6-7
Interest Rate Parity Carefully Defined
No matter how you quote the exchange rate ($ per ¥ or ¥ per $) to find a forward rate, increase the dollars by the dollar rate and the foreign currency by the foreign currency rate:
£
S$/£
Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist). F$/£ (1 + i$) = (1 + i$) F$/£= S$/£× (1 + i£) × (1 + i£ ) S$/£


Xiaojing Chen
chenxj@ 67703822 D 429
6-2
Chapter Outline
Interest Rate Parity
– – – – Covered Interest Arbitrage IRP and Exchange Rate Determination Currency Carry Trade Reasons for Deviations from IRP
6-14
Arbitrage Strategy II
If F360($/£) < $2.01/£: 1. Borrow £500 at t = 0 at i£= 2.49%. 2. Exchange £500 for $1,000 at the prevailing spot rate; invest $1,000 at 3% for one year to achieve $1,030. 3. Translate $1,030 back into pounds; if F360($/£) < $2.01/£, then $1,030 will be more than enough to repay your debt of £512.45.
A trader with $1,000 could invest in the U.S. at 3.00%. In one year his investment will be worth: $1,030 = $1,000 (1+ i$) = $1,000 (1.03) Alternatively, this trader could:
6-5
Alternative 2: Send your $ on a round trip to Britain
$1,000 S$/£
IRP
Step 2:
Invest those pounds at i£ Future Value = $1,000
$1,000
Alternative 1: Invest $1,000 at i$ $1,000×(1 + i$) =
6-13
Step 2: Buy pounds £ = 500 $1,000×
$1,000 £ 1 $2.00
Arbitrage I
Step 3: Invest £ at 500 i£ = 2.49%. 500 £ 512.45 In one year £ will be worth £ 512.45 = £ (1+ i£) 500 Step 4: Repatriate to the U.S. £ 500
One Choice: Invest $1,000 at 3%. FV = $1,030
= $2.01/£
$1,030 F£(360) $1,030 = £ 512.45 × £ 1
6-11
IRP& Exchange Rate Determination
According to IRP only one 360-day forward rate F360($/£) can exist. It must be the case that
6-10
Other Choice:
Buy £ at $2/£ 500 . £ = 500 $1,000×
$1,000 £ 1
£ 500
Arbitrage I
Step 2: $2.00 Invest £ at 500 i£ = 2.49%. 500 £ 512.45 In one year £ will be worth Step 3: £ 512.45 = Repatriate to the £ (1+ i£) 500 U.S. at F360($/£ )
F360($/£) = $2.01/£
Why?
If F360($/£) $2.01/£, an astute trader could make money with one of the following strategies.
6-12
Arbitrage Strategy I
If F360($/£) > $2.01/£: 1. Borrow $1,000 at t = 0 at i$ = 3%. 2. Exchange $1,000 for £500 at the prevailing spot rate (note that £500 = $1,000 ÷ $2/£.); invest £500 at 2.49% (i£) for one year to achieve £512.45. 3. Translate £512.45 back into dollars; if F360($/£) > $2.01/£, then £512.45 will be more than enough to repay your debt of $1,030.
Step 1: Borrow $1,000. More F£(360) $1,030 < £ 512.45 × than $1,030 Step 5: Repay £ 1 your dollar loan with $1,030. If F£(360) > $2.01/£ £ , 512.45 will be more than enough to repay your dollar obligation of $1,030. The excess is your profit.
– – – – Efficient Market Approach Fundamental Approach Technical Approach Performance of the Forecasters
6-3
Interest Rate Parity Defined
IRP is a “no arbitrage” condition. If IRP did not hold, then it would be possible for an astute trader to make unlimited amounts of money by exploiting the arbitrage opportunity. Since we don’t typically observe persistent arbitrage conditions, we can safely assume that IRP holds.
6-6
IRPபைடு நூலகம்
S$/£
(1+ i£) × F$/£
Interest Rate Parity Defined
The scale of the project is unimportant. $1,000 (1+ i£) × F$/£ = $1,000×(1 + i$) S$/£ F$/£ × (1+ i£) (1 + i$) = S$/£ IRP is sometimes approximated as: i$ – i£ ≈ F – S S
International Parity Relationships and Forecasting Foreign Exchange Rates
Chapter Six
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
or F¥/$ = S¥/$ F$/¥= S$/¥ × × …be careful—it’s easy to get this wrong.
6-8
1 + i¥ 1 + i$
1 + i$ 1 + i¥
IRP and Covered Interest Arbitrage
If IRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example. Consider the following set of foreign and domestic interest rates and spot and forward exchange rates.
Spot exchange rate 360-day forward rate U.S. discount rate British discount rate S($/£ = $2.0000/£ ) F360($/£ = $2.0100/£ ) i$ = 3.00% i£ = 2.49%
6-9
IRP and Covered Interest Arbitrage