May

1

From 1951 to 2019, there were 15 6-month periods ending on April 30 in which the S&P 500 index declined. The average net change over the next 6 months was -3.8%, a statistically significant underperformance compared to the 4.2% average 6-month gain during the entire 69-year period.

Date         Index close   net change last 6 months      net change next 6 months
    4/29/1960      54.37                  -5.5%                     -1.8%
    4/30/1962      65.24                  -4.9%                    -13.4%
    4/29/1966      91.06                  -1.5%                    -11.9%
    4/30/1970      81.52                 -16.1%                      2.1%
    4/30/1973     106.97                  -4.1%                      1.2%
    4/30/1974      90.31                 -16.6%                    -18.2%
    4/29/1977      98.44                  -4.3%                     -6.2%
    4/30/1982     116.44                  -4.5%                     14.8%
    4/30/1984     160.05                  -2.1%                      3.8%
    4/30/1990      330.8                  -2.8%                     -8.1%
    4/29/1994     450.91                  -3.6%                      4.8%
    4/30/2001    1249.46                 -12.6%                    -15.2%
    4/30/2008    1385.14                 -10.6%                    -30.1%
    4/30/2009     872.81                  -9.9%                     18.7%
    4/29/2016     2065.3                  -0.7%                      2.9%

                        Average                                     -3.8%
                        Standard deviation                          12.8%
                        N                                              15
                        t                                           -2.42
                        Average of all 6 month periods               4.2%

Hernan Avella writes: 

Thanks Steve. Some notes:

- If you include the monthly data from 1928 (free yahoo finance), you effect disappears the average next 6 month goes from -3.80% to -0.12%
- Since you have such a small sample perhaps better to look at the trimmed mean or the median……the median of your sample is -1.8%
- Another (arguably better) way to check for significance is calculate your own p value with the bootstrap and the empirical distribution of 6 month returns, using the trimmed mean and winsorized variance.
- Related to above, Victor recommended a fine book a while back.
- Whether one can make more money adding this layer of complexity is still to be determined.
 


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