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Free FRM Quantitative Analysis Practice Questions & Answers

400 exam-style Quantitative Analysis questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.

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Question 31

Portfolio return has mean 8% and standard deviation 15%. Using a normal distribution, what is the 95% VaR over one year?

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Question 32

Two assets have returns with correlation 0.3. Asset A has volatility 20%; Asset B has volatility 30%. Portfolio weights are 50/50. The portfolio variance is:

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Question 33

Bayes' theorem allows:

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Question 34

Monte Carlo simulation in risk management is used to:

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Question 35

The log-normal distribution is commonly used for asset prices because:

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Question 36

A manager claims their fund beat the benchmark by 3% with a tracking error of 6%. The information ratio is:

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Question 37

Maximum Likelihood Estimation (MLE) finds parameter values that:

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Question 38

Jensen's inequality states that for a convex function f and random variable X:

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Question 39

The law of large numbers states that:

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Question 40

If X ~ N(μ, σ²), then aX + b follows:

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Question 41

A 99% confidence interval for the mean of a large sample is:

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Question 42

The t-distribution converges to the standard normal as:

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Question 43

Conditional probability P(A|B) is defined as:

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Question 44

The kurtosis of the normal distribution is:

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Question 45

The moment generating function (MGF) of a random variable X is:

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Question 46

The relationship between VaR and Expected Shortfall for a normal distribution is:

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Question 47

If annual volatility is 20%, what is the approximate daily volatility assuming 252 trading days per year?

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Question 48

The null hypothesis in a VaR backtesting test is:

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Question 49

In Monte Carlo VaR, the accuracy of the VaR estimate improves as:

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Question 50

A portfolio has VaR of $10M at 99% confidence (one-day). Assuming normal distribution and independent daily returns, what is the 10-day VaR?

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Question 51

The Copula approach in joint loss modelling is used because:

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Question 52

The Extreme Value Theory (EVT) approach to tail risk modelling:

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Question 53

In bootstrapping for VaR estimation:

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Question 54

Extreme Value Theory's Generalised Pareto Distribution (GPD) is used for:

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Question 55

The characteristic function of a random variable X is:

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Question 56

In the context of hypothesis testing, the power of a test is:

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Question 57

A sufficient statistic T(X) for a parameter θ is defined as:

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Question 58

The probability integral transform states that:

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Question 59

The Kullback-Leibler (KL) divergence between distributions P and Q is:

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Question 60

The variance of a sum of random variables X and Y is:

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Free FRM Quantitative Analysis Practice Questions & Answers

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