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

138 Optimizing Optimization

1800 2000 2200 2400 2600 2800 3000

A

B

Realized wealth

Sample paths of wealth

Wealth (Optimized portfolio–sharpe)

Wealth (Optimized portfolio–R-Ratio (0.1,0.35))

Observations

0.9

0

0.8

1.1

1.2

0.3

1.4

1.5

Sample paths of total return

Total-return (sharpe)

Total-return (R-Ratio (0.1, 0.35))

2400 2600 2800 3000

Observations

1800 2000 2200

Realized total return

–0.1

–0.2

0

0.1

0.2

0.3

0.4

0.5

Figure 5.4 Final wealth and total return realized in 1,000 days using either the Rachev
ratio with parameters α  0.35; β  0.1 or the Sharpe ratio.