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186 RISK BUDGETING   TABLE 13.9 Normalized Active Confidence Levels and Active


Risk Budget Confidence Relative to U.S. Large Cap . . s F Active U.S. Large Cap Equity U.S. Small Cap Equity International Equity Emerging Markets Equity Core+ Fixed Income High Yield Overlay   Historical IR Equal Net IR Risk Budget 1.00 1.00 50.7 0.10 0.23 2.9 0.40 0.88 39.9 0.10 0.13 0.9 1.25 0.20 2.2 0.03 0.09 0.4 0.12 0.24 3.0 U.S. Large Cap. For reference, the normalized confidence levels are contrasted in Table 13.9 with the active risk budget. What is striking about Table 13.9 is the impact of switching the set of views. When we assume that the net information ratio is constant, then there is a very close qualitative ordering between the risk budget and the relative confidence levels. This ordering breaks down when we use the historical information ratios. For a simple example, let's look at Core+ Fixed Income. The allocation to Core+ Fixed Income is only 2.2 percent of the active risk budget. When we assume that the net information ratio is the same across all active strategies, the active risk budget implies that we are 25 percent more confident in our view on U.S. Large Cap than in our view on Core+ Fixed Income. Alternatively, when we use the adjusted historical information ratios, the relationship between the two sources of active risk is reversed. In fact, the allocation to Core+ Fixed Income is now implying a confidence level that is 25 percent larger than that of U.S. Large Cap. Given that we believe that historical averages are poor predictors of future returns, we might be inclined to use an assumption of a constant net information ratio as a starting view, and then adjust this view depending on the policy question. How can our analysis be applied to investment policy choices, and what do those choices imply about how we think about views and confidence levels? There are three distinct investment policy decisions that investors must make. Each of these is a risk budgeting choice. The first choice is the split between asset class risk and active risk. This is a decision about the efficient allocation of total portfolio risk between active and asset class risk. Once an active risk level has been selected, the second choice is the efficient allocation of active risk across asset classes. The final choice is the efficient allocation of risk to individual managers within an asset class. Let's look first at the implications of changing the split between asset class risk and active risk. An easy way to do this in the context of our example is to assume that the asset allocation is fixed at the allocations of Table 13.3 and scale up each asset class's active risk level. Doing so will increase the total tracking error, increase the total portfolio risk, and increase the contribution of active risk to the total risk budget. Table 13.10 shows the results of this analysis for our example. The table also shows the implied returns for each level of active risk. As the fig-