Chapter 5 :BOND PRICES AND INTEREST RATE RISK Mr. Al Mannaei Third Edition

What is Bond ? Debt instrument issued by a government or a corporation in order to finance projects or activities. A form of loan. –Issuer :lender : At maturity borrower will pay lender face value + interest. Negotiable instruments. 2

What is Bond ? Why issuing bonds? Governments : to finance infrastructure projects: schools, roads, power stations..etc. Corporations : to finance commercial project, expand the business, increase capital and reduce tax. 3

What is Bond ? Mona bought a bond for $980 issued by ALBA with 3 years maturity, the coupon rate is 6%, paid annually ? –Who are the borrower & the lender? –What is the $980 ? –How much mona will receive every year* ? –Can Mona sell the bond before maturity ? –How much mona will receive at maturity ? * in other word, how much alba have to pay each year. Year 1 Year 2 Year 3 (Maturity) 4

What is Bond ? What is the Maturity (Time) of bonds ? Range : from to What is the frequency of payment ? Is payment guaranteed ? Risk & Return ? Why corporation pay higher interest than government ? Listed vs. over the counter (OTC) ?! 5

How to price a bond ? The price of a bond is the present value of the future cash flows promised, discounted at the market rate of interest. 6

How to price a bond ? WherePB = price of bond or present value of promised payments; Ct = coupon payment in period t, where t = 1, 2, 3,…, n; Fn = par value (principal amount) due at maturity; i = market interest rate (discount rate or market yield); and n = number of periods to maturity. 7

Coupon rate & Market Yield What is the difference between coupon rate & Market Yield ?! Example : You buy 1 year government bond for $1030. The bond pays 7% coupon annually. What is your profit ?! In percentage (%) ?!

Coupon rate & Market Yield Example (Continue) : if you sell the bond after 6 months for $1050. Calculate the market yield ?!

How to price a bond ? Example 1 : Consider 3 Years Bond with face value of $1000 and Coupon rate 8%, Current market rate is 10%, Calculate the price of the Bond ? 10

How to price a bond ? Example 1 : Consider 3 Years Bond with face value of $1000 and Coupon rate 8%, Current market rate is 10%, Calculate the price of the Bond ? 11

How to price a bond ? Example 2 : Consider 3 Years Bond with face value of $1000 and Coupon rate 5%, Current market rate is 5%, Calculate the price of the Bond ? 12

How to price a bond ? Example 2 : Consider 3 Years Bond with face value of $1000 and Coupon rate 5%, Current market rate is 5%, Calculate the price of the Bond ? 13

How to price a bond ? Example 3: Consider a 1 year bond with a face value of $1000 and a coupon rate of 8% compounded annually, current market yield is 5%, calculate the price of the bonds ? 14

How to price a bond ? Example 3: Consider a 1 year bond with a face value of $1000 and a coupon rate of 8% compounded annually, current market yield is 5%, calculate the price of the bonds ? 1.Press (CMPD) bottom press EXE 2.Press EXE on (Set) choose END press EXE 3.Press EXE on (n) entre 1 press EXE 4.Press EXE on (I) entre 5 press EXE 5.Ignore PV ( press down ) 6.Press EXE on PMT ENTRE 80 press EXE 7.Go back for PV press SOLVE. 15

How to price a bond ? Example 3: Consider a 1 year bond with a face value of $1000 and a coupon rate of 8% compounded annually, current market yield is 5%, calculate the price of the bonds ? n= 1 I=5 PV= ? PMT=80 FV=1000 C/Y=1 16

Coupon rate & Market IR How Does the Market IR & Coupon rate affect Bond price ? 17

Coupon rate & Market IR How Does the Market IR & Coupon rate affect Bond price ? If : Coupon rate Greater Market IR >>> bond price higher than par ( issued at premium ) Coupon rate Lower Market IR >>> bond price lower than par ( issued at discount) Coupon rate = Market IR >>> bond price equal par (issued at par) 18

Market IR & Bond Price Negative relationship between i & Bond Price –Increasing i ; decrease Bond Price. –Decreasing i ; increase Bond Price. Positive relationship between Coupon & Bond Price –Increasing Coupon ; increase Bond Price. –Decreasing Coupon ; decrease Bond Price. 19

Question What is the price of a $1000 face value with a 10% coupon if the market rate of return is 10%? 20

How to price a bond ? Example 4: Consider a 2 year bond with a face value of $1000 and a coupon rate of 5% compounded Semi-annually, current market yield is 6%, calculate the price of the bonds ? 21

How to price a bond ? Example 4: Consider a 2 year bond with a face value of $1000 and a coupon rate of 5% compounded Semi-annually, current market yield is 6%, calculate the price of the bonds ? 22

Risk related with Bonds Credit or default risk: chance that issuer may be unable or unwilling to pay as agreed. 23

Risk related with Bonds Reinvestment risk: potential effect of variability of market interest rates on return at which payments can be reinvested when received. Price risk: Inverse relationship between bond prices and interest rates. 24

Zero Coupon Bonds No periodic coupon payments. Issued at discount from par. Single payment of par value at maturity. 25

Zero Coupon Bond How to price Zero Coupon Bonds ? Annual Semi-annual, Quarterly, monthly, daily PB is simply PV of FV represented by par value, discounted at market rate. 26

Example if you want to purchase a Company XYZ zero- coupon bond that has a $1,000 face value and matures in 3 years compounded annually, and you would like to earn 10% per year on the investment, what is the price of the bond ? 27

Example if you want to purchase a Company XYZ zero- coupon bond that has a $1,000 face value and matures in 3 years compounded semi-annually, and you would like to earn 10% per year on the investment, what is the price of the bond ? 28

Example In the previous example if the compounding frequency increase, Bond price will : –Decrease –Increase –No Change Yearly, semi-annually, monthly, daily. Compounding Frequency increase Compounding Frequency decrease 29

Problem Carol purchases a one-year discount bond with a face value of $1,000 for $ What is the yield of the bond? 30

Zero bond Mariam bought a bond mature after 3 years for 1000 BD. The coupon rate and market yield = 8%. Marwa bought zero-bond mature after 3 years for 1000 BD. The market yield is 8%. What if both bond defaulted after year 2 ?! Year

Bond Yields Market Yield (Interest Rate) –Yield to Maturity –Expected Yield –Realized Yield 32

Yield to Maturity (YTM) YTM : Investor's expected yield if bond is held to maturity and all payments are reinvested at same yield. The longer until maturity, the less valid the reinvestment assumption Example: –Bond A mature after 30 years pay 8%. –Bond B mature after 5 years pay 8%. –Which bond most likely will change the coupon rate ?! 33

Yields calculation The Bond price, Coupon rate & maturity will be given and the Yield (i) has to be calculated. The Yields can be calculated through –Trail & error. –Financial calculator. 34

YTM Example Investor buys 5% percent coupon (semiannual payments) bond for $951.90; bond matures in 3 years. Solve the bond pricing equation for the interest rate (i) such that price paid for the bond equals PV of remaining payments due under the bond. 35

YTM Example Investor buys 5% percent coupon (semiannual payments) bond for $951.90; bond matures in 3 years. Solve the bond pricing equation for the interest rate (i) such that price paid for the bond equals PV of remaining payments due under the bond. 36

YTM Example Investor buys 5% percent coupon (semiannual payments) bond for $951.90; bond matures in 3 years. Solve the bond pricing equation for the interest rate (i) such that price paid for the bond equals PV of remaining payments due under the bond. I :n:FV:PV: PMT: Answer : 37

Expected Yield Predicted yield for a given holding period Almost same as YTM but the expected holding period is shorter. 38

Realized Yield Realized Yield: actual rate of return, given the cash flows actually received and their timing. Differ from YTM & Expected yield, due to : –Change in the amount of promised payments. –Change in market interest rates. 39

Realized Yield Investor pays $1,000 for 10-year 8% coupon bond; sells bond 3 years later for $ Solve for i such that $1,000 (the original investment) equals PV of 2 annual payments of $80 followed by a 3 rd annual payment of $

Realized Yield Investor pays $1,000 for 10-year 8% coupon bond; sells bond 3 years later for $ Solve for i such that $1,000 (the original investment) equals PV of 2 annual payments of $80 followed by a 3 rd annual payment of $

Realized Yield Investor pays $1,000 for 10-year 8% coupon bond; sells bond 3 years later for $ Solve for i such that $1,000 (the original investment) equals PV of 2 annual payments of $80 followed by a 3 rd annual payment of $ I :n:FV:PV: PMT: Answer : 42

Bond price volatility (price risk) Percentage change in price for given change in interest rates where %∆PB = percentage change in price P t = new price in period t P t – 1 = bond’s price one period earlier 43

Bond price volatility (price risk) 44

Bond price volatility (price risk) 45

Bond price volatility (price risk) 46

Bond theorems Bond prices are inversely related to bond yields. The price volatility of a long-term bond is greater than that of a short-term bond, holding the coupon rate constant. The price volatility of a low-coupon bond is greater than that of a high-coupon bond, holding maturity constant 47

Price Risk Reinvestment Risk Price risk and reinvestment risk work against each other. You bought one year bond at par, where interest rate and coupon rate= 5%. After three months the interest rate fall to 3% ?! 48

Price risk and reinvestment risk work against each other. –if interest rates fall : Bond prices rise but >> Coupons are reinvested at lower return. –if interest rates rise : Bond prices fall but >> Coupons are reinvested at higher return. 49

Duration A measure of the volatility of bond price to a change in interest rates. Expressed as a number of years. It is NOT the length of time it takes to get back the original investment ( Payback Period ). 50

Bond : Duration will always be less than its time to maturity. Zero-Bond : Duration is equal to its time to maturity. Zero Bond Regular Bond 51

Duration –CF : Coupons payment – t: time of payment –i: interest –n: number of years 52

Duration Example Suppose we have a bond with a 3-year term to maturity, an 8% coupon paid annually, and a market yield of 10%. Duration is: 53

Duration If the yield increases to 15%: What is the relationship between yield & Duration ? 54

Duration What is the relation between coupon rates and duration ?! Duration equals term to maturity for zero coupon securities. 55

Duration concepts Higher coupon rates mean shorter duration (less price volatility). Bond A has 5 coupon rate, IR 10%, 2 years Bond B has 8 coupon rate, IR 10%, 2 years Which of the above bonds has lower duration ? Duration equals term to maturity for zero coupon securities. What is the duration for 3 years zero bond ? 56

Duration concepts Longer maturities mean longer durations (greater price volatility). Bond A has 8 coupon rate, IR 10%, 5 years Bond B has 8 coupon rate, IR 10%, 2 years Which of the above bonds has lower duration ? The higher the market rate of interest, the shorter the duration. Bond A has 8 coupon rate, IR 20%, 2 years Bond B has 8 coupon rate, IR 10%, 2 years Which of the above bonds has lower duration ? 57

Duration where:w i = proportion of bond i in portfolio and D i = duration of bond i. 58

Duration 59

Duration Using the 3-year, 4% coupon bond in Exhibit 5.6 (previous slide ), If yield increases to 12%: 60

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