1. Flexible Asset Allocation With Stepwise Correlation BY ILYA KIPNIS

2. 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).

3. 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).

4. 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.

5. 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.

6. 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, wMom = 1, wVol =.5, wCor =.5  Top 6 with stepwise correlation, wMom = 1, wVol = 0, wCor = 1  Top 6 with no stepwise correlation, wMom = 1, wVol =.5, wCor =.5  Top 6 with stepwise correlation, wMom = 0, wVol =.5, wCor =.5

7. 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 single-pass correlation.

8. Results of Six-Asset Configurations SW Correlation Single Correlation SW No Vol Cor Wt 1 SW Zero Momentum Wt Annualized Return 0.1290.1090.121 0.063 Annualized Std Dev 0.1250.1220.1460.046 Sharpe (Rf = 0%) 1.0260.8890.8261.352 Worst Drawdown 0.1550.173 0.2210.069

9. 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 – weightMom = weightCor = 1, weightVol = 0, no stepwise correlation.  With weightMom = weightCor = 1 and weightVol = 0, the stepwise and single- pass return streams are identical.

10. 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 0.1340.0950.134 Annualized Std Dev 0.1160.113 0.1210.0640.121 Annualized Sharpe (Rf=0%) 1.0741.0971.1071.4791.107 Worst Drawdown 0.1380.1530.146 0.065 0.146

11. 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/IlyaKipnis/IKTradingwww.github.com/IlyaKipnis/IKTrading  More can be read on my blog, www.quantStratTrader.wordpress.comwww.quantStratTrader.wordpress.com

12. Questions?