The more significant fund with the smaller edge

Question

An allocator compares two funds. Fund X reports $p = 0.0001$ for its alpha; fund Y reports $p = 0.02$ . The allocator says, "X's alpha is clearly far larger, its p-value is tiny."

Explain the flaw in this reasoning, and construct a concrete case where fund Y actually has the larger alpha despite the larger p-value.

Accepted Answer

The flaw. A p-value blends effect size, sample length, and noise. Fund X might simply have a very long, very clean track record that makes even a modest alpha extremely significant, while fund Y has a short, volatile record that leaves a genuinely bigger alpha looking only moderately significant. Significance is not magnitude. A concrete case. Suppose: - Fund X: alpha = 1.5\% per year, standard error = 0.375\%, so z = 4.0, giving p \approx 0.0001. This might be 25 years of steady data. - Fund Y: alpha = 6.0\% per year, standard error = 2.6\%, so z \approx 2.3, giving p \approx 0.02. This migh…

The more significant fund with the smaller edge

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