Calculating the New Combined Return Vector
Having specified the scalar (τ ) and the covariance matrix of the error term (Ω ),
all of the inputs are then entered into the Black-Litterman formula and the New
Combined Return Vector ( E[R]) is derived. The process of combining the two sources of
information is depicted in Figure 1. The New Recommended Weights (wˆ ) are calculated
by solving the unconstrained maximization problem, Formula 2. The covariance matrix
of historical excess returns (Σ ) is presented in Table 5.