FRM Part I practice questions

Question 1

A portfolio has a return of 12%, a standard deviation of 18% and a beta of 1.2. The risk-free rate is 3%. Its Treynor ratio is closest to:

1. A0.050
2. B0.075
3. C0.090
4. D0.500

Question 2

The collapse of Barings Bank is most directly attributed to:

1. AAn unhedged commodity basis exposure
2. BA single trader controlling both trading and settlement functions
3. CA liquidity mismatch in the repo book
4. DA model error in option pricing

Question 3

Two portfolios show identical Sharpe ratios but different Treynor ratios. This most likely indicates that:

1. AOne portfolio holds significant undiversified specific risk
2. BOne portfolio is leveraged
3. CThe risk-free rate was measured differently
4. DBoth portfolios are fully diversified

Question 4

Under an enterprise risk management framework, the primary responsibility for setting risk appetite lies with:

1. AThe chief risk officer
2. BThe board of directors
3. CInternal audit
4. DThe trading desk heads

Question 5

A risk that can be transferred at a known cost, such as a hedgeable currency exposure, is best managed by:

1. AHolding economic capital against it
2. BHedging it
3. CScenario analysis only
4. DAccepting it as an unknown unknown

Question 6

A test for a rare condition has 95% sensitivity and 95% specificity. The condition affects 1% of the population. Given a positive result, the probability the condition is present is closest to:

1. A16%
2. B48%
3. C85%
4. D95%

Question 7

A GARCH(1,1) model is estimated with α = 0.08 and β = 0.90. Persistence and the implication for volatility are:

1. A0.98 — volatility mean-reverts slowly
2. B0.98 — volatility mean-reverts quickly
3. C0.82 — the model is non-stationary
4. D1.00 — the model reduces to EWMA

Question 8

An analyst regresses one random walk on an unrelated random walk and obtains an R² of 0.78 with a significant t-statistic. The correct conclusion is that:

1. AA genuine economic relationship exists
2. BThe regression is spurious because both series are non-stationary
3. CThe sample size is too small
4. DHeteroskedasticity is present

Question 9

Lowering the significance level of a hypothesis test from 5% to 1% will:

1. AReduce Type I error and reduce Type II error
2. BReduce Type I error and increase Type II error
3. CIncrease Type I error and reduce Type II error
4. DLeave both error rates unchanged

Question 10

Compared with GARCH(1,1), the EWMA model:

1. AIncludes a long-run variance term and mean-reverts
2. BOmits the long-run variance term and does not mean-revert
3. CRequires a normality assumption GARCH does not
4. DCannot be estimated from historical returns

Question 11

The standard deviation of spot price changes is 0.65, the standard deviation of futures price changes is 0.81, and their correlation is 0.80. The minimum variance hedge ratio is closest to:

1. A0.64
2. B0.80
3. C0.99
4. D1.25

Question 12

Initial margin posted to a central counterparty is intended to cover:

1. ACurrent mark-to-market exposure
2. BPotential future exposure over the close-out period
3. CThe clearing member's default fund contribution
4. DAccrued interest on the position

Question 13

An investor buys a call with a strike of $40 for a premium of $3. The breakeven price at expiry is:

1. A$37
2. B$40
3. C$43
4. D$46

Question 14

A hedger uses a futures contract on a related but different asset. The residual exposure is best described as:

1. ACounterparty risk
2. BBasis risk
3. CLiquidity risk
4. DOperational risk

Question 15

On a reset date, the value of the floating leg of a plain vanilla interest rate swap is:

1. AZero
2. BPar
3. CThe notional plus accrued interest for the full remaining term
4. DIndeterminate without the forward curve

Question 16

A portfolio worth $200m has a daily volatility of 1.2% and a mean daily return of zero. The 1-day 99% VaR is closest to:

1. A$2.4m
2. B$3.9m
3. C$5.6m
4. D$8.5m

Question 17

A loan has a probability of default of 3%, loss given default of 45% and exposure at default of $10m. Expected loss is:

1. A$135,000
2. B$300,000
3. C$450,000
4. D$1,350,000

Question 18

Which statement about expected shortfall is correct?

1. AES is never greater than VaR at the same confidence level
2. BES is sub-additive; VaR need not be
3. CES ignores the shape of the tail
4. DES requires an assumption of normality

Question 19

Historical simulation VaR differs from delta-normal VaR chiefly because it:

1. AAssumes returns are normally distributed
2. BRequires no distributional assumption
3. CCannot handle option positions
4. DAlways produces a lower VaR estimate

Question 20

A delta-neutral options book is long gamma. A large move in the underlying in either direction will produce:

1. AA loss
2. BA gain
3. CNo profit or loss, since the book is delta neutral
4. DA gain only if the move is upward