Understanding Asset Allocation: In Search of the Upside
- The Measurement of Risk
- Asset Allocation and Retirement
- Ranging the Possibilities: Monte Carlo Simulations
It is striking how little most people understood about risk as recently as three decades ago. Risk, of course, is that piece of information all investors need to knowand should desire to keep as low as possible in relation to the returns they expect to see on their investments. Fortunately, developments in modern portfolio theory provide a framework for addressing the ways risk can affect expected returns.1 The developments have been nothing short of dramatic.
The Measurement of Risk
We now have the Sharpe ratio at our disposal, a well-known formula useful for evaluating alternative investments and determining when to add additional assets to a portfolio.2
The Sharpe ratio summarizes two measures—mean return and variance—within a single measure. Mean return can be considered the average return an investment or investment class is expected to deliver over time, while variance can be considered the average range of asset performance around the mean return. To calculate the Sharpe ratio, subtract the risk-free rate returns (that is, Treasury bill [T-bill] returns) from the asset returns in question and divide that result by the standard deviation of the return of the asset class in question less that of the risk-free rate. In this manner, risk is pinpointed. One way to think of this is to consider a person who borrows money to invest. After doing so, that person’s net gain is the difference between the return of the investment and the funds borrowed; the greater the difference (on the positive side), the greater the reward. Similarly, the higher the Sharpe ratio, the lower the risk in relation to the reward. The Sharpe ratio is calculated using the mean and standard deviation of an excess return. That is the net of the asset class return and the risk free rate (that is, three months’ T-bill yields). A related measure is obtained when the ratio is calculated based on the mean and return of a single investment. This ratio is also known as the information ratio.
Then, there’s the capital asset pricing model (CAPM), which similarly looks at the relationship between an investment’s risk and its expected market return—or, more specifically, the ways investment risk should affect its expected return.3 One major insight of the CAPM is that not all risks should affect asset prices. As would be the case if two assets moved in the same direction, the volatility of the portfolio consisting of the two assets would remain the same as the individual assets. In contrast, if the two assets move in the opposite direction, the volatil-ity of a portfolio consisting of the two assets would be much lower than that of each of the assets by themselves. The latter represents an example of a risk that can be diversified away by combining it with other assets in a portfolio, which should not be considered a risk. Hence, when considering adding asset to a portfolio, one needs to take into account whether the asset moves with the portfolio and whether the addition of the asset will reduce or increase the volatility of the portfolio. If the asset does not add to the volatility of the portfolio, it should not be priced for risk, or more plainly, investors would not demand an additional return or premium over and above the current expected return. The only risk that should be priced is the risk that cannot be diversified away, the residual risk or systematic risk. The CAPM is firm on this point. What should matter to the investor, therefore, is the incremental impact on the overall portfolio volatility—not the individual investment volatility. With this in mind, an investor can effectively apply the Sharpe ratio: When adding an asset to a portfolio improves the Sharpe ratio, the asset adds to the return of a portfolio over and above the increased volatility of the new overall portfolio.
Investing suddenly seems very simple. Indeed, in the days of the Sharpe ratio and the CAPM, the market portfolio—a portfolio that has bought the market (given that the overall market is in equilibrium)—has become the efficient portfolio. An efficient portfolio is a portfolio that contains returns that have been maximized in relation to the risk level that individual investors desire. In a market that is in equilibrium, where the number of winners and losers must balance out, adding one additional asset class or stock does not increase the portfolio’s risk return ratio. This means the portfolio containing risky assets with the highest Sharpe ratio must be the market portfolio.