Bonds 1 AWAD RAHEEL

 Bond Characteristics ◦ Reading the financial pages  Interest Rates and Bond Prices  Current Yield and Yield to Maturity  Bond Rates and Returns  Corporate Bonds and the Risk of Default 2AWAD RAHEEL

Terminology  Bond - Security that obligates the issuer to make specified payments to the bondholder.  Coupon - The interest payments made to the bondholder.  Face Value (Par Value or Principal Value) - Payment at the maturity of the bond.  Coupon Rate - Annual interest payment, as a percentage of face value. 3AWAD RAHEEL

WARNING The coupon rate IS NOT the discount rate used in the Present Value calculations. The coupon rate merely tells us what cash flow the bond will produce. Since the coupon rate is listed as a %, this misconception is quite common. 4AWAD RAHEEL

The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return. 5AWAD RAHEEL

Example What is the price of a 5.5 % annual coupon bond, with a Rs1,000 face value, which matures in 3 years? Assume a required return of 3.5%. 6AWAD RAHEEL

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Example (continued) What is the price of the bond if the required rate of return is 5.5 %? 8AWAD RAHEEL

Example (continued) What is the price of the bond if the required rate of return is 15 %? 9AWAD RAHEEL

Example (continued) What is the price of the bond if the required rate of return is 3.5% AND the coupons are paid semi-annually for 3 years? 10AWAD RAHEEL

Example (continued) Q: How did the calculation change, given semi- annual coupons versus annual coupon payments? 11AWAD RAHEEL

 Example (continued)  Q: How did the calculation change, given semi-annual coupons versus annual coupon payments? Time Periods Paying coupons twice a year, instead of once doubles the total number of cash flows to be discounted in the PV formula. Discount Rate Since the time periods are now half years, the discount rate is also changed from the annual rate to the half year rate. 12AWAD RAHEEL

 Current Yield - Annual coupon payments divided by bond price.  Yield To Maturity – Interest/Discount rate for which the present value of the bond’s payments equal to its price. 13AWAD RAHEEL

 Calculating Current Yield  Suppose you are purchasing 3 years bond with coupon rate of 10%. How do you calculate the rate of return the bond offer?  Current Rate of Return = 100/1000 = 10% AWAD RAHEEL14 Cash Paid to You in Year You Pay123Rate of Return Rs %

 Now suppose that the market price of 3 years bond is Rs with annual income of Rs100. What is the rate of return now?  So you pay and receive 100 annually.  Income as proportion of initial outlay is  100/ =.088 = 8.8% AWAD RAHEEL15 Cash Paid to You in Year You Pay123Rate of Return Rs ?

 Problems due to current yield rates AWAD RAHEEL16

Calculating Yield to Maturity (YTM=r) If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r. 17AWAD RAHEEL

Example What is the YTM of a 5.5 % annual coupon bond, with a Rs1,000 face value, which matures in 3 years? The market price of the bond is Rs1, AWAD RAHEEL

WARNING Calculating YTM by hand can be very tedious. It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator. 19AWAD RAHEEL

Rate of Return – Earnings per period per rupee invested. 20AWAD RAHEEL

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Price path for Premium Bond Price path for Discount Bond Today Maturity 23AWAD RAHEEL

 Bond shows interest rate risk as its price fluctuate with interest rate change.  Do all bonds get effected equally?  Long term bonds are more sensitive to interest rate than prices of short term bonds. AWAD RAHEEL24

30 yr bond 3 yr bond When the interest rate equals the 5.5% coupon rate, both bonds sell at face value 25AWAD RAHEEL Interest Rate (%) Bond price 0

 Bonds are also available with real interest rates.  If nominal rate is 3.5% and inflation rate is 2%, then real interest rate will be:  Real interest rate = =.0147 = 1.47% 1.02  As inflation rate is uncertain, so is real interest rate. AWAD RAHEEL26

 In inflation indexed bonds real cash flows are fixed while nominal cash flows (interest and principal) are changed as CPI changes.  e.g. Real cash flow of 2 years indexed bonds at 3% would be:  Now suppose that inflation turns out to be 5% in year 1 and 4% in year 2. then nominal cash flow would be:  Here cash payments are justified to give 3% real interest rate AWAD RAHEEL27 Year 1 Year 2 Real Cash FlowRs 30Rs 1030 Year 1 Year 2 Nominal Cash FlowRs 30x1.05= Rs Rs 1030x1.05x1.04 =Rs

Yield on UK nominal bonds Yield on UK indexed bonds 28AWAD RAHEEL

 Like governments, corporate also borrow money by selling bonds.  Credit risk – The risk that bond issuer may default on its bonds.  Default premium – The additional yield on a bond investor require for bearing credit risk.  Investment grade – Bonds rated BBB and above. ( 1% default rate of AAA since 1971)  Junk bonds – Bonds having grade less than BBB (about 50% bonds rated CCC by S&P defaulted within 10 yrs) 29AWAD RAHEEL

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 Zero coupons ◦ No coupon offered and receive face value of bond at maturity date.  Floating rate bonds ◦ Rate can be pegged to some measure of current market e.g. T Bills plus 2%  Convertible bonds ◦ Option to convert into shares latter. ◦ Investor accept lower interest rates on convertible bonds. 31AWAD RAHEEL

 Innovations are always in process for bonds e.g.  Catastrophe (or cat) bonds: ◦ Offer high return but reduced when specific type of disaster occurs.  Longevity bonds: ◦ Bond payments get higher if more population survived extra year. ◦ Pension funds are common buyer of these bonds as they have to pay extra if life expectancy increases. AWAD RAHEEL32

Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date. Yield Curve - Graph of the term structure. 33AWAD RAHEEL