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Questions and Answers of Banking

If XYZ does nothing to manage copper price risk, what is its profit 1 year from now, per pound of copper? If on the other hand XYZ sells forward its expected copper production, what is its estimated
Compute estimated profit in 1 year if Telco sells collars with the following strikes:a. $0.95 for the put and $1.00 for the call.b. $0.975 for the put and $1.025 for the call.c. $0.95 for the put and
Compute estimated profit in 1 year if Telco buys paylater calls as follows (the net premium may not be exactly zero): a. Sell one 0.975-strike call and buy two 1.034-strike calls. b. Sell two
Suppose that Wirco does nothing to manage the risk of copper price changes. What is its profit 1 year from now, per pound of copper? Suppose that Wirco buys copper forward at $1. What is its profit 1
What happens to the variability of Wirco's profit if Wirco undertakes any strategy (buying calls, selling puts, collars, etc.) to lock in the price of copper next year? You can use your answer to the
Golddiggers has zero net income if it sells gold for a price of $380. However, by shorting a forward contract it is possible to guarantee a profit of $40/oz. Suppose a manager decides not to hedge
Consider the example in Table 4.6. Suppose that losses are fully tax-deductible. What is the expected after-tax profit in this case?
Suppose that firms face a 40% income tax rate on all profits. In particular, losses receive full credit. Firm A has a 50% probability of a $1000 profit and a 50% probability of a $600 loss each year.
Suppose that firms face a 40% income tax rate on positive profits and that net losses receive no credit. (Thus, if profits are positive, after-tax income is (1− 0.4) × profit, while if there is a
a. Suppose that Auric insures against a price increase by purchasing a 440-strike call. Verify by drawing a profit diagram that simultaneously selling a 400 strike put will generate a collar. What is
Suppose that LMN Investment Bank wishes to sell Auric a zero-cost collar of width 30 without explicit premium (i.e., there will be no cash payment from Auric to LMN). Also suppose that on every
Suppose the 1-year copper forward price were $0.80 instead of $1. If XYZ were to sell forward its expected copper production, what is its estimated profit 1 year from now? Should XYZ produce copper?
Use the same assumptions as in the preceding problem, without the bid-ask spread. Suppose that we want to construct a paylater strategy using a ratio spread. Instead of buying a 440-strike call,
Using the information in Table 4.11, verify that a regression of revenue on price gives a regression slope coefficient of about 100,000.
Using the information in Table 4.9 about Scenario C:a. Compute Ïƒtotal revenue when correlation between price and quantity is positive.b. What is the correlation between price and revenue?
Using the information in Table 4.9 about Scenario C:a. Using your answer to the previous question, use equation (4.7) to compute the variance-minimizing hedge ratio.b. Run a regression of revenue on
Using the information in Table 4.9 about Scenario C:a. What is the expected quantity of production?b. Suppose you short the expected quantity of corn. What is the standard deviation of hedged revenue?
Suppose that price and quantity are positively correlated as in this table:There is a 50% chance of either price. The futures price is $2.50. Demonstrate the effect of hedging if we do the
Compute estimated profit in 1 year if XYZ buys a put option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case.
Compute estimated profit in 1 year if XYZ sells a call option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case.
Compute estimated profit in 1 year if XYZ buys collars with the following strikes:a. $0.95 for the put and $1.00 for the call.b. $0.975 for the put and $1.025 for the call.c. $1.05 for the put and
Compute estimated profit in 1 year if XYZ buys paylater puts as follows (the net premium may not be exactly zero):a. Sell one 1.025-strike put and buy two 0.975-strike puts.b. Sell two 1.034-strike
If Telco does nothing to manage copper price risk, what is its profit 1 year from now, per pound of copper that it buys? If it hedges the price of wire by buying copper forward, what is its estimated
Compute estimated profit in 1 year if Telco buys a call option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case.
Compute estimated profit in 1 year if Telco sells a put option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case.
Construct Table 5.1 from the perspective of a seller, providing a descriptive name for each of the transactions.
The S&R index spot price is 1100 and the continuously compounded risk-free rate is 5%. You observe a 9-month forward price of 1129.257.a. What dividend yield is implied by this forward price?b.
Suppose the S&P 500 index futures price is currently 1200. You wish to purchase four futures contracts on margin.a. What is the notional value of your position?b. Assuming a 10% initial margin,
Suppose the S&P 500 index is currently 950 and the initial margin is 10%. You wish to enter into 10 S&P 500 futures contracts.a. What is the notional value of your position? What is the
Verify that going long a forward contract and lending the present value of the forward price creates a payoff of one share of stock whena. The stock pays no dividends.b. The stock pays discrete
Verify that when there are transaction costs, the lower no-arbitrage bound is given by equation (5.12).S0 × P5.5 + 0.7 × BSCall(S0, S0, σ , r, 5.5, δ)
Suppose the S&R index is 800, and that the dividend yield is 0. You are an arbitrageur with a continuously compounded borrowing rate of 5.5% and a continuously compounded lending rate of 5%.
Suppose the S&P 500 currently has a level of 875. The continuously compounded return on a 1-year T-bill is 4.75%. You wish to hedge an $800,000 portfolio that has a beta of 1.1 and a correlation
Suppose you are selecting a futures contract with which to hedge a portfolio. You have a choice of six contracts, each of which has the same variability, but with correlations of −0.95, −0.75,
Suppose the current exchange rate between Germany and Japan is 0.02 = C/¥. The euro-denominated annual continuously compounded risk-free rate is 4% and the yen-denominated annual continuously
Suppose the spot $/¥ exchange rate is 0.008, the 1-year continuously compounded dollar-denominated rate is 5% and the 1-year continuously compounded yen denominated rate is 1%. Suppose the 1-year
A $50 stock pays a $1 dividend every 3 months, with the first dividend coming 3 months from today. The continuously compounded risk-free rate is 6%.a. What is the price of a prepaid forward contract
Suppose we wish to borrow $10 million for 91 days beginning next June, and that the quoted Eurodollar futures price is 93.23.a. What 3-month LIBOR rate is implied by this price?b. How much will be
A $50 stock pays an 8% continuous dividend. The continuously compounded riskfree rate is 6%.a. What is the price of a prepaid forward contract that expires 1 year from today?b. What is the price of a
Suppose the stock price is $35 and the continuously compounded interest rate is 5%.a. What is the 6-month forward price, assuming dividends are zero?b. If the 6-month forward price is $35.50, what is
Suppose you are a market-maker in S&R index forward contracts. The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0.a. What is the no-arbitrage
Repeat the previous problem, assuming that the dividend yield is 1.5%.a. What is the no-arbitrage forward price for delivery in 9 months?b. Suppose a customer wishes to enter a short index futures
The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0.a. Suppose you observe a 6-month forward price of 1135. What arbitrage would you undertake?b.
The S&R index spot price is 1100, the risk-free rate is 5%, and the continuous dividend yield on the index is 2%.a. Suppose you observe a 6-month forward price of 1120. What arbitrage would you
Suppose that 10 years from now it becomes possible for money managers to engage in time travel. In particular, suppose that a money manager could travel to January 1981, when the 1-year Treasury bill
The spot price of a widget is $70.00 per unit. Forward prices for 3, 6, 9, and 12 months are $70.70, $71.41, $72.13, and $72.86. Assuming a 5% continuously compounded annual risk-free rate, what are
Using Table 6.6, what is your best guess about the current price of gold per ounce?
Consider production ratios of 2:1:1, 3:2:1, and 5:3:2 for oil, gasoline, and heating oil. Assume that other costs are the same per gallon of processed oil. a. Which ratio maximizes the per-gallon
evening Suppose you know nothing about widgets. You are going to approach a widget merchant to borrow one in order to short-sell it. (That is, you will take physical possession of the widget, sell
The current price of oil is $32.00 per barrel. Forward prices for 3, 6, 9, and 12 months are $31.37, $30.75, $30.14, and $29.54. Assuming a 2% continuously compounded annual risk-free rate, what is
Given a continuously compounded risk-free rate of 3% annually, at what lease rate will forward prices equal the current commodity price? (Recall the copper example in Section 6.3.) If the lease rate
Suppose that copper costs $3.00 today and the continuously compounded lease rate for copper is 5%. The continuously compounded interest rate is 10%. The copper price in 1 year is uncertain and copper
Suppose the gold spot price is $300/oz, the 1-year forward price is 310.686, and the continuously compounded risk-free rate is 5%.a. What is the lease rate?b. What is the return on a cash-and-carry
a. What are some possible explanations for the shape of this forward curve?b. What annualized rate of return do you earn on a cash-and-carry entered into in December of Year 0 and closed in March of
a. Suppose that you want to borrow a widget beginning in December of Year 0 and ending in March of Year 1. What payment will be required to make the transaction fair to both parties?b. Suppose that
a. Suppose the March Year 1 forward price were $3.10. Describe two different transactions you could use to undertake arbitrage.b. Suppose the September Year 1 forward price fell to $2.70 and
Consider Example 6.1. Suppose the February forward price had been $2.80. What would the arbitrage be? Suppose it had been $2.65. What would the arbitrage be? In each case, specify the transactions
Suppose you observe the following zero-coupon bond prices per $1 of maturity payment: 0.96154 (1-year), 0.91573 (2-year), 0.87630 (3-year), 0.82270 (4-year), 0.77611 (5-year). For each maturity year
What is the rate on a synthetic FRA for a 90-day loan commencing on day 90? A 180-day loan commencing on day 90? A 270-day loan commencing on day 90? Discuss.
What is the rate on a synthetic FRA for a 180-day loan commencing on day 180? Suppose you are the counterparty for a borrower who uses the FRA to hedge the interest rate on a $10m loan. What
Suppose you are the counterparty for a lender who enters into an FRA to hedge the lending rate on $10m for a 90-day loan commencing on day 270. What positions in zero-coupon bonds would you use to
Using the information in Table 7.1, suppose you buy a 3-year par coupon bond and hold it for 2 years, after which time you sell it. Assume that interest rates are certain not to change and that you
As in the previous problem, consider holding a 3-year bond for 2 years. Nowsuppose that interest rates can change, but that at time 0 the rates in Table 7.1 prevail. What transactions could you
Consider the implied forward rate between year 1 and year 2, based on Table 7.1.a. Suppose that r0(1, 2) = 6.8%. Show how buying the 2-year zero-coupon bond and borrowing at the 1-year rate and
Suppose the September Eurodollar futures contract has a price of 96.4. You plan to borrow $50m for 3 months in September at LIBOR, and you intend to use the Eurodollar contract to hedge your
A lender plans to invest $100m for 150 days, 60 days from today. (That is, if today is day 0, the loan will be initiated on day 60 and will mature on day 210.) The implied forward rate over 150 days,
Consider the same facts as the previous problem, only now consider hedging with the 3-month Eurodollar futures. Suppose the Eurodollar futures contract that matures 60 days from today has a price on
Consider the bonds in Example 7.8. What hedge ratio would have exactly hedged the portfolio if interest rates had decreased by 25 basis points? Increased by 25 basis points? Repeat assuming a
Using the information in the previous problem, find the price of a 5-year coupon bond that has a par payment of $1,000.00 and annual coupon payments of $60.00. Discuss.
Compute Macaulay and modified durations for the following bonds:a. A 5-year bond paying annual coupons of 4.432% and selling at par.b. An 8-year bond paying semiannual coupons with a coupon rate of
Consider the following two bonds which make semiannual coupon payments: a 20 year bond with a 6% coupon and 20% yield, and a 30-year bond with a 6% coupon and a 20% yield.a. For each bond, compute
An 8-year bond with 6% annual coupons and a 5.004% yield sells for $106.44 with a Macaulay duration of 6.631864. A 9-year bond has 7% annual coupons with a 5.252% yield and sells for $112.29 with a
A 6-year bond with a 4% coupon sells for $102.46 with a 3.5384% yield. The conversion factor for the bond is 0.90046. An 8-year bond with 5.5% coupons sells for $113.564 with a conversion factor of
a. Compute the convexity of a 3-year bond paying annual coupons of 4.5% and selling at par.b. Compute the convexity of a 3-year 4.5% coupon bond that makes semiannual coupon payments and that
Suppose a 10-year zero-coupon bond with a face value of $100 trades at $69.20205.a. What is the yield to maturity and modified duration of the zero-coupon bond?b. Calculate the approximate bond
Suppose you observe the following effective annual zero-coupon bond yields: 0.030 (1-year), 0.035 (2-year), 0.040 (3-year), 0.045 (4-year), 0.050 (5-year). For each maturity year compute the
Suppose you observe the following 1-year implied forward rates: 0.050000 (1 year), 0.034061 (2-year), 0.036012 (3-year), 0.024092 (4-year), 0.001470 (5-year). For each maturity year compute the
Suppose you observe the following continuously compounded zero-coupon bond yields: 0.06766 (1-year), 0.05827 (2-year), 0.04879 (3-year), 0.04402 (4-year), 0.03922 (5-year). For each maturity year
Suppose you observe the following par coupon bond yields: 0.03000 (1-year), 0.03491 (2-year), 0.03974 (3-year), 0.04629 (4-year), 0.05174 (5-year). For each maturity year compute the zero-coupon bond
Using the information in Table 7.1,a. Compute the implied forward rate from time 1 to time 3.b. Compute the implied forward price of a par 2-year coupon bond that will be issued at time 1.
Suppose that in order to hedge interest rate risk on your borrowing, you enter into an FRA that will guarantee a 6%effective annual interest rate for 1 year on $500,000.00. On the date you borrow the
Using the same information as the previous problem, suppose the interest rate on the borrowing date is 7.5%. Determine the dollar settlement of the FRA assuminga. Settlement occurs on the date the
Suppose that 1- and 2-year oil forward prices are $22/barrel and $23/barrel. The 1 and 2-year interest rates are 6% and 6.5%. Show that the new 2-year swap price is $22.483. Discuss.
Using the zero-coupon bond prices and oil forward prices in Table 8.9, what is the price of an 8-period swap for which two barrels of oil are delivered in even-numbered quarters and one barrel of oil
Using the zero-coupon bond prices and natural gas swap prices in Table 8.9, what are gas forward prices for each of the 8 quarters?
Using the zero-coupon bond prices and natural gas swap prices in Table 8.9, what is the implicit loan amount in each quarter in an 8-quarter natural gas swap?In table 8.9
What is the fixed rate in a 5-quarter interest rate swap with the first settlement in quarter 2? Discuss.
Using the zero-coupon bond yields in Table 8.9, what is the fixed rate in a 4-quarter interest rate swap? What is the fixed rate in an 8-quarter interest rate swap? Discuss.
What 8-quarter dollar annuity is equivalent to an 8-quarter annuity of = C1?
Using the assumptions in Tables 8.5 and 8.6, verify that equation (8.13) equals 6%. Discuss.
Using the information in Table 8.9, what are the euro-denominated fixed rates for 4- and 8-quarter swaps?
Using the information in Table 8.9, verify that it is possible to derive the 8-quarter dollar interest swap rate from the 8-quarter euro interest swap rate by using equation (8.13). Discuss.
Suppose that oil forward prices for 1 year, 2 years, and 3 years are $20, $21, and $22. The 1-year effective annual interest rate is 6.0%, the 2-year interest rate is 6.5%, and the 3-year interest
Consider the same 3-year oil swap. Suppose a dealer is paying the fixed price and receiving floating. What position in oil forward contracts will hedge oil price risk in this position? Verify that
Consider the 3-year swap in the previous example. Suppose you are the fixed-rate payer in the swap. How much have you overpaid relative to the forward price after the first swap settlement? What is
Consider the same 3-year swap. Suppose you are a dealer who is paying the fixed oil price and receiving the floating price. Suppose that you enter into the swap and immediately thereafter all
Supposing the effective quarterly interest rate is 1.5%, what are the per-barrel swap prices for 4-quarter and 8-quarter oil swaps? (Use oil forward prices in Table 8.9.) What is the total cost of
Using the information about zero-coupon bond prices and oil forward prices in Table 8.9, construct the set of swap prices for oil for 1 through 8 quarters.
Using the information in Table 8.9, what is the swap price of a 4-quarter oil swap with the first settlement occurring in the third quarter? Discuss.
Given an 8-quarter oil swap price of $20.43, construct the implicit loan balance for each quarter over the life of the swap. Discuss.

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