280 Gianni Pola
Ta b le 2 .Maximal probabilitiesp∗
3m 1m 2w 1w
Probability 68.40% 72.50% 76.28% 77.76%concavestrategies.^4 This feature makes the model particularly appealing in oscillating
markets.
We conclude this section by making a comparison with aconvexstrategy. We
run a Constant–Proportional–Portfolio–Insurance (CPPI) model [5] with a 2-years
horizon: the model has been designed to protect the capital at maturity. We assume
that the risky basket is composed by the equity market (multiplier has been set to 6)
and trading is weekly based. In order to make a comparison, we assume the same
Value-at-Risk budget risk as in the previous case.
Table 3 offers a comparison between the two approaches. (The ODAA results
refers to a weekly based strategy;N=104.) The CPPI strategy works pretty well
to protect the capital (99.60%), but it presents a lower probability of achieving large
returns. (The probability of beating a 7% target return at maturity is 33.64%.) Distri-
bution of performance at maturity is positive skewed and platykurtic, thus revealing a
very stable strategy. Conversely, the ODAA strategy presents a higher probability of
delivering its target return (77.76%), but a lower probability of protecting the capital.
ODAA performance distribution is negative skewed and leptokurtic. Higher-order
risk is paid off by the the large probability of achieving more ambitious returns.
The applications presented in this section should be considered for illustrating the
methodology. The views expressed in this work are those of the author and do not
necessarily correspond to those of Credit Agricole Asset Management. ́
Ta b le 3 .Comparison between the ODAA and CPPI strategy
ODAA CPPI
Mean perf N (ann) 5.68% 6.15 %
Median perf N (ann) 7.03% 3.64%
Skewness perf N −2.80 1.35
Kurtosis perf N 11.08 4.44
Vol (ann) 2.70% 3.05%
Sharpe (ann) 1.51 0.44
Prob 0% 91.40% 99.60%
Prob cash 85.58% 53.21%
Prob 7% 77.76% 33.64%(^4) The exposure diagram reports on theX–axis the portfolio value and on theY–axis the risky
exposure. Concave (resp. convex) strategies are characterised by a concave (resp. convex)
exposure diagram.