When conducting statistical hypothesis tests, we reject the null hypothesis if the sample evidence is strong enough to raise doubts about the hypothesis. In contrast, the decision to fail to reject the null hypothesis does not mean that the null hypothesis is true -- we can only say that the evidence is not strong enough to reject the hypothesis. For this reason, we make a stronger statement when we reject a hypothesis than when we fail to reject a hypothesis.

The authors explain in Chapter 7 of Quantitative Investment Analysis that we can use this asymmetry to our advantage. If we have a particular hypothesis that we want to support, we can set it up as an alternative hypothesis. Then, the decision to reject the null hypothesis provides stronger evidence in support of the favored alternative. In contrast, if we use the preferred hypothesis as the null hypothesis, then the strongest conclusion we can draw in support of the hypothesis is that we fail to reject it.

To illustrate, suppose you lead a team of asset managers, and you want to show that your portfolio returns are significantly above the market return. You could define the null hypothesis as excess returns are greater than or equal to zero, but the best outcome would be a failure to reject this null. In contrast, you could set the null as excess returns are less than or equal to zero, and the best outcome would be a rejection of this null. Your best option is to choose the second option since it would provide stronger evidence in support of your team. However, is this practice fair to potential investors in your portfolio? Do you think your promotional materials should include a footnote to explain the decision process?