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 $3 (note that this is in dollars, not Yuan!). Assume that you care about your profits in dollars and that thecurrentspot exchange rate is 6.7 Yuan/$. IfSis the CNY/$ exchange rate in November, then theYuanprice that maximizes your dollar profits is:

Price (Yuan)=(100+3*S)/2

What is the Yuan price that maximizes your profits if exchange rates stay constant?

What is the dollar price?

What is your profit per unit sold, in dollars?

What is your total profit, in dollars?

Plot your total profit in dollars as a function of the future exchange rate from 6-7.5 Yuan/$.

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 theprofitof the long side of each of these derivatives, in Yuan, if the eventual spot rate is CNY 6/$? CNY 6.5/$? CNY 7/$? CNY 7.5/$?

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.

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.