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

Modeling, estimation, and optimization of equity portfolios with heavy-tailed distributions 139

A

1800 2000 2200 2400 2600 2800 3000

0.9

0.95

1

1.05

1.15

1.2

1.25

Realized wealth

1.3

1.4

1.1

Observations

Wealth (Optimized portfolio – sharpe)

Wealth (Optimized portfolio – RHMR)

Sample paths of wealth

B

2400 2600 2800 3000

Observations

1800 2000 2200

Realized total return

–0.1

–0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Total-return (sharpe)

Total-return (RHMR)

Sample paths of total return

Figure 5.5 Final wealth and total return realized in 1,000 days using either the Rachev
high moment ratio or the Sharpe ratio.