Week Two Problem Set

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Week Two Problem Set Problem 1 Answer A decline of the dollar could affect FI. €10,000,000 is equivalent to €10,000,000*$1.50/€ = $15,000,000 based on the current spot exchange rate. Let's take an example where the dollar depreciates to $1.55/€ in six months. In that case, the same €10,000,000 will be worth $15,500,000, meaning that FI will have lost $5,000,000. When the value of the dollar declines, one euro will be worth more, and when it appreciates, the opposite is true. The amount of money required is €10,000,000*$1.60/€ = $16,000,000 if the loan is canceled and the FI is not hedged, assuming the spot rate in six months is $1.6/€. If the FI chooses to use € futures for hedging, it should purchase € futures in order to lock in the exchange rate immediately and get euros after six months. After six months, if the FI had hedged, the net amount required to fund the loan would have been €10,000,000*$1.53/€ - $15,000,000 = $15,300,000 - $15,000,000 = $300,000. At the current spot currency rate of $1.50/€, $15,000,000 is worth. Thus, only $300,000 more funding is required by hedging. Problem 2 Answer  The manager should be worried about the dollar appreciating, as this would result in a higher cost for the payment in euros. By hedging with either options or futures, the manager can protect against this potential depreciation and ensure that the payment can be made at the expected exchange rate of $1.60/€.  In this situation, Union Corp should buy Puts to hedge the payment. This is because the Put option gives the buyer the right to sell euros at a predetermined exchange rate (in this case, $1.60/€) on or before the expiration date. This means that if the euro depreciates against the

dollar and the spot rate falls below $1.60/€, Union Corp can exercise the Put and sell euros at the predetermined higher exchange rate, minimizing their losses on the payment. On the other hand, if Union Corp buys Calls, they would have the right to buy euros at the predetermined exchange rate if the spot rate rises above $1.60/€. In this scenario, if the euro appreciates and the spot rate rises above $1.60/€, Union Corp would still have to pay the higher spot rate to acquire the euros, resulting in a higher cost for the payment. Therefore, buying Puts would be a more suitable option for hedging against potential appreciation of the dollar.  If futures are used to hedge, the company should sell € futures. This means that the company would enter into a contract to sell euros at a predetermined exchange rate on the maturity date. Similar to buying Puts, this will allow the company to lock in a specific exchange rate and protect against potential appreciation of the dollar. If the euro depreciates against the dollar, the company can still sell euros at the higher predetermined exchange rate, minimizing their losses on the payment. However, if the euro appreciates and the spot rate rises above the predetermined rate, the company would have to sell euros at a lower rate, resulting in a loss on the futures contract but offset by a lower cost for the payment. Therefore, selling € futures would be a suitable way for the company to hedge against potential appreciation of the dollar while also allowing for potential cost savings if the euro depreciates.  The net payment on the payable will vary depending on the spot price in six months. Assuming a Put option was used to hedge the payment, the net payment would be: - If the spot price in six months is $1.50/€: the Put option would be exercised and the net payment would be €5 million at the predetermined exchange rate of $1.60/€, resulting in a payment of $8 million.

- If the spot price in six months is $1.60/€: the Put option would expire worthless, but the company would still make the payment at the predetermined spot rate of $1.60/€, resulting in a net payment of $8 million. - If the spot price in six months is $1.70/€: the Put option would expire worthless and the company would have to make the payment at the spot rate of $1.70/€, resulting in a net payment of $8.5 million. Therefore, using an option contract to hedge the payment would result in a net payment of $8 million in two out of the three scenarios, providing a level of certainty and protection against potential appreciation of the dollar.  Assuming a futures contract was used to hedge the payment, the net payment would be: - If the spot price in six months is $1.50/€: the futures contract would be settled at the predetermined exchange rate of $1.60/€, resulting in a net payment of $8 million. - If the spot price in six months is $1.60/€: the futures contract would be settled at the predetermined exchange rate of $1.60/€, resulting in a net payment of $8 million. - If the spot price in six months is $1.70/€: the futures contract would be settled at the spot rate of $1.70/€, resulting in a net payment of $8.5 million.  The method of hedging that is preferable will depend on the specific risk management goals and preferences of Union Corp. Both options and futures can be effective tools for hedging against potential appreciation of the dollar and minimizing losses on the payment, but they also have different characteristics and potential costs. Options give the buyer the right (but not the obligation) to buy or sell a specific amount of currency at a predetermined exchange rate, while futures contracts involve a binding agreement to buy or sell a specific amount of currency at a specific price on a predetermined date. This means that options provide more flexibility and allow the buyer to choose whether or not to exercise the option, while futures contracts are more binding and have less flexibility. In terms of cost, options typically have a higher upfront premium cost, while futures contracts may involve margin calls and potential losses if the price moves against the company's position.

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Therefore, the preferable method of hedging will depend on the company's risk management strategy and goals. Problem 3 Answer  In this scenario, an arbitrageur would take advantage of the discrepancy between the exchange rates and the option pricing to make a risk-free profit. First, the arbitrageur would borrow $1,000,000 from the US at a 6% interest rate and convert it into Swiss Francs at the exchange rate of $.51/SF, resulting in 1,960,784 SF. This amount would then be invested in a risk-free Swiss bond at a 4% interest rate for three months, earning a total of 19,608 SF in interest. Next, the arbitrageur would purchase the SF Call option with an exercise price of $.50/SF for a cost of $19,608 (1,960,784 SF x $.01/SF). This option gives the arbitrageur the right to buy SF at the exercise price of $.50/SF, regardless of the market price, within the three-month expiration period. Now, the arbitrageur has two options: If the market price of SF at the expiration date is higher than $.50/SF, the option will be exercised, and the arbitrageur will buy SF at the exercise price of $.50/SF. The arbitrageur can then convert the SF back into US dollars at the current exchange rate of $.51/SF, resulting in a profit of $9,804 (1,960,784 SF x ($.51/SF - $.50/SF)). This is because the US risk-free investment has earned $19,608 in interest, covering the cost of the option, and the remaining $9,804 is the arbitrageur's profit. If the market price of SF at the expiration date is lower than $.50/SF, the option will not be exercised, and the arbitrageur will not exercise the option. The arbitrageur can then convert the SF back into US dollars at the current exchange rate of $.51/SF, resulting in a profit of $19,608 from the interest earned on the Swiss bond. By engaging in this type of arbitrage, the arbitrageur can make a risk-free profit regardless of the market movement. This is because the interest earned on the Swiss bond will cover the cost of

the option and provide a profit, while the option provides a hedge against any potential loss from the exchange rate.  An arbitrageur would purchase the SF Put option at $.01/SF. They would also borrow $1 at the US risk-free rate of 6%, which would cost them $1.015 after three months (1+0.06)^0.25. Then, they would exchange the borrowed $1 for SF at the current exchange rate of $.48/SF, resulting in 2.1 SF. The arbitrageur would exercise the put option, which would allow them to sell the 2.1 SF for $.50/SF, resulting in $1.05. The arbitrageur would then use the $1.05 to repay the borrowed $1, and they would be left with a profit of $.05 without taking on any risk. This is because the profit from exercising the put option ($1.05) is greater than the cost of borrowing $1 ($1.015). The arbitrageur would repeat this process many times until the market price of the put option reaches its fair value of $.021/SF.  In this scenario, an arbitrageur would take advantage of the price discrepancy between the SF Put option and Call option. They would first calculate the cost of purchasing one SF Call option, which is $.04 x 100,000 = $4,000. Then, they would calculate the cost of short selling one SF Put option, which is $.0075 x 100,000 = $750. Next, the arbitrageur would borrow $100,000 at the Swiss risk-free rate of 4% per year for three months, which would result in a total interest expense of $1,000. They would convert the borrowed Swiss francs into US dollars at the current exchange rate of $.52/SF, resulting in a total of $52,000. The arbitrageur would then use the $52,000 to purchase 130 SF Call options ($52,000 / $.40). They would also simultaneously short sell 130 SF Put options, generating $97,500 ($750 x 130) in cash. After three months, the SF Call options would expire and if the exchange rate is above $.50/SF, the options would be exercised and the arbitrageur would receive $100,000 (130 x $.50 x 100,000). They would use this amount to repay their loan of $100,000 plus the interest expense of $1,000, resulting in a profit of $98,000 ($100,000 - $1,000 - $1,000). If the exchange rate is below $.50/SF, the options would not be exercised and the arbitrageur would keep the premium of $4,000 from the SF Call options and repay their loan of $100,000 plus the interest expense of $1,000, resulting in a loss of $97,000 ($100,000 - $1,000 - $4,000).

Problem 4 Answer The spread between the interest rates offered to A and B is 0.4% (or 40 basis points) on sterling loans and 0.8% (or 80 basis points) on U.S. dollar loans. The total benefit to all parties from the swap is therefore 80 -40= 40 basis points It is therefore possible to design a swap which will earn 10 basis points for the bank while making each of A and B 15 basis points better off than they would be by going directly to financial markets. One possible swap is shown in Figure S7.5. Company A borrows at an effective rate of 6.85% per annum in U.S. dollars. Business B borrows money in sterling at an effective annual rate of 10.45%. Ten basis points are earned by the bank. Currency swaps like this one function in the following ways. The principal quantities are selected to be approximately equal in both dollars and sterling. When the swap is started, these principal amounts flow in the opposite direction of the arrows. The principal amounts flow in the same way as the arrows at the conclusion of the swap's life, and interest payments follow suit during the duration of the swap. Keep in mind that the swap exposes the bank to some exchange rate risk. It pays out 55 basis points in pounds and earns 65 basis points in US dollars. Forward contracts could be used to hedge this currency rate risk.

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Problem 5 Answer For fixed rate investments, the difference between the interest rates offered to X and Y is 0.8% annually, while for floating rate assets, it is 0.0% annually. This indicates that the swap's apparent annual gain to all parties is 0.8 percent. Of this, the bank will receive 0.2% annually. That leaves X and Y with 0.3% annually apiece. Put differently, firm X should be eligible for an annual fixed-rate return of 8.3%, whereas company Y should receive a floating-rate return equal to LIBOR + 0.3%. The necessary swap is displayed in Figure S7.3. firm X earns 8.3%, firm Y earns LIBOR + 0.3%, and the bank earns 0.2%.

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