LM6: fixed-inome bond valuation - prices and yields

market discount rate

the rate of return required by investors given the risk of the bond investment

Par

• PV = FV

• PMT = market discount rate

Discount

• PV < FV

• PMT < market discount rate

premium

• PV > FV

• PMT > market discount rate

YTM

• is the internal rate of return that equates the PV of future cash flows to the price of the bond

• it is the implied market discount rate given the price of the bond

a bond investor’s rate of return will equal the YTM if

• the investor holds the bond to maturity

• the issuer makes full coupon and principal payments on the scheduled date

• the investor reinvests all coupon payments at the same YTM

the full price (PVfull)

reflects the amount paid by the buyer and received by the seller on the trade settlement date

accrued interest (AI)

is the portion of the next coupon payment owed to the seller of a bond

flat price (PVflat)

is used for quotations to avoid misleading investors about a bond’s market price trend

inverse relationship

the price of a bond is inversely related to its YTM

coupon effect

lower coupon → higher duration → higher interest rate risk

maturity effect

longer time to maturity → higher duration → higher interest rate risk

constant-yield price trajectory

the price of a bond approaches par value as the maturity date nears assuming that the YTM remains the same

convexity effect

the percentage price change for a bond is greater than the YTM goes down than when it goes up by the same amount

matrix pricing

• is used to value illiquid bonds by using prices and yields of comparable but more frequently traded bonds with the same or similar features

• is used in underwriting new bonds to get an estimate of the required yield spread over the benchmark rate