VRM11 - Bond Yields and Return Calculations

Question 1

Distinguish between gross and net realised returns and calculate the realised return for a bond over a holding period including reinvestments

Answer 1

Gross return is all income from the investment, net takes into account financing costs

Question 2

Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing

Answer 2

YTM is a single discount rate which if applied to all cashflows, the PV of cashflows would equal the bonds market price

PV = sum(i = 1 to 2T) (1 / (1 + y/2))^i + 100 / (1 + y/2)^T

Question 3

Calculate the price of an annuity and a perpetuity

Answer 3

Annuity = C/y [ 1 - 1/(1+y/2)^2T ]

Perpetuity = c / y

Question 4

Explain the relationship between YTM and spot rates

Answer 4

If no coupon, spot rate = YTM

Question 5

Define the coupon effect and explain the relationship between coupon rate, YTM and bond prices

Answer 5

Coupon effect is where correctly priced bonds with equal maturities and different coupons have different YTMs

• where y = coupon rate, bond sells for face value
• where y > c, bond sells for less than face value
• where c < y, bonds sells for more than face value

Question 6

Explain the decomposition of the profit and loss for a bond position or portfolio including carry roll-down, rate change, and spread change effects

Answer 6

Carry roll down estimates return if there is no change to some aspect of the interest rate environment

Rate change is return when interest rates differ from that in carry roll down

Spread change is when a bond’s spread relative to other bonds changes