Bootstrap standard error of a correlation

Question

You want a standard error for the correlation between two assets' returns, a statistic whose textbook standard error is awkward. You bootstrap the paired observations and keep five replicate correlations:

$0.30, \quad 0.35, \quad 0.40, \quad 0.45, \quad 0.50.$

Estimate the bootstrap standard error of the correlation.

Accepted Answer

As always, the bootstrap standard error is the standard deviation of the replicate values (sample version, dividing by B - 1 = 4). Step 1, mean of the replicates. \bar{	heta}^ = \frac{0.30 + 0.35 + 0.40 + 0.45 + 0.50}{5} = \frac{2.00}{5} = 0.40. Step 2, squared deviations from 0.40. (-0.10)^2 + (-0.05)^2 + 0^2 + (0.05)^2 + (0.10)^2 = 0.01 + 0.0025 + 0 + 0.0025 + 0.01 = 0.025. Step 3, divide by B - 1 = 4 and take the square root. 	ext{SE}{	ext{boot}} = \sqrt{\frac{0.025}{4}} = \sqrt{0.00625} \approx 0.079. Correlation is bounded in [-1, 1] and its sampling distribution is skewed near the ed…

Bootstrap standard error of a correlation

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