Developing an Optimal Active Risk Budget 189 tive risk assigned to a specific manager, the implied alpha to that manager, and
the confidence in that manager relative to a numeraire manager. For example, suppose that we have a portfolio of three International Equity managers. Furthermore, suppose that the correlation of excess returns between the managers is .38 (from Table 13.2), and that the tracking error target for the portfolio of managers is 460 basis points (from Table 13.3). Table 13.12 shows the tracking error targets for each manager, their allocations, and the risk budget for this portfolio of managers. In Table 13.5, International Equity was allocated roughly 40 percent of the total active risk budget, under the assumption that the portfolio of managers had a target tracking error of 460 basis points. Implicit in this decision was the view that in the aggregate, International Equity managers were more likely to add value in line with the historical performance than managers in other asset classes. Table 13.12 is telling us that the third manager has been allocated around 50 percent of the active risk in International Equity. Now our question is, what does this allocation of risk imply about our confidence in any particular manager's ability to deliver alpha? The confidence levels for each manager, normalized to manager 2, are shown in Table 13.13. These have been calculated using two sets of views. The first view is that the information ratio for each manager is the median information ratio. The second view is that managers have different information ratios. More specifically, we've assumed that the first manager's expected information ratio is .25, while expected information ratios for the second and third managers are .57 and .75 respectively. As expected, the risk budget reveals quite different information about our confidence in each manager's ability to deliver alpha, depending on the view. When we assume an equal information ratio for each manager, then the risk budget is effectively TABLE 13.12 International Manager Weights Tracking Risk Allocation Error (bps) Budget Manager 1 20.0% 500 14.4% Manager 2 35.0 575 35.3 Manager 3 45.0 675 50.3 Total 100.0 450 100.0 TABLE 13.13 Relative Confidence Levels Confidence Relative to Manager 2 Constant IR Differential IR Manager 1 0.5 1.6 Manager 2 1.0 1.0 Manager 3 1.5 1.1
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