Equity Allocation Predicts Next Quarter's Market Return

It predicts fully one-fourth of the variation in market returns

Still slogging through Michael Howell’s Capital Wars. The going is slow because Howell makes a lot of serious claims and, as you know dear reader, I like to check things with my own hands. At one point he argues that the proportion of assets held in equities is a good measure of risk appetite so that it predicts 2-year ahead equity returns. That obviously perked me up. He has a scatter plot that looks suspiciously like he did not detrend the series again:

Sure enough, when he next compares the performance of the ratio to CAPE as a long-term predictor of equity returns, you can tell by visual inspection that he had indeed not bothered to detrend the series properly.

As usual, though, he’s on to something. That something was the predictive information contained in the share of equities in the aggregate portfolio of American investors. We obtain the share of directly and indirectly held corporate equities in the total assets of US households, as well as every other variable we look at here, from Fred. Here’s the series before and after first-differencing.

Turns out, equity allocation does not predict two-year ahead market returns. But it strongly predicts next quarter’s market returns! How much predictive information does it contain exactly?

We find an astonishing degree of return predictability. Detrended equity share predicts fully one-fourth of the next quarter’s variation in market returns. The Durbin-Watson test cannot reject the null of zero residual autocorrelation (DW = 2.07, P = 0.634), so the result is not due to autocorrelation — the bane of time-series analysis.

This level of return predictability is so astonishing that one is forced to undertake stringent robustness tests. We find that equity allocation predicts 1-qtr fwd market returns after controlling for contemporaneous market returns, margin balances at broker-dealers (a proxy of market-wide leverage); dealer leverage, net worth, or balance sheet capacity; as well as traditional return forecasting factors like the term spread (T10Y2Y) and the credit spread (BAA10Y). It does so whether we restrict the sample to 1986Q1-2020Q4, 1995Q1-2020Q4, or 2009Q1-2020Q4. Note that all variables have been robustly standardized to have zero mean and unit variance. So the slope coefficient measures effect size. We find that a one standard deviation unit shock to equity allocation (equivalent to a change of 1.4 percentage points in equity share) predicts fully one-half standard deviation units higher market returns or 3.3 percent per quarter. This is an obscene level of return predictability. The Durbin-Watson test allows us to rule out spurious results due to autocorrelated residuals (DW = 2.02, P = 0.528).

We also carry out vector autoregressions and Granger causality tests with market returns and detrended equity share. Controlling for lagged terms reduces the standardized slope only slightly to b = 0.43 and it remains significant at the 1 percent level (P < 0.001). We cannot reject the null of zero residual autocorrelation even at the 10 percent level in the Portmanteau test (P = 0.236), so the results are not due to autocorrelation. The Granger test yields an F-statistic of 21.37, allowing us to reject the null that equity allocation does not predict market returns at the 1 percent level of confidence (P < 0.001).

Digging further into it reveals that equity allocation contains much the same information as that jointly contained in household net worth and household leverage. All three are good return-forecasting factors.

The predictive information about future returns contained in household leverage is, as we shall see, less than that contained in household net worth.

We find that if we control for net worth, equity share has the larger gradient (b = 0.26, P = 0.050) that sits on the boundary of the standard level of statistical significance, whereas the gradient of net worth is smaller and statistically indistinguishable from zero even at the 10 percent level (b = 0.18, P = 0.250). The Durbin-Watson test statistic does not allow us to reject the null of zero residual autocorrelation (DW= 2.09, P = 0.681). In a vector autoregression specification with 1 qtr lagged values, the Granger test allows us to reject the null that equity allocation does not predict market returns (F = 4.66, P = 0.032), but not that net worth does not predict market returns (F = 1.39, P = 0.239). In a specification with lagged values for 2 quarters, we find again that equity allocation predicts market returns (F = 3.54, P = 0.030), but net worth does not (F = 1.14, P = 0.321).

Similarly, we find that controlling for household leverage, equity share has a large and significant gradient (b = 0.55, P < 0.001). Meanwhile, household leverage falls into insignificance with equity share in the regression (b = -0.16, P = 0.356). The Durbin-Watson again rules out a spurious result due to autocorrelation (DW = 2.08, P = 0.663). In the vector autoregression with 1-qtr lagged values, we find that equity allocation Granger-causes market returns (F = 14.4, P < 0.001), but household leverage does not (F = 0.91, P = 0.341). In the specification with lagged values for 2 quarters, we find that equity allocation again predicts market returns (F = 5.53, P = 0.004), but household leverage does not (F = 0.68, P = 0.510).

Including both household net worth and leverage, however, does push the slope of the equity share into insignificance. Mechanically, this is due to multicollinearity. Indeed, we find that household net worth and leverage together explain 93 percent of the variation in equity share, with the Durbin-Watson test again allowing us to rule out residual autocorrelation (DW = 1.74, P = 0.099). Economically, the import is that the share of risky equities in the aggregate assets of US investors contains information on their risk appetite. As institutional investors rotate into risk assets, the flood of money buoys equity returns; as they rotate away from risk assets to safety, the tidal outflow lowers equity returns. In other words, equity allocation is an excellent proxy of the equity risk premium — fluctuations in expected excess returns on equities track fluctuations in equity allocation.

Finally, we also find that equity allocation predicts 1-qtr fwd credit spread — the difference between the yield on Moody’s Baa corporate bonds and the 10-year Treasury note. The Granger test statistic is large and robust (F = 16.6, P < 0.001). The credit spread, on the other hand, does not predict equity allocation (F = 0.73, P = 0.393). Again, these results are not due to screwed-up residuals. The Portmanteau test cannot reject the null that the residuals are white noise (P = 0.308).

Meanwhile, we find only weak predictability of the term spread — the difference in yields between 10-year and 2-year US Treasuries. The Granger test statistic is only marginally significant for equity allocation predicting the term spread (F = 3.83, P = 0.052). The term spread, meanwhile, does not try to predict equity allocation at all (F = 0.83, P = 0.363). Again, the Portmanteau test cannot rule out the hypothesis that the residuals are white noise (P = 0.846).

Variables that contain strongly predictive information on future market returns are useful in at least three ways. First, they’re a proxy of market-wide risk premia that is of interest to investors, macroeconomists, central bankers, and other policymakers. Second, they’re the key ingredient of any dynamic pricing model because you need good return-forecasting factors to span the price of the systematic risk being modeled. Third and last, but certainly not the least, they open up the possibility of market-timing strategies. That is why the stability of the return-predictability that we documented over successively more recent periods — 1986Q1-2020Q4, 1995Q1-2020Q4, or 2009Q1-2020Q4 — is so interesting.

Can someone please coach Howell on detrending?