Monday, May 5, 2008


200 RISK BUDGETING Because the active risk budget identifies the sources of active risk, it also provides important information



investing money


about the structure of an investor's active equity portfolio. In fact, there is a direct relation between the active risk budget and an investor's views about active returns: In the absence of constraints, the total portfolio information ratio is maximized when active risk is allocated so that the marginal contribution to active performance equals the marginal contribution to active risk for all active investments. Constraints can alter this ideal relation, but any allocation of active risk that maximizes the information ratio (for a given level of active risk) is called an optimal active risk budget/ The process of finding this optimal active risk budget is the risk budgeting process. A simple example may help illustrate these points. Suppose an investor has two sources of active performance: a portfolio of two structured managers and a portfolio of four traditional managers. To simplify our discussion, we'll assume that active returns-the returns over the benchmark-are uncorrected across all managers, an assumption that we'll relax later on. (As shown in Table 14.1, traditional and structured managers are unlikely to have completely uncorrected excess returns.) Reflecting the results of our historical analysis, we'll also assume that each structured manager has a tracking error of 215 basis points, while each traditional manager has a tracking error of 800 basis points. Finally, we'll assume that each manager is equally weighted within its type-namely, each structured manager invests 50 percent of the structured portfolio and each traditional manager invests 25 percent of the traditional portfolio. In this simple example, risk budgeting means deciding how much of the active risk budget to allocate to each group of managers. To make this decision, we must first calculate the active risk level for each portfolio of managers. Under our simple assumptions, the tracking error for the portfolio of structured managers is around 150 basis points, while the tracking error for the portfolio of traditional managers is 400 basis points.7 (These calculations assume each portfolio of managers has a beta of 1.0 relative to the benchmark index.) Recall that when there are no constraints, we should allocate active risk such that the marginal contribution to active risk equals the marginal contribution to active return for all investments (or managers). Thus, the next step is to estimate active returns for groups of managers. For simplicity, let's assume that structured managers have expected information ratios of 0.45, while traditional managers have expected information ratios of 0.30. These assumptions roughly correspond to the top or first-quartile figures in Table 14.1, and imply that the investor has some skill in manager selection. Using these assumptions, the expected information ratio and active return for the group 6Oi course, this works only if we assume that active risk is uncorrelated with the underlying strategic asset allocation. If the active returns are negatively correlated with the underlying assets, then the total portfolio information ratio could be improved by using a suboptimal active portfolio. In practice, the correlation between active risk and the strategic asset allocation is quite low. 7The tracking error of 150 basis points for the portfolio of two structured managers is calculated as the square root of the following sum: (V2 x 215)2 + 2 x lk x lk x 0 x 215 x 215 + (V2 x 215)2. The zero in the middle term represents the correlation assumption. A similar approach applies to the portfolio of four traditional managers.


Read also about: return money investment investing money hand

No comments: