Interest Yields, Interest-Rate

Risk, and Derivative Securities

INTERNATIONAL MONETARY AND

FINANCIAL ECONOMICS

Third Edition

Joseph P. DanielsDavid D. VanHoose

Copyright © South-Western, a division of Thomson Learning. All rights reserved.

2

Interest Rates

• To understand the risks owing to interest rate variations, how to minimize those risks, or how to profit from them requires an understanding of how interest rates and the prices of financial instruments are related.

• Principal is the amount of credit extended when one makes a loan or purchases a bond.

3

Interest Yields

• Interest is the payment by the issuer of a financial instrument that compensates the purchaser for the use of their funds.

• The interest rate is the amount of interest expressed as a percentage of the principal.

• Capital gain is a rise in the value of a financial instrument at the time it is sold relative to its market value at the time it was purchased.

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Discounted Present Value

• Discounted present value is the value today of a payment to be received at a future date.

• Calculating discounted present value:– The value today of a payment to be received at a

future date. • Payment one year from now/(1+ r).

– Discounted present value of payment to be received n years in the future:

• Payment n years from now/(1+ r)n.

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Compounded Annual Interest RateYear 3% 5% 8% 10% 20%

1 .971 .952 .926 .909 .8332 .943 .907 .857 .826 .694

3 .915 .864 .794 .751 .578

4 .889 .823 .735 .683 .482

5 .863 .784 .681 .620 .402

6 .838 .746 .630 .564 .335

7 .813 .711 .583 .513 .279

8 .789 .677 .540 .466 .233

9 .766 .645 .500 .424 .194

10 .744 .614 .463 .385 .162

Present Values of a Future Dollar

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Calculating the Yield to Maturity

• Perpetuity:– A bond with an infinite term to maturity.– Perpetuity price = C/r.

• Simple rule:– Prices of existing bonds are inversely related to

changing market interest rates.

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Term to Maturity and Interest-Rate Risk

• Interest rate risk is the possibility that the market value of a financial instrument will change as interest rates vary.

• Capital loss is a decline in the market value of a financial instrument at the time it is sold as compared with its market value at the time it was purchased.

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The Term Structure

• Term Structure of interest rates is the relationship among yields on financial instruments with identical risk, liquidity, and tax characteristics but differing terms to maturity.

• Yield Curve is a chart illustrating the relationship among yields on bonds that differ only in their term to maturity.

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Yield Curves

Typically, yield curves slope upward: interest yields rise at longer terms to maturity.

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Yield Curves

• Economists offer three fundamental explanations for why yield curves are typically upward sloping.– Segmented Markets– Expectations Theory – Preferred Habitat Theory

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Segmented Markets Theory

• Segmented markets theory is a theory of the term structure of interest rates that views bonds with differing maturities as nonsubstitutable, so their yields differ because they are determined in separate markets.

• Drawbacks to theory:

– Yields tend to move together.

– Does not explain natural tendency of the yield curve to slope upward or downward.

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Expectations Theory

• Expectations theory explains how expectations about future yields can cause yields on instruments with different maturities to move together.

– It can provide insight into why the yield curve may systematically slope upward or downward:

• An upward-sloping yield curve indicates a general expectation by savers that short-term interest rates will rise.

• A downward-sloping yield curve indicates a general expectation that short-term interest rates will decline.

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The Preferred Habitat Theory

• Preferred habitat theory is a theory of the term structure of interest rates that views bonds as imperfectly substitutable, so yields on longer-term bonds must be greater than those on shorter-term bonds even if short-term interest rates are not expected to rise or fall.

• Term premium is the amount by which the yield on a long-term bond must exceed the yield on a short-term bond to make individuals willing to hold either bond if they expect short-term bond yields to remain unchanged.

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The Risk Structure of Interest Rates

• Risk structure of interest rates is the relationship among yields on financial instruments that have the same maturity but differ because of variations in default risk, liquidity, and tax rates.

• Default risk is the chance that an individual or a firm that issues a financial instrument may be unable to honor its obligations to repay the principal and/or to make interest payments.

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Excess Returns

• If uncovered interest parity fails to hold, a saver can anticipate earning excess returns.

• Peso problem is an upward bias in depreciation expectations resulting from a perceived small probability of a large currency realignment.

• The peso problem is but one reason for persistent excess returns in emerging economies.

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Nominal versus Real Rates of Interest

• Nominal interest rate is a rate of return in current-dollar terms that does not reflect anticipated inflation.

• Real interest rate is the anticipated rate of return from holding a financial instrument after taking into account the extent to which inflation is expected to reduce the amount of goods and services that this return could be used to buy.

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The Fisher Equation

• The Fisher Equation is a condition relating interest rates and prices.

• It postulates that the real interest rate for a given time period is equal to the nominal interest rate minus the rate of inflation that is expected to prevail over that period:

r = R – πe.• Typically this equation is rewritten for the nominal

rate:R = r + e.

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Ex Ante PPP

• Recall that relative purchasing power parity is:

π – π* = (Se+1 – S)/S.

• For expected price changes, we can express ex ante PPP as:

πe – π*e = (Se+1 – S)/S.

• In other words, the difference in expected rates of inflation is equal to the expected rate of depreciation of the domestic currency.

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Real Interest Parity

• Recall that UIP is expressed as:R – R* = (Se

+1 – S)/S.

• We can set ex ante PPP and UIP equal to each other:πe – π*e = (Se

+1 – S)/S = R – R*.

• Rearranging we obtain:R - πe = R* - π*e, or r = r*,

• which is real interest parity. • Real interest parity postulates that, in equilibrium, the

real rates of interest on similar financial instruments are equal.

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Hedging, Speculation, and Derivative Securities

• Individuals who trade in international financial markets face risks arising from variations in asset returns and foreign exchange risks that arise from exchange-rate volatility.

• Hedging is a strategy of using other financial instruments to reduce financial-market and foreign-exchange-market risks.

• Derivative Security is a financial instrument whose return depends on the returns of other financial instruments.

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Long and Short Positions

• Long Position is an obligation to purchase a financial instrument at a given price and at a specific time.

• Short Position is an obligation to sell a financial instrument at a given price and at a specific time.

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Common Currency Derivatives

• Foreign-exchange forward contract is an agreement that ensures the future delivery of a foreign currency at a specified rate of exchange.

• Currency futures contract is an agreement to deliver a standardized amount of a specific nation’s currency at a designated future date.

• Currency option is a contract granting the right to buy or sell a given amount of a nation’s currency at a certain price within a specific period of time.

• Currency swap is an exchange of payment flows denominated in different currencies.

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Currency Futures

• Currency futures contracts entail daily cash flow settlements.

• To hedge with a futures contract, the firm must post an initial margin, or bond performance requirement.

• The firm must also maintain a maintenance margin, or minimum bond performance requirement.

• Future contract gains or losses are marked-to-market at the end of each trading day.

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Chicago Mercantile Exchange Inc.

Buyers and sellers engage in transactions with brokerage firms that are members of the Chicago Mercantile Exchange (CME). Brokers process these orders in the CME’s trading pits or via its electronic trading system, and CME’s Clearing House member firms execute the transactions.

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Currency Options

• A currency option gives the holder the right to purchase or sell a currency at a given price.

• The price at which holders of an option can exercise their right to buy or sell is the option’s exercise price.

• Call options allow the holder to purchase the underlying currency.

• Put options allow the holder to sell the underlying currency.

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American Options and European Options

• American options grant the holder the right to exercise the right to purchase or sell the underlying currency at any time before or including the date at which the contract expires.

• European options grant the holder the right to exercise the right to purchase or sell the underlying currency only at on the date that the contract expires.

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Potential Profit and Limited Loss of Call Options

The holder of thirty-two €62,500 call options, with a premium of $0.0068 per euro faces a limited loss of $13,600. At a spot exchange rate of $1.2268 per euro, the earnings from exercising the options is just enough to cover the premiums paid for the options. At a spot exchange rate of $1.240 per euro, the holder earns a net profit of $26,400.

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Potential Profit and Limited Loss of Put Options

The holder of twenty €62,500 put options with a premium of $0.0226 per euro faces a limited loss of $28,250. At a spot exchange rate of $1.0574 per euro, the earnings from exercising the options is just enough to cover the premiums paid for the options. At a spot exchange rate of $1.040 per euro, the holder earns a net profit of $21,750.

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Currency Swaps

• Currency swaps are an exchange of payment flows denominated in different currencies.

• Swap partners are sometimes easier to find than counterparties to forward contracts, because swaps directly match traders that require flows denominated in currencies held by one another.

• Swaps may allow borrowers to arrange better loan terms by borrowing in their domestic currency and engaging in a currency swap for a foreign currency, thereby avoiding payment of a risk premium.

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A Sample Currency Swap

IBM receives yen earnings from selling computers in Japan, and Toshiba receives dollar earnings from selling computers in the United states. The two companies could use a currency swap contract to trade their yen and dollar earnings to make payments to holders of their stocks and bonds.