I 2 c n f n 1 i n discount bond yieldcoupon par

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i ) 2 + + C n + F n ( 1 + i ) n Discount bond, yield>coupon Par, Premium, and Discount Bonds Par bond If a bond’s coupon rate is equal to its yield, the price will equal the face value Discount bond If a bond’s coupon rate is less than its yield, the price will b e less than the face value Likely to happen when interest rates are rising Premium bond If a bond’s coupon rate is more than its yield, the price will be higher than the face value Likely to happen when interest rates are falling Semiannual Compounding Most bonds issued in Europe pay annual coupons, but bonds issued in the U.S. usually pay semi-annual coupons Equation 8.2 P B = C m 1 + i m + C m ( 1 + i m ) 2 + C m ( 1 + i m ) 3 + + C m + F mn ( 1 + i m ) mn Calculator Example – Bond Valuation What is the price of a three-year, 5% coupon bond with a market yield of 8% and semi- annual coupon payments? Semi-annual yield = 8%/2=4% Semi-annual coupon payment = $50/2=$25 Number of periods = 3x2=6 Zero Coupon Bonds
Zero Coupon bonds pay face value at maturity, but do not make coupon payments The yield of a zero coupon bond is therefore the present value of the par value Zero coupon bonds pay cash only at maturity ; they sell for less than similar bonds which make periodic interest payments Equation 8.3 P Z = F mn ( 1 + i m ) mn What is the price of a zero coupon bond with a $1,000 face value, 10-year maturity, and semi- annual compounding? The market rate on similar bonds is 12%. P Z = $ 1000 ( 1 + 0.12 2 ) 20 = $ 1000 ( 1 + 0.06 ) 20 = $ 311.80 Yield to Maturity 到期收益率 Yield to Maturity (YTM) is the rate that makes the present value of the bond’s cash flows equal to the price of the bond i.e., YTM is the rate a bondholder earns if the bond is held to maturity and all coupon and principal payments are made as promised YTM changes daily as interest rates change Yield goes down, the price goes down Long term bonds are more sensitive than small bonds Effective Annual Yield In bond trading, the effective annual rate (EAR) is called the effective annual yield (EAY) EAY = ( 1 + quoted rate m ) m 1 Simple annual yield is yield per period multiplied by the number of compounding periods ; for bonds with annual compounding, simple annual yield is two times the semi-annual yield Calculator Example – YTM and EAY An investor buys a 30-year bond with a $1,000 face value for $800. The bond’s coupon rate is 8% and interest payments are made semi-annually. What are the bond’s yield to maturity and effective annual yield? Bond Yields Realized Yield is the return earned on a bond given the cash flows actually received by the investor 实际收益率是投资者实际收到的现金流量所产生的收益 It represents the interest rate at which the present value of actual cash flows generated by the investment equals the bond’s price The realized yield is important because it allows investors to see what they actually earned on their investments Interest Rate Risk Bond theorems are statements about the math used in bond pricing

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