Using Big-Data Techniques to Construct Hedge Portfolios

Researchers and practitioners typically rely on models for guidance, but “most asset pricing models are too stylized to explicitly capture all sources of risk in the economy,” write Yale’s Stefano Giglio and Chicago Booth’s Dacheng Xiu. Rather than exclude some important risk factors from the analysis, Giglio and Xiu are using big-data techniques to help isolate risks so they can be measured and traded.

The risk premium is how much compensation investors can obtain in exchange for bearing certain risks. If professionals and academics exclude important risk factors while trying to estimate the risk premium of the factor they are trying to hedge, it can severely bias the estimate. Therefore researchers typically add a few arbitrary factors as “controls,” even when those factors are not explicitly predicted by a model, hoping that those additions correspond to the risk factors investors actually care about.

For example, it is common for researchers to add the market return as a factor in an analysis even if a theoretical model doesn’t include it, because it is reasonable to assume that investors care about market risk.

Giglio and Xiu instead propose a three-pass method to estimate risk premia that uses big-data techniques to address the potential omitted factors. Their solution marries the well-known Fama-MacBeth two-pass regression, an important tool contributed by Chicago Booth’s Eugene F. Fama and the late James D. MacBeth, with principal component analysis, a statistical technique that can be used to extract factors from a large panel of asset returns. The key of the methodology lies in an econometric theory guaranteeing that even if the true risk factors that drive asset prices are not known, the factors extracted using PCA are equally effective in controlling for the other risk factors—and therefore in isolating the risk factor of interest—for the purpose of estimating the risk premium of the factor of interest.

Giglio and Xiu apply this technique to a large panel of equity and nonequity portfolios and find that properly controlling for omitted risk factors has an economically and statistically significant effect on the estimates of risk premia for many factors. They find that many macroeconomic factors do not carry any risk premium, while factors related to financial frictions such as liquidity command high risk premia.

The method has implications for practitioners trying to hedge or trade any arbitrary factor, such as market liquidity or the number of words in Federal Open Market Committee statements, for which there isn’t a tradable insurance contract or a hedging portfolio. Giglio and Xiu’s method indicates whether the factor carries risk compensation—and constructs a portfolio that allows investors to trade away this risk.