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Developing an Optimal Active Risk Budget 187 TABLE 13.10 Impact of Increasing Active Risk Scaling Factor Total


Tracking Error (bps) Total Portfolio Volatility Contribution of Active Risk Implied Implied Alpha (bps) IR   0.5 70 11.0 0.4% 1 0.01 1 140 11.1 1.6 4 0.03 2 280 11.3 6.2 15 0.05 5 700 13.0 29.1 95 0.14 10 1,400 17.8 62.2 380 0.27 ures in the table indicate, scaling up the level of active risk increases the associated implied return. In fact, at roughly 1,400 basis points of tracking error, the implied information ratio for the active portfolio exceeds the Sharpe ratio for the underlying asset classes.8 Of course, investors cannot simply scale up the active risk in each asset class linearly. In active strategies such as U.S. Large Cap, constraints such as the no net short constraint become binding at higher risk levels. By contrast, strategies such as active overlay are typically not subject to the same constraint. The implication is that at higher risk levels, we should start to anticipate some deterioration in the information ratio for more constrained strategies. Consequently, at higher risk levels we would want to analyze confidence levels on the basis of differences in the net information ratio.3 In addition to the overall level of active risk, investors are also interested in the efficient allocation of active risk (i.e., an optimal active risk budget). To see the impact on the risk budget and associated implied confidence levels, let's work through the following example. Suppose that we triple the allocation of active risk to the Overlay strategies, and shift 10 percent of the portfolio from active U.S. Large Cap to U.S. Small Cap. The results of these shifts are shown in Table 13.11. As we can see, the confidence on active U.S. Small Cap and Overlay strategies relative to U.S. Large Cap has increased. As well, the allocation of active risk has shifted away from U.S. Large Cap and into the other two strategies (as illustrated by the change in the relative risk allocation columns). In fact, the rebalanced active risk budget appears to be more diversified. This example illustrates a basic idea, which is that there is a very close correspondence between the allocation of active risk and the relative confidence placed on views. Why would an investor choose to assign more confidence to the active returns in one asset class versus another? Given that most investors have access to the same data and would share the same basic ranking of the historical information ratios, 8Assuming that we hold the relative confidence levels roughly fixed, improving the Sharpe ratio by increasing the level of active risk relative to the risk on the underlying asset classes means, as a first approximation, that the investor is also increasing the implied level oft, or the weight on views. One interpretation would be that the investor believes that markets take a long time to correct to equilibrium. ^Higher costs at higher risk levels could also cause information ratio deterioriation.