Traditional Factor-Based Models & Their Challenges
Factor-model based asset pricing field is a fast-growing niche in the quant hedge fund space. It is a traditional and empirical area that is widely accepted in industry. Factor literature is a treasure of insights, many of which deliver high returns. Even if some factors may fail to generate profits themselves, they are still very useful explaining the cross-sectional variation of expected stock returns, although their explanatory powers for different left-hand-side portfolios in a multi-factor model are different.
Harvey, Liu, and Zhu (2016) [1] documented 314 factors on top journals, and only included statistically significant ones. In reality there are even more factors. The most popular common risk factors include size, book-to-market ratio, momentum, profitability and so on. However, traditional factors do not seem to do a good job in recent decades. One of the papers explaining this in detail is “Alice’s Adventures in Factorland: Three Blunders That Plague Factor Investing” [2].
This paper explained why factor premiums vanish due to reasons like crowding and transaction costs. There is also one common misunderstanding of factors: creating a portfolio of several long-short factors can diversify most of the risks in factor investing.
In reality, factor returns are far from normal. The worst drawdowns for the portfolios of factors were similar to the average of the worst single-factor drawdowns, because the large drawdowns of individual factors often happen at the same time. This may be due to time varying cross-factor correlations or serial correlation of returns. In conclusion, we should rein in our expectations about factor returns as well as pay close attention to their tail risks.
So, what can we do about factor investing? There are several choices we can make.
Just as what a lot of practitioners are doing, we can discover new factors. For example, we can use different data sources like alternative data to do alpha research. Tons of new factors are discovered each year, and so-called alpha factors are actually undiscovered beta factors.
In the paper, they examined all 46 common factors published, and there’s evidence showing cumulative factor performance before and after publication to have significant differences, meaning that anomalies of a factor were likely to be exploited by investors after publication. When we try to locate a new factor, we need to test its exposure to common risk factors as well as the economic rationale behind it before researching the factor.
As for existing factors, different factors generally work differently under different market conditions. We may need to combine them wisely due to our insight about the market. Another thing we can do is to make meaningful adjustments to existing factors. Take momentum for an example. It is a common risk factor which has been studied and proven effective across assets and countries.
The basic idea behind it is simple: buying past winners and selling past losers. Instead of measuring past returns to determine winners and losers, we can compute the momentum differently, like measuring past alpha proposed by Carhart [3], and he found mutual funds with past high four-factor alphas tend to have better performance in the future. Gulen and Petkova [4] found “Absolute Strength Momentum”.
The term “absolute” refers to the fact that the stock is being evaluated relative to the historical benchmark which is stable over time. For all of the variations, one thing is generally true: they make economic sense. But for actual deployment, we may need to locate their hidden risks, check crowding and so on.
Another choice we have is to introduce state of the art techniques to take advantage of big data (See Coqueret and Guida [5]). For example, instead of making a forecast of future price, we can build up a system to learn the policy, and the policy will tell the system whether to buy or sell a stock. This is an idea from Reinforcement Learning, and it can be compared with commonly used regression-based approaches.
But the problem with techniques like this is also obvious: their economic intuition is opaque. Lots of factors discovered to be statistically significant are simply results of data mining. This is something we need to avoid. But these techniques themselves have proven to be very helpful in many industries for recent years. They have even been accepted by a lot of Hedge Funds like Rebellion Research and already made substantial profits.
So, what if we kind of combine Machine Learning or Reinforcement Learning with traditional factor-based models? In a way that we can explain the output of our model but make better use of the data we have without getting overfit to historical data due to data mining. The combination between tradition and innovation can be a trend.
Or as the revered Machine Learning expert, teacher and author of Machine Learning for Factor Investing Tony Guida says, “For me ML and factors/signals are the perfect matrimony, each dataset is a small relative part of truth. ML is a very effective, fast and non linear way of harvesting higher dimensional interaction between signals.”
Written by Yi Hu & Edited by Alexander Fleiss
Sources:
[1] Harvey, C., Y. Liu, and H. Zhu. 2016. ... and the Cross- Section of Expected Returns. Review of Financial Studies 29, no. 1 (January): 5–68.
[2] Arnott, R., C. R. Harvey, V. Kalesnik, and J. Linnainmaa. 2019. Alice’s adventures in factorland: Three blunders that plague factor investing. Journal of Portfolio Management 45:18–36.
[3] Carhart, M.M., 1997. On persistence in mutual fund performance. The Journal of finance, 52(1), pp.57-82.
[4] Gulen, H. and Petkova, R., 2018. Absolute strength: Exploring momentum in stock returns. Available at SSRN 2638004.
[5] Coqueret, G., & Guida, T. 2020. Machine Learning for Factor Investing: R Version. CRC Press.