CAIA Quantitative Methods and Statistics

Question 1

What does the Sharpe ratio measure?

Accepted Answer

Excess return per unit of total risk

Answer

The Sharpe ratio is calculated as (Rp - Rf) / σp, representing excess return over the risk-free rate per unit of total portfolio risk (standard deviation).

Question 2

Which statistical measure best captures 'fat tail' risk in alternative investment return distributions?

Accepted Answer

Kurtosis

Answer

Kurtosis measures the degree of fat tails (excess probability of extreme outcomes) relative to a normal distribution; excess kurtosis above 3 signals leptokurtic (fat-tailed) distributions common in alternatives.

Question 3

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

Accepted Answer

95%

Answer

The empirical rule states that approximately 68% of observations fall within ±1σ, 95% within ±2σ, and 99.7% within ±3σ of the mean.

Question 4

Why is the geometric mean return typically lower than the arithmetic mean return for a volatile investment?

Accepted Answer

Geometric mean accounts for compounding and is reduced by variance drag

Answer

The geometric mean approximates the arithmetic mean minus half the variance (g ≈ r - σ²/2), so higher volatility creates a larger variance drag, widening the gap between the two measures.

Question 5

What does negative skewness in the distribution of hedge fund returns indicate?

Accepted Answer

The distribution has a long left tail with more extreme negative outcomes

Answer

Negative skewness means the left tail is longer, indicating a higher probability of large negative returns (crash risk) relative to a normal distribution — a common feature of strategies that sell optionality.

CAIA - Chartered Alternative Investment Analyst Association Practice Test

CAIA - Chartered Alternative Investment Analyst Association Practice Test

CAIA Quantitative Methods and Statistics