Exam 10: Derivatives: Risk Management With Speculation, Hedging, and Risk Transfer

A five-year currency swap involves two AAA borrowers and has been set at current market interest rates. The swap is for US$100 million against AUD 200 million at the current spot exchange rate of AUD/$ 2.00. The interest rates are 10% in U.S. dollars and 7% in Australian dollars, or annual swaps of US$10 million for AUD 14 million. A year later, the interest rates have dropped to 8% in U.S. dollars and 6% in Australian dollars, and the exchange rate is now AUD/$ 1.9. a. What should the market value of the swap be in the secondary market? Assume now that the swap is instead a currency-interest rate swap whereby the dollar interest is set at LIBOR. b. What would the market value of the currency-interest rate swap be if these conditions prevailed a year later?

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Question 1

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a. The new value of the swap is derived by considering the market value of two streams of cash flows:
$\bullet$ P_$: a bond in dollars with four years remaining, with annual cash flows of $10 million, and a principal repayment of $100 million;
$\bullet$ P_AUD: a bond in Australian dollars with four years remaining, with annual cash flows of AUD
14 million, and a principal repayment of AUD 200 million.
The swap to receive AUD and pay dollars is worth in AUD:
Swap= P_AUD (6%)- spot AUD/$ * P_$ (8%).
Swap = $\left( \frac { 14 } { 1.06 } + \frac { 14 } { 1.06 ^ { 2 } } + \frac { 14 } { 1.06 ^ { 3 } } + \frac { 214 } { 1.06 ^ { 4 } } \right) - 1.9 \left( \frac { 10 } { 1.08 } + \frac { 10 } { 1.08 ^ { 2 } } + \frac { 10 } { 1.08 ^ { 3 } } + \frac { 110 } { 1.08 ^ { 4 } } \right)$ Swap = 206.93 - 1.9 (106.63) = AUD 4.34 million.
The U.S. dollar value of the swap is 4.34/1.9 = $ 2.28 million.
Of course, the seller of this swap who receives dollars for Australian dollars will realize a corresponding loss.
b. Without further information, we can assume that the value of a bond with a floating rate stays constant. Therefore, the swap value will change only because of a change in the AUD interest rate and a change in the exchange rate. This second swap is now worth:
Swap = 206.93 - 1.9 (100) =AUD 16.93 million.
Swap =$ 8.91 million.

A differential swap, or switch LIBOR swap, involves the LIBOR rates in two different currencies but with both legs denominated in the same currency. A Japanese insurance company engages in a differential swap whereby it receives the six-month Japanese yen LIBOR and pays the six-month U.S. dollar LIBOR plus 50 bp but with both legs denominated in yen. No principal is exchanged at the end. The current LIBOR for the yen and the dollar are 6% and 4%, respectively, and the principal is 100 million yen. Hence, the first swap payment will be based on a differential of 1.5% in yen [6% = (4%-0.5%)]. The current yield pick-up is 150 bp. There is no currency risk on this swap. Provide some intuitive explanation for the pricing of such a swap, knowing that at the time, the dollar yield curve was very steep (long-term rates are much higher than short-term rates) and the yen yield curve was almost flat.

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Question 2

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This is not an easy task. Some preliminary remarks can be useful.
a. In a standard floating-for-floating currency swap, the terms would be yen LIBOR against dollar LIBOR flat. The 50-basis-point addition on the dollar LIBOR of the differential swap comes from the fact that all cash flows on the dollar leg (interest and principal) are denominated in yen, not in dollars.
b. The forward exchange rates reflect the differences in the two interest rates term structures. This impacts on the pricing of the differential swap.
The difficulty in valuing a differential swap is the valuation of the dollar LIBOR (in yen) leg. The "fair" spread to add (here 50 basis points) is the spread that makes the market value of this leg equal to the market value of the yen LIBOR leg. The basic pricing idea is to replicate the dollar LIBOR
(in yen) leg by using forward dollar LIBOR rates and forward ¥/$ exchange rates. This is detailed in R. Litzenberger, "Swaps: Plain and Fanciful," Journal of Finance, July 1992 (pages 842-844).

You are a young investment banker considering the issuance of a guaranteed note with stock index participation for a client. The current yield curve is flat at 8% for all maturities. Long-term at-the-money options on the stock market index are traded by banks. Two-year at-the-money calls trade at 17.84% of the index value; three-year at-the-money calls trade at 20% of the index value. You are hesitant about the terms to set in the structured note. You know that if you guarantee a higher coupon rate, the level of participation in the stock appreciation will be less. Your boss asks you to compute the "fair" participation rate that would be feasible for various guaranteed coupon rates and maturities. In other words, based on the current market conditions (as described above), estimate the participation rates that are feasible with a maturity of two or three years, and a coupon rate of: 0%, 1%, 2%, 3%, 5%, and 7%.

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Question 3

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The guaranteed note can be decomposed as the sum of a straight bond with a coupon C plus p times a call option on the index (p is the participation rate).
For a two-year note, we have: $100 = \frac { C } { 1.08 } + \frac { C } { 1.08 ^ { 2 } } + \frac { 100 } { 1.08 ^ { 2 } } + p \times 17.84$ hence $p = \frac { 14.266 - 1.7833 \times C } { 17.84 }$ For a three-year note, we have: $100 = \frac { C } { 1.08 } + \frac { C } { 1.08 ^ { 2 } } + \frac { C } { 1.08 ^ { 3 } } + \frac { 100 } { 1.08 ^ { 3 } } + p \times 20$ hence $p = \frac { 20.617 - 2.5771 \times C } { 20 }$ The next table gives the fair participation rates for various coupon rates:
$\begin{array}{ccc}\text { Coupon Rate } & \boldsymbol{p} \text { (2-Year Bond) } & \boldsymbol{p} \text { (3-Year Bond) } \\\hline 0 \% & 80 \% & 103 \% \\1 \% & 70 \% & 90 \% \\2 \% & 60 \% & 77 \% \\3 \% & 50 \% & 64 \% \\5 \% & 30 \% & 39 \% \\7 \% & 10 \% & 13 \%\end{array}$

A manager holds a diversified portfolio of British stocks worth £5 million. He has short-term fears about the market but feels that it is a sound long-term investment. He is a firm believer in betas, and his portfolio's $\beta$ is equal to 0.8. What are the alternatives open to temporarily reduce the risk on his British portfolio?

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Question 4

In 1990, the French bank, BNP, issued exchangeable bonds denominated in French francs (FF). These are bonds issued for FF 100 on April 1, 1990, with an annual coupon of FF 5, plus an exchange right. The bonds can be redeemed for FF 100 on April 1, 1996. The right can be exchanged on April 1, 1991, with payment of an additional FF 100, for another bond identical to the old bond (annual coupon of FF 5 and redeemed for FF 100 on April 1, 1996). If you exercise your right, you will have paid an additional FF 100 on April 1, 1991, but you will then hold two BNP bonds with maturity in 1996. a. Under what scenario would you exercise the exchange right (exchange the right plus FF 100 for an additional bond) on April 1, 1991? What is the attraction of such an exchangeable bond for investors? b. On April 1, 1990, the yield curve is flat at 6%. You can buy a call on a five-year bond with a coupon of 5%. The call has a strike price of 100% and expires on April 1, 1991. Its premium is 2%. Construct a replication portfolio to determine at what price the exchangeable bond can be issued by BNP.

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Question 5

You are currently borrowing €10 million at three-month Euribor + 75 basis points. The Euribor is at 3%. You expect to borrow this amount for five years but are worried that Euribor will rise in the future. You can buy a 4% cap on three-month Euribor over the next five years with an annual cost of 0.75% (paid quarterly). Describe the evolution of your borrowing costs under various interest rate scenarios (i.e., above and below 4%).

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Question 6

You're a banker. A client wishes to buy a guaranteed note with a 100% indexation to the stock index's growth. In other words, he doesn't want any coupon but requires 100% of the index growth. You wonder about the maturity of such a note. You check the prices of various index calls traded on the market for different maturities. Their strike is the current index level and their price is expressed as a percentage of this level. (For instance if the CAC is worth 3,000, the strike is 3,000 and the one-year maturity call trades at 11% of 3,000. You also check the price of a zero-coupon in percentage for various maturities. The following graph shows, for each maturity, the price of the option, that of the zero-coupon, and 100%-zero. a. What is the maturity of the guaranteed note (coupon =0%, indexation =100%)? Justify. b. If as a banker, you want to make a profit, should you lengthen or shorten the maturity of that note? Explain why. c. Everything remaining constant (that is, same volatility and interest rate), should the maturity of the guaranteed note be shorter or longer if the index pays a low dividend rather than a high one? Why?

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Question 7

The current yield curve on the international bond market in euro is flat at 4% for top-quality borrowers. A French company of good standing can issue plain-vanilla straight and floating-rate bonds at the following conditions: $\bullet$ Bond A: Straight Bond. Five-year straight bond with a fixed coupon of 4%. $\bullet$ Bond B: FRN. Five-year dollar FRN with a semiannual coupon set at LIBOR. An investment banker proposes to the French company to issue bull and/or bear FRNs at the following conditions: $\bullet$ Bond C: Bull FRN. Five-year FRN with a semiannual coupon set at: 7.60% - LIBOR. $\bullet$ Bond D: Bear FRN. Five-year FRN with a semiannual coupon set at: 2*LIBOR - 4.2%. The floor on all coupons is zero. The investment bank also proposes a five-year floor option at a strike of 2.1%. This floor will pay to the French company the difference between 2.1% and LIBOR, if it is positive, or zero if LIBOR is above 2.1%. The cost of this floor is spread over the payment dates and set at an annual 0.05%. The bank also proposes a five-year cap at a strike of 7.60%. The annual premium on the cap is 0.1%. The company can also enter in a five-year interest-rate swap 4% fixed against LIBOR. a. Assume that the French company issues Bonds C and D in equal proportions. Is it more advantageous than issuing Bonds A and B in equal proportion and why? b. Find out the borrowing cost reduction that can be achieved by issuing the bull note compared to issuing a fixed-coupon straight bond at 4%. c. Find out the borrowing cost reduction that can be achieved by issuing the bull note compared to issuing a plain-vanilla FRN at LIBOR. d. Find out the borrowing cost reduction that can be achieved by issuing the bear note compared to issuing a fixed-coupon straight bond at 4%. e. Find out the borrowing cost reduction that can be achieved by issuing the bear note compared to issuing a plain-vanilla FRN at LIBOR.

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Question 8

If the average premium on gold call options declines, does this mean that they are becoming undervalued and, therefore, should be bought? Using valuation models, give at least two possible reasons for this decline.

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Question 9

A small French bank has the following balance sheet, based on historical (nominal) values. Assets Liabilities Loan of 100 million: Debt of 50 million: 3 years, @ 3-month Euribor +1/2 5-year maturity, @ 10\% Net worth: 50 million All assets and liabilities are denominated in euros. The net worth is calculated as the difference between the value of assets and liabilities. The current interest rate term structure in euro is flat at 8%. The risk premium over Euribor required on the loan to a client remains at 50 basis points. a. Value the balance sheet based on market value. b. The bank anticipates a sharp drop in French interest rates. Would this drop be good for the bank? The current market conditions for interest rate swaps with a maturity of three or five years are 8% against Euribor. c. Assume that the bank simply wishes to immunize its market value against any movements in interest rates (drop or rise). What swap would you make to hedge this interest rate risk? d. Assume that the bank is quite confident in its interest rate prediction (a drop). What would you suggest? The next day, all interest rates drop to 7%. e. Value the balance sheet again, assuming that the floating rate debt remains at 100% and that the bank has undertaken the swap that you recommended. How much did the bank save by undertaking this swap?

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Question 10

Strumpf Ltd. decides to issue a convertible bond with a maturity of two years. Each bond is issued with a nominal value of £ 100 and an annual coupon C; of course, C has to be determined. Each bond can be redeemed for £ 100 or converted into one share of Strumpf at the option of the bondholder. The current stock price of Strumpf is £90. The yield curve for an issuer like Strumpf is flat at 6%. Barings is ready to issue long-term options on Strumpf shares. The premiums on calls with one-year and two-year expirations are given below: a. American-type calls are more expensive than European-type calls. Is it reasonable? b. Assume that the bond can only be converted at maturity, after payment of the second coupon. What should be the fair coupon rate C, consistent with the above market conditions? c. Assume that the bond is issued with the coupon rate determined above. The yield curve suddenly moves from 6% to 6.1% and the option premiums stay the same. What should be the new market price of the convertible bond? d. Assume now that the bond can be converted on two dates (rather than one as above). These dates are the first year (right after the first coupon payment) and the second year as above. It is not possible to convert the two-year bond at any other date. Is it possible to construct an arbitrage portfolio allowing to price the fair coupon C with the above data? Be precise in your explanation and state what type of options you would need to price the bond.

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Question 11

You wish to establish the theoretical futures price on a Euribor contract quoted on the London International Financial Futures Exchange (LIFFE) in London. The futures contract is for a 90-day Euribor rate at expiration of the futures contract. You look at the current term structure of Euribor interest rates. Following the standard conventions for short-term rates, all interest rates are quoted as annualized linear rates. In other words, the interest paid for a maturity of T days is equal to the annualized rate quoted, divided by 360 and multiplied by T. The observed rates are as follows: 60-Day 90-D\pi 150-Day 180-Da\% Euribar Rate 4.125\% 4.250\% 4.500\% 4.550\% a. What should be the Euribor futures price quoted today with an expiration date in exactly 90 days? b. What should be the Euribor futures price quoted today with an expiration date in exactly 60 days?

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Question 12

Let's consider a Swiss franc futures contract traded in the United States. On February 18 (a Friday), the March contract closed at 0.7049 dollar per Swiss franc. The size of the contract is 125,000 Swiss francs. The initial margin is $2,600 per contract and the maintenance margin is $1,600. Assume that you buy one March contract on February 19 at 0.7049 $/SFr and you deposit, in cash, an initial margin of $2,600. Listed below are the futures quotations (settlement prices) observed on three successive days: Feb. 18 Feb. 20 Feb. 21 Feb. 22 0.7049 0.7009 0.6949 0.7089 What are the cash flows associated with the marking-to-market procedure?

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Question 13

A few years ago when the French franc (FF) still existed, the MATIF futures exchange in Paris had a very active market for the French government bond contract. The underlying asset is a notional long-term government bond with a yield of 10%. The size of the contract is FF 500,000 of nominal value. Futures prices are quoted in percentage of the nominal value. On April 1, the French term structure of interest rate is flat. The bond futures price for delivery in June is equal to 106.21%. The three French government bonds that can be used for delivery have the following characteristics: Market Prica Duration Convarsinn Factar Band A 107.46\% 7.00 101.171\% Band B 105.57\% 7.90 98.1441\% Band C 106.32\% 8.80 99.3104\% a. Is the futures price consistent with the spot bond prices? (Find the bond cheapest to deliver.) b. Estimate the interest rate sensitivity (duration) of the futures price. c. You are an insurance company with a portfolio of French government bonds. The portfolio has a nominal value of FF 100 million and a market value of FF 110 million. Its average duration is 3.5. You are worried that social unrest in France could lead to an increase in French interest rates. Rather than selling the bonds, you wish to temporarily hedge the French interest rate risk. How many futures contracts would you sell and why? Note to the instructor: The section on optimal hedge ratios for bond portfolios has been removed from the 5th edition. We include a brief summary of the theoretical derivations given at the end of the solution.

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Question 14

In Hong Kong, the size of a futures contract on the Hang Seng stock index is HK $50 times the index. The margin (initial and maintenance) is set at HK $32,500. You predict a drop in the Hong Kong stock market following some economic problems in China and decide to sell one June futures contract on April 1. The current futures price is 7,200. The contract expires on the second-to-last business day of the delivery month (expiration date: June 27). Today is April 1, and the current spot value of the stock market index is 7,140. a. Why is the spot value of the index lower than the futures value of the index? b. Indicate the cash flows that affect your position if the following prices are subsequently observed: April 1 April 2 April 3 April 4 Hang Seng Futures 7,200 7,300 7,250 6,900

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Question 15

Digital options: Digital (or binary) options can only have two payoffs at maturity. If the strike condition set in the option is met, the buyer will receive the full prespecified payoff. If not, the buyer receives no payoff. This is different from a traditional option where there exists an infinite number of payoffs. For example, we could have a digital option on the French CAC index, stating that the option buyer will get €200 if the CAC index is above 4,000 at expiration and zero otherwise. On this digital option, the buyer will get exactly 200 as soon as the CAC index is above the 4,000 level at expiration, whether it be 4,001, 4,100, or 5,000. a. Draw the profit and loss curve at expiration as a function of the CAC index for these two options: $\bullet$ Traditional call on the CAC index: Exercise price: 4,000; premium: 40. $\bullet$ Digital call on the CAC index: Exercise price: 4,000; payoff if exercised: 200; premium: 40. b. What are the relative advantages of the two options? c. Assume that the volatility of the French stock market increases suddenly. Should the premium on the digital call increase more (or less) than the premium on the traditional call?

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Question 16

An American investor wants to invest in a diversified portfolio of Japanese stocks but can invest only a rather small sum. The investor also worries about fiscal and transaction cost considerations. Why would futures contracts on the Nikkei index be an attractive alternative?

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Question 17

You specialize in arbitrage between the futures and the cash market on the Paris Bourse. The CAC stock index is made up of 40 leading stocks. The futures price of the CAC contract with delivery in a month is 2,120. The size of the contract is €10 times the index. The spot value of the index is given as 2,000. Actually, there are transaction costs in the cash market; the bid-ask spread is around 40 points. You can buy a basket of stocks representing the index for 2,020 and sell the same basket for 1,980. Transaction costs on the futures contracts are assumed to be negligible. During the next month, the stocks in the index will pay dividends amounting to 5 per index. These dividends have already been announced, so there is no uncertainty about this cash flow. The current one-month interest rate in euros is 6¹/₂ -⁵/₈%. a. Do you detect any arbitrage opportunity? b. What profit could you make per contract? c. What is the theoretical value of the futures bid and ask prices?

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Question 18

Assume that an AAA customer pays 8% on a five-year loan and can contract a five-year interest rate swap (paying fixed) at 8% against LIBOR. Assume that a BBB customer pays (8 +0 m)% on a five-year loan and can contract a five-year interest rate swap (paying fixed) at (8 + µ)% against LIBOR. Should a customer pay the same credit-quality spread (m and µ) on a loan and on a swap?

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Question 19

The current dollar yield curve on the dollar international bond market is flat at 7% for top-quality borrowers. A company of good standing can issue plain-vanilla straight and floating-rate dollar bonds under the following conditions: $\bullet$ Bond A: Straight bond. Five-year straight dollar bond with a coupon of 7.25%. $\bullet$ Bond B: FRN. Five-year dollar FRN with a semiannual coupon set at LIBOR plus 0.25% and a cap of 14%. The cap means that the coupon rate is limited to 14% even if the LIBOR passes 13.75%. An investment banker proposes to a French company to issue bull and/or bear FRNs under the following conditions: $\bullet$ Bond C: Bull FRN. Five-year FRN with a semiannual coupon set at: 13.75% - LIBOR. $\bullet$ Bond D: Bear FRN. Five-year FRN with a semiannual coupon set at: 2 * LIBOR - 7% and a cap of 20.5%. Coupons on all bonds cannot be negative. The investment bank also proposes a five-year floor option at 3.5%. This floor will pay to the French company the difference between 3.5% and LIBOR, if it is positive, or zero if LIBOR is above 3.5%. The cost of this floor is spread over the payment dates and set at an annual 0.1%. The investment bank also proposes a five-year cap option at a strike of 13.75%. The cost of this cap is spread over the payment dates and set at an annual 0.05%. The company can also enter into a five-year interest rate swap at 7% fixed against LIBOR. a. Explain why it would be attractive to the French company to issue these FRNs compared to current market conditions for plain-vanilla straight bonds and FRNs. b. Find out the borrowing cost reduction that can be achieved by issuing bull notes compared to a fixed-coupon rate of 7.25%. c. Find out the borrowing cost reduction that can be achieved by issuing bear notes compared to an FRN at LIBOR plus 0.25%.

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Question 20

Showing 1 - 20 of 49

If the average premium on gold call options declines, does this mean that they are becoming undervalued and, therefore, should be bought? Using valuation models, give at least two possible reasons for this decline.

An American investor wants to invest in a diversified portfolio of Japanese stocks but can invest only a rather small sum. The investor also worries about fiscal and transaction cost considerations. Why would futures contracts on the Nikkei index be an attractive alternative?

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Foreign Exchange Parity Relations

Foreign Exchange Determination and Forecasting

International Asset Pricing

Equity: Markets and Instruments

Equity: Concepts and Techniques

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The Case for International Diversification

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