ECON5319-Lecture10-2011

ECON5319-Lecture10-2011 - The Global Economy ECON 5319...

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The Global Economy ECON 5319 Interest Rates and Exchange Rates William J. Crowder Ph.D.
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What is an Interest Rate? • To understand the concept of an interest rate we need to familiarize ourselves with the concept of present value. • A dollar paid to you one year from now is less valuable than a dollar paid to you today. • That is because a dollar received today can be saved and earn interest.
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Future Values 2 3 Let = .10 In one year $100 X (1+ 0.10) = $110 In two years $110 X (1 + 0.10) = $121 or 100 X (1 + 0.10) In three years $121 X (1 + 0.10) = $133 In years $100 X (1 + ) n i n i
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Simple Present Value n PV = today's (present) value CF = future cash flow (payment) = the interest rate CF PV = (1 + ) i i
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Yield to Maturity • The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today
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Four Types of Credit Market Instruments • Simple Loan • Fixed Payment Loan • Coupon Bond • Discount Bond
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Simple Loan—Yield to Maturity 1 PV = amount borrowed = $100 CF = cash flow in one year = $110 = number of years = 1 $110 $100 = (1 + ) ) $100 = $110 ) = $100 = 0.10 = 10% For simple loans, the simple interest rate equ n i i i i als the yield to maturity
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Fixed Payment Loan Yield to Maturity 23 The same cash flow payment every period throughout the life of the loan LV = loan value FP = fixed yearly payment = number of years until maturity FP LV = . . . + 1 + (1 + ) ) ) n n ii i i +++
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Coupon Bond Yield to Maturity 23 Using the same strategy used for the fixed-payment loan: P = price of coupon bond C = yearly coupon payment F = face value of the bond = years to maturity date CC C C F P = . . . + 1+ (1+ ) (1 n n ii i i +++ + +) n i
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• When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate • The price of a coupon bond and the yield to maturity are negatively related • The yield to maturity is greater than the coupon rate when the bond price is below its face value
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Consol or Perpetuity • A bond with no maturity date that does not repay principal but pays fixed coupon payments forever / / cc c c PC i P C i iC P = = = = = price of the consol yearly interest payment yield to maturity of the consol Can rewrite above equation as For coupon bonds, this equation gives current yield, which is an easy-to-calculate approximation of yield to maturity
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Discount Bond Yield to Maturity For any n-day discount bond F - P 365 = P F = Face value of the discount bond P = current price of the discount bond The yield to maturity equals the increase in price over the year divided b i n ⎡⎤ × ⎢⎥ ⎣⎦ y the initial price. As with a coupon bond, the yield to maturity is negatively related to the current bond price.
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Yield on a Discount Basis Less accurate but less difficult to calculate i db = F - P F X 360 days to maturity i = yield on a discount basis F = face value of the Treasury bill (discount bond) P = purchase price of the discount bond Uses the percentage gain on the face value Puts the yield on an annual basis using 360 instead of 365 days Always understates the yield to maturity The understatement becomes more severe the longer the maturity
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Bond Prices and Interest Rates
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Rate of Return
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This note was uploaded on 07/16/2011 for the course ECON 5319 taught by Professor Crowder during the Spring '11 term at UT Arlington.

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ECON5319-Lecture10-2011 - The Global Economy ECON 5319...

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