Do the odds favour a rebound in equities?

First we identify all the weeks when the bull-bear spread has been lower than -30, which is 37 times since 1987. Three of these observations have been within the last 12 weeks. In our analysis we then calculate the forward 1, 4, 8, and 12-week return going long the S&P 500 Index if the spread is below -30. The table below shows the excess return over S&P 500 on such a strategy which is done by subtracting the average S&P 500 return since 1987 for these different time horizons. If a signal has any informational value then it should be able to beat the passive returns by just being invested in US equities.

The average excess return in percentage is -0.11% for the 1-week holding period but then jumps to 1.33% for the 4-week horizon and 1.29% and 1.49% for the 8-week and 12-week holding period respectively. This looks good at first sight, but the average always comes with variance and if we apply a standard t-test on the samples of each holding period scenario then we see that the probability of these different samples being statistically significant from zero excess return is not very high. The best test statistic is for the 4-week holding period at t = 1.28 which correspond to a p-value of 0.21, which is not statistically significant under normal circumstances. In a low signal-to-noise process such as the equity market the question is whether the odds are good enough to bet on. The confidence interval is -0.79% to 3.46% after all, so we let each trader decide for himself whether the odds are stacked in favour of a rebound. One should note that many of the most bearish readings are clustered in time which means that the 34 observations that we are calculating our statistics on are not truly independent and thus the statistical significance is weaker than the numbers displayed below suggest.

Outside the world of statistics, yesterday’s price action felt technical across both bond and equities as there was no real news driving the move. It seems the market might be positioning itself differently ahead of the important US CPI print on Tuesday where a lower than estimated inflation figure could ignite a short-term rally equities. These considerations are worth melting into the decision process of whether this is a good time to go long again.