Forward Rates

Bill Reese

International Finance

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Learning Objectives

In this unit we will learn: Why people might trade forward exchange rate

contracts How covered interest arbitrage determines

forward rates What interest rate parity is

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Spot vs. Forward Rates

Spot Rate The price of a currency in terms of another

currency for a trade today

Forward Rate Price agreed upon today for a trade to be

executed at a specified future date (30, 60, 90, 180 or 360 days)

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Forward Rates

Purpose: to lock in an exchange rate and thus eliminate XR risk

XR risk: the risk that the XR may move in an unfavorable direction Risk averse investors may prefer certain forward

rate to risky future spot rate

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Forward Rate Example

Purchasing manager for Best Buy Places an order for 10,000 Sony televisions for

Christmas Must pay Sony in 6 months when delivered – pay

in Yen Agreed price is ¥300 million

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Forward Rate Example

Spot XR is .008 $/¥• ¥300 million x .008 $/¥ = $2.4 million

Suppose yen appreciates to .010 $/¥• ¥300 million x .010 $/¥ =

$3 million• XR loss of $600,000

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Forward Rate Example

Note: $/¥ When yen appreciates, XR increases

Yen is currency being priced Currency in denominator

Yen buys more dollars Takes more dollars to buy a yen

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Forward Rate Example

Suppose 180-day forward contract is available at .0085 $/¥ Agree to sell dollars (buy yen) in 180 days at

117.65 ¥/$ (1/.0085 = 117.65)

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Forward Rate Example

Buy ¥ 300 million at .0085 $/¥ for $2,550,000 Locked-in price No XR risk

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Forward Contracts

Like Girl Scout Cookies Order taken for future delivery specifying:

Good Quantity Delivery date Price

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Forward Contracts

Usually with banks Individually tailored No money exchanged at time of agreement Counterparty risk

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Forward Contracts

Forward premium Forward rate > spot rate

Forward discount Forward rate < spot rate

Our example Spot rate = .0080 $/¥ Forward rate = .0085 $/¥

Forward premium

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Forward Contracts

Forward premiums and discounts

Indirect quotes

Premium (discount) = SR – FR x 360

FR length

= 125 – 117.65 x 360 = 12.5%

117.65 180

Negative value would be a discount13

Forward Rates

Forward rate ≠future spot rate (necessarily) Determined by absence of arbitrage

condition Covered interest arbitrage

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Example

Spot rate = .73 $/CD Six-month forward rate = .73 $/CD U.S. interest rate = 5.0% Canadian interest rate = 5.5%

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Today

Borrow $100 at 5% in U.S. Convert to CD at spot rate: $100 ÷.73 $/CD =

CD 136.99 Invest CD in Canada at 5.5% for six months Enter into 6-month forward contract to sell

CD at .73 $/CD

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Six Months from Now

Investment grows to CD 140.76• 136.99(1+.055/2) = 140.76

Convert CD to $ with forward contract• CD 140.76 x .73 $/CD = $102.75

Pay off debt • $100 (1+.05/2) = $102.50

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Covered Interest Arbitrage

Started with nothing Ended up with something

Paid off debt of $102.50 with $102.75 from forward contract – leaving $0.25

Riskless profit Cannot last in competitive markets

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Covered Interest Arbitrage

Investors will notice Everyone buys CD in spot mkt

CD appreciates

Everyone sells CD in forw mkt CD sells at forward discount

Rates adjust until arbitrage opportunity disapears

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Interest Rate Parity

Prevents covered interest rate arbitrage Country with higher interest rate

Currency sells forward at a discount

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Interest Rate Parity

(1 + i) = Forward Rate

(1 + i*) Spot Rate

Where i = domestic int. rate and i*= foreign int. rate

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Interest Rate Parity

(1 + .05/2) = Forward Rate

(1 + .055/2) .73 $/CD

Solving for forward rate:

.728224 $/CD

Gives you just enough to pay off the loan ($102.50)

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Interest Rate Parity

Country with higher interest rates• Currency sells forward at discount

Eliminates possibility for covered interest arbitrage

Transactions costs and taxes leaves range for forward rate

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