FT AlphaVille linked to an interesting blog post by Nick Maggiulli on Dollars and Data that examined the long-run stock return predictability in terms of equity allocations. Nick shows that high allocations predict lower ten-year returns. Here’s a replication of the main result.
The result must be taken with a pinch of salt. Is it a feature or a bug? The cause for concern is that overlapping regressions generate spurious correlations. There is good reason to be skeptical of the extremely high coefficient estimate (r=-0.897, p<0.001). It likely reflects the medium-term cycle in Equity Allocation. (We use the same metric as Nick and in the original blog post at PhilosophicalEconomics.) Econometrically, regression estimates rely on the assumption that the series is stationary (no detectable temporal patterns like trends and cycles) which is manifestly violated here. See next figure.
What is required for kosher statistical inference is to transform the series so that it is at least roughly stationary. The best way to do that is to difference the series. Here we look at changes in the natural logarithm (ie, compounded rate of return) of the SP500 Index and Equity Allocation. The two series are manifestly stationary and appear to be strongly contemporaneously correlated.
Indeed, contemporaneous percentage changes in Equity Allocation strongly predict quarterly returns on the SP500. Our gradient estimate (b=1.25, t-Stat=30.7) implies that 1 percent higher allocation to equities predicts a 1.25 percent quarterly return on the SP500 over and above the unconditional mean of 1.79 percent per quarter. Equity Allocation explains 78 percent of the variation in stock market returns. See next figure.
The empirical evidence is rather consistent with the idea that fluctuations in the stock market reflect investor herd behavior. Specifically, the stock market goes up when investors rebalance to equities and goes down when investors rotate out of equities to bonds and cash. This is not only an important amplifier of dealer risk appetite and monetary policy shocks but also an important source of fluctuations in its own right. So stocks are getting culled across the board as we speak precisely due to investor rebalancing prompted by higher yields. (In turn, higher yields reflect either the expectation that the Fed will hike faster, a higher term risk premium, or both. The two can be disentangled using the ACM term-structure model as I illustrated not too long ago. [P.S. It’s risk premium; although Matt Klein doesn’t seem to buy the ACM decomposition.)
Tying market fluctuations empirically to investor herd behavior goes some way towards explaining the excess volatility of the stock market that has long puzzled economists. My wager is that stock markets fluctuate dramatically more than reassessments of underlying fundamentals could possibly warrant because of fluctuations driven by investor rebalancing.
The question is whether this is due to the herd behavior of small investors, or whether it is due to the inadvertently-coordinated rebalancing among large asset managers because they face similar mandates. If the former, that leads us to questions of investor sentiment. If the latter, it leads us straight back to market structure. In particular, it draws our attention to the buy side. Instead of paying exclusive attention to dealers and wholesale funding markets, perhaps we should also interrogate the investor behavior of large asset managers as an independent source of fluctuations in the price of risk.
In either case, knowing that rebalancing investor herds drive stock market fluctuations is not very useful since data on equity allocation is only available at the end of the quarter. Or is it not? Can we not think of Equity Allocation (hence implicitly investor herd behavior) as a risk factor for pricing the cross-section of stock excess returns? Indeed we can. Turns out, percentage changes in Equity Allocation are priced in the cross-section of expected excess returns. We illustrate this with 100 Size-Value portfolios from Kenneth French’s library.
What we find is that instead of a linear pricing relationship whereby higher betas imply monotonically higher expected returns in excess of the risk-free rate, the relationship is quadratic. Portfolios whose equity allocation betas is moderately high outperform portfolios with extreme betas in both directions. So an easy way to make money is to hold portfolios that are, depending on your risk appetite, long or overweight moderate beta stocks, and short or underweight extreme beta stocks.
Note that stock portfolios that are more sensitive to tidal investor flows are generally more volatile. See next figure.
The big puzzle that thus emerges is why these frontier assets (stock portfolios that are highly sensitive to investor rebalancing) don’t sport high expected returns. For the fundamental insight of modern asset pricing is that risk premia (expected returns in excess of the risk-free rate) exist because investors require compensation to hold systematic risk (but not idiosyncratic risk since that can be easily diversified away). In other words, assets that pose a greater risk to investors’ balance sheets ought to sport higher returns. We have shown that the tidal effect of inadvertently-coordinated investor rebalancing is a significant and systematic risk factor for all investors. So why isn’t there a monotonic relationship between the sensitivity of portfolio returns to investor rebalancing and the risk premium embedded in the cross-section? Why is the price of risk quadratic and not linear in beta? Clearly, we are missing a theoretical piece of the puzzle.