Question

Explain the impact of the steepening of the yield curve on two bonds portfolios. Both portfolios have equal Macaulay’s duration. The first portfolio is designed as a bullet (100% allocation to the mid-maturity in the yield curve) and the other as a barbell (allocation split between the short and the long maturities in the yield curve). You must demonstrate your answer with an example.

1. Explain the bullet and barbell strategy and why investor are indifferent between choosing one or the other when no expectations regarding changes in the terms structure.

2. Explain the link between yield curve flattening or steepening on the two investment strategies.

3. Show using an example: create the two portfolios and ensure durations are matched.

4. Explain how when yield curve flattens/steepens the effect on the two strategies.

Answer 1

Ans:

a) Bullet Startegy : This is the strategy considered by the investor, where he will buy the bonds of same maturity to earn higher yield, interest rate volatility high, but return can be high.

b) Barebell Strategy : It is strategy where, investor is risk averse and would better like to manage risk . So, he invest in short and long maturities of bonds together.

As the duration is same for bith portfolios, the returns would not be different and hence, investor are indifferent.

2) In case if yield curve is flattening means the long term yield will go down and prices of the bond will rise bullet strategy would not be effective.

If yield curve steepens , means the long term yield will rise and hence the bond of long maturity price will go down . And can be bought at cheaper price.

3) Let's consider 3 bonds with face value = 100

Bond	Coupon	Maturity	Price	YTM	Duration_m
A	0.085	5	100	0.085	4.0054435
B	0.095	20	100	0.095	8.8815081
C	0.0925	10	100	0.0925	6.43409

For bullet strategy if we take 100% investment in C, duration is 6.43

For barebell strategy we need to invest in A (short term bond) and B(long term).

Let x be the % to be invested in A and 1-x for B , as duration should equal:

x*4.005 +(1-x)*8.88 = 6.43 , on solving we get , x = 50.2% and 1-x = 49.8%

4) In case if yield flattens , the long term yield will go down and short term will rise, that would give advantage when we consider portfolios with too short and long maturities as these are too far end, where we can get the maximum benefit. But same is not the case when bullet is used as minimum gain will achieved, since, the long term yield go down.

In case if the yield curve steepning the long term yield will rise, give a far better returns if we will use bullet strategy . While in case of barebell the loss will be booked as short term yield is low and long term high.