Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)

110 Optimizing Optimization

of the hedge fund returns are significantly nonnormal. Moreover, much of this
nonnormality survives into the mean – variance efficient portfolios, which implies
that log-wealth utility is fairly insensitive to higher moments. However, mean –
variance optimization performs poorly for investors with kinked utility or
S-shaped value functions.

Table 4.5 Turnover required to shift from mean – variance to full-scale efficiency

Log-wealth

utility

Kinked utility S-shaped value functions

At  5% At  1% At 0% At  0.5%

Equity hedge 4% 21% 31% 40% 53%

Convertible arbitrage 0% 66% 63% 56% 40%

Event driven 0% 84% 30% 31% 42%

Merger arbitrage 0% 36% 42% 12% 14%

All hedge funds 15% 34% 56% 57% 55%