Covered Interest Parity and exchanged ratae

CIP and Covered Interest Arbitrage

The Global EconomyECON 5319

Interest Rates and Exchange Rates

William J. Crowder Ph.D.

CIP and Covered Interest Arbitrage

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.

CIP and Covered Interest Arbitrage

Future ValuesLet i= .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)2 In three years$121 X (1+ 0.10)=$133 or 100 X (1+ 0.10)3 In n years$100 X (1+ i)n

CIP and Covered Interest Arbitrage

Simple Present ValuePV= today's (present) value CF= future cash flow (payment) i= the interest rate CF PV= n (1+ i )

CIP and Covered Interest Arbitrage

Yield to Maturity The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today

CIP and Covered Interest Arbitrage

Four Types of Credit Market Instruments Simple Loan Fixed Payment Loan Coupon Bond Discount Bond

CIP and Covered Interest Arbitrage

Simple Loan—Yield to MaturityPV= amount borrowed=$100 CF= cash flow in one year=$110 n= number of years= 1$110$100= (1+ i )1 (1+ i )$100=$110$110 (1+ i )=$100 i= 0.10= 10% For simple loans, the simple interest rate equ als the yield to maturity

CIP and Covered Interest Arbitrage

Fixed Payment Loan Yield to MaturityThe same cash flow payment every period throughout the life of the loan LV= loan value FP= fixed yearly payment n= number of years until maturity FP FP FP FP LV=+++ ...+ 2 3 1+ i (1+ i) (1+ i) (1+ i)n

CIP and Covered Interest Arbitrage

Coupon Bond Yield to MaturityUsing the same strategy used for the fixed-payment loan: P= price of coupon bond C= yearly coupon payment F= face value of the bond n= years to maturity date C C C C F+++. . .++ P= 2 3 n 1+i (1+i) (1+i) (1+i) (1+i)n

CIP and Covered Interest Arbitrage

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

CIP and Covered Interest Arbitrage

Consol or Perpetuity A bond with no maturity date that does not repay principal but pays fixed coupon payments foreverPc= C/ ic Pc= price of the consol C= yearly interest payment ic= yield to maturity of the consol Can rewrite above equation as ic= C/ Pc For coupon bonds, this equation gives current yield, which is an easy-to-calculate approximation of yield to maturity

CIP and Covered Interest Arbitrage

Discount Bond Yield to MaturityFor any n-day discount bond F - P 365 i= × n 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 pided by the initial price. As with a coupon bond, the yield to maturity is negatively related to the current bond price.

CIP and Covered Interest Arbitrage

Yield on a Discount BasisLess accurate but less difficult to calculate F-P 360 idb= X F days to maturity idb= yield on a discount basis F= face valu

e 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

CIP and Covered Interest Arbitrage

Bond Prices and Interest Rates

CIP and Covered Interest Arbitrage

Rate of ReturnThe payments to the owner plus the change in value expressed as a fraction of the purchase price Pt+1 - Pt C+ RET= Pt Pt RET= return from holding the bond from time t to time t+ 1 Pt= price of bond at time t Pt+1= price of the bond at time t+ 1 C= coupon payment C= current yield= ic Pt Pt+1 - Pt= rate of capital gain= g Pt

CIP and Covered Interest Arbitrage

Rate of Return and Interest Rates The return equals the yield to maturity only if the holding period equals the time to maturity A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise