CAIA Quantitative Methods and Statistics

Question 1

What does the Sharpe ratio measure?

Accepted Answer

Excess return per unit of total risk

Answer

Excess return per unit of systematic risk

Answer

Total return per unit of downside risk

Answer

Risk-adjusted return relative to a benchmark

Question 2

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

Accepted Answer

Kurtosis

Answer

Standard deviation

Answer

Skewness

Answer

Variance

Question 3

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

Accepted Answer

95%

Answer

68%

Answer

90%

Answer

99%

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

Geometric mean ignores compounding effects

Answer

Arithmetic mean penalizes negative returns more heavily

Answer

They are equal unless leverage is applied

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

The distribution has a long right tail with more extreme positive outcomes

Answer

Returns are normally distributed around the mean

Answer

Volatility is lower than measured by standard deviation

Question 6

Value at Risk (VaR) at the 95% confidence level over a one-day horizon is best defined as:

Accepted Answer

The maximum loss at the 95% confidence level over one day

Answer

The average loss when losses exceed the 95th percentile threshold

Answer

The probability that losses exceed a given threshold over one day

Answer

The portfolio standard deviation scaled to a one-day period

Question 7

Why is autocorrelation in returns particularly important when evaluating alternative investment funds?

Accepted Answer

Positive autocorrelation can signal smoothed or stale pricing in illiquid assets, understating true volatility

Answer

Autocorrelation measures systematic risk exposure and helps compute beta accurately

Answer

Autocorrelation corrects for survivorship bias in historical databases

Answer

Negative autocorrelation indicates market timing skill