 # Dynamic Intermediary Asset Pricing at Arbitrary Frequencies

I’ve grown sick of rough cut estimates and back of the envelope reasoning. I decided to run a full dynamic asset pricing model to test the hypothesis that we can instrument intermediary risk appetite at daily frequency with innovations in the volatility risk premium. Put simply, I decided to do things the kosher way.

The following estimates are based on the 3-pass estimator of Adrian et al. (2011). I obtain the vol risk premium by deducting 22-day realized volatility from expected volatility (VIX). AR(1) innovations to this series is our single risk factor. As return forecasting factors, that will span the risk premium on our instrument, we use lagged terms for: vol risk premium, term spread, return on term spread, Baa spread, corporate spread, high yield spread, return on the S&P 500, and vol term premium — the difference between the risk premia in VIX and VX.

 Loadings on price-of-risk factors in a dynamic asset pricing model with constant betas and time-varying prices of risk. Lambda Std Error P Intercept 0.083 0.029 0.005 VIX risk premium -0.504 0.023 0.000 Baa spread -0.071 0.030 0.020 Corp spread -0.132 0.035 0.000 HY spread -0.030 0.038 0.421 S&P 500 return -0.045 0.051 0.381 Term spread -0.093 0.032 0.004 Term spread return 0.079 0.013 0.000 VIX-VX -0.197 0.026 0.000 The price of risk is an affine function of our return-forecasting factors with slope coefficients Lambda. All return-forecasting factors are standardized to have mean 0 and variance 1, and lagged 1 quarter. Risk factor is contemporaneous AR(1) innovations in the vol risk premium defined as the difference between realized 22-day volatility of S&P 500 returns and the daily closing value of VIX. Estimates in bold are significant at the 5 percent level. Estimates based on Adrian et al. (2011)’s 3-pass OLS estimator at daily frequency.

What is great about dynamic asset pricing is that you obtain conditional prices — you can actually trade on this information. What He et al. (2017) have shown is that options contain the strongest signal of dealer risk-appetite. We can therefore instrument the latter by the former. The volatility risk premium, the spread between expected volatility and realized volatility, is a good measure of the risk premium embedded in option prices where we can expect the intermediary risk appetite signal to be strongest. That’s how we can do intermediary asset pricing at daily frequency! As a return forecasting factor, vol risk premium stands out. In fact, a single factor forecasting model with vol risk premium as the return forecasting factor is as good as the full model with return on the S&P 500 as the response. See the Matlab results and the scatter plot of the single factor return-forecasting regression. Note that the slopes of the return forecasting regression are quite different from the risk loadings displayed in the preceding table.  In effect, we have a single factor model with lagged vol risk premium as the price-of-risk factor and contemporaneous innovation in vol risk premium as the cross-sectional pricing factor. This is as parsimonious as it gets. The icing on the cake is that, since we can read dealer risk appetite off the volatility risk premium, we can do dynamic intermediary asset pricing at arbitrary frequencies — with real time data that we can trade on.