Chapter 23
Futures, Swaps, and Risk Management
Mutliple Choice
1.Which one of the following stock index futures has a multiplier of $250 times the index value?
A.Russell 2000
B.S&P 500 Index
C.Nikkei
D.DAX-30
E.NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
2.Which one of the following stock index futures has a multiplier of $10 times the index value?
A.Russell 2000
B.Dow Jones Industrial Average
C.Nikkei
D.DAX-30
E.NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
3.Which one of the following stock index futures has a multiplier of $100 times the index value?
A.Russell 2000
B.FTSE 100
C.Nikkei
D.NASDAQ 100
E.Russell 2000 and NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
4.Which one of the following stock index futures has a multiplier of $100 times the index value?
A.Russell 2000
B.FTSE 100
C.S&P Mid-Cap
D.DAX-30
E.Russell 2000 and S&P Mid-Cap
The multiplier is used to calculate contract settlements. See Table 23.1.
5.Which one of the following stock index futures has a multiplier of $100 times the index value?
A.CAC 40
B.S&P 500 Index
C.Nikkei
D.DAX-30
E.NASDAQ 100
The multiplier is used to calculate contract settlements. See Table 23.1.
6.Which one of the following stock index futures has a multiplier of 10 euros times the index?
A.CAC 40
B.DJ Euro Stoxx - 50
C.Nikkei
D.DAX-30
E.CAC 40 and DJ Euro Stoxx - 50
The multiplier is used to calculate contract settlements. See Table 23.1.
7.Which one of the following stock index futures has a multiplier of 10 euros times the index?
A.FTSE 100
B.DJ Euro Stoxx - 50
C.Nikkei
D.DAX-30
E.FTSE 100 and DJ Euro Stoxx - 50
The multiplier is used to calculate contract settlements. See Table 23.1.
8.Which one of the following stock index futures has a multiplier of 25 euros times the index?
A.FTSE 100
B.DJ Euro Stoxx - 50
C.Nikkei
D.DAX-30
E.FTSE 100 and DJ Euro Stoxx - 50
The multiplier is used to calculate contract settlements. See Table 23.1.
9.You purchased one S&P 500 Index futures contract at a price of 950 and closed your position when the index futures was 947, you incurred:
A.a loss of $1,500.
B.a gain of $1,500.
C.a loss of $750.
D.a gain of $750.
E.None of these is correct.
(−$950 + $947) × 250 = −$750.
10.You took a short position in two S&P 500 futures contracts at a price of 910 and closed the position when the index futures was 892, you incurred:
A.a gain of $9,000.
B.a loss of $9,000.
C.a loss of $18,000.
D.a gain of $18,000.
E.None of these is correct.
($910 − $892) × 250 × 2 = $9,000.
11.If a stock index futures contract is overpriced, you would exploit this situation by:
A.selling both the stock index futures and the stocks in the index.
B.selling the stock index futures and simultaneously buying the stocks in the index.
C.buying both the stock index futures and the stocks in the index.
D.buying the stock index futures and selling the stocks in the index.
E.None of these is correct.
If one perceives one asset to be overpriced relative to another asset, one sells the overpriced asset and buys the other one.
12.Foreign Exchange Futures markets are ______and the Foreign Exchange Forward markets are ______.
A.informal; formal
B.formal; formal
C.formal; informal
D.informal; informal
E.organized; unorganized
The forward market in foreign exchange is a network of banks and brokers allowing customers to enter forward contracts to purchase or sell currency in the future at a currently agreed upon rate of exchange. The currency futures markets are formal markets established by the Chicago Mercantile Exchange where contracts are standardized as to size and daily marking to market is observed. A clearinghouse is also involved.
13.Suppose that the risk-free rates in the United States and in the United Kingdom are 4% and 6%, respectively. The spot exchange rate between the dollar and the pound is $1.60/BP. What should the futures price of the pound for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs?
A.$1.60/BP
B.$1.70/BP
C.$1.66/BP
D.$1.63/BP
E.$1.57/BP
$1.60(1.04/1.06) = $1.57/BP.
14.Suppose that the risk-free rates in the United States and in the United Kingdom are 5% and 4%, respectively. The spot exchange rate between the dollar and the pound is $1.80/BP. What should the futures price of the pound for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs?
A.$1.62/BP
B.$1.72/BP
C.$1.82/BP
D.$1.92/BP
E.None of these is correct
$1.80(1.05/1.04) = $1.82/BP.
15.Suppose that the risk-free rates in the United States and in Japan are 5.25% and 4.5%, respectively. The spot exchange rate between the dollar and the yen is $0.008828/yen. What should the futures price of the yen for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs?
A.$0.009999/yen
B.$0.009981/yen
C.$0.008981/yen
D.$0.008891/yen
E.None of these is correct
$0.008828 (1.0525/1.045) = $0.008891/yen.
16.Let RUS be the annual risk free rate in the United States, RUK be the risk free rate in the United Kingdom, F be the futures price of $/BP for a 1-year contract, and E the spot exchange rate of $/BP. Which one of the following is true?
A.if RUS > RUK, then E > F
B.if RUS < RUK, then E < F
C.if RUS > RUK, then E < F
D.if RUS < RUK, then F = E
E.There is no consistent relationship that can be predicted.
If RUS > RUK, then (1 + RUS)/(1 + RUK) > 1 and E < F.
17.Let RUS be the annual risk free rate in the United States, RJ be the risk free rate in Japan, F be the futures price of $/yen for a 1-year contract, and E the spot exchange rate of $/yen. Which one of the following is true?
A.if RUS > RJ, then E < F
B.if RUS < RJ, then E < F
C.if RUS > RJ, then E > F
D.if RUS < RJ, then F = E
E.There is no consistent relationship that can be predicted.
If RUS > RJ, then (1 + RUS)/(1 + RJ) > 1 and E < F.
Consider the following:
18.What should be the proper futures price for a 1-year contract?
A.1.703 A$/$
B.1.654 A$/$
C.1.638 A$/$
D.1.778 A$/$
E.1.686 A$/$
1.03/1.04(1.67 A$/$) = 1.654 A$/$.
19.If the futures market price is 1.63 A$/$, how could you arbitrage?
A.Borrow Australian Dollars in Australia, convert them to dollars, lend the proceeds in the United States and enter futures positions to purchase Australian Dollars at the current futures price.
B.Borrow U. S dollars in the United States, convert them to Australian Dollars, lend the proceeds in Australia and enter futures positions to sell Australian Dollars at the current futures price.
C.Borrow U. S. dollars in the United States and invest them in the U. S. and enter futures positions to purchase Australian Dollars at the current futures price.
D.Borrow Australian Dollars in Australia and invest them there, then convert back to U. S. dollars at the spot price.
E.There is no arbitrage opportunity.
E0(1 + rUS) − FO(1 + rA); use the U. S. $values for the currency: 0.5988(1.04) − 0.6135(1.03) = −0.009153; when relationship is negative, action b will result in arbitrage profits.
20.If the market futures price is 1.69 A$/$, how could you arbitrage?
A.Borrow Australian Dollars in Australia, convert them to dollars, lend the proceeds in the United States and enter futures positions to purchase Australian Dollars at the current futures price.
B.Borrow U. S. dollars in the United States, convert them to Australian Dollars, lend the proceeds in Australia and enter futures positions to sell Australian Dollars at the current futures price.
C.Borrow U. S. dollars in the United States and invest them in the U. S. and enter futures positions to purchase Australian Dollars at the current futures price.
D.Borrow Australian Dollars in Australia and invest them there, then convert back to U. S. dollars at the spot price.
E.There is no arbitrage opportunity.
0.5988(1.04) − 0.5917(1.03) = 0.013301; when this relationship is positive; action a will result in arbitrage profits.
21.Assume the current market futures price is 1.66 A$/$. You borrow 167,000 A$ and convert the proceeds to U. S. dollars and invest them in the U. S at the risk-free rate. You simultaneously enter a contract to purchase 170,340 A$ at the current futures prices (maturity of 1 year). What would be your profit (loss)?
A.Profit of 630 A$
B.Loss of 2300 A$
C.Profit of 2300 A$
D.Loss of 630 A$
E.None of these is correct
[A$167,000 / 1.67 × 1.04 × 1.66] − (A$167,000 × 1.03) = A$630.
22.Which of the following is/are example(s) of interest rate futures contracts?
A.Corporate bonds.
B.Treasury bonds.
C.Eurodollars.
D.Treasury bonds and Eurodollars
E.Corporate bonds and Treasury bonds
Interest rate futures are traded on Treasury bonds and Eurodollars. Examples that use these contracts to hedge are given in the textbook.
23.You hold a $50 million portfolio of par value bonds with a coupon rate of 10 percent paid annually and 15 years to maturity. How many T-bond futures contracts do you need to hedge the portfolio against an unanticipated change in the interest rate of 0.18%? Assume the market interest rate is 10 percent and that T-bond futures contracts call for delivery of an 8 percent coupon (paid annually), 20-year maturity T-bond.
A.398 contracts long
B.524 contracts short
C.1048 contracts short
D.398 contracts short
E.None of these is correct
0.9864485 × $50 M = $49,322,425; $50,000,000 − $49,322,425 = $677,575 loss on bonds; $100.00 − $82.97 = $17.03 × 100 = $1703 gain on futures; $677,575/$1,703 = 398 contracts short.
24.A swap
A.obligates two counterparties to exchange cash flows at one or more future dates.
B.allows participants to restructure their balance sheets.
C.allows a firm to convert outstanding fixed rate debt to floating rate debt.
D.obligates two counterparties to exchange cash flows at one or more future dates and allows participants to restructure their balance sheets.
E.obligates two counterparties to exchange cash flows at one or more future dates, allows participants to restructure their balance sheets, and allows a firm to convert outstanding fixed rate debt to floating rate debt.
A firm can enter into agreement to pay a floating rate and receive a fixed rate. Swaps involve an exchange of cash flows rather than securities.
25.Credit risk in the swap market
A.is extensive.
B.is limited to the difference between the values of the fixed rate and floating rate obligations.
C.is equal to the total value of the payments that the floating rate payer was obligated to make.
D.is extensive and is equal to the total value of the payments that the floating rate payer was obligated to make.
E.None of these is correct.
Swaps obligate two counterparties to exchange cash flows at one or more future dates. Swaps allow firms to restructure balance sheets, and the firm is obligated only for the difference between the fixed and floating rates.
26.Trading in stock index futures
A.now exceeds buying and selling of shares in most markets.
B.reduces transactions costs as compared to trading in stocks.
C.increases leverage as compared to trading in stocks.
D.generally results in faster execution than trading in stocks.
E.All of these are correct.
Trading in stock index futures now exceeds buying and selling of shares in most markets, reduces transactions costs as compared to trading in stocks, increases leverage as compared to trading in stocks, and generally results in faster execution than trading in stocks.
27.Commodity futures pricing
A.must be related to spot prices.
B.includes cost of carry.
C.converges to spot prices at maturity.
D.All of these are correct.
E.None of these is correct.
Commodity futures are similar to other types of futures contracts but the cost of carrying must be considered. The cost of carrying includes interest costs, storage costs, and allowance for spoilage.
28.Arbitrage proofs in futures market pricing relationships
A.rely on the CAPM.
B.demonstrate how investors can exploit misalignments.
C.incorporate transactions costs.
D.All of these are correct.
E.None of these is correct.
No-arbitrage relationships are stronger than arguments such as the CAPM, but may be less precise if transactions or storage costs are not known.
29.One reason swaps are desirable is that
A.they are free of credit risk.
B.they have no transactions costs.
C.they increase interest rate volatility.
D.they increase interest rate risk.
E.they offer participants easy ways to restructure their balance sheets.
For example, a firm can change a floating-rate obligation into a fixed-rate obligation and vice versa.
30.Which two indices had the lowest correlation between them during the 2001-2006 period?
A.S&P and DJIA; the correlation was 0.957
B.S&P and NASDAQ; the correlation was 0.899
C.DJIA and Russell 2000 the correlation was 0.758
D.S&P and NYSE; the correlation was 0.973
E.NYSE and DJIA; the correlation was 0.931
The correlations are shown in Table 23.2.
31.Which two indices had the highest correlation between them during the 2001-2006 period?
A.S&P and DJIA; the correlation was 0.957
B.S&P and Russell 2000 the correlation was 0.899
C.DJIA and Russell 2000 the correlation was 0.758
D.S&P and NYSE; the correlation was 0.973
E.NYSE and DJIA; the correlation was 0.931
The correlations are shown in Table 23.2.
32.The value of a futures contract for storable commodities can be determined by the ______and the model ______consistent with parity relationships.
A.CAPM, will be
B.CAPM, will not be
C.APT, will not be
D.APT, will be
E.CAPM and APT; will be
Both the CAPM and the APT can be used for this purpose and both will be consistent with parity relationships.
33.In the equation Profits = a + b*($/₤ exchange rate), b is a measure of
A.the firm's beta when measured in terms of the foreign currency.
B.the ratio of the firm's beta in terms of dollars to the firm's beta in terms of pounds.
C.the sensitivity of profits to the exchange rate.
D.the sensitivity of the exchange rate to profits.
E.the frequency with which the exchange rate changes.
The slope of a line that plots profits vs. exchange rates gives the average amount by which profits will change for each unit change in the exchange rate.
34.Hedging one commodity by using a futures contract on another commodity is called
A.surrogate hedging.
B.cross hedging.
C.alternative hedging.
D.correlative hedging.
E.proxy hedging.
Cross-hedging is used in some cases because no futures contract exists for the item you want to hedge. The two commodities should be highly correlated.
You are given the following information about a portfolio you are to manage. For the long-term you are bullish, but you think the market may fall over the next month.
35.If the anticipated market value materializes, what will be your expected loss on the portfolio?
A.14.29%
B.16.67%
C.15.43%
D.8.57%
E.6.42%
The change would represent a drop of (1200− 1400)/1400=14.3% in the index. Given the portfolio's beta, your portfolio would be expected to lose 0.6*14.3%=8.57%
36.What is the dollar value of your expected loss?
A.$142,900
B.$16,670
C.$85,700
D.$30,000
E.$64,200
The dollar value equals the loss of 8.57% times the $1 million portfolio value = $85,700.
37.For a 200-point drop in the S&P500, by how much does the value of the futures position change?
A.$200,000
B.$50,000
C.$250,000
D.$500,000
E.$100,000
The change is 200 points times the $250 multiplier, which equals $50,000.
38.How many contracts should you buy or sell to hedge your position? Allow fractions of contracts in your answer.
A.sell 1.714
B.buy 1.714
C.sell 4.236
D.buy 4.236
E.sell 11.235
The number of contracts equals the hedge ratio = Change in portfolio value / Profit on one futures contract = $85,700/$50,000 = 1.714. You should sell the contract because as the market falls the value of the futures contract will rise and will offset the decline in the portfolio's value.
39.You sold S&P 500 Index futures contract at a price of 950 and closed your position when the index futures was 947, you incurred:
A.a loss of $1,500.
B.a gain of $1,500.
C.a loss of $750.
D.a gain of $750.
E.None of these is correct.
($950 − $947) = $3 × 250 = $750.
40.You took a short position in three S&P 500 futures contracts at a price of 900 and closed the position when the index futures was 885, you incurred:
A.a gain of $11,250.
B.a loss of $11,250.
C.a loss of $8,000.
D.a gain of $8,000.
E.None of these is correct.
($900 − $885) = $15 × 250 × 3 = $11,250.
41.Suppose that the risk-free rates in the United States and in the Canada are 3% and 5%, respectively. The spot exchange rate between the dollar and the Canadian dollar (C$) is $0.80/C$. What should the futures price of the C$ for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs.
A.$1.00/ C$
B.$1.70/ C$
C.$0.88/ C$
D.$0.78/ C$
E.$1.22/ C$
$0.80(1.03/1.05) = $0.78/ C$.
42.Suppose that the risk-free rates in the United States and in the Canada are 5% and 3%, respectively. The spot exchange rate between the dollar and the Canadian dollar (C$) is $0.80/C$. What should the futures price of the C$ for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs.
A.$1.00/ C$
B.$0.82/ C$
C.$0.88/ C$
D.$0.78/ C$
E.$1.22/ C$
$0.80(1.05/1.03) = $0.82/ C$.
43.Suppose that the risk-free rates in the United States and in the United Kingdom are 6% and 4%, respectively. The spot exchange rate between the dollar and the pound is $1.60/BP. What should the futures price of the pound for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs.
A.$1.60/BP
B.$1.70/BP
C.$1.66/Bp
D.$1.63/BP
E.$1.57/BP
$1.60(1.06/1.04) = $1.63/BP.
You are given the following information about a portfolio you are to manage. For the long-term you are bullish, but you think the market may fall over the next month.
44.If the anticipated market value materializes, what will be your expected loss on the portfolio?
A.7.58%
B.6.52%
C.15.43%
D.8.57%
E.6.42%
The change would represent a drop of (915-990)/990=7.58% in the index. Given the portfolio's beta, your portfolio would be expected to lose 0.86*7.58%=6.52%
45.What is the dollar value of your expected loss?
A.$142,900
B.$65,200
C.$85,700
D.$30,000
E.$64,200
The dollar value equals the loss of 6.52% times the $1 million portfolio value = $65,200.
46.For a 75-point drop in the S&P500, by how much does the futures position change?
A.$200,000
B.$50,000
C.$250,000
D.$500,000
E.$18,750
The change is 75 points times the $250 multiplier, which equals $18,750.
47.How many contracts should you buy or sell to hedge your position? Allow fractions of contracts in your answer.
A.sell 3.477
B.buy 3.477
C.sell 4.236
D.buy 4.236
E.sell 11.235
The number of contracts equals the hedge ratio = Change in portfolio value / Profit on one futures contract = $65,200/$18,750 = 3.477. You should sell the contract because as the market falls the value of the futures contract will rise and will offset the decline in the portfolio's value.
48.Covered interest arbitrage ______.
A.ensures that currency futures prices are set correctly
B.ensures that commodity futures prices are set correctly
C.ensures that interest rate futures prices are set correctly
D.ensures that currency futures prices are set correctly and ensures that commodity futures prices are set correctly
E.None of these is correct