prob-stats — Quantitative Finance Practice Questions

101 free Quantitative Finance questions on prob-stats: 33 easy, 54 medium, and 14 hard, every one exam-realistic and fully explained once you sign in. This is the fastest way to turn prob-stats from a weakness into a scoring area — drill it in 10-question reps with immediate feedback.

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1. What is the estimated OLS slope hatβ?
2. Assuming 252 trading days in a year, what is the annualized historical volatility?
3. If the correlation between two assets is ρ = 0.6, what is the R^2 of a linear regression of one asset's return
4. If the slope β is positive, what is the correlation coefficient ρ between x and y?
5. What is the defining property of the 'Cumulative Distribution Function' F(x)?
6. Which 'standardized moment' should they measure to quantify this?
7. What is the probability the stock outperforms given the signal fired?
8. Which statistical property describes a time series where the mean, variance, and autocorrelation structure are
9. What is the estimated OLS beta (slope) of the stock?
10. What is the long-run probability of being in the Stressed state?
11. A strategy delivers a sample mean daily return of 0.06% with a sample daily volatility of 1.5% over n = 256 tr
12. What is the long-run (unconditional) daily volatility of the asset?
13. Given that X is observed at 28%, what is the conditional expected return of Y?
14. What is the 95% confidence interval for the true daily mean return?
15. Given four observations of (x, y) as (1, 2), (2, 2), (3, 4), (4, 4), what is the calculated least-squares slop
16. If X is observed to be 28%, what is the conditional expectation E[Y|X=0.28]?
17. If the sum of squared deviations from the sample mean is 0.0018, what is the unbiased sample variance estimate
18. If stock X is observed to have a return of 0.10, what is the conditional expected return of stock Y?
19. A symmetric 2 × 2 covariance matrix has eigenvalues λ_1 = 0.… — What does this imply about the validity of the
20. If the current conditional variance is σ_t^2 = 0.00025, what is the forecasted conditional variance for two st
21. If Asset X is observed to return 23%, what is the conditional expected return of Asset Y?
22. In a simple linear regression of a stock's excess returns (y) on the market's excess returns (x), the sample c
23. What is the variance of the number of heads (H) observed, using the Law of Total Variance?
24. Which property of a Gaussian copula most significantly distinguishes it from a t-copula in the context of fina
25. If yesterday's conditional variance was σ^2_t-1 = 0.0004 and the return was r_t-1 = -3%, what is today's condi
26. If you observe the mean return over 400 days to be 0.10% per day, what is the standard error of this sample me
27. If the signal fires for a specific stock, what is the updated posterior probability that the stock actually po
28. In the long-run stationary distribution, what fraction of the time is the market in the 'Stressed' state?
29. A risk model tracks two assets, X and Y. X has a standard normal distribution. Y = X^2 is a deterministic func
30. Over a sample of n = 400 days, what is the t-statistic for the null hypothesis that the true mean is zero?