Bob Bowman, CFA, is an analyst who has been recently assigned to the currency trading desk at Ridgeway Securities, a hedge fund management firm based in New York. Ridgeway’s stellar reputation as a top tier hedge fund manager has been built upon many years of its portfolio outperforming both the market and its peer group. Ridgeway’s portfolio is globally diversified, with less than 35% of its assets currently invested in U.S. securities. Ridgeway seeks to enhance its portfolio returns through the active use of currency futures that correspond to its investments. From time to time, Ridgeway will also take advantage of arbitrage opportunities that arise in the currency markets. In his new position, Bowman will be reporting to the head currency trader, Jane Anthony. Among Bowman’s new responsibilities, he will be performing an ongoing analysis of global currency rates. His analysis is expected to include projections of future exchange rates and a sensitivity analysis of exchange rates in a variety of interest rate scenarios. Using his projections as a starting point, he will then be expected to suggest possible trading strategies for Ridgeway. Bowman knows that his analysis will begin with the underlying principles of the five basic international parity relationships. However, he does realize that certain principles will be more useful than others when applied to a “real-world” situation. To test his knowledge of the subject, Anthony has asked Bowman to prepare a presentation on the interrelationships between exchange rates, interest rates, and inflation rates. For the presentation, Bowman will need to prepare a brief analysis of current market conditions and formulate some basic trading strategies based upon his projections. He also will need to demonstrate his ability to calculate predicted spot rates for currencies, given some basic inflation rate and interest rate assumptions.
Bowman begins his task by gathering the following current market statistics:
1 year U.S. Interest Rates = 8%
1 year U.K. Interest Rates = 10%
1 year $/? forward rate = 1.70
Current $/? spot rate = 1.85
Bowman knows that if the forward rate is lower than what interest rate parity indicates, the appropriate strategy would be to borrow:
|
A) |
pounds, convert to dollars at the forward rate, and lend the dollars. | |
|
B) |
pounds, convert to dollars at the spot rate, and lend the dollars. | |
|
C) |
dollars, convert to pounds at the spot rate, and lend the pounds. | |
If the forward rate is lower than what the interest rate parity indicates, the appropriate strategy would be: borrow pounds, convert to dollars at the spot rate, and lend dollars. (Study Session 4, LOS 18.h)
Bowman also knows that if the forward rate is higher than what interest rate parity indicates, the appropriate strategy would be to borrow:
|
A) |
dollars, convert to pounds at the forward rate, and lend the pounds. | |
|
B) |
dollars, convert to pounds at the spot rate, and lend the pounds. | |
|
C) |
pounds, convert to dollars at the spot rate, and lend the dollars. | |
If the forward rate is higher than what interest rate parity indicates, the appropriate strategy would be: borrow dollars, convert to pounds at the spot rate, and lend the pounds. (Study Session 4, LOS 18.h)
Based on the information above, Bowman would like to calculate the forward rate implied by interest rate parity. The answer is:
Given the above relationship, interest rate parity does not hold.
(If interest parity held, 1.70 = 1.85 × (1.08 / 1.10), but 1.85 × (1.08 / 1.10) = 1.82).
Therefore, an arbitrage opportunity exists.
To determine whether to borrow dollars or pounds, express the foreign rate in hedged US$ terms (by manipulating the equation for IRP). We get:
(1.70 / 1.85) × 1.10 = 1.0108, which is less than 1.08 (U.S. rate), so we should start by borrowing British pounds and lending U.S. dollars.
Arbitrage Example:
- Today:
- borrow 5,000 GBP @ 10%
- buy $9,250 with the proceeds of the loan (5,000 GBP × 1.85).
- lend $9,250 @ 8%
- buy 5,500 GBP one year in the future @ 1.70 $/￡. This guarantees your loan repayment of 5,000 GBP × 1.1 = 5,500 GBP.
- One year later, close out your position:
- collect the proceeds of your loan: $9,990 = $9,250 × 1.08
- buy 5,500 GBP with your forward contract → cost = 5,500 GBP × 1.70 = $9,350
- pay off your loan of 5,500 GBP
- reap your profits: $9,990 ? $9,350 = $640
- Alternately, you could say that the arbitrage profit is 376.47 GBP. Bob Bowman is a US investor so we left his profits in USD. 640 USD = 1.70 × 376.47 GBP.
(Study Session 4, LOS 18.h)
A junior colleague asks Bowman for the mathematical equation that describes interest rate parity. Which of the following equations most accurately describes interest rate parity? (S0 is the spot exchange rate expressed in dollars per unit of foreign currency, F0,T is the forward exchange rate, and rUS and rFX are the risk-free rates in the U.S. and foreign country.)
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A) |
F0,t = S0 [(1+rUS) / (1+rFX)]. | |
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B) |
S1 = F0,t [(1+rUS) / (1+rFX)]. | |
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C) |
F0,t = S0 [(1+rFX) / (1+rUS)]. | |
Interest Rate Parity
Interest rates between countries and their exchange rates (spot and futures) must be in equilibrium at all times or else there will be arbitrage opportunities. Interest rate parity says that:
F0,t = S0 [(1+rUS) / (1+rFX)]
Where:
| S0 |
= |
the current exchange rate in the spot market |
| F0,t |
= |
the current exchange rate in the forward of futures market |
| rUS |
= |
the risk-free interest rate in the U.S. |
| rFX |
= |
the risk-free interest rate in the foreign market |
Note: the above currency quotes are expressed in $/FX. (Study Session 4, LOS 18.h)
Now, suppose Bowman has the following information available to him: the current spot exchange rate for Indian Rupees is $0.02046. Inflation over the next 5 years is expected to be 3% in the U.S. and 5% in India. Bowman must calculate the U.S. Dollar/Indian Rupee expected future spot exchange rate in 5 years implied by purchasing power parity (PPP). The answer is:
The PPP assumption is that the future spot exchange rate will change exactly as the inflation rates affect the values of each currency. For the computation, raise the U.S. inflation rate to the 5th power (because of 5 years) and divide it by the Indian inflation rate raised to the 5th power. Then multiply the result by the spot exchange rate. ((1.03)5 / (1.05)5) × 0.02046 = $0.01858. (Study Session 4, LOS 19.h)
Bowman routinely calculates the expected spot rate for the Japanese Yen per U.S. dollar. He knows that the current spot exchange rate is 189.76 Yen/USD. He is also aware that the interest rates in Japan, Great Britain, and the U.S. are 8%, 4%, and 5% respectively. Calculate the expected spot rate for Yen/USD in a one year period.
The exact methodology of the covered interest rate parity (IRP) is:
expected spot rate in one period (FC/DC) = spot rate today (FC/DC) × [(1 + RFC) / (1 + RDC)].
Setting up this equation gives us E(S1) = 189.76 Yen/USD × (1.08 / 1.05) = 195.18 Yen/USD. (Study Session 4, LOS 18.h)
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发表于 2011-3-6 12:11
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