164 INSTITUTIONAL FUNDS possible to that of the strategic portfolio.
Given that we have matched the level, the only way to make the tactical views consistent with the expected excess returns from the strategic asset allocation is to shrink the magnitude of the tactical views by a factor of approximately 11.6. Having done so, we can match them exactly. What are these incredibly small implied views in the tactical portfolio telling us? These implied views are the changes in expected excess returns for which it is optimal to move from the original strategic portfolio to the new portfolio with the tactical deviations as we specified. The condition for optimality is that the return per unit of portfolio risk is the same across all assets. In this case, we can think of the portfolio of tactical deviations as one asset, and what the factor of 11.6 is telling us is that if the Sharpe ratio of these positions is really .2 then we ought to significantly increase the size of the deviations. Conversely, given the size of the positions (the size of which was set to create 100 basis points of risk) the Sharpe ratio can't be .2; it can only be .008. We might think of this result as suggesting that tactical exposures that contribute relatively small amounts of uncorrelated risk to a portfolio have implied Sharpe ratios that are quite small-in fact, incredibly small. There is a very important message for investors hidden in these calculations. Let's put into simple words what we have just shown. First, we examined a very simple global portfolio of equity exposures. We called this the strategic asset allocation portfolio, and we think of it as a crude proxy for the basic risk faced by almost all investors, the risk of the global equity markets. We then considered a portfolio of tactical deviations. We think of this portfolio as an example of an asset with positive expected returns and which has returns that are uncorrelated with the market portfolio. In fact, in our particular example, the historical returns of the tactical portfolio happen to have been slightly negatively correlated with those of the market portfolio. We then chose to add a small amount of this essentially uncorrelated asset to the strategic portfolio. We chose the amount of tracking error, 100 basis points, to approximate the amount of tactical asset allocation risk that many institutional investors tend to look at. We then made what we thought was a conservative assumption about the expected returns of that tactical portfolio, and the implied views told us that either our return assumption was over 10 times too big, or the risk of our position was much too small. Let's boil this observation down to its essential components. We started with a strategic global equity portfolio with expected excess return of 385 basis points per year and with a volatility of 14.8 percent. We think these are realistic values for a global equity portfolio. Many investors in recent years have significantly reduced their return estimates, and might think the expected excess return we use to be relatively optimistic. (If so, their pessimism just strengthens our argument.) Suppose there is an uncorrelated asset with an unknown Sharpe ratio. We investigate the optimal amounts of this uncorrelated risk to add to the strategic portfolio as a function of the assumed Sharpe ratio of the uncorrelated risk. The surprising results are shown in Table 12.5, which parallels Figure 12.1. For each Sharpe ratio assumption, we solve for the optimal combination of the uncorrelated asset risk from the tactical asset allocation portfolio and market risk holding fixed the total portfolio volatility. We report the risk decomposition, the portfolio Sharpe ratio, the additional basis points of excess return that are added, and the percentage increase in portfolio excess return.
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