# Probabilistic Value And Momentum Factor Rotation

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Includes: DIA, IWM, QQQ, SPY

## Summary

Value and momentum have historically generated alpha that is statistically significant against the market.

The combination of value and momentum works even better.

Using a probabilistic approach to rotating between value and momentum is another method of capturing long term risk premia.

Value and momentum are the premier market anomalies. Historically, investing in either strategy would have yielded superior risk adjusted returns relative to the market. It has also been proven that a combination of value and momentum does an even better job at capturing long term risk premia. However, is there a strategy that does even better than a portfolio split between value and momentum? Perhaps a style rotation? Utilizing a strategy called probabilistic momentum, rotating between value and momentum when the probability for outperformance is in your favor yields results that are as strong, if not superior, to simply allocating equally between the two.

The process for probabilistic value and momentum is as follows:

▪ Take the information ratio of value over momentum from the past 6 months.

▪ The information ratio becomes the t-statistic.

▪ This t-statistic is then used to calculate the probability of outperformance.

▪ If value has a 60% or greater probability, the portfolio rotates 100% into value. I stay in value until the probability of momentum becomes 60% or greater and vice versa.

Taking the top decile from both momentum and value a value weighted portfolio was created and tested.

Results are as follows:

Clearly the highest deciles of momentum and value outperform the market individually. A 50-50 portfolio has a higher Sharpe and Information Ratio than momentum or value alone. Our probabilistic rotation between value and momentum had the highest mean risk-adjusted return despite a slightly lower Sharpe and Information Ratio relative to the 50-50 portfolio. Drawdown is also slightly larger than the 50-50 portfolio. Now is this statistically different than the other portfolios? Put another way, does the probabilistic portfolio generate reliable alpha? Here we compute alpha using the CAPM, Fama-French 3 and 4 factor portfolios(zero investment portfolios mimicking value(HML), small minus big(NYSEARCA:SMB), market(MKT), and momentum(UMD). Also, a 6-factor model is used which contains the four Fama-French factors along with quality minus junk(QMJ) and betting against beta(NYSEARCA:BAB).

*monthly

Alpha is clearly statistically significant against all factor mimicking portfolios, boasting high t-statistics. This exercise also allows us to understand the portfolio's factor exposures. It is clear that the probabilistic portfolio is heavily exposed to movements in the overall market with coefficients greater than one. It should be obvious that we have exposure to value(HML) and momentum(UMD) and since the portfolio is heavily exposed to the market it should come as no surprise that there is negative exposure towards betting against beta(BAB). There is also exposure to small cap stocks versus large cap stocks. What is interesting is the negative loading towards quality minus junk. Although the exposure is relatively small, it is still statistically significant. It appears that the screen generates stocks that are of poor quality. This could make logical sense. Some of the value stocks chosen may not be particularly good investments from a business standpoint but could still be selling below some measure of intrinsic value(in our case the book-to-market ratio). Also, momentum stocks tend to be driven by short-term sentiment(technicals, surprises, analyst revisions etc.) more so than the underlying business itself. So by measures of quality(profitability, growth, payout, and safety) they are poor investments. However, they have captured the attention of the investment public for some reason and we are essentially "jumping on the train".

Being a quant, I like to deal with probabilities and bet when the probability of success is in my favor. Clearly a combination of value and momentum stocks is superior to holding portfolios of value or momentum individually. The probabilistic approach is an interesting exercise in capturing long term risk premia and has proven to generate alpha that is statistically significant against the market and boasts high Sharpe and Information Ratios.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.