# FRM Part 2 Question Bank by AnalystPrep - Solutions

## Question 1

**Correct Answer: A).**

*Recall that: αVaR = -µ _{P/L} + σ_{P/L}z_{α} ,*

*Therefore, the 95% VaR is: -14.1 + 28.2Z _{0.95} = -14.1 + 28.2 × 1.645 = 32.289*

*The 99% VaR is: -14.1 + 28.2Z _{0.99} = -14.1 + 28.2 × 2.326 = 51.4932*

## Question 2

**Correct Answer: C).**

*Recall that from the CIR model, we have:**dr = k (θ − r)dt + σ√rdw*

*From the data provided in the question:**σ = 0.0317, r = 0.0211, θ = 0.0764, k = 0.57, dw = 0.16*

*Therefore:**dr = 0.57(0.0764 − 0.0211) × ^{1}⁄_{12} + 0.0317√0.0211 × 0.16*

*⇒ dr = 0.00336 = 0.336%*

*The short rate in the first month under this CIR model is:**2.11% + 0.336% = 2.446%*

## Question 3

**Correct Answer: A).**

*For Black-Scholes-Merton model and in the absence of arbitrage opportunities, the put-call parity satisfies:**p _{BS} + S0 e^{−qT} = c_{BS} Ke^{−rt}*

*For the market prices, put-call parity holds when arbitrage opportunities are absent such that:**p _{MKT} + S0 e^{−qT} = c_{MKT} Ke^{−rt}*

*The difference between the two equations is:**p _{BS} − p_{MKT} = c_{BS} − c_{MKT}*

*From the question we have that:**c _{BS} = 0.0249, p_{BS} = 0.051 and p_{MKT} = 0.0317*

*Thus:**0.0501 − 0.0317 = 0.0249 − c _{MKT}*

*⇒ c*

_{MKT}= 0.0065## Question 4

**Correct Answer: A).**

*A default correlation equal to 0 implies the portfolio is a binomial-distributed random variable because there is no correlation with other firms/credits. In this case, the number of defaults would be binomially distributed with n = 100 and θ = 0.03*

*What’s more each credit has a volume of $10,000 (=$1000,000/100)*

*The expected loss = 1,000,000 × 0.03 = 30,000*

*If there are 4 defaults, the credit loss is $10,000 × 4 = $40,000*

*Credit VaR = credit loss – expected loss = 40,000 – 30,000 = $10,000*

## Question 5

**Correct Answer: D).**

*Recall that BCVA, which is an obvious extension of DVA, is calculated by using the following formula:*

*BCVA = EPE × Spread _{c}− ENE × Spread_{p}*

*From the question, we have: EPE = 0.136, Spread _{c} = 267, ENE = 0.09, and Spread_{p} = 191*

*Therefore:*

*BCVA = 0.136 × 267 bps − 0.09 × 191 bps*

*= 19.122 bps*

## Question 6

**Correct Answer: C).**

*Recall that:*

*RAROC = (Expected revenues − Costs − Expected losses − Taxes + Return on risk capital +/− Transfers)/Economic capital*

*Therefore:*

*RAROC = (89.5 − 8.89 − 50.98 − 10 + 24.01)/69.5*

*= 0.6279*

## Question 7

**Correct Answer: A).**

*The amount the bank pays is given by*

*200,000 × (99.50% + 10% × 0.25) = 204,000*

## Question 8

**Correct Answer: A).**

*Sharpe Ratio = (Rp − Rf )/σ*

*Sharpe Ratio = (10 – 3)/ 5*

*Sharpe Ratio = 1.4*

*Information Ratio = (Rp − Rb)/(Tracking error)*

*Information Ratio = (10 – 8)/10*

*Information Ratio = 0.2*

## Question 9

**Correct Answer: A).**

*Liquidity duration = Q _{i}/(0.15 × V_{i})*

*Q _{i} = Number of shares held in security i*

*V*

_{i}= Daily volume of security i*Liquidity duration = 10,000/(0.15 × 100,000) = 0.67*