Heuristic portfolio optimization: Bayesian updating with the Johnson family of distributions 261
2 January 2003 and 23 December 2008 from M { 2, 3 } randomly chosen
FTSE 100 stocks:
L()
()w () ()ww
w
TA wwTA GS
TA TA GS(^11)
Dim
[]UU
(11.8)
where Dim( w TA ) is the dimension of the portfolio weight vector, 1[.] is an
indicator function, and U is the expected utility function. 18 The results from
N 250 simulations are reported in Table 11.1. Even with a limited number
of steps, iterations, and restarts, it appears that the TA algorithm produces sim-
ilar results to a global grid-search procedure.
11.5 Data reweighting
Dealing with an unknown and changing data-generating process is undoubt-
edly the greatest challenge that one faces when trying to model asset returns,
especially when “ success ” is measured in terms of out-of-sample performance.
18 Our original intention was to consider M { 2,3,4 } stocks. However, including a fourth stock
would entail 1.7 billion grid-point evaluations per simulation, and 425 billion evaluations in
total. This highlights the infeasibility of a grid-search approach, especially when a relatively fine
grid is used.
Table 11.1 Threshold acceptance versus grid searchN (^) Steps 2 Assets 3 Assets
N (^) Restarts 10 N (^) Restarts 20 N (^) Restarts 10 N (^) Restarts 20
100 0.0070 0.0053 0.0189 0.0140
(^) 0.0394 0.0383 0.0689 0.0626
250 0.0038 0.0022 0.0133 0.0072
(^) 0.0207 0.0114 0.0515 0.0352
500 0.0038 0.0008 0.0046 0.0024
(^) 0.0310 0.0037 0.0233 0.0117
750 0.0035 0.0023 0.0070 0.0024
(^) 0.0336 0.0291 0.0502 0.0211
1000 0.0031 0.0003 0.0051 0.0009
(^) 0.0298 0.0012 0.0313 0.0061
This table describes the mean (upper entry) and standard deviation (lower entry) of L ( w TA ), based on
N 250 simulations using N (^) Iter 3. The grid-search procedure is based on 2 runs with 200 points
in the first run and 100 in the second. We set z 0.65 for convenience, and assume a coefficient
of relative risk aversion equal to two, i.e., α 2, with no disappointment aversion, i.e., A 1. All
calculations are performed using an Intel Core 2 Duo 1.86GHz Processor and 2GB RAM.