Index 305
lognormal curve, formula for , 174
overview , 171
probability of returns with a 3
parameter lognormal , 172 – 3
style analysis , 176
style statistic , 176
see also Gain/Loss Optimization ;
Heuristic portfolio optimization ;
Mean – variance (MV) analysis ;
Second-order cone programming
(SOCP)
Portfolio selection problem , 130
performance ratios, review of , 132 – 4
portfolio strategies, empirical
comparison among , 134 – 6 ,
137 – 9
Portfolio strategies, empirical comparison
among , 134 – 6 , 137 – 9
Portfolio theory, themes in , 117
Power utility , 104
Principal components analysis (PCA) ,
118 , 123
Q
Quadratic utility , 249
Quantile estimator, under
misspecifi cation , 275 – 8
R
Rachev higher moments ratio (RHMR) ,
133 , 135
Rachev ratio (RR) , 132 , 134 , 135 , 136 ,
137 , 138
Return estimation, of WPA , 111
Return scenarios, generation of ,
126 – 30
Return volatility , 143
Risk:
budgets , 113
estimation , 111
model information , 76
regimes , 94
problem , 101
WPA solution , 101 – 4
and reward , 204
conditional moments , 205 – 7
drawdown , 208
partial moments , 205
quantiles , 207 – 8
Robust optimization , 58 – 9
background , 58
BITA Robust applications, to
controlling FE , 61
explicit risk budgeting , 65 – 6
FE constraints , 61 – 2
mean forecast intervals , 65
mean – variance optimization,
reformulation of , 59 – 61
preliminary results , 62 – 4
Rom, Brian , 162
Root mean square error (RMSE) , 256 ,
275 , 276S
S-PLUS ™ , 287
Second risk model , 25 , 26 , 27 , 51
constraint , 32 – 3
Second-order cone programming (SOCP),
for robust portfolio optimization ,
3 , 88
alpha uncertainty , 4 – 6
fund of funds , 18 – 22
risk constraints , 12 – 16
risk measures , 16 – 18
SunGard APT case , 12
medium-term model risk , 12 , 13 , 14
short-term model risk , 12 , 14
systematic and specifi c risk, constraints
on , 6 – 12
Sharpe ratio (SR) , 132 , 205 , 226 , 236
SIA optimizer , 169
Skewness – kurtosis plane , 253
Specifi c risk, constraints on , 6 – 12
and alpha uncertainty:
with portfolio specifi c volatility , 11
with portfolio systematic volatility ,
11
portfolio , 7
portfolio specifi c volatility , 10
portfolio volatility with , 9
Standard deviation , 173
Standard mean – variance optimal portfolio
problem , 241 – 4
Starting portfolio , 43 , 45
Statistical axioms , 284 – 5
Statistical risk model:
constraining active risk with , 27
constraining total risk with , 31 – 2