Model Selection in Portfolio Management

Abstract

Model selection starts with a dataset and a number of candidate models that can explain that data. The AIC
and BIC criteria prevents choosing the best fitting model by penalizing for the number of parameters in a
model and instead selects the model that performs best when assessed to unseen data. Their performance
depends on the sample size and the noise in the data.
In portfolio management, it is common to find a combination of financial products such that an objective
is optimized. A common risk measure criterion that gets maximized is the Sharpe ratio. Since portfolio management
is also done based on historic data, but wanted to be optimized for unseen data, model selection
can be applied to portfolio management as well.
Finding the optimal weights in a portfolio is done by solving a linear system of equations. Applying this
to subsets of stocks which are contained in the AEX index, leads to higher in-sample Sharpe ratios than using
equal weights or just following the AEX index. The out-of-sample Sharpe ratio gets overestimated by noise
fit and estimation error. The Sharpe Ratio Information Criterion (SRIC) corrects for this. This criterion gives
an unbiased estimate for the out-of-sample Sharpe ratio and can be used for model selection in portfolio
management. Using a trend following strategy, investing proportionally to the returns, also increases your
expected out-of-sample Sharpe ratio.