Question

4. Ms. Sternin is a U.S. arbitrageur. The one-year interest rate offered in the U.S. is 1.0%, while the one-year interest rate offered in Australia is 3.25%. The spot rate is .96 AUD/USD. Kramerika Bank offers Ms. Sternin a one-year forward contract at 1.05 AUD/USD.

(1) Determine the arbitrage-free one-year forward contract exchange rate.

(2) Can Ms. Sternin make a risk-free profit? If yes, describe a covered arbitrage strategy.

(3) Determine Ms. Sternin's profits.

(4) Calculate the forward premium and compare it to the interest rate differential. Based on these numbers, what kind of capital flows will the U.S. economy experience?

3. The U.S. and Mexico both produce orange juice. A gallon of orange juice sells in the U.S. for USD 5.75. An equivalent gallon of juice sells in Mexico for MXN 70. The spot rate is .09 USD/MXN.
(a) According to purchasing power parity (PPP), what should be the USD/MXN exchange rate?
(b) Take the U.S. as the domestic country. Calculate the real exchange rate, Rt. Which country is more efficient?

(c) The Mexican GDP per capita is MXN 95,000. Translate this amount to (nominal) USD and to PPP USD prices. (d) Suppose the price of a gallon of juice in Mexico decreases to MXN 63 over the next year, while the price of an equivalent U.S. gallon of orange juice increases to USD 6.05. According to the linearized version of relative PPP, what should be the USD/MXN exchange rate one-year from now?
(e) Next year, the exchange rate is 12.8 MXN/USD. Generate a trading signal based on PPP.

1. Assume a USD is worth JPY 81.26, (St=81.26 JPY/USD). Also, a JPY is worth CAD .0124 (St=.0124 CAD/JPY).

i. What is the cross rate CAD/USD?
ii. Suppose Kwiki Bank quotes St=.93 USD/CAD. Is arbitrage possible? (Why?)
iii. If yes, describe a triangular arbitrage strategy and determine an arbitrageur’s profits.

2. It is October 2012. Iris Oil Inc., a Houston-based energy company, has a CAD 300 million receivable due in June 2013. Iris Oil decides to use options to reduce FX risk. Available options with June maturity are:

X calls puts
.94 USD/CAD 2.49 0.29

.98 USD/CAD 1.68 1.77
1.00 USD/CAD 0.17 4.83

where X represents the strike price and premiums are expressed in USD cents –i.e., 1.77 equals to USD 0.0177. Today, the exchange rate is .98 USD/CAD.
A. Calculate the premium cost and use a graph to describe the net cash flows (in USD) in June for Iris Oil under the following choices:
i) in-the-money option
ii) out-of-the money option
B. Suppose Iris Oil can sell CAD forward at Ft,June = .99 USD/CAD. Calculate the cash flows (in USD) in June for Iris Oil under the forward contract. What are the pros and cons of the forward contract relative to the option alternative?

Answer 1

(1)

(a) Current Spot Rate = 0.96 AUD/USD

Australian Interest Rate = 3.25 % and US Interest Rate = 1 %

Arbitrage Free Exchange Rate = 0.96 x [1+Australian Interest Rate / 1+US Interest Rate] = 0.96 x [1.0325 / 1.01] = 0.982 AUD/USD

(b) Forward Rate being offered = 1.05 AUD/USD

As the forward rate and arbirtage free rates do not match, there is indeed a chance for an arbitrage. The same will be executed as described below:

- Borrow 0.96 AUD to purchase 1 USD and sell a forward contract on USD

- The AUD borrowings would lead to a liability of (0.96 x 1.0325) = 0.9912 AUD one year later.

- The 1 USD can be invested at the US Interest Rate of 1 % to yield 1 x 1.01 = 1.01 USD one year later.

- The USD investment proceeds of 1.01 USD can be sold under the forward contract to yield = 1.05 x 1.01 = 1.0605 AUD

- Profit = Investment Yield in AUD - Borrowing Liability in AUD = 1.0605 - 0.9912 = 0.0693 AUD

(c) Arbitrage Profit = Investment Yield in AUD - Borrowing Liability in AUD = 1.0605 - 0.9912 = 0.0693 AUD

(d) Forward Rate = 1.05 AUD/USD and Spot Rate = 0.96 AUD/USD

Forward Premium = (Forward Rate - Spot Rate) / Spot Rate = (1.05 - 0.96) / 0.96 = 0.09375 or 9.375 %

Interest Rate Differential = 3.25 - 1 = 2.25 %

As the Australian Interest Rate is higher than the US Interest Rate, the AUD would lose value(depreciate) with respect to the USD. Hence, as is observable 1 USD could buy 0.96 AUD initially but the same amount of USD could purchase 1.05 AUD later. A higher interest rate in Australia however would lead to a flow of investors towards AUD denominated assets (as they offer 3.25 % interest compared to the US Rate of 1 %). This higher demand of AUD denominated assets would propr up demand for AUD as well, thereby rebalancing the depreciating AUD (with respect to USD). Hence, the capital flow for Australia would be inwards.

NOTE: Please raise separate queries for solutions to the remaining unrelated questions.