A lower-tail one-sided test on drawdown risk

Question

A risk analyst worries a strategy actually loses money, so the pre-registered alternative is that the mean return is negative (mean $< 0$ ). The test statistic comes back as $z = -1.65$ .

Compute the one-sided (lower-tail) p-value for $z = -1.65$ , and explain why you use the lower tail here.

Accepted Answer

Which tail. The alternative is "mean < 0," so evidence for it lives in the lower tail: very negative z-values. The one-sided p-value is the area below the observed statistic: p{	ext{one}} = \Phi(-1.65) = 0.0495 \approx 0.05. By symmetry of the normal curve, \Phi(-1.65) = 1 - \Phi(1.65), and \Phi(1.65) \approx 0.9505, giving 0.0495. Why the lower tail. A one-sided test only rewards evidence in the direction you pre-registered. Since the concern is losses, only strongly negative results count against the null of "no loss." A large positive z (great returns) would give a one-sided p near 1, cor…

A lower-tail one-sided test on drawdown risk

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