In this chapter we review in detail the quality of the various numerical approximations we have introduced in Part IV of the book. As we shall see, the good news is that they tend to be surprisingly successful, and can therefore greatly lighten the computational burden of the optimization. They will also suggest an approach to asset allocation using Bayesian nets which is not only computationally lighter, but also intuitively more appealing.

We begin by looking at the quality of the mean-variance approximation.

How good is the mean-variance approximation?

In this section we are trying to ascertain how accurate the mean-variance Gaussian approximation presented in Sections 25.2 and 25.3 actually is, once the moments of the full distribution obtained by the Bayesian net are matched.

The answer is apparent from Figure 27.2, which shows the allocations as a function of (1 – k) obtained using the Gaussian approximation. This figure can be compared with the allocations obtained using the full Monte-Carlo optimization and the logarithmic utility function, shown again in Figure 27.1 for ease of comparison.

The similarity between the two sets of optimal weights is remarkable, and is shown even more clearly in Figure 27.3, which displays the allocations as a function of (1 – k) for the the three methods. Again, it is apparent that the Gaussian approximation, once the moments are matched, is extremely accurate.