom. An investment in an auto stock will have a rate of return of 8 percent in a recession, 5 percent in a normal period, and 18 percent in a boom. Auto firms are cyclical: They do well when the economy does well. In contrast, gold firms are often said to be countercyclical, meaning that they do well when other firms do poorly. Suppose that stock in a gold mining firm will provide a rate of return of 20 percent in a recession, 3 percent in a normal period, and 20 percent in a boom. These assumptions are summarized in Table 3.15.

It appears that gold is the more volatile investment. The difference in return across the boom and bust scenarios is 40 percent ( 20 percent in a boom versus +20 percent in a recession), compared to a spread of only 26 percent for the auto stock. In fact, we can confirm the higher volatility by measuring the variance or standard deviation of returns of the two assets. The calculations are set out in Table 3.16.

Since all three scenarios are equally likely, the expected return on each stock is simply the average of the three possible outcomes.8 For the auto stock the expected return is 5 percent; for the gold stock it is 1 percent. The variance is the average of the squared deviations from the expected return, and the standard deviation is the square root of the variance.

The gold mining stock offers a lower expected rate of return than the auto stock, and more volatility a loser on both counts, right? Would anyone be willing to hold gold mining stocks in an investment portfolio? The answer is a resounding yes. To see why, suppose you do believe that gold is a lousy asset, and therefore hold your entire portfolio in the auto stock. Your expected return is 5 percent and your standard deviation is 10.6 percent. We ll compare that portfolio to a partially diversified one, invested 75 percent in autos and 25 percent in gold. For example, if you have a $10,000 portfolio, you could put $7,500 in autos and $2,500 in gold.

First, we need to calculate the return on this portfolio in each scenario. The portfolio return is the weighted average of returns on the individual assets with weights equal to the proportion of the portfolio invested in each asset. For a portfolio formed from only two assets,

Portfolio rate = (fraction of portfolio _ rate of return) of return in first asset on first asset + (fraction of portfolio _

rate of return ) in second asset on second asset

For example, autos have a weight of .75 and a rate of return of 8 percent in the recession, and gold has a weight of .25 and a return of 20 percent in a recession. Therefore, the portfolio return in the recession is the following weighted average:9 Portfolio return in recession = [.75 Г— ( 8%)] + [.25 Г— 20%] = 1%

Table 3.17 expands Table 3.15 to include the portfolio of the auto stock and the gold mining stock. The expected returns and volatility measures are summarized at the bottom of the table. The surprising finding is this: When you shift funds from the auto stock to the more volatile gold mining stock, your portfolio variability actually decreases. In fact, the volatility of the auto-plus-gold stock portfolio is considerably less than the volatility of either stock separately. This is the payoff to diversification. We can understand this more clearly by focusing on asset returns in the two extreme scenarios, boom and recession. In the boom, when auto stocks do best, the poor return on gold reduces the performance of the overall portfolio. However, when auto stocks are stalling in a recession, gold shines, providing a substantial positive return that boosts portfolio performance.

The gold stock offsets the swings in the performance of the auto stock, reducing the best-case return but improving the worst-case return. The inverse relationship between the returns on the two stocks means that the addition of the gold mining stock to an all-auto portfolio stabilizes returns.

A gold stock is really a negative-risk asset to an investor starting with an all-auto portfolio. Adding it to the portfolio reduces the volatility of returns. The incremental risk of the gold stock (that is, the change in overall risk when gold is added to the portfolio) is negative despite the fact that gold returns are highly volatile.

In general, the incremental risk of a stock depends on whether its returns tend to vary with or against the returns of the other assets in the portfolio. Incremental risk does not just depend on a stock s volatility. If returns do not move closely with those of the rest of the portfolio, the stock will reduce the volatility of portfolio returns. We can summarize as follows:

1. Investors care about the expected return and risk of their portfolio of assets. The risk of the overall portfolio can be measured by the volatility of returns, that is, the variance or standard deviation.

2. The standard deviation of the returns of an individual security measures how risky that security would be if held in isolation. But an investor who holds a portfolio of securities is interested only in how each security affects the risk of the entire portfolio. The contribution of a security to the risk of the portfolio depends on how the security s returns vary with the investor s other holdings. Thus a security that is risky if held in isolation may nevertheless serve to reduce the variability of the portfolio, as long as its returns vary inversely with those of the rest of the portfolio.

Merck and Ford Motor

Let s look at a more realistic example of the effect of diversification. Figure 3.17a shows the monthly returns of Merck stock from 1994 to 1999. The average monthly return was 3.1 percent but you can see that there was considerable variation around that average. The standard deviation of monthly returns was 7.1 percent. As a rule of thumb, in roughly one-third of the months the return is likely to be more than one standard eviation above or below the average return.10 The figure shows that the return did indeed differ by more than 7.1 percent from the average on about a third of the occasions. Figure 3.17b shows the monthly returns of Ford Motor. The average monthly return on Ford was 2.3 percent and the standard deviation was 7.2 percent, about the same as that of Merck. Again you can see that in about a third of the cases the return differed

from the average by more than one standard deviation.

An investment in either Merck or Ford would have been very variable. But the fortunes of the two stocks were not perfectly related.11 There were many occasions when a shows the returns on a portfolio that was equally divided between the stocks. The monthly standard deviation of this portfolio would have been only 5.1 percent that is, about 70 percent of the variability of the individual stocks.