Markets are only efficient to zeroth order

Mimicking the SPY

I am interested in portfolios one can actually hold. There is a very practical difference between sorting stocks on some signal and actually harvesting the alpha — negative or positive — associated with the signal from the cross-section of equities. What is alpha? Alpha is defined as the difference in expected returns between two portfolios you can actually hold that is not due to greater exposure to systematic risk. One can try to isolate alpha by constructing market-neutral portfolios. I cannot talk about products offered by Systematic Portfolios according to the SEC’s rules. But I can document puzzles that have nothing to do with the economics of my firm. Here’s a first-order puzzle. The SPY has a negative premium over a market-weighted portfolio of the most liquid five hundred tickers of US equities.

We obtain the market capitalization of point-in-time SPY constituents from NASDAQ. We filter on a number of liquidity proxies. All our portfolios except the SPY are rebalanced monthly and market-weighted — “liquid_507_constituents” is our mimicking portfolio for the SPY. We construct the L/S by putting a dollar on our portfolio and a dollar against the SPY. L/S_3X is three dollars on each side.

We find a “flight-to-safety premium” in these blue-chip US equities. The L/S gains in times of market distress. The L/S is a negative-beta, low-risk asset with a volatility comparable to a portfolio of ultrashort-duration bonds. Levering up to the practical upper bound (“3X”) gets us closer to our reference level of volatility of 10% per annum. Despite being anti-correlated with the SPY (-0.15), the expected return on the 3X is 5% per annum.

This shows that the market is only efficient to zeroth order — at first-order, it fails. Note that the t-test for the equality of means is not significant. That’s good. It means that the longonly portfolio mimics all the fluctuations of the SPY but still contains a premium over the SPY. An alpha of 5% per annum is just sitting there for the taking! If the most liquid market for risk were efficient, this premium would not exist. There should be no systematic information contained in the L/S. Yet, there is; as evidenced by the alpha and especially the diachronic pattern.

The theory of the astonishing alpha of the market-weighted portfolio documented above is that it is the compensation for intermediaries responsible for closing the gap between the main ETF and its constituents. Our result is consistent with the literature on “limits to arbitrage.” Leverage constraints on arbitrage capital explain the existence and tightness of the premium. In periods of intermediary balance sheet stress, when balance sheet capacity is scarce, the risk premium expands; in periods of robust balance sheet growth, it becomes stationary around zero. We can therefore think of this alpha as a sensitive intermediary risk premium; sorta like that contained in the slope of the VIX futures curve.

If we were not constrained by regulations to any level of leverage, we could lever up to market levels of volatility of about 20% per annum. Then we would’ve earned 10% per annum on a negative-beta asset. Again, I am not talking my book — we are not selling any variant of this asset. But the fact that it exists is interesting and important. It suggests that markets are only efficient to zeroth order.