Peter Urbani's Statistics - Co-Skewness worth 290bp
This month we look at the impact of different objective functions on the out-of-sample performance of optimised strategy allocations, and in particular of the important contribution of co-skewness to the overall skewness of the portfolio for those who care about higher moments
We show that the inclusion of higher moments to your portfolio construction process is worth +290 bp per annum over and above the performance of a broad Hedge Fund Index (Dow Jones Blue Chip Index). We also show that optimal weights for those who prefer higher odd moments (Mean, Skew etc.) are generally higher in the direction of those assets exhibiting positive relative skewness, or co-skewness, with either a benchmark or the portfolio itself. To illustrate, we conduct out-of-sample back testing on the 10 Main Dow Jones CSFB Blue Chip Hedge Fund Strategy Indices from Jan 2006 to Dec 2012. The initial look-back period is 24 months and rebalancing takes place bi-annually.
Objective functions used include; maximising the Sharpe ratio, which is equivalent to the classical minimum variance portfolio of MarkowitzĂ˘â‚¬â„˘s MPT, Maximising the ratio of the CAGR to both the normal, best fit and modified conditional value at risk (CVaR) or Expected Shortfall. This is sometimes called the STAR Ratio. As a control we compare the results to the benchmark index, and both a buy and hold and rebalanced equally weighted index.
The results show that the Modified and Best Fit methods outperform the Minimum Variance / Maximum Sharpe ratio method, the Benchmark Index and ......................
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