Quantitative Analysis Flashcards

In a normal distribution, approximately what percentage of observations fall within two standard deviations of the mean?

Answer: 95%

Approximately 95% of observations fall within ±2 standard deviations in a normal distribution, following the empirical 68-95-99.7 rule.

Which statistical measure describes the asymmetry of a probability distribution?

Answer: Skewness

Skewness measures the asymmetry of a distribution, with positive skewness indicating a longer right tail and negative skewness indicating a longer left tail.

A leptokurtic distribution compared to a normal distribution has:

Answer: Excess kurtosis greater than 0

A leptokurtic distribution has excess kurtosis greater than 0 (kurtosis > 3), indicating heavier tails and a higher peak than a normal distribution, which is critical for risk modeling.

The covariance between two assets is 0.006, and their standard deviations are 0.10 and 0.15. What is their correlation coefficient?

Answer: 0.40

Correlation = Covariance / (σ1 × σ2) = 0.006 / (0.10 × 0.15) = 0.006 / 0.015 = 0.40.

Which statement best describes the Central Limit Theorem (CLT)?

Answer: The distribution of sample means approaches normality as sample size increases regardless of the underlying distribution

The CLT states that the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population's underlying distribution.

In hypothesis testing, a Type I error occurs when:

Answer: We reject a true null hypothesis

A Type I error (false positive) occurs when we reject a null hypothesis that is actually true, with its probability equal to the significance level α.

For a two-asset equal-weighted portfolio where each asset has variance 0.04 and the assets have a correlation of 0.50, the portfolio variance is:

Answer: 0.03

Portfolio variance = (0.5)²(0.04) + (0.5)²(0.04) + 2(0.5)(0.5)(0.2)(0.2)(0.5) = 0.01 + 0.01 + 0.01 = 0.03.