Serial Correlation Of S&P 500 Total Returns

According to a Bloomberg article, the rare S&P 500 total return 12-month winning streak can be attributed to positive serial correlation. However, monthly returns appear to have negative serial correlation, i.e., they are mean-reverting.

The chart below shows the SPY ETF total return and the 1-lag 36-month, 48-month and 50-month autocorrelation of returns.

It may be seen that the autocorrelation is negative. Actually it is negative for most lag values from 1 to 10. it is also negative for most periods from 12 to 60 months. One must increase the period to more than 100 months to get a positive serial correlation.

In fact, returns are mean reverting and the probability of a negative return after a positive return is higher. The 12-month winning streak is a highly unlikely event under these conditions.

The other explanation is that the S&P 500 total return is NOT a random but a quasi-random process. Central bank interventions and passive investing remove most of the randomness at least during certain periods. When these forces subside, the process becomes more random. So it is random and it is not, depending on prevailing conditions. Maybe this is a better way of looking at this process.

Bloomberg article

 

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