# How to correctly use Fama-French factors (from investment portfolio perspective)?

I have several questions regarding Fama-French and other (for instance, BAB) equity return factors for practical purposes (portfolio construction, portfolio risk analysis, portfolio return analysis). I am interested in answer for any of the questions below. I am familiar with "factor zoo", so below when I write "factors" I mean Fama-French 5 factors + Momentum + BAB + FMAX + tail risk + liquidity risk (Pastor or Sadka approach).

1. Portfolio construction stage.
1.1 Do practioners really use factors to construct portfolios (for instance, a combination of factor ETFs or manual construction of portfolio based on factor selection)?
1.2 If so, is there any literature covering prediction of factor (SMB, HML, ...) returns? As data on Kennet French site demonstrates, some factors (SMB, HML for example) have demonstrated really weak performance over past decade... In fact, I have basic idea, that HML upside is driven by low interest rates, but it's too obvious and superficial...

2. Portfolio risks.
2.1 Besides the standard risk-management procedures, can factors be used to understand what are main risk factors underlying specific equity portfolio?
2.2 If so, how can we use this knowledge to hedge such risks? We are interested mostly in tail risk, aren't we? So we shall model someway the relationship between risk factors in tail situation (copula/ something else?) and build some stress scenario under this model?
2.3 Say we identified portfolio exposure to some factor risks. Which instruments might be used to hedge? Long put options on market index/factor ETF or something else?

3. Portfolio return analysis.
3.1 Academic papers really enjoy criticizing hedge funds for zero alpha after regressing hedge fund returns on some return factors. But isn't the devil in good factor selection for portfolio exposure? I mean, may be there is no need to generate some alpha for portfolio managers, since investor mostly benefits not from alpha, but from correct factor selection in portfolio, and as for me, it's really not so easy to predict which factors will perform well in the future and how much they will reward. And regressing past fund returns gives us static averaged over time view on historical fund strategy and factor selection only, thus benefits from such a knowledge seem to be limited...

## 1. Portfolio construction stage

#### 1.1

Yes, practitioners really use factor strategies, see style investing. Prominent examples are DFA and AQR. Both firms were co-founded by former PhD students of Eugene Fama.

#### 1.2

Factor timing is a different word for time-varying conditional risk premia. Firstly, remember that measuring unconditional expected returns is difficult enough. Nonetheless, as an example, you might be interested in Cooper et al. (2004, JF). They find that momentum strategies work well in economic booms, but not so well during recessions. Regarding your idea about HML's recent weak performance, check out Lettau and Wachter (2007, JF) who suggest that the value premium is related to equity duration and thus sensitive to interest rates.

## 2. Portfolio risks

#### 2.1

The key question is: ''What is the purpose of a factor model?'' Is it about explaining returns or average returns? Economic theory tells us something about expected returns and systematic risk and if we want to test these theories, we only care about average returns. If we want to hedge our portfolios and reduce total risk, we have a different objective. Look at SMB. It carries little pricing power (it doesn't really help to lower alphas) but it explains a lot of variation in returns (increases $$R^2$$ a lot). The point of factor regressions is to find how sensitive your returns are to set of well-known factors. Regardless of whether these factors approximate the SDF and are motivated by a general equilibrium model, you can use the estimated sensitivities to understand what drives the total variation in realised returns of your portfolio.

#### 2.2

In theory, agents only care about systematic risk (covariation with a stochastic discount factor) and asset pricing models aim to identify systematic risk. You personally seem more scared of tail risk. To be precise, you're probably only really concerned with left tail risk (I don't think you fear really high returns). For example, you should be wary about too much momentum exposure for it is known to have occasional crashes, see Daniel and Moskowitz (2016, JFE).

#### 2.3

Regarding hedging instruments: yes, long puts are an option. Even simpler, you could try to reduce your exposure to a certain risk factor. For example, if you discover a value tilt which you find too risky, just lower that exposure by longing growth stocks.

## 3. Portfolio return analysis

The question is what the purpose of factor regressions is. When used for performance evaluation, the question tends to be: ''Can we achieve the same return using cheap long-short portfolios, or is the manager worth his fees?'' This is different to asking whether everything is ''correctly'' priced. Thus, it's fair to see whether a manager actually outperforms any set of factors. If not, I best invest in these factors (essentially for free).