Flexible Asset Allocation With Stepwise Correlation BY ILYA

Flexible Asset Allocation With Stepwise Correlation BY ILYA KIPNIS

The Basic Idea Momentum is a well known anomaly (Antonacci 2012, Faber 2007, among others). Rank ordering selection is also robust to estimation errors (Chriss, Almgren 2004 & 2005). Add volatility ranking and basic correlation ranking to the mix and you have the original FAA (Keller 2012).

Stepwise Correlation Rank Innovation proposed by David Varadi (2014) When selecting assets, we don’t care about all correlations—only between assets actually selected. Starts with an initial asset, then selects based on minimum average correlation, and ranks in that order. In other words, it’s path dependent. Best asset chosen from ranking of non-correlation factors (momentum and volatility).

Stepwise Correlation Example The orders are slightly different depending on the initial asset. After all, better to build portfolio around selected assets rather than care about relationships not present in the portfolio. Easy to tell by similarity of colors that it’s robust to starting seed, but will nevertheless generate slightly different sequences.

How It Works Five numerical parameters: weight on return, weight on volatility, weight on correlation, lookback period (in months), and how many assets (top N) to invest in. Other parameters: whether or not to use stepwise correlation rank. Procedure: every month, look back over the previous months (specified with the lookback parameter). Rank every security by cumulative return and annualized volatility. Rank the weighted sum of ranks. Use the best as the seed for stepwise correlation rank. Take the rank of the weighted sum of ranks of all three metrics. Equal weight the top N assets. Set to zero any asset with negative momentum. Invest that in cash.

An Example Take the close prices of the following 30 ETFs (in inception since 2003, data from start of 2003 to 2015 -05 -22) XLB, XLE, XLF, XLP, XLI, XLU, XLV, XLK, XLY, RWR, EWJ, EWG, EWU, EWC, EWY, EWA, EWH, EWS, IYZ, EZU, IYR, EWT, EWZ, EFA, IGE, EPP, LQD, SHY, IEF, TLT Run the following configurations with a 4 -month lookback: Top 6 with stepwise correlation, w. Mom = 1, w. Vol =. 5, w. Cor =. 5 Top 6 with stepwise correlation, w. Mom = 1, w. Vol = 0, w. Cor = 1 Top 6 with no stepwise correlation, w. Mom = 1, w. Vol =. 5, w. Cor =. 5 Top 6 with stepwise correlation, w. Mom = 0, w. Vol =. 5, w. Cor =. 5

Example (Continued) At Small Percentage of Universe (20% in this case), Stepwise Correlation has room to work. Results seem intuitive. Momentum drives returns, factoring in volatility helps, stepwise correlation outperforms singlepass correlation.

Results of Six-Asset Configurations SW Correlation Single Correlation SW No Vol Cor SW Zero Wt 1 Momentum Wt 0. 129 0. 109 0. 121 0. 063 Annualized Std 0. 125 Dev 0. 122 0. 146 0. 046 Sharpe (Rf = 0%) 1. 026 0. 889 0. 826 1. 352 Worst Drawdown 0. 155 0. 173 0. 221 0. 069 Annualized Return

Second Example (12 assets, From 6) When using 12 out of 30 assets, the stepwise effect doesn’t have as large (if any) an impact at all. Add in one more configuration – weight. Mom = weight. Cor = 1, weight. Vol = 0, no stepwise correlation. With weight. Mom = weight. Cor = 1 and weight. Vol = 0, the stepwise and singlepass return streams are identical.

Results of 12 asset configurations (Stepwise makes no difference in Cor Wt 1 cases) SW Correlation Single Correlation SW No Vol Cor Wt 1 SW Zero Momentum Wt Single Cor No Vol Cor Wt 1 Annualized Return 0. 125 0. 134 0. 095 0. 134 Annualized Std Dev 0. 116 0. 113 0. 121 0. 064 0. 121 Annualized Sharpe (Rf=0%) 1. 074 1. 097 1. 107 1. 479 1. 107 Worst Drawdown 0. 138 0. 153 0. 146 0. 065 0. 146

Conclusions Incorporating momentum rank delivers higher returns than leaving it out. Stepwise Correlation ranking helps at smaller percentages of the total universe. Its effects dilute when more securities added in to wash out idiosyncratic risk. Code available at www. github. com/Ilya. Kipnis/IKTrading More can be read on my blog, www. quant. Strat. Trader. wordpress. com

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