In this post I’d like to show an example of constructing a monthly-rebalanced long-short portfolio to exploit alpha signals while controlling for factor exposures.
This example covers the time period between March 2005 and 2014. I use 477 stocks from S&P500 universe (data source: Quandl) and Fama-French 3 factors (data source: Kenneth French’s website) to conduct backtests. My alpha signal is simply the cross-sectional price level of all stocks – overweighting stocks that are low on price level and underweighting the ones that are high. By doing this I’m effectively targeting the liquidity factor so it worked out pretty well during the 2008 crisis. But that’s beside the point, for this post is more about the process and techniques than a skyward PnL curve.
At each rebalance, I rank all stocks based on the dollar value of their shares, then assign weights to them based on their ranks inversely, i.e., expensive stocks are getting lower weights and vice versa. This gives me naive exposure to my alpha signal. However, my strategy is probably exposed to common factors in the market. By the end of the day, I could have a working alpha idea and a bad performance driven by untended factor bets at the same time. This situation calls for a technique that gives me control for factor exposures while still keeping the portfolio close to the naive alpha bets.
Good news: the basic quadratic programming function is just the tool for the job – its objective function can minimize the sum of squared weight differences from to the naive portfolio while the linear constraints stretching factor exposures where we want them to be. For this study I backtested 3 scenarios: naive alpha portfolio, factor neutral portfolio and a portfolio that is neutral on MKT and HML factor but tilts towards SMB (with a desired factor loading at 0.5). As an example, the chart below shows the expected factor loadings of each 3 backtests on the 50th rebalance (84 in total). Regression coefficients are estimated with 1-year weekly returns.
After the backtests, I got 3 time-series of monthly returns for 3 scenarios. Tables below show the results of regressing these returns on MKT, SMB and HML factors. All three strategies yield similar monthly alpha, but the neutral portfolio mitigated factor loadings from the naive strategy significantly, while the size tilt portfolio kept material exposure to the SMB factor.
Tables below summarize the annualized performance of these backtests. While the neutralized portfolio generates the lowest annualized alpha, it ranks the highest in terms of information ratio.
Interpretation: the naive and size portfolio gets penalized for having more of their returns driven by factor exposures, either unintended or intentional. The neutral portfolio, with slightly lower returns, gets a better information ratio for representing the “truer” performance of this particular alpha idea.
The idea above can be extend to multiple alpha strategies and dozens of factors, or even hundreds if the universe is large enough to make it feasible. The caveat is that there is such thing as too many factors and most of them don’t last in the long run (Hwang and Lu, 2007). It’s just not that easy to come across something that carries both statistical and economic significance.