Mathematical and Statistical Methods for Actuarial Sciences and Finance

Optimal dynamic asset allocation in a non–Gaussian world 279

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Fig. 1.ODAA optimal solution

value ofx 1 = 0 .9982 moves the optimal strategy to the maximum allowed risky
exposure (i.e. 7% VaR99m).
Maps fork= 2 , 3 , 4 , 5 , 6 ,7 exhibit similar characteristics as fork=1. The main
difference is that askincreases the portfolio rebalancing gets sharper and sharper.
The ODAA maximal probabilityp∗is 68.40%. In order to make a comparison with
more standard approaches, we run the same exercise for a Markowitz constant-mix
investor: in this case the optimal solution requires the full budget-risk to be invested,
with a maximal probability of 61.90%. The ODAA model gets more and more efficient
as the rebalancing frequency increases. Table 2 reports the maximal probabilities for
rebalancing frequency of three months (N=8), one month (N=24), two weeks
(N=52) and one week (N=104). In fact, this result is a direct consequence of
the Dynamic Programming approach pursued in this paper. It is worth emphasising
that the Markowitz constant-mix approach does not produce similar results: in fact
the probability is rather insensitive to the rebalancing frequency.
The allocation grids reported in Figure 1 clearly show that an (optimal) total return
fund manager should adopt acontrarianrebalancing policy [9]: the investor should
increase the risky exposure in the presence of market drawdowns and reduce it in
case of positive performance. The contrarian attitude of the model is a peculiarity of