# FRM Part 2 Question Bank by AnalystPrep - Solutions

## Question 1

Recall that: αVaR = -µP/L + σP/Lzα ,

Therefore, the 95% VaR is: -14.1 + 28.2Z0.95 = -14.1 + 28.2 × 1.645 = 32.289

The 99% VaR is: -14.1 + 28.2Z0.99 = -14.1 + 28.2 × 2.326 = 51.4932

## Question 2

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) × 112 + 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

For Black-Scholes-Merton model and in the absence of arbitrage opportunities, the put-call parity satisfies:
pBS + S0 e−qT = cBS Ke−rt

For the market prices, put-call parity holds when arbitrage opportunities are absent such that:
pMKT + S0 e−qT = cMKT Ke−rt

The difference between the two equations is:
pBS − pMKT = cBS − cMKT

From the question we have that:
cBS = 0.0249, pBS = 0.051 and pMKT = 0.0317

Thus:
0.0501 − 0.0317 = 0.0249 − cMKT
⇒ cMKT = 0.0065

## Question 4

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

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

From the question, we have: EPE = 0.136, Spreadc = 267, ENE = 0.09, and Spreadp = 191

Therefore:

BCVA = 0.136 × 267 bps − 0.09 × 191 bps

= 19.122 bps

## Question 6

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

The amount the bank pays is given by

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

## Question 8

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