Portfolio Design: A Modern Approach to Asset Allocation

HOW MUCH MORE ATTRACTIVE ARE STOCKS THAN BONDS?

Many investors, though, see the equity premium as a necessary price for the extra risk of investing in stocks. After all, the standard deviation of the S&P 500 series is 14.6 percent in Table 2.1. But that explanation needs to be examined more closely because, as reported in Table 2.1, the standard deviation of the bond return is also quite high at 9.5 percent. To compare stocks and bonds, it’s useful to ask the following question: If an investor were to choose between these two assets, which would be more attractive in risk-adjusted terms?7

To assess the return on stocks versus the return on bonds, the first step is to adjust each return for risk. The Sharpe ratio adjusts each return by first subtracting the risk-free rate, rF, then dividing by the standard deviation. If rj is the return on asset j and σj is its standard deviation, then the Sharpe ratio for asset j is

To calculate the Sharpe ratio, we use the arithmetic returns and standard deviations in Table 2.1. It’s possible to define a Sharpe ratio using geometric returns, but only if the standard deviation is defined over a similar long horizon.8 Using the returns in Table 1, the Sharpe ratios are defined by

The Sharpe ratio for stocks is more than twice the size of the ratio ...