General considerations

The analysis of the sensitivity of the allocation weights to the uncertain inputs is closely linked to the issue of the (lack of) stability of the allocations – a stability issue with which portfolio managers are very familiar. This instability is one of the greatest drawbacks of Markowitz-like solutions. The allocations produced by the Black–Litterman model are somewhat more stable, but, for reasons that we discuss below, not always significantly so. Are the allocations produced by the Bayesian-net technology more stable, or are they plagued by the same instability problems?

Now, as we began using the Bayesian-net technology, we did not know for sure whether the allocations produced by the procedure described in this book would be greatly affected by small changes in the marginal (root) probabilities, in the conditional probabilities, in the expected returns, in the stressed sampling distributions that we associate with the leaves, etc. We did know, however, that, unless we could find a satisfactory solution to the stability problem, the usefulness of any asset-allocation approach, including the Bayesian-net approach of which we are so fond, was going to be limited.

With an eye to this stability issue, we can begin the discussion by making two general observations.

The first is that we do not expect Bayesian nets in themselves to be responsible for any additional instability over and above what is already produced by the Markowitz-like optimization. If anything, we explain later why they should have a modest stabilizing effect.