Tactical Global Asset Allocation and Stock Selection

Campbell R. Harvey,
Fuqua School of Business, Duke University, Durham, NC
National Bureau of Economic Research, Cambridge, MA

Risk versus Prediction Regressions

Risk regression:

That is like the traditional market model regression:

R_t = intercept + beta x R_mt + residual_t

The R² of this regression is high (90%) and the beta is the risk "sensitivity" or "exposure" or "loading" and R_m is the "risk factor". Notice that everything is contemporaneous - time t for both left hand side and right hand side.

We could augment the regression with additional risk factors:

R_t = intercept + beta₁ x R_mt + beta₂ x Doil_t + residual_t
Now we have a second risk sensitity "beta₂" to the change in the oil price. We talked about other factors like: unexpected world inflation, changes in expected world inflation, changes in world industrial production, changes in world interest rates and term structure.

Prediction regression:

R_t = intercept + d₁ x Z_t-1 + residual_t
where Z_t-1 is a lagged predictor variable and d₁ is a simple regression coefficient. Z_t-1 might be the lagged dividend yield. Indeed, Z_t-1 might be the same data as a risk factor, such as oil price changes - but, *importantly,* the variable is lagged in the prediction regression and NOT lagged in the risk regression.

The prediction regressions are not risk regressions. It is hard to find predictability so the R² is low (say 5%).

Hope this clarification helps.

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