(I actually did this work before the post on the lack of asymmetric response in interest rates.) In the same manner as in our analysis of interest rates, we can create a time series of independent annual upside and downside response estimators for the S&P 500 Index. The chart below illustrates the covariance of those estimators.

From the chart we see data that illustrates support for a significant positive downside response coefficient and no support for a non-zero upside response coefficient. Furthermore, there is no evidence of covariance between the estimators (remember, our null hypothesis of is E_y = D_y).