Download Multiple Choice - Marriott School

Practice Problems II Key
Part I. Multiple Choice (30 points: 3 points each)
There are ten multiple-choice questions. Choose only one answer for each question. You
do not have to explain why you have selected a particular one. If you feel that a question
is ambiguous, feel free to write a justification for your answer on the test sheet.
1. Which of the following statements is correct?
A) Bonds with higher coupon rates have higher durations
B) The higher the yield-to-maturity, the higher the duration
C) Long term bonds generally have shorter durations than short term bonds
D) The duration of a zero coupon bond is its time-to-maturity
2. Purchasing power parity implies
A) The law of one-price holds
B) Nominal exchange rates should be 1.0
C) Currencies of countries with high inflation will appreciate
D) The demand curve for dollars slopes upward.
3. Which of the following will not shift the demand curve for dollars to the right?
A) Increase in foreign preference for American goods.
B) Decrease in foreign wealth
C) Increase in interest rates on U.S. bonds
D) Reduction in riskiness of U.S. investment
4. Based on the given information, the volatility of option A must be _______ the
volatility of option B.
Put
A
B
A)
B)
C)
D)
T
0.5
0.5
X
55
50
S
50
55
Option Price
12
9
higher than
equal to
lower than
impossible to determine without more information
5. A futures contract that matures in six months is trading at a futures price of $95. The
current spot price of the asset is $90 and the risk-free rate is 8% (annually). To take
advantage of this arbitrage, you would need to
A) Borrow money at risk-free rate, long stock, short the futures contract.
B) Loan out money at risk-free rate, long stock, short the futures contract.
C) Borrow money at risk-free rate, short stock, long the futures contract.
D) Loan out money at risk-free rate, short stock, long the futures contract.
6. A defensive bank manager would want the duration of his bank to be
A) Positive if he expects interest rates to increase
B) Positive if he expects interest rates to decrease
C) Close to zero
D) Positive if he expects interest rates to decrease
E) Negative if he expects interest rates to decrease
7. The purpose of a clearing corporation
A) Determine who is cleared to be a broker on the CBOE trading floors
B) Determine which stocks are cleared to have options written on them
C) Guarantee that options expire “in the money”
D) Remove default risk from the option contract
8. Which of the following is not a problem with duration analysis?
A) Can only analyze parallel shifts in the yield curve
B) Time horizon to determine duration is ambiguous
C) Only valid for small changes in interest rates
D) The risk of duration drift
9. Assume you are in the 30% tax bracket. A treasury bond promises a YTM of 6% over
the next year while a municipal bond promises a YTM of 4%. You should
A) Buy the treasury bond since it provides a higher after-tax yield.
B) Buy the municipal bond because it promises a higher after tax yield
C) Buy the treasury bond since it provides a lower after-tax yield.
D) Buy the municipal bond because it promises a lower after tax yield
10. The Basel Accord
A) Established a regime of fixed exchange rates across countries
B) Established a set of capital requirements for banks across countries
C) Allows banks to branch across state lines in the United States.
D) Established a system to detect money laundering in Switzerland.
Part II. Free Response
1. Explain what is meant by “regulation Q”. (4 points)
A regulation that allowed the Fed to set maximum limits on the interest rate that
could be paid on time deposits.
2. A client has a liability to pay 10 million yen in three months, and has asked that you
help him hedge the currency risk he is facing.
A) What position in futures contracts would allow the client to hedge the
currency risk? (3 points)
A long futures position on yen. The client has to buy yen in three months. By
going long the futures contract, he is locked in to the price he will pay for the
yen.
B) What position in options would allow the client to hedge the currency risk? (3
points)
A long call position on yen. The client has to buy yen in three months. By
going long the call contract, he is locked in the highest price he will have to
pay for the yen. (If the yen exchange rate does not go above the strike price,
the client will not exercise the call.)
3. The current price of Zions stock, which is currently not paying dividends, is $75 per
share. In one year from now, the value of Zions will be either $80 or $70. The
effective annual risk-free rate is 4% per year. Find the value of a European call option
on one share of Zions stock with a strike of $78. using the binomial option pricing
model. (5 points)
When Zions is at 80, the payoff to the call option is 2.
When Zions is at 70 the payoff to the call option is 0.
Delta=2/10=0.20
.2(70)+B(1.04) =0 implies B=-.2(70)/ (1.04) =-13.46
So a portfolio long 0.2 shares of stock and short $13.46 in bonds will replicate the
call.
Price of Call = .2(75) – 13.46 = 1.54
4. The nominal yield on U.S. bonds is 4%, and the dollar is expected to appreciate
relative to Mexican pesos by 8% over the next year. If capital is mobile, so that
interest rate parity holds, what must be the nominal yield on bonds in Mexico? (3
points)
4%+8%=12%
5. Assume a basket of goods in the U.S. costs 100 dollars, and the same basket of goods
in Brazil costs 24,500 “reais”. According to the theory of purchasing power parity,
what should be the dollar exchange rate in terms of reais? (3 points)
24,500 reais= 100 dollars, implying
245 reais = 1 dollar
6. As a management assistant assigned to the bank’s asset/liability management
committee, you have been asked to calculate the duration of a loan on which the
borrower pays $8000 per year for four years. Assume the yield to maturity on the
loan is 5%. What is the modified duration? (5 points)
Time
1
2
3
4
TOTALS
Cash
8000
8000
8000
8000
PV
7619.04762
7256.23583
6910.70079
6581.6198
weights
0.268583
0.255793
0.243612
0.232012
Duration
0.268583
0.511586
0.730837
0.928047
28367.604
1
2.439053
Modified duration is 2.44/1.05=2.32
7. Analyze the following quotes on currency markets in terms of supply and demand:
A) The dollar pulled back ahead of a report on the fourth-quarter U.S. trade deficit,
which is expected to show a large increase to $219.5 billion from $195.8 billion in
the third quarter. (2 points)
A rising trade deficit indicates either an increase in American preference for foreign
goods, or a decrease in foreign preference for American goods.
In either case, the demand for dollars is weaker, indicating a shift to the left of the
demand curve, which lowers the dollar exchange rate.
B) The dollar slid broadly amid reports suggesting that expectations for interest-rate
increases by the Federal Reserve are overdone. (2 points)
The news suggests a decrease (relative to expectations) in the real interest rate in the
U.S. relative to foreign rates. Demand for dollars therefore should decrease, the
demand curve for dollars should shift left, causing the dollar to depreciate.
C) The dollar pulled ahead today following the announcement of officials at Standard
and Poor’s that the credit rating firm had decided to downgrade Argentina’s
sovereign debt.
U.S. bonds have decreased in relative riskiness. The demand curve for U.S. bonds
shifts right, leading to an increase in the dollar exchange rate.
8. You are responsible for the risk management operations for a local bank. The
balance sheet for the bank is as follows:
The number under “rate” for each asset and liability is the effective monthly rate earned
or paid by the bank each month. The number under “Duration” is the modified duration.
A) If you classify all assets and liabilities with a duration of 5 years or less as
“interest rate sensitive”, what is the bank’s gap? (3 points)
IRS Assets = 350 million
IRS Liabilities = 400 million
Gap = -50 million
B) If effective monthly interest rates increase by 45 basis points over the next
month, what will be the effect on the bank’s monthly net income? (3 points)
-50*0.0045 =-0.225
The bank’s monthly net income will drop by 0.225 million, or $225,000.
C) What is the modified duration of the bank’s assets and liabilities? (3 points)
Duration of assets = (350/750)*5+(400/750)*20 = 13
Total Liabilities = 500
Duration of liabilities = (100/500)*0.50+(300/500)*5+(100/500)*10 = 5.1
D) If interest rates increase by 45 basis points over the next month, what will be
the effect on bank equity? (3 points)
Change in Assets=-13*750*.0045=-43.88
Change in Liabilities=-5.1*500*.0045=-11.48
Change in bank equity=-43.88-(-11.48)=-32.4 (million)
9. A futures contract for Cisco stock is trading at a futures price of F0=$70 per share.
The spot price of Cisco is $69.50 per share. Assume the effective annual risk-free
rate is 3% and the futures contract matures in five months. How would you take
advantage of the arbitrage opportunity? How much would you make? Assume each
contract is for one share (5 points).
69.50(1.03)5/12=70.36
Long the futures, Short the stock, get 69.50, deposit proceeds in risk-free account..
In five months, money is risk-free account has grown to $70.36. Use to honor futures
position and buy stock for $70. Use purchased stock to close out short position.
Keep 36 cents. (Of course you would do this many times over, so the actual gains
would be much larger.)
10. The current price of Best Buy stock, which is currently not paying dividends, is $75
per share. In three months from now, the value of Best Buy will be either $82.5 or
$67.5. The effective annual risk-free rate is 2% per year. Find the value of a
European put option on one share of best Buy stock with a strike of $80. The option
expires in 3 months. (5 points)
When Best Buy is at 82.5, the payoff to the put option is 0.
When best Buy is at 67.5 the payoff to the put option is 12.5.
Delta=-12.5/15 = -0.833
Portfolio payoff in “up” state
-0.833(82.5)+B(1.02)1/4=0 implies B=68.38
So a portfolio short 0.833 shares of stock and long $68.38 in bonds will replicate the
put option.
Price of Put = -.833(75)+68.38 = 5.91
11. The dollar exchange rate in terms of yuan is 10.00, the dollar exchange in terms of
roubles is 30.00. What is the rouble exchange rate in terms of yuan? (3 points)
One dollar costs 30 roubles, or 30 roubles cost one dollar. One rouble therefore
costs 1/30 dollars. One dollar costs 10 yuan, or 1/30 dollars costs 10/30 yuan. The
rouble exchange rate in terms of yuan is therefore 10/30=0.333.
12. The modified duration of your bank assets is 15, while the modified duration of bank
liabilities is 4. The ratio of liabilities to assets is 80%. Total assets are 1 billion.
A) If interest rates increase by 75 basis points over the next year, what will be the
percent change in equity? (3 points)
Change in assets=-15*1billion*.0075=-0.113 billion
Change in liabilities=-4*0.80*.0075=-0.024 billion
Change in equity is -.113-(-0.024)=-.089 billion or -89 million
Original equity was .2*1B=200 million, so equity has fallen by 44.5 percent
B) A futures contract on zero-coupon bonds exists. Each contract is on 1 million
face value of bonds that mature in two years. The futures contract matures in
one year. What is the no arbitrage futures price? Assume the yield is 8 percent
(2 points).
Current spot price of bonds = 1M/(1.082)=857,339
Futures price = 857,339*(1.08) = 925,926
C) If you wanted to protect your bank equity in the event that rates increase by 75
basis points, how many futures contracts would you need to short? (4 points)
Payoff from 1 short futures contract would be (F0-ST)
In the event that rates increase by 75 basis points, the future spot prince would be
1M/1.0875 = 919,540 (since when the futures contract matures the bond still has
one year left before it matures).
Hence, the payoff to one short futures position would be 925,926-919,540 =
6385.70
You want the payoff from the total position to be 89 million.
Need to short approximately 13,937 futures contracts.
D) A put option on zero-coupon bonds exists. Each contract is on 1million face
value of bonds that mature in two years. The put matures in one year. Assume
the put premium is $1000 , and the strike price is the same as your futures
price found in part (B) above. If rates increase by 75 basis points, how would
the put protect your equity?
In the event that rates increase, the value of $1 million in bonds would be
1M/1.0875 = 919,540 (since when the futures contract matures the bond still has
one year left before it matures). You could then buy the bonds for 919,540 in the
market, and sell them via the put contract for 925,926 for a payoff of 6385.70.
The profit from the put position, including the premium would then be 5385.70
per contract. By going long enough put contracts, you could offset the loss in
bank equity.
13. Assume if rates increase by 200 basis points, the equity for a bank drops by $18
million. The bank can enter a swap. The notional amount for is on 100,000. The fixed
side will pay 9% fixed on the notional amount. The floating side will pay Libor + 4%
on the same notional amount. Assume Libor is currently 5% and changes along with
other changes in interest rates.
a. What are the net cash flows to either party from one swap contract at
current rates?
Party paying Fixed: pays .09*100,000=9000, receives .09*100000=9,000
Party paying Floating: pays 9,000, receives 9,000
Net cash flows to either side are zero.
b. If rates increase by 200bp, what are net cash flows to either side of the
swap contract?
Party paying Fixed: pays .09*100,000=9000,
receives .11*100000=11,000
Net = 2000
Party paying Floating: pays 11,000, receives 9,000
Net=-2000
c. What position does the bank want to take (paying fixed or floating)? How
many contracts should it take this position on if it wants to perfectly offset
the loss to equity in the case that rates increase by 200bp?
The bank wants to pay fixed and receive floating on 18m/2000=9,000
contracts.