3) According to the CAPM, would the expected rate of return on a security with a beta less than zero be more or less than the risk-free interest rate? Why would investors be willing to invest in such a security? (Hint: Look back to the auto and gold example in the lecture slides)

Asset versus Portfolio Risk Volatility of returns can be a misleading measure of risk for an individual asset held as part of a portfolio. Consider the following example: There are three equally likely scenarios for the economy, a recession, normal growth and a boom. Auto firms are cyclical. They do well when the economy does well. Gold firms are countercyclical. They do well when other firms do poorly. Expected Return and Volatility for Auto Firm Expected Return and Volatility for Gold Firm Asset versus Portfolio Risk It appears that gold is the more volatile stock based on standard deviations. However, it also has a lower expected rate of return. In other words, it is a loser on both counts. Would anyone be willing to hold gold mining stocks in an investment portfolio? The answer is yes. Now suppose that you invest 75% in auto and 25% in gold firms. Portfolio return in recession = (0.75 -8) + (0.25 20) = -1% Portfolio return in normal growth = (o.75 5) + (0.25 3) = 4.5% Portfolio return in boom = (0.75 18) + (0.25 -20) = 8.5% Asset versus Portfolio Risk The volatility of the auto-plus-gold stock portfolio is considerably less than the volatility of either stock separately. This is the most important benefit of diversification. Asset versus Portfolio Risk 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 does well and boosts portfolio performance. The gold stock reduces the best-case return but improves the worst-case return and therefore provides a stabilizing effect. A gold stock can be considered to be a negative-risk asset since the incremental risk of the gold stock is negative. A security that is risky held in isolation may nevertheless serve to reduce the variability of the portfolio if its returns do not move in lockstep with the rest of the portfolio