# What is the benefit of High-minus-Low as in Fama French model?

Can anyon explain the concept of using High-minus-Low in finance literature.

• In 1985 Rosenberg Reid and Lanstein showed that a strategy of investing in stocks with high book to market ratio and shorting stocks with low B/M would have earned high returns historically. jpm.iijournals.com/content/11/3/9 Fama French think this is because High-Minus-Low is a undiversifiable risk factor which earns return Jan 28 '19 at 17:04
• In any case, whether it is a risk factor or not, it seems to "explain" (in a statistical sense) the cross-section of stock returns, i.e. how long-term returns differ from one stock to another. Jan 28 '19 at 20:12
• Are you referring to (1) forming portfolios based upon some variable $X$ then computing the difference between the high $X$ portfolio return and the low $X$ portfolio return or (2) the Fama-French $HML$ factor in particular which they form by sorting securities based upon book to market ratio? Jan 29 '19 at 18:47
• @MatthewGunn I am actually referring to (1) because I have seen some also use other type of High minus Low such as High unemployment minus Low unemployment. Actually, my teacher say that the gap between high minus low is the risk premium itself, but we don't know what kind of risk this is, so we just build a factor for it. Is it correct? Thank you for your answer!
– town
Jan 30 '19 at 16:15

"High-minus-Low" refers to portfolio analysis, which is one of the most commonly used statistical methodologies in empirical asset pricing. There are several benefits of this technique in comparison to regression-models presented in Bali/Engle/Murray (2016), p. 33:

While the most common application of portfolio analysis is to examine future return predictability, the portfolio methodology can also be employed to understand variation in the characteristics of the entities (stocks) across the different portfolios.

Perhaps the most important benefit of portfolio analysis is that it is a nonparametric technique. This means that it does not make any assumptions about the nature of the cross-sectional relations between the variables under investigation.

In fact, portfolio analysis can be helpful in uncovering nonlinear relations between variables that are quite difficult to detect using parametric techniques.

The main statistical argument is, that we frequently want to test whether the time-series mean for each of the portfolios differs from some null hypothesis mean value (wich is often assumed to be zero). Most importantly, we want to examine whether the time-series mean of the difference portfolio is statistically distinguishable from zero. As commented, we commonly use the most extreme portfolios, to test if a certain cross-sectional relation between stocks exists, because the difference for the control-variable (sorting-variable) is highest for these extreme portfolios.

Reference

Bali, Turan G., Robert F. Engle, and Scott Murray (2016): Empirical asset pricing: the cross section of stock returns. John Wiley & Sons

• If my answer was helpful for you, i would be pleased if you mark it as accepted. Jan 31 '19 at 9:10