# Chapter 6 example example a bond with a 65 annual

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Chapter 6: Example Example: A bond with a 6.5% annual coupon has three years to maturity. If investors require a 5.1% return, what is the price of the bond? Assume the bond is issued at par. Coupon = 6.5% * 1000 = 65 Discount rate = 5.1% Price of bond = PV of coupons + PV of principle
Chapter 6: Premiums vs. Discounts Par: Coupon rate = Discount rate Discount: Coupon rate < Discount rate Premium: Coupon rate > Discount rate All else held equal, the price of a premium bond falls over time the price of par bond stays constant over time the price of a discount bond rises over time
Chapter 6: Bond Yield 3 methods of measuring return an investor would receive on bond investment: Current yield Yield to Maturity (YTM or yield) Rate of Return Current yield = annual coupon payment / bond price Yield To Maturity: discount rate for which the present value of the bond’s payments equal the price.
Chapter 6: Example Suppose you buy the bond and sell it after one year, and interest rates have not changed. The price of the bond will be P = 100/(1+r) + 100/(1+r)^2 + 1,000/(1+r)^2 =1,092.97 Your return is = 100 +1,092.97 −1,136.36 = 5% = ytm 1,136.16 what if interest rates rise or fall ? Instead if you hold it till maturity, reinvesting coupons, and interest rates do not change, your return is =[100 (1.05)^2 +100(1.05)+1100 - 1,136.36]/1136.16 =15.7625% or, on an annualized basis, your return is =(1.157625)^(1/3) −1=5%= ytm If interest rates rise (i.e., future bond prices fall), then your return is higher than the YTM implied by current prices , for a holding period till maturity . Vice versa if interest rates fall. Exception: zero-coupon bonds, for which YTM = return till maturity regardless of interest rate movements.
Chapter 6: Interest Rate Risk & Yield Curve All else equal, a longer maturity bond has higher interest rate risk. All else equal, a lower coupon bond has higher interest rate risk. The principal measure of interest risk of a bond is called its duration The yield curve, at any point in time, plots the yield to maturity of otherwise identical bonds that differ only in their time to maturity. Since longer maturity bonds have higher interest rate risk, all else equal, investors would require a higher rate of return on longer maturity bonds, or else they would not be willing to hold these bonds.
Chapter 6: Managing Risk A bond issuer faces the risk that interest rates may fall, but he is locked into paying a fixed coupon. One option is to make the bond callable, the issuer reserves the right to retire the bond before maturity at a pre- specified call price. all else equal, a callable bond should trade at a lower price than an otherwise identical non-callable bond. Similarly, to protect investors, bonds may be puttable the buyer/holder reserves the right to demand repayment before maturity all else equal, a puttable bond should trade at a higher price than an otherwise identical non-puttable bond.