Question

Module 9 – Foreign Exchange Rate Risk Homework Exercise Part 1 1.

Suppose that the EUR:USD is trading at 1.3342; the GBP:JPY is trading at 67.7600; and the EUR:GBP is trading at 0.8165. What should the USD:JPY rate be?

2. If a price index for US goods stands at 118.93 and the same price index for European goods (i.e., computed from the same consumption basket) stands at 183.34; what is the fair (under the theory of PPP) spot exchange rate EUR:USD.

3. Suppose that the EUR:USD spot exchange rate is $1.4825. The one year interest rate in the US is 0.50% and the one year interest rate in the Euro Zone is 3.25%. Calculate the one-year forward EUR:USD exchange rate. Assume that interest rate parity holds and that the interest rates quoted are simple rates with annual compounding.

4. The spot GBP:USD rate is being quoted by a dealer bank at 92/97. The figure is 1.70. What is the dealer's bid and what is the dealer's offer?

5. A dealer is quoting the 90 day forward rate for GBP:USD at 45/37. Based on the spot rates in D above, what is the dealer's "outright quote" for 90 day cable in terms of dollars.

Part 2

1. The related spreadsheet contains data for the end-of-day value of the EUR:USD spot exchange rate. Day -101 is 101 days ago and day 0 is today. Thus, this is historic price data. From this historic price data, calculate the historic annual "vol" for this exchange rate.

2. On day 0, your analysis of the Fed's Quantitative Easing strategy leads you to conclude that the euro is about to rise dramatically. So you take $1 million of your wealth, convert it to euros at the Day 0 exchange rate, and invest it in German T-bills paying 2 percent annually. You have decided you will liquidate your position in one year. Calculate your 95% one-year VaR based on historic volatility. [Note 1: Treat the 2% yield on German T-bills as a simple interest rate with annual compounding. Note 2: The spot exchange rate today is the rate associated with Day 0, i.e., 1.3556. The one-year forward rate is currently quoted at 1.3690.]

3. Now suppose that there is a one-year EUR:USD option trading on the U.S. option markets. The price of this option implies a EUR:USD volatility of 18.70%. Based on this alternative measure of volatility, what is the 95% one-year VaR on your speculative position?

4. Briefly describe the difference between an "historic volatility" derived from price data (exchange rate changes in this case) and an "implied volatility" extracted from an option premium. Which do you think is likely to be the better indicator of future volatility?

Part 3

The AIM Holding Company, Inc. is an American based holding company that has subsidiaries selling various types of insurance in the United States and in a number of foreign countries. AIM-Europa is the holding company's European subsidiary.

AIM-Europa sells lifetime annuity policies across the Euro Zone (the countries that use the euro as their currency). To be clear, a policy pays a fixed number of euros each month for the life of the policyholder and ceases immediately upon the policyholder's death. The proceeds from the sale of these annuities are transferred to the U.S. where the money is invested in U.S. corporate bonds. In all cases, the monthly payouts to the policyholders were calculated to return 3% per annum based on the policyholder's life expectancy. While the actual life-spans of the individual annuity holders are uncertain, AIM-Europa relies on actuarial studies to estimate life expectancies and payouts.

At present, if AIM-Europa does not sell any more policies, its current situation is as follows: It is obligated to pay out €22,500,000 monthly for the next 20 years. As already noted, this payout represents a return to the policy holders of 3% per annum. The U.S. bond portfolio that supports the annuity policies has been structured to generate $47,431,600 per month, which represents a 4% annual return, for the next 20 years. Both the 3% return to the annuity holders and the 4% return to the company assume monthly compounding. Note that the EUR:USD spot exchange rate is currently $1.3980.

1. What risks do you see AIM-Europa exposed to that could make it difficult for it to meet its obligations to the annuity holders down the road? Identify at least three such risks and describe them briefly. No math is necessary.

2. Challenge Question (optional – extra credit) Suppose that there is a currency swap dealer that is prepared to write a fixed-forfixed currency swap such that the swap dealer is prepared to pay AIM-Europa a fixed rate of 3% in euros in monthly installments in exchange for AIM-Europa paying the dealer a fixed rate of 3.45% in dollars, again in monthly installments. (a) Graphically structure all the cash flows so that you illustrate (1) the relationship between AIM-Euopa and it annuity holders; (2) AIM-Euopa and the U.S. bond portfolio; and (3) AIM-Europa and the swap dealer. Determine the notional principal on the dollar leg and the notional principal on the euro leg such that the euro exposure is completely neutralized. Calculate the amount of notional principal in euros, so that the euro risk is gone, and the amount of dollar notionals so that the notionals employed are fair. (b) Assuming that all other costs incurred by the business (other than the annuity payouts) amount to $3 million per month, is the business profitable? (c) Which of the risks that you identified in Part A does this structure address (i.e., manage)? (d) What possible ancillary business advantages do you see from hedging the exchange rate risk?

Answer 1

(1)

EUR:USD means "1 EUR = how many USD"

Therefore, from given data,

$/€ = 1.3342

¥/£ = 67.7600

£/€ = 0.8165

Therefore, ¥/$ = ¥/£ × £/€ × €/$ = 67.7600 × 0.8165 × (1/1.3342) = 41.4676

Therefore, USD:JPY = 41.4676

(2)

Fair EUR:USD (under PPP) = European Price Index/US price index = 183.34/118.93 = 1.5416

(3)

1 year forward EUR:USD = Spot EUR:USD × (1+Interest rate in US)/(1+Interest rate in Euro Zone)

= 1.4825 × (1+0.005)/(1+0.0325) = 1.4430

(4)

GBP:USD rate is quoted 92/97 and the figure is 1.70

Therefore, the quote is 1.7092/1.7097

Bid price is the price at which dealer is willing to buy and offer price is the price at which dealer is willing to sell. Dealer will always be willing to by at a lower price and sell at a higher price, so that he makes profit.

In this case,

Bid Price is 1.7092 & Offer Price is 1.7097

Note: We are supposed to answer not more than 4 sub questions in one question. Please don't rate the answer negatively for that reason.