There is a problem of time-scale in intermediary asset pricing. Fluctuations in the risk-bearing capacity of broker-dealers drive fluctuations in asset prices. While we have data on dealer balance sheets on a quarterly basis, dealers care more about day-to-day or even intra-day fluctuations. By working with quarterly numbers, we fold away the vast bulk of asset price variation that dealers care about the most. This works for the purposes of investors more patient than day traders. But it is hardly satisfactory from an analytical perspective. Here we suggest a way to get around this problem by identifying a proxy for dealer risk appetite that is available on a daily basis.
The measure we have in mind is the term premium on expected volatility embedded in option prices. CBOE’s VIX is the price of insurance against market turmoil over the following month; VX is the same for the following quarter; their difference is the term premium embedded in expected volatility. Both track each other closely. But spikes in their difference contain information on financial conditions. Simply put, spikes in the term premium on expected volatility correspond to “risk-off” episodes when dealer risk constraints bite, asset prices fall, and short-term expected volatility spikes above its medium-term counterpart. Put another way, when the price of short term insurance against market moves exceeds the same for the longer term, that’s a signal that dealers are shedding risk, thereby driving asset prices down and (both realized and expected) volatility up. The term risk premium in expected volatility thus turns out to be a highly sensitive barometer of dealer risk appetite.
We posit that the term risk premium is priced into the cross-section of stock excess returns. We extract daily return data for 100 portfolios sorted on market capitalization and book-to-market ratio from Kenneth French’s website. The data is from Jan 4, 2010 to Oct 31, 2019. We begin by noting that daily returns are even more strongly correlated with the 3-month VIX than the 1-month VIX. We can infer that the vol term risk premium contains additional information beyond that contained in the VIX.
The capital asset pricing model posits that the pricing factor is market returns. It does a truly shitty job in pricing US stocks. The price of this risk is indistinguishable from zero.
Recall that we are working with returns on portfolios sorted on size and value. Yet, size (“SMB”) performs as poorly as market returns as a pricing factor. So much for the workhorse model.
Contrary to theoretical expectations, the price of value turns out to be negative. That is, stocks that are more sensitive to returns on relatively high book values (“value stocks”) actually do worse than stocks that are less sensitive to this factor. One can still mine this premium the “wrong” way around. But there is no reason to believe that this pattern will continue to hold.
According to theoretical expectations, market volatility should not be priced in. But it is. VIX has a robust price meaning that if you hold a portfolio that is more sensitive to fluctuations in VIX, you earn higher returns. This makes no sense if your marginal investor is the traditional hypothetical investor who cares about her consumption. But it makes ample sense in a world where the marginal investor in asset markets is a financial intermediary whose risk constraint is proportional to market volatility. In particular, dealers want to maintain a constant probability of default, that is in turn a constant function of daily volatility and market leverage. If we live in this latter world, we should expect VIX to be priced in the cross-section of asset returns.
VX does nearly as well as VIX, although the price is slightly lower, suggesting that dealers care much more about short-term expected volatility, ie over a horizon measured in days and weeks, rather than medium-term expected volatility over a horizon measured in months. This fact will help us interpret the term risk premium in expected volatility (VIX-VX).
We find that the term risk premium in expected volatility (“vdiff”) is also priced in the cross-section of stock returns. Portfolios that are more sensitive to our barometer of risk-off events sport higher returns. This is strong evidence that the term premium contains information on the response function of the dealers.
We know from previous work that, at longer time-scales, say at the quarterly frequency, stock markets returns are predictable. Specifically, measures of risk premia such as the term spread &c, and balance sheet measures of dealer risk-appetite, predict market returns. Return predictability is of existential importance to dynamic asset pricing, where the price of risk is assumed to be an affine function of return forecasting factors. Return predictability is quite modest for daily data. However, we do find some predictability. Specifically, we find that (one-day lagged) market returns and return on VX, but not VIX, weakly predict market returns in the sense that the slope is significant at the 10 percent level. Meanwhile, the slope of one-day lagged return on the term risk premium on expected volatility is significant at the standard 5 percent level.
These patterns suggest that the term risk premium on expected volatility embedded in option prices contains significant information on dealer risk-appetite. Spikes in this spread correspond to risk-off episodes when dealers balance sheets are overloaded and they must shed risk. Investors are compensated for this systematic risk — that is, it is priced into the cross-section of stock returns. And the price of this risk is very significant. What looks like intermittent market turmoil is simply the balance sheet retrenchment of key intermediaries.
Note that stocks are a very minor component of dealer balance sheets, and the universe of investors in US stocks is very broad. By comparison, OTC derivatives and fixed-income securities like corporate bonds, treasuries, asset-backed securities and other structured products, are traded almost exclusively over-the-counter, ie, within the dealer ecosystem. We can thus expect these assets to be priced even more tightly by intermediary risk-appetite. Indeed, there is good evidence that this is the case. I would love to my hands on return data for these asset classes. But it is hard to come by. He et al. (2017) looked at a number of assets and found that the capital ratio of dealers (the inverse of dealer leverage) prices securities across asset classes at the quarterly frequency. The next figure displays their prices of risk along with the 95 percent confidence intervals.
The next figure reports the percentage of cross-sectional variation in expected excess returns explained by factor betas for dealer capital ratios computed by He et al. The relationship is much tighter for derivatives and fixed-income, compared to stocks. Pricing commodities and FX is much more difficult because these are much more sensitive to exogenous shocks. But, as we have seen in the case of the oil price, intermediary pricing still works for these asset classes.
Ideally, we’d like to do this in real-time with daily returns on fixed-income securities. That would then allow us to trade short-term anomalies and harvest a greater portion of the risk premium on balance sheet capacity.
Postscript. Return predictability is much stronger at daily frequencies than previously reported. We extract the volatility risk premium from VIX and VX by deducting realized volatility (sampled over 22 days for the former and 66 days for the latter).
Turns out that return predictability is even stronger at daily frequencies. Vol risk premium (VIX – realized volatility) explains 6 percent of next day’s return variation. That’s a very striking degree of return predictability. By comparison, the best performance for a return forecasting factor at the quarterly frequency was found to be 3 percent.
The term spread, the difference between the yield on the 10-year and 2-year notes, also predicts one-day forward return on the S&P 500, although nowhere near as well as the vol risk premium. These results are highly suggestive of a system structure wherein the market price of risk is determined in over-the-counter derivatives markets that live directly on dealer balance sheets. When balance sheet capacity is plentiful, options traders bid away the volatility risk premium, along with the equity risk premium, thus compressing the next day’s market return. When balance sheet capacity is scarce, options traders are leverage-constrained, the volatility risk premium expands, along with the equity premium, thus predicting higher market returns the next day.