Bond PricingBond Pricing

Bond Pricing

Fundamentals

Valuation

? What determines the price of a bond?

? Contract features: coupon, face value (FV), maturity

? Risk-free interest rates in the economy (US treasury yield curve)

? Credit risk premium (risk premium required for default risk of firm).

Terminology and Conventions

? Face Value (FV) : is usually $1000. ? Coupon: quoted as % of FV and usually paid

semi-annually. Thus, a 5% coupon on a face value of $1000 implies that the bond pays $25 every 6 months. ? Price is usually expressed as a % of FV. ? Yield to maturity (YTM): the return you earn on the bond, if you bought the bond at its current price and held it to maturity.

? The convention in the bond market is that the YTM is quoted in nominal annual terms, which is twice the equivalent semi-annual yield.

Two Simple Questions

? If I know the yield to maturity (or the holding-

period return), how much should I pay for it? ? If I buy a bond at some price, P, and hold it to

maturity, then what would be the yield to maturity (or the return) that I earn?

Calculation of the Price, knowing the YTM

? If I know what return (YTM) I require from the bond, how should I price it?

? Answer: Discount the cash flows at a discount rate that is equal to the YTM.

An Example (1/2)

? What should be the price of a Treasury Bill with a 5 1/8 % coupon, maturing in 1.5 years, when the first of the semi-annual coupons is due exactly 6 months from today? The bond is priced to yield (YTM) 5.82%.

? Answer: 25.625/(1+ 5.82%/2)^1 + 25.625/(1+5.82%/2)^2 + 1025.625/(1+5.82%/2)^3 = $990.15.

? Note

? Semi-annual Coupon = (1/2) (5.125%)(1000)= $25.625 ? Discount factor = (0.0582/2) for a six month period.

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