LM10: Interest rate risk and return

Fixed-rate bond investors have three sources of return

• receipt of promised coupon and principal payments on the schedule dates

• reinvestment of coupon payments

• potential capital gains/losses on the sale of the bond prior to maturity

the horizon yield matches the original YTM if

• the investor holds the bond to maturity

• there is no default by the issuer

• coupon payments are reinvested at the original YTM

reinvestment risk

is the risk that the future value of reinvested coupon payments increases when interest rates rise and decreases when interest rates fall

price risk

is the risk that the sale price on a bond that matures after the horizon date decreases when interest rates rise and increases when interest rates fall

price risk dominates reinvestment risk for short-term investors

while reinvestment risk dominates market price risk for long-term investors

macaulay duration

is the weighted average of the time of receipt of a bond’s cash flow, where the weights of each cash flow in the calculation are each cash flow’s share of the bond’s full price

investment horizon = macaulay duration

• duration gap = 0

• reinvestment risk offsets price risk

• investor is hedged against interest rate risk

investment horizon > macaulay duration

• duration gap is negative

• reinvestment risk dominates price risk

• investor is at risk of lower interest rates

investment horizon < macaulay duration

• duration gap is positive

• price risk dominates reinvestment risk

• investor is at risk of higher interest rates

duration gap

• macaulay duration - investment horizon