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Active Space

Let's consider now an application in active space. To do so, we now need to include benchmark returns for stocks (US) and bonds (FI). We estimate the covariance matrix Q for all four returns series, which we will refer to as the combined covariance matrix V_c:

Again, the top left quadrant is the 2 × 2 covariance matrix (V) for the program returns while the bottom right 2 × 2 matrix are benchmark covariances. The top right and bottom left 2 × 2 matrices estimate covariances across programs and benchmarks. The covariances in active space can be estimated by transforming V_c as in equation (8) generating V_a = m'V_cm:

Thus, the active risks on stocks and bonds are the square roots of the diagonal (2.70, 1.83).

In the previous example, equilibrium returns were the forward-looking expectations = (7.1, 5.3). Since these returns are what managers expect to prevail over the long run, then they are, in essence, managers’ expectations of equilibrium. Views, on the other hand, denote short-run deviations from equilibrium. From the previous example, the return view vector = (9, 6) suggests ...