Skip to main content

TL;DR

An interval \( [\hat{\theta} - z_{\alpha/2}\cdot SE, \hat{\theta} + z_{\alpha/2}\cdot SE] \) that, over repeated sampling, contains the true parameter with probability \( 1-\alpha \). It quantifies estimation uncertainty.

By Valenke Exam Prep Team·Last updated 2026-06-03

Confidence Interval

An interval \( [\hat{\theta} - z_{\alpha/2}\cdot SE, \hat{\theta} + z_{\alpha/2}\cdot SE] \) that, over repeated sampling, contains the true parameter with probability \( 1-\alpha \). It quantifies estimation uncertainty.

Why it matters for interviews

Confidence intervals for Sharpe ratios, betas, and strategy returns quantify how uncertain parameter estimates are. Wide intervals signal insufficient data -- a common issue in strategy development.

Definition and Mathematical Foundation

An interval \( [\hat{\theta} - z_{\alpha/2}\cdot SE, \hat{\theta} + z_{\alpha/2}\cdot SE] \) that, over repeated sampling, contains the true parameter with probability \( 1-\alpha \). It quantifies estimation uncertainty.

Application in Quantitative Finance

Confidence intervals for Sharpe ratios, betas, and strategy returns quantify how uncertain parameter estimates are. Wide intervals signal insufficient data -- a common issue in strategy development.

Related Terms

Ready to practice for the Quant Trading Interview?

Adaptive practice powered by Item Response Theory targets your weak areas. Start with 3 free sessions.

Start free practice →

Frequently Asked Questions

What is the correct interpretation of a 95% confidence interval?
If you repeated the sampling procedure many times, 95% of the constructed intervals would contain the true parameter. It does NOT mean there is a 95% probability the parameter is in this specific interval.
How do you construct a confidence interval for the Sharpe ratio?
The Sharpe ratio \( SR = \bar{r}/s \) has approximate standard error \( \sqrt{(1 + SR^2/2)/n} \). With 3 years of monthly data (n=36), a Sharpe of 1.0 has SE \( \approx 0.20 \), giving wide intervals.
What is the relationship between confidence intervals and hypothesis tests?
A 95% CI excludes values rejected at the 5% level. If the CI for the mean does not contain 0, the t-test rejects \( H_0: \mu = 0 \) at 5%. They are dual perspectives on the same information.