When even the wide interval straddles zero

Question

For a new factor's average return (in basis points), the 95% confidence interval is $[-1.2,\ 3.4]$ and the 90% confidence interval is $[-0.5,\ 2.7]$ .

Using only these intervals, decide whether the return is significant at the 5% and 10% levels, and state what the result does and does not prove.

Accepted Answer

The duality rule. The return is significant at level \alpha if and only if the (1-\alpha) confidence interval excludes the null value 0. Apply it. - The 95% interval [-1.2,\ 3.4] contains 0, so not significant at the 5% level. - The 90% interval [-0.5,\ 2.7] also contains 0, so not significant even at the looser 10% level. So the two-sided p-value is above 0.10. What this does not prove. Failing to reject is not the same as proving the factor's return is zero. The 95% interval stretches from -1.2 up to +3.4 bps, so it remains consistent with a meaningful positive return, a meaningful negative…

When even the wide interval straddles zero

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