What a 95% confidence interval really claims

Question

A researcher estimates a strategy's Sharpe ratio and reports a 95% confidence interval of $[0.4, 1.2]$ , saying "there is a 95% probability the true Sharpe lies between 0.4 and 1.2."

Give the correct interpretation of a confidence interval, explain what is wrong with the sentence, and describe how to get a statement about the probability the true value is in a range.

Accepted Answer

Correct interpretation. The 95\% refers to the procedure, not to this one interval. If you repeated the whole experiment many times and built a 95\% confidence interval each time, about 95\% of those (random) intervals would contain the true, fixed Sharpe. The confidence level is a property of the method's long-run coverage. What is wrong. In the frequentist framework the true Sharpe is a fixed (unknown) number, not random. A specific realized interval like [0.4, 1.2] either contains it or does not, there is no "95\% probability" about this particular interval. The random thing is the interva…

What a 95% confidence interval really claims

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