Reading a confidence interval for a difference

Question

You estimate that Portfolio X outperformed Portfolio Y by 2.0 percentage points over the period, with a standard error on that difference of 0.9 percentage points.

Construct the 95% confidence interval for the true outperformance, state what it lets you conclude about significance, and list the pitfalls in interpreting it.

Accepted Answer

Build the interval. With a roughly normal sampling distribution, 	ext{CI} = 2.0 \pm 1.96 	imes 0.9 = 2.0 \pm 1.76 = [0.24\%,\ 3.76\%]. What it tells you about significance. The interval excludes zero. By the duality between confidence intervals and tests, that is exactly equivalent to rejecting H0: 	ext{difference} = 0 at the 5% level (two-sided). So X's outperformance is statistically significant, but only barely, since the lower end sits just above zero at 0.24%. What you can conclude. The data are consistent with a true outperformance anywhere from a slim 0.24 points to a substantial 3.…

Reading a confidence interval for a difference

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