Factors

• Groups of stocks with certain characteristics seem to have higher expected returns.
• These stocks also usually tend to move together.
• Maybe they are exposed to some risk that some investors regard as undesirable.
• Maybe you want to take on that risk to get the return.

• The return of the group of stocks is called a factor.
• Investing in the factor means you will be correlated with the factor.
  • So, if we regress your return on the factor, you will have a positive slope coefficient (beta).
  • Hence the name “smart beta.”
• Example: Fama-French factors: Small Minus Big, High book-to-market Minus Low book-to-market, Conservative Minus Agressive, Robust Minus Weak.

• The “exposed to some risk” story is a way to reconcile factor investing with the efficient markets hypothesis.
• It is also possible that stocks are just mispriced in systematic ways.
• For example, there is evidence that analysts recognize that “quality” stocks are worth more than “junk” stocks, but they underestimate how much more.

Industry examples

Factor investing at BlackRock

Factor investing at AQR

Some data

• Sort into quintiles each month.
• Value weighted return of each group
• Re-sort at the beginning of the next period and continue.

Factor investing with machine learning

• Find factors worth investing in.
• Decide how to optimally combine them.
• Using ML, we can in principle throw in lots of characteristics and let the machine decide which are useful, but preprocessing is usually useful.
• Need to backtest, which is a variation of the usual ML train-and-test.
• Gu, Kelly, and Xiu, 2020