Interest Rate Parity (IRP)

Interest Rate Parity (IRP)

• Interest rates differ across countries.
• Investors should be aware of foreign exchange risk.
• Foreign exchange risk can offset potential advantages from interest rate differentials.
• IRP explains how differences in interest rates between countries are offset by forward exchange rates.
• Understanding IRP requires knowing interest rate arbitrage.

Arbitrage

• Arbitrage involves buying and selling to create zero net investment and earn a return.
• Electronic money transfers have easily determined prices, i.e. the interest rate.
• IRP suggests exchange rates adjust to eliminate incentives for funds to flow between countries for better returns.
• Interest rate arbitrage maintains the IRP relationship.

Recent Annual Interest Rates

• Eurodollars: 3.70%
• UK: 9.56%
• Canada: 6.76%
• Germany: 9.42%
• Switzerland: 7.67%
• Netherlands: 9.25%
• France: 10.14%
• Italy: 13.91%
• Belgium: 9.11%
• Japan: 4.39%

IRP Example

• Borrowing Eurodollars at 3.70% and investing in Italian lira at 13.91% may appear to generate arbitrage profit.
• Initial spot rate (Lira/$): 1,700
• One-year forward rate ($/Lira): 0.000535509
• The covered (hedged) interest rate formula factors in forward and spot rates.
• Direct quote is 1/1700 = 0.000588235
• The covered (hedged) interest rate is 3.697% or 3.70%.
• The inter-currency interest differential is zero because the lira forward rate equals the IRP forward rate which means there is no profitable arbitrage.

Key Messages of IRP

• Spot and forward rates link via arbitrage to interest rates in different currencies.
• The interest rate differential between domestic and foreign currencies determines the forward premium or discount.
• Lower interest rate currencies should have a forward premium relative to higher interest rate currencies.
• Interest rate differentials should equal the forward premium or discount in efficient markets with no transaction costs.
• Risk-free return on a covered (hedged) foreign investment equals the domestic risk-free interest rate, eliminating profitable arbitrage.

Example 1 (Using IRP)

• One-year UK interest rate: 10%
• UK pound (sterling) spot rate: $1.75/£
• One-year US interest rate: 6%
• The forward exchange rate formula is: F($/£) = S0($/£) * [(1 + i$) / (1 + i£)]
• The forward rate should be lower than the spot rate.
• Calculation: F($/£) = 1.75 * [(1 + 0.06) / (1 + 0.10)] - 1 = 1.6864
• Investing in £'s earns 4% higher interest, so the forward exchange rate should be about 4% lower in dollar terms.
• The IRP-based F($/£) = 1.6864, which is approximately 4% lower than the spot rate of $1.75/£.

Example 2 (No arbitrage opportunity if IRP holds)

• Investor 1 invests $10,000 domestically.
• Investor 2 invests $10,000 in the UK and uses a forward contract to eliminate foreign exchange risk.
• At F($/£) = 1.6864, Investor 2 will earn a 6% dollar interest rate.
• This equals the 6% earned by Investor 1 domestically.
• Covered interest rate formula: (1 + i£) * [F/S] - 1 Covered interest rate: (1 + 0.10) * (1.6864 / 1.75) - 1 = 6%
• No arbitrage opportunities exist when F($/£) equals the IRP forward rate meaning The IRP holds.

Example 3 (Profitable arbitrage opportunity when IRP does not hold)

• Forward exchange rate is $1.70/£ instead of $1.6864.
• $1 million can be borrowed at quoted interest rates.
• $1.70/£ exceeds the IRP-based forward rate of $1.6864/£.
• The covered interest rate with the higher $1.70/£ forward rate is: (1 + 0.10)*(1.70/1.75) - 1 = 6.857%.
• 6.857% exceeds the domestic 6% $-interest rate.
• The difference of 6.857% - 6% = 0.857% creates a profitable arbitrage opportunity.
• Borrowing $1 million at 6% and investing it at 6.857% covered interest rate generates arbitrage profit.
• Arbitrage profit example: $1,000,000 * 0.857% = $85.

Example 4

• US interest rate: 8%
• Japan interest rate: 2%
• Spot rate for the yen: $0.007692
• Need to determine the 90-day forward rate on the Japanese yen, assuming interest rate parity holds.
• The interest rates are annual.
• The 90-day i$ = 8%/4 = 2% and 90-day i_yen = 2%/4 = 0.5%.
• F($/yen) = 0.007692 * [(1 + 0.02) / (1 + 0.005)] = $0.00781 or 0.781%.

Example 5

• Three-month interest rates in Japan: 7%
• Three-month interest rates in the United States: 9%
• Spot rate: ¥142:$1
• 90-day forward rate: ¥139:$1

Alternative 1

• Borrow dollars at a 90-day interest rate of 9%/4 = 2.25%.
• Buy yen with the borrowed dollars at S($/yen) = $1/¥.
• Invest yen at a 90-day interest rate of 7%/4 = 1.75%. Forward sell today the yen amount which gives a covered interest rate of: (1 + 0.0175) * (1/139) / (1/142) - 1 = (1.0175) * (142/139) - 1 = 0.03946 or 3.946%

Alternative 2

• It is more profitable to borrow yen and invest in dollars.
• This will give covered yen interest rate of (1 + 0.0225) * (139/142) - 1 = 0.0009 or 0.09%.
• Which is far less than the 90-day borrowing rate of 7%/4 = 1.75%.
• Borrow dollars to invest in yen. Arbitrage profit per $ arbitraged is 1.696%.