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

Modeling, estimation, and optimization of equity portfolios with heavy-tailed distributions 137

2000 2200 2400 2600 2800 3000

Realized wealth

1800

0.8

0.9

1

1.1

1.2

1.3

1.5

Wealth (optimized portfolio – heuristic - RR(0.1,0.35))

Wealth (optimized portfolio – fmincon - RR(0.1,0.35))

Realized total return

1800 2000 2200 2400 2600 2800 3000

–0.1

–0.2

0

0.1

0.2

0.3

0.4

0.5

Total-return – heuristic - (R-Rato (0.1,0.35))

Total-return – fmincon - (R-Rato (0.1,0.35))

A

B

Observations

Observations

Figure 5.3 Final wealth and total return realized in 1,000 days using the Rachev
ratio with parameters α  0.35; β  0.1 and maximizing it either with the Angelelli –
Ortobelli heuristic or the function fmincon of Matlab.