Chapter 5 part 2 FIN Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Bond Theorem 2 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

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1- Find out the relationship between bond prices and bond yield? 2- Compare between price volatility of long and short run bond 3- Compare between price volatility of low – coupon and high coupon bonds. You will find that 1- There is a negative (an Inverse) relationship between bond prices and bond yield. 2- The price volatility of a long - term bond is greater than that of a short – term bond, holding the coupon rate constant. i.e. Bond volatility increases as maturity increases. 3- The price volatility of a low – coupon bond is greater that that of a high – coupon bond, holding maturity constant. i.e. Bond volatility decreases as coupon rate increases. 4 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Bond Price Volatility (Price Risk) A simple measure of bond volatility is the % change in bond price for a given change in yield. % change PB = {(new PB – old PB) / Old PB} * 100 Example 5 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Interest Rate Risk and Duration Interest rate risk comprises price risk and reinvestment risk. Price risk is the variability in bond prices caused by their inverse relationship with interest rates. Reinvestment risk is the variability in realized yield caused by changing market rates at which coupons can be reinvested. Price risk and reinvestment risk work against each other. – As interest rates fall (rise): Bond prices rise (falls) but Coupons are reinvested at lower (higher) return. 6 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Interest Rate Risk and Duration cont. Duration is a measure of interest rate risk that considers both coupon rate and term to maturity. It refers to the period necessary to offset price risk and reinvestment risk, and thus eliminate interest rate risk. It is measured as the ratio of the sum of the time weighted discounted cash flows divided by the current price of the bond. It is equal to the PV of all cash flows weighted according to length of time to receipt, divided by the price of the bond. 7 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Duration is calculated using the formula: where:D = duration of the bond CFt = interest or principal payment at time t t = time period in which payment is made n = number of periods to maturity i = the yield to maturity (interest rate) 8 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Example 1: Fc = 1000, 5 years maturity, coupon rate = 5%, and market yield (rate)= 8% Calculate: 1.Coupon payment 2.Price of the bond 3.Duration Note: For coupon bonds, Duration value is less than maturity of the bond. BUT for zero coupon bonds, duration value equals to maturity. 9 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Class work 1: A $1000, 2 years, 10% coupon bond is priced at $1000 in the market. The duration of the bond is …………………. Class work 2: The duration of a $1000, 2 years, 7% loan (interest paid annually) is ………….. When market loan rates are 8%? Class work 3: No. 10 page 134 textbook Calculate the duration of a $1000, 8-year zero coupon bond using annual compounding and a current market rate of 7%. 10 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

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Duration Concepts (all else equal): Higher coupon rates mean shorter duration and less price volatility. Duration equals term to maturity for zero coupon securities. Longer maturities mean longer durations and greater price volatility. The higher the market rate of interest, the shorter the duration. 12 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Duration can be calculated for an entire portfolio as follows (cancelled): where:w i = proportion of bond i in portfolio and D i = duration of bond i. 13 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Duration is used as a measure of price risk Example: Using the 3-year, 4% coupon bond in Exhibit 5.6— If yield increases to 12%: 14 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2

Class Works: Class work 1: (study guide, P. 52) What is the market price of a BD 1000 face value zero coupon bond with a 5 – year maturity priced to yield 11%, compounded annually? A- BD B - BD 1000 C- BD 650 D- BD Class work 2: In class work 1, calculate the duration. Class work 3: In class work 2, assume interest rate decreases by 2% and the price decreases by BD 34. what is price volatility?

Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2 16 Class work 4: Duration is a measure of: A- a bond’s price B- a bond’s contractual maturity. C- bond price volatility D- the length of time it takes to get back the original Class work 5: A $1000, 3 years, 5% coupon (semiannually) bond is priced at $978.3 in the market. 1- The yield to maturity is …………….. 2- The duration of the bond is ………… 3- If the interest rate increases by 3%, the price volatility is ……………….

Duration & Manage Interest Rate Risk Financial institutions use duration to manage interest rate risk and actually achieve the desired yield for the desired holding period.  Zero-coupon approach: zero-coupon bonds have no reinvestment risk. The duration of a “zero” equals its term to maturity. Buy a “zero” with the desired holding period and lock in the YTM. Must hold to maturity to evade price risk.  Duration matching: To realize yield to maturity, investors select bonds with durations matching their desired holding periods.  Maturity matching: Selecting a term to maturity equals to the desired holding period eliminates price risk, but not reinvestment risk. 17 Dr. Hisham Abdelbaki FIN 221 Chapter 5 Part 2