What Is the Conditional Autocorrelation on the Stock Market?

Abstract

We derive lower and upper bounds on the conditional market autocorrelation index at various investment horizons without using the precise form of the utility function. The bounds are derived in terms of option prices and can be computed at daily frequency for any given horizon. The bounds incorporate all the information contained in the entire distribution of returns. We use options on the S&P 500 index to quantify the bounds and document that asset prices imply a negative upper bound on the market conditional autocorrelation index. The upper bound on the market conditional autocorrelation index is highly volatile, skewed, and exhibits fat tails. It varies from -28% to -3% and takes extremely negative values during crisis or recession periods while being close to zero during normal times. On average, the upper bound on the market conditional autocorrelation index is -14%. We also document that periods of extremely negative market conditional autocorrelation index coincide with periods of a high Sharpe ratio, and we show that leading asset pricing models cannot reproduce both the negative market conditional autocorrelation index and the negative average market conditional autocorrelation index implied by asset prices.