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P1. Mock Exam D

FRM 2012 Practice Questions

By David Harper, CFA FRM CIPM

www.bionicturtle.com

FRM 2012 n PART 1: MOCK EXAM D n 1 www.bionicturtle.com

Table of Contents

Question 1: On- and off-balance-sheet foreign exchange (FX) risk hedges ..................... 3

Question 2: Capital asset pricing model (CAPM) .................................................... 3

Question 3: EWMA covariance ......................................................................... 3

Question 4: Collateralization in over-the-counter (OTC) market ................................. 4

Question 5: Role of rating agencies in financial markets .......................................... 4

Question 6: Geometric Brownian motion (GBM) Monte Carlo simulation ........................ 4

Question 7: Chase Manhattan Bank/Drysdale Securities ........................................... 5

Question 8: Arbitrage pricing model (APT) .......................................................... 5

Question 9: Eurodollar futures and duration-based hedges ....................................... 5

Question 10: Limitations of Value-at-Risk (VaR). Coherent Risk Measures. ..................... 5

Question 11: Chi-square distribution ................................................................. 6

Question 12: Basis risk .................................................................................. 6

Question 13: Spectral risk measures .................................................................. 6

Question 14: Hypothesis testing (Stock & Watson) ................................................. 7

Question 15: Currency swap valuation ............................................................... 7

Question 16: Tax argument for risk management .................................................. 8

Question 17: Black-Scholes with dividends .......................................................... 8

Question 18: American option lower bounds ........................................................ 9

Question 19: Dynamic delta hedging ................................................................. 9

Question 20: Bond price using spot rates ............................................................ 9

Question 21: Difference between two means ..................................................... 10

Question 22: Commodity lease rates ............................................................... 10

Question 23: Expected loss (M. Ong) ............................................................... 10

Question 24: Bond maturity and retirement ....................................................... 11

Question 25: Dollar value of an '01 (DV01; aka, DVBP, PV01) ................................... 11


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Question 1: On- and off-balance-sheet foreign exchange (FX) risk hedges

1. A U.S. bank raises $200 million in liabilities, that pay an interest rate of 4.0%, in order to fund two investments: $100 million invested into U.S. dollar denominated assets and the remaining $100 million invested into Euro- (EUR) denominated assets. The expected net (of default risk) yield on the USD assets is 6.0% and the net yield on the EUR-denominated assets is 8.0%. In this way the expected return on the investment (ROI) is 3.0% as the difference between the blended ROA of 7.0% (average of 6.0% and 8.0%) and the cost of funds (COF) of 4.0%. However, the bank is un-hedged with respect to currency risk. At the beginning of the year, the exchange rate is EUR/USD $1.40. At the end of the year, the exchange rate has moved to EUR/USD $1.26. The nominal returns for the year were exactly as expected. What is the one-year realized ROI if we account for the currency shift?

Note #1: please assume all interest rates are effective annual rates (EARs). For example, an effective annual rate of 8.0% is equivalent to 8.0% per annum with (discrete) annual compounding. Note #2: In the initial exchange rate of EUR/USD $1.40, EUR is the base currency and USD is the quote currency, so this quote format refers to USD $1.40 per one unit of EUR.

a) ROI of +5.90% because the EUR appreciated against the USD b) ROI of -4.30% because the EUR appreciated against the USD c) ROI of +1.90% because the EUR depreciated against the USD d) ROI of -2.40% because the EUR depreciated against the USD

Question 2: Capital asset pricing model (CAPM)

2. Assume the riskfree rate is 4% and the expected (overall) market return is 12% with 20%

volatility. Our portfolio (P) has volatility of 30% and a correlation with the market of 0.4.

According to CAPM, what is the portfolio's expected return?

a) 6.0% b) 8.8% c) 11.2% d) 12.0%

Question 3: EWMA covariance

3. Assume two assets, A and B. Asset A closed trading yesterday with daily volatility of 1.0% and

daily return of +1.0%; i.e., sigma A(n-1) = 1.0% and return A(n-1) = 1.0%. Asset B closed trading

yesterday with daily volatility of 2.0% and a daily return of +2.0%; i.e., sigma B(n-1) = 2.0% and

return B(n-1) = 2.0%. Yesterday's correlation (coefficient) between the two assets was 0.40. If

we use the EWMA model with a lambda parameter of 0.90 to update covariance, what is today's

updated estimate of the correlation between the assets?

a) 0.38 b) 0.40 c) 0.44 d) 0.46

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