Assignment:
Question 1
The current Nov. '17 forward rate for the Chinese Yuan (CNY) against the U.S. Dollar ($) is CNY 6.7/$. Your firm has a large expense in China coming up (CNY 3 million) and you want to lock in your dollar cost.
a. What is the current dollar cost of the expense?
b. What kind of future do you want to take out (CNY to $ or $ to CNY)?
c. Suppose that this transaction is denominated in Yuan, and the future is not deliverable. That is, the future is cash-settled. What is the notional value of the future you would ideally like? For future questions, assume that you can have this exact amount.
d. If the true exchange rate at maturity is CNY 7.14/$, what will be the profit or loss in yuan?
e. What will be the profit or loss in dollars?
f. What is the total number of dollars you owe when combining your expense and the profit/loss from the future?
g. Make two payoff graphs. The first is the payoff of this future denominated in yuan. The second is the payoff of this future denominated in dollars. The y-axis of these graphs should be the payoff and the x-axis should be the eventual spot rate. Plot values at least from an eventual spot rate of CNY5/$ to CNY8/$. (Note: This will require doing steps (e) and (f) above for many values between 5 and 8).
h. You should notice that one of these graphs is not linear. Which one is it and why is this true? How can you transform the graph so that it becomes linear?
Question 2
Suppose that you are a clothing brand interested in selling t-shirts in China. It will take you a month to get operations going. You face a demand curve of: D = 10,000 - 100P, where P is the price you charge in Yuan. The marginal cost of production is $3 (note that this is in dollars, not Yuan!). Assume that you care about your profits in dollars and that the current spot exchange rate is 6.7 Yuan/$. If S is the CNY/$ exchange rate in November, then theYuan price that maximizes your dollar profits is:
Price (Yuan) = 100 + 3 * S / 2
a. What is the Yuan price that maximizes your profits if exchange rates stay constant?
b. What is the dollar price?
c. What is your profit per unit sold, in dollars?
d. What is your total profit, in dollars?
e. Plot your total profit in dollars as a function of thefuture exchange rate from 6-7.5 Yuan/$.
f. Suppose that you have access to the following derivatives, all denominated in Yuan with a maturity of Nov' 17:
i. A future with a contract price of CNY 6.7 / $.
ii. A put with a strike of CNY 7 / $ for a price of 0.37 Yuan per dollar of exposure.
iii. A put with a strike of CNY 6.5 / $ for a price of 0.10 Yuan per dollar of exposure.
What is the profit of the long side of each of these derivatives, in Yuan, if the eventual spot rate is CNY 6/$? CNY 6.5/$? CNY 7/$? CNY 7.5/$?
g. For each derivative and spot rate listed in (f), list the profits in dollars. Remember that you pay for the option now, but receive any value from them at the time of maturity, and the exchange rate at these two times may not be the same.
h. You ask your analysts to come up with a portfolio of derivatives to hedge your risk. They come back with the following suggestions:
i. 4,540 long forwards, 4,750 short puts with a strike of CNY 7/$, and 4,750 short puts with a strike of CNY 6.5/$.
ii. 5,400 long forwards
iii. 5,650 long forwards, 1,500 long puts with a strike of CNY 7/$, and 250 long puts with a strike of CNY 6.5/$
Which of these portfolios of derivatives will best hedge your exposure? Answers without work will receive no credit. For each of the eventual spot rates listed in (f) and (g), calculate the combined profits/losses of each of the derivative portfolios and your t-shirt sale profits. You may use any metric you like to determine which has the least exchange rate exposure.