Combining two estimates that are correlated
Asked at Two Sigma, DE Shaw
Two analysts each give an unbiased estimate of fair value, each with a standard deviation of . But they read the same order flow, so their errors are correlated with .
What is the standard deviation of the simple average of the two, and how does correlation change the value of a second opinion?
Show a hint
With equal variances, symmetry says the best weights are still each. But the variance of the average now carries a covariance term.