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

A swap dealer provides the following quotations for a yen/$ currency swap. The quotes are for a yen fixed rate against the U.S. Treasury yield flat, with annual payments. A client wishes to enter a five-year swap, paying yen and receiving $. The current yield on five-year U.S. Treasury bonds is 7.20%, using the semiannual method, which amounts to 7.33%, using the annual European method. What will the exact terms of the swap be if the client accepts these quotations?

A dollar-Swiss franc swap with a maturity of five years was contracted by Papaf Inc. three years ago. Papaf swapped $100 million for CHF 250 million. The swap payments were annual, based on market interest rates of 8% in dollars and 4% in CHF. In other words, Papaf Inc. contracted to pay dollars and receive CHF. The current spot exchange rate is 2 CHF/$, and the current interest rates are 6% in CHF and 10% in $ (the term structures are flat). a. What is the swap payment at the end of year three? Does Papaf pay or receive? b. On the final date of the swap, the spot exchange rate is 1.5 CHF/$. What is the final swap payment at the end of year five?

A money manager holds $50 million worth of top-quality international bonds denominated in dollars. Their face value is $40 million, and most issues are highly illiquid. She fears a rise in U.S. interest rates and decides to hedge, using U.S. Treasury bond futures. Why would it be difficult to achieve a perfect hedge (list the various reasons)?

A Swiss portfolio manager has a significant portion of the portfolio invested in dollar-denominated assets. The money manager is worried about the political situation surrounding the next U.S. presidential election and fears a potential drop in the value of the dollar. The manager decides to sell the dollars forward against Swiss francs. a. Give some reasons why the Swiss money manager should use futures rather than forward currency contracts? b. Give some reasons why the Swiss money manager should use forward currency contracts rather than futures?

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 4% in U.S. dollars and 7% in Australian dollars, or annual swaps of $4 million for AUD 14 million. A year later, the interest rates have dropped to 3% in U.S. dollars and 6% in Australian dollars, and the exchange rate is now AUD/$ 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?

A small German bank has the following portfolio of loans in U.S. dollars, valued at market value: Assets \ 50 million of a five-year FRN at LIBOR plus 0.5 \% Liabilities \ 10 million of a five-year loan at a fixed rate of 9 \% The German bank fears a long-term depreciation of the U.S. dollar relative to the euro and believes in stable U.S. interest rates. a. What is its currency exposure? b. What type of swap arrangements should it contract? c. What should the principal of the swaps be?

Guaranteed note. You are a young banker offering a client to issue a guaranteed note. The yield curve is flat at 9% for each maturity. Options on the stock index are offered by banks. A at-the-money call with a two-year maturity trades at 12% of the index value, whereas a three-year call is worth 15% of the index. You wonder about the characteristics of the bond. If you offer a high coupon, the indexation will be low. Therefore, you decide to compute the indexation levels in accordance to the current market conditions for maturities of two and three years and coupon levels of 0%, 2%, and 5%.

The average premium on currency calls has decreased, whereas the premium on currency puts has increased. What explanations can you provide?

Bank PAPOUF decides to issue two bonds and wonders what the fair interest rate on these bonds should be: A. A one-year currency option bond. The bond is issued in dollars with a face value of $100. The bondholder can choose to have the coupon and principal paid in dollars or in SFr, at a specified exchange rate of SFr/$ = 2, that is, receive either $100 or SFr 200 as principal repayment, and receive either $C or SFr 2C as interest if C is the coupon set in dollars. The coupon rate is c = C/100. B. A two-year currency option bond. The bond is issued in dollars, with a face value of $100 and pays an annual coupon C'. The bondholder can choose to have the coupons and principal paid in dollars or in SFr, at a specified exchange rate of SFr/$ = 2, that is, receive either $100 or SFr 200 as principal repayment, and receive either $C' or SFr 2C' as interest, if C' is the coupon set in dollars. The coupon rate is c'= C'/100. Current market conditions are given below: $\bullet$ Interest Rates 1-Year 2-Year Zero-coupon rates US$ 8% 8% SFr 4% 4% $\bullet$ Spot exchange rate: SFr/$= 2 $\bullet$ Currency options: SFr call, strike price 50 U.S. cents, expiration one year: 2 U.S. cents. SFr call, strike price 50 U.S. cents, expiration two years: 5 U.S. cents. a. Compute the coupon C on Bond A that would be consistent with market conditions at time of issue. b. Compute the coupon C' on Bond B that would be consistent with market conditions at time of issue.

A small Dutch bank has the following balance sheet (in euros), based on historical or nominal values. Assets Liabilities Loan of 200 million: FRN borrowing of 150 million: 3 years, @ 7\% @ 3-month Euribor, 5-year maturity Net worth: 50 million All assets and liabilities are denominated in euros. The bank borrows short-term on the Euro-currency market. The bank and its client are AAA quality. The net worth is calculated as the difference between the value of assets and liabilities. The current euro term structure for AAA borrowers is flat at 6.5%. a. Value the balance sheet based on market value. b. Compute the interest-rate sensitivity (duration) of the asset. Infer the interest rate sensitivity of the net worth of the bank. For example, how much would stockholders lose if euro interest rates moved up by 0.10%? (Assume that the interest rate sensitivity of an floating-rate note (FRN) is zero, as the coupon is reset to the market interest rate.) c. The bank fears a rise in all euro interest rates. The current market conditions for interest rate swaps in euros are as follows: $\bullet$ With a maturity of three years are: 6.5% against Euribor. $\bullet$ With a maturity of five years are: 6.75% against Euribor. What would you do to hedge this interest rate risk? d. The next day, all interest rates move up to 8%. Value again the balance sheet, assuming that the floating-rate debt remains at 100% and that the bank has undertaken the swap that you recommended. Is the hedge perfect? Why?

A traditional interest rate swap has a notional capital of 100 and exchange LIBOR (the floating leg) against 6% (fixed leg). At maturity of the swap there is no capital exchange as the same notional capital of 100 is "exchanged" on both legs. Assume that the swap has a five-year maturity. A company needs to create an immediate cash flow to offset an immediate loss and decides to use an amortizing swap. Its off-balance sheet items are accounted at their book or historical values. The floating leg is LIBOR, paid quarterly, with a notional capital of 100. The fixed leg also has a notional capital of 100, however, there is only an initial cash flow of X on the fixed leg of the amortizing swap and no other cash flow (zero coupons). Hence, there is no capital exchanged at maturity of the swap (capital identical on both legs). The swap is priced (the value of X is set) so that the initial swap value is zero. The company enters the amortizing swap to pay floating and receive fixed. In other words, its cash flows on the swap are as follows: $\bullet$ Receive X at time 0. $\bullet$ Pays LIBOR every quarter for five years. $\bullet$ No cash flow at maturity. a. Why is the amortizing swap interesting for this company, which wants to window-dress an immediate loss? How will it impact its future earnings? b. The term structure is flat at 6%. What should be the "fair" value of X? c. The company expects a loss of 10 million, what should be the notional capital of the amortizing swap that should be contracted? d. Assume now that the company must value all off-balance sheet items at their market value. What would happen to the value of the swap immediately after the payment of X is received by the company? Are amortizing swaps useful in deferring losses with this accounting convention?

Derive a theoretical price for each of the following futures contracts quoted in the United States and indicate why and how the market price should deviate from this theoretical value. In each case, consider one unit of underlying asset. The contract expires in exactly three months, and the annualized interest rate on three-month dollar London InterBank Offered Rate (LIBOR) is 12%. All interest rates quoted are annualized. Contract a. Gold Futures: b. Currency Futures: c. Eurodollar Futures: (3-month \ LIBOR): d. Stock Index Futures: Useful Information Spot gold price=\ 300 per ounce; cost of storage= \ 0.50 per ounce per month \ / spot exchange rate =1.10dollars per euro; 3-month euro interest rate =4 \% 6 -month \LIBOR interest rate =10 \% Current value of stock index =1,200 ; annual dividend yield=2 \%

You are an investment banker working in Switzerland where yields are very low (1% for all maturities). You are planning to offer a five-year Swiss franc/British pound bond with the following characteristics: $\bullet$ Issuer: Brit Ltd., a top-quality British company. $\bullet$ Issue amount: SFr 100 million. $\bullet$ Coupon in SFr: 5% (or SFr 5 million). $\bullet$ Reimbursed value: £40 million. This bond qualifies as a Swiss franc bond for the portfolio of a Swiss insurance company. The current spot exchange rate is 2.5 Swiss francs per British pound. The yield curve in British pounds is flat at 7%. The pound/franc swap rates are 7% in pounds against 1% in francs for all maturities. a. Assume that Swiss insurance companies can account for their Swiss franc bond holdings at historical costs. Give a reason why it would be attractive to invest in this bond. b. Is the coupon rate set at fair pricing (i.e., consistent with current market conditions)? c. The British company desires to borrow in pounds and does not wish to carry any currency risk on its debt. The investment banker needs to design a coupon swap that would hedge the currency risk on that dual-currency bond for Brit Ltd. The designed swap should have a zero value at time of contracting. Give one possible design for the swap and calculate its associated swap rate. d. What is the pound yield paid by the British company, once it has hedged its currency risk on the dual-currency bond using the swap described above? What is the annual cost-saving in British pounds compared to a straight pound bond?

The current market conditions for an AAA client are 8% on a one-year dollar loan, and 8% fixed U.S. dollars for 9% fixed British pounds on a one-year dollar/pound currency swap. Let's consider a BBB client borrowing at (8 + m)% on a one-year dollar loan. The same client can enter a dollar/pound currency swap, paying (8 + µ)% fixed dollars and receiving 9% fixed pounds. Assume that the customer has a probability of p% to default within a year. In case of default, the bank knows that it will recover nothing on either transaction. The probability of default p (e.g., 5%) is known and independent of movements in interest and exchange rates. The spot exchange rate is S₀ = 1 $/£. Assuming that you can observe the prices of $/£ currency options, suggest some approach to determine the fair values of m and µ. (Assume that the bank has a large number of clients whose probabilities of default are independent; therefore, the bank can diversify away the uncertainty of default on this specific client.)

A Dutch institutional investor has decided to bet on a drop in U.S. dollar bond yields. It engages in a leveraged strategy, borrowing $100 million at LIBOR plus 0.25% and investing the proceeds in attractive, newly issued, long-term dollar international bonds. Suddenly, the investor becomes worried that bond yields have hit bottom and will rise because of inflationary pressures. The investor wishes to keep the specific international bonds that have been selected, partly because of their attractiveness and partly because of their lack of market liquidity. What kind of swap could be arranged to hedge this U.S. dollar bond yield risk?

You are the treasurer of a major Japanese construction company. Today is January 15. You expect to receive €10 million at the end of March, as payment from a client on some construction work in France. You know that you will need this sum somewhere else in Europe at the end of June. Meanwhile, you wish to invest these €10 million for three months. The current three-month interest rate in euros is 4%, but you are worried that it will quickly drop. Listed below are Euribor futures quotations on EUREX: Maturity (manth-end) Price February 96.02\% March 96.08\% June 96.20\% September 96.25\% a. Knowing that Euribor contracts have a size of €1 million, what should you do to freeze a lending rate when you will receive the money? b. At the end of March, when you receive the money, the three-month Euribor is equal to 3%. How much money (number of euros) have you gained by engaging in the above transaction (as opposed to doing nothing on January 15)?

Pouf is a rapidly growing and pleasant country in the Austral hemisphere. Its inhabitants are called Poufans, and its currency is the pof. The bond market is fairly active with many issues by Poufan companies, but there are no foreign investors or issuers. The current yield on pof bonds is 10%. Poufan investors have to pay a 15% tax on interest income received. The newly elected Poufan government wishes to internationalize its bond market and attract foreign issuers. To do so, it decides to remove any taxation of income on bonds issued by foreign corporations in Pouf. Several changes take place after the enactment of this tax provision: $\bullet$ Several well-known foreign corporations issue pof-denominated bonds in the Poufan bond market. $\bullet$ Several well-known Poufan corporations issue international bonds denominated in U.S. dollars. $\bullet$ Several dollar/pof swaps are arranged. Try to provide a sensible explanation for this phenomenon.

Titi, a Japanese company, issued a six-year international bond in dollars convertible into shares of the company. At time of issue, the long-term bond yield on straight dollar bonds was 10% for such an issuer. Instead, Titi issued bonds at 8%. Each $1,000 par bond is convertible into 100 shares of Titi. At time of issue, the stock price of Titi is 1,600 yen, and the exchange rate is 100 yen = 0.5 dollars ($/¥ = 0.005, ¥/$ = 200). a. Why can the bond be issued with a yield of only 8%, below the market rate for straight dollar bonds? b. What would happen if: $\bullet$ The stock price of Titi increases? $\bullet$ The yen appreciates? $\bullet$ The market interest rate of dollar bonds drops? A year later, the new market conditions are as follows: $\bullet$ The yield on straight dollar bonds of similar quality has risen from 10% to 11%. $\bullet$ Titi stock price has moved up to ¥ 2,000. $\bullet$ The exchange rate is $/¥ 0.006. c. What would be a minimum price for the Titi convertible bond? d. Could you try to assess the theoretical value of this convertible bond as a package of other securities, such as straight bonds issued by Titi, options or warrants on the yen value of Titi stock, and futures and options on the dollar/yen exchange rate?

Why are futures contracts commonly believed to be less subject to default risk than forward contracts?

The Kingdom of Papou issues a very-bull bond with a coupon equal to: 14.6 - 2 * LIBOR. Of course, the coupon cannot be negative. The Kingdom could have issued a FRN at LIBOR + ¼ %, or a straight bond at 5.30%. The current market conditions for swaps are 5% against LIBOR. You could also trade in caps and floors with different exercise prices (these are levels of interest rates). The premium are paid annually. Exercise Annual Premium Intarast Rate Cap Fladr 7.3\% 0.2\% 2\% 14.6\% 0.1\% 10\% a. You are a buyer of this very-bull bond. Tell us what it is equivalent to, in terms of buying/selling: FRN, straight bonds, caps or floors. b. Assume that the Kingdom actually wanted to issue a straight bond (fixed coupon). The bank will put in place a "de-mining" portfolio with swaps and options so that this very-bull bond plus the "de-mining" portfolio is equivalent to a straight bond. What is exactly the "de-mining" portfolio? (Be very precise and tell us if the Kingdom must pay fixed, receive LIBOR or vice versa, etc.) c. What is the cost advantage for the Kingdom compared to issuing bonds at 5.30%? d. Same question assuming that the Kingdom wanted to issue an FRN at LIBOR +¼%?