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Answer for assignment 2

1. Alice purchased a put option on British pounds for $.04 per unit. The strike price was $1.80, and the spot rate at the time the pound option was exercised was $1.70. Assume there are 31,250 units in a British pound option, what was Alice’s net profit on the option?

As a buyer of the put option, Alice could purchase one pound sterling from the spot market at $1.70, sell it at the price of $1.80.

After taking into account the premium of 0.04, the net profit from the put option is

(1.80 – 1.70 – 0.04)*31,250 = $1,875

2. Assume the following information:

Value of the Canadian dollar in U.S. dollars: $0.90

Value of New Zealand dollar in U.S. dollars: $0.30

Value of the Canadian dollar in New Zealand dollars NZ $2.80

Given this information, is triangular arbitrage possible? If so, explain the steps that would reflect triangular arbitrage, and compute the profit from this strategy if you had $1 million to use.

The hypothetical CAD-NZD cross rate is = $0.90/$0.30 = NZ$3 per CAD

Since the quoted price is below the hypothetical rate, arbitrage is possible by using the NZD to purchase CAD

Starting with $1 million USD,

1. Exchange USD 1,000,000 for 1,000,000 / 0.3 = NZD 3,333,333.33

2. Exchange NZD 3,333,333 for 3,333,333.33 / (2.80) = CAD 1,190,476.19

3. Exchange CAD 1,190,476.19 for 1,190,476.19* (0.9) = USD 1,071 428.57,

Making a riskless profit of $71,428.57

3. Assume the following information:

Spot rate of Brazilian real: $0.250

180-day forward rate of Brazilian real: $0.240

180-day Brazilian interest rate: 7%

180-day U.S. interest rate: 4%

Given this information, is covered interest arbitrage worthwhile for American investors to invest in the Brazilian deposit? Explain your answer.

To show that the covered interest arbitrage is worthwhile, observe that the forward discount of the Brazilian dollar (-0.01/0.25) = -0.04, is less than the US-Brazilian interest differential of 0.04 – 0.07 = -0.03, so a covered interest arbitrage on the Brazilian deposit is impossible

To show that it is not possible, suppose you have $1 million,

1. Today, convert USD 1 million to 1/0.25 = BRL 4 million

2. Today, sell 4 million * (1.07) = BRL 4.28million forward at the rate of $0.240 real

3. In 180 days, fulfill the contract by converting 4.28million real to 4.28(0.24) = 1.0272 million.

The same $1 million would have yield $1.04million. Therefore the covered interest arbitrage is not worth the investment.

4. You believe that the future value of the Thai Bhat will be determined by purchasing power parity (PPP). You expect that inflation in Thailand will be 9 percent next year, while inflation in the United States will be 3 percent next year. Today the spot rate of the Thai Baht is $.031. What is the expected spot rate of the Thai Baht in one year?

According to the PPP formula, (future spot – 0.31)/0.31 = (1.03)/(1.09) – 1 = -0.055046

Therefore future spot for Thai baht is 0.31*(1 – 0.055046) = 0.0292936

5. Assume that the three-year annualized interest rate in the United States is 5 percent and the three-year annualized interest rate in Brazil is 8 percent. Assume interest rate parity holds for a three-year horizon. Assume that the spot rate of the Brazilian real is $0.25. If the forward rate is used to forecast exchange rates, what will be the forecast of the Brazilian real’s spot rate in three years?

Three year annualized interest rate in the US, i_US = (1.05)³ – 1 = 0.157625

Three year annualized interest rate in Brazil, i_Brazil = (1.08) ³ – 1= 0.2597

The forward rate (F – S)/S = (1+ i_US) / (1 + i_Brazil) – 1 = -0.08104

At spot rate S = 0.25, the forward rate equals, F = 0.25(1 – 0.08104) = 0.022974

6. Assume that you obtain a quote for a one-year forward rate on the Argentine peso. Assume that Argentina’s one-year interest rate is 50 percent, while the U.S. one-year interest rate is 10 percent. Over the next year, the peso depreciates by 25 percent. Do you think the forward rate overestimated the spot rate one year ahead in this case? Explain.

The international Fischer effect suggests that the Argentine peso should depreciate by 1.1/1.5 – 1 = 0.267 or 26.7 percent. Since the peso depreciates by 25 percent, the forward rate underestimates the spot rate one year from today.

7. Assume the following information:

90-day U.S. interest rate: 3.4%

90-day Malaysian interest rate: 3.0%

90-day forward rate of Malaysian ringgit: $0.400

Spot rate of Malaysian ringgit: $0.394

Assume that the Delta Co. in the United States will need 300,000 ringgit in 90 days. It wishes to hedge this payables position. Would it be better off using a forward hedge or a money market hedge? Substantiate your answer with estimated costs for each type of hedge.

Using the forward hedge, Delta Co would need 300 000 (0.4) = $ 120,000

To hedge the payable position in ringgit one year from today, we follow these three steps

1. Amount of ringgit needed today cover 300,000 payable,

=MYR 300,000/1.03 = MYR 291 262.14

2. Amount of dollar needed today to convert into ringgit,

= USD 291 262.14(0.394) = USD 114 757.28

3. Amount of dollar needed 1 year from today to repay the dollar loan

= USD 114 757.28(1.034) = USD 118,659.03

In this case the money market hedge on payable is the cheaper option

8. As treasurer of Sigma Corp. (a U.S. exporter to Australia), you must decide how to hedge (if at all) future receivables of 250,000 Australian dollars 90 days from now. Put options are available for a premium of $.03 per unit and an exercise price of $.70 per Australian dollar. The forecasted spot rate of the A$ in 90 days follows:

With the probability of 30%, future spot rate is $0.74

With the probability of 50%, future spot rate is $0.69

With the probability of 20%, future spot rate is $0.65

Given that you hedge your position with options, calculate the expected return of U.S. dollars to be received in 90 days based on the forecasted spot rate of the A$.