Barbell, bullet, laddered - online question

CFA Level III Portfolio Management
#1

Neeson comments, “The durations for almost half of the bonds in the Wharton portfolio are clustered around 4 years, and the durations of the remainder around 12 years, while the durations of the Lawson portfolio bonds are clustered between 6 years and 8 years. In general, a laddered bond portfolio approach would improve liquidity management for both, although the Lawson portfolio would experience an increase in cash flow reinvestment risk and the Wharton portfolio would experience a decrease in convexity.”

Q. Is Neeson most likely correct in his assessment of the effects of a laddered bond portfolio approach on the Wharton and Lawson portfolios?

A. Yes
B. No, because the Lawson portfolio is a bullet portfolio where the duration of its assets are matched to the duration of its liabilities
C. No, because the duration of the Wharton liabilities is greater than that of the Lawson liabilities owing to the younger age of its participants

Solution: A is correct
A laddered portfolio has lower convexity and dispersion than a barbell portfolio but more than a bullet portfolio, given comparable duration and cash flow yields. Lower convexity and dispersion are desirable aspects in liquidity management. In a laddered portfolio, there is always a bond close to redemption enhancing liquidity. As bonds mature, the final coupon and principal are available for distribution or can be reinvested in a long-term bond at the back of the ladder. The Wharton portfolio is more of a barbell, has higher convexity than the Lawson portfolio, and would see a larger reduction in cash flow reinvestment risk with the reduction of convexity.

I do not understand anything from this solution (other than the fact that B and C are incorrect). Is the question poorly worded? Or what is it here that does not match?
Many thanks!

#2

The durations for almost half of the bonds in the Wharton portfolio are clustered around 4 years, and the durations of the remainder around 12 years

Since we are given four maturities, we have 4, 6, 8, and 12. Wharton’s holding looks like 4, 6, 8, 12. That’s a relatively barbelled structure.

the durations of the Lawson portfolio bonds are clustered between 6 years and 8 years

Lawson’s holding looks like 4, 6, 8, 12. That’s a relatively bulleted structure. They also used the word “clustered,” which is a giveaway that it is a bulleted structure.

Therefore, we now know that Wharton = barbell, and Lawson = bullet. Both of them are trying to switch to a laddered portfolio.

In a barbelled portfolio, the cash inflow from bond maturity is either on the 4 years, or the 12 years. Compare that to a laddered portfolio where, assuming simplicity, the holding is distributed equally on the 4, 6, 8, and 12 bonds. That means you have big cash inflows four times as opposed to only two (one four years from now, and another 12 years from now), which is what it would be on the barbelled scenario. The similar case can be made on the bulleted, where you will have cash inflow spread out on 4, 6, 8 and 12 as opposed to only 6 and 8. Therefore, the first statement of improving liquidity is accurate for both Wharton and Lawson.

On moving to laddered structure, Lawson - heretofore bulleted - will now have to reinvest some of his shorter-term bonds (e.g. the 4 year) to satisfy a liability sometime in the future (I am assuming his liabilities are further down the road, since he was holding a 6 and 8 year bond), thus introducing cash flow reinvestment risk.

On moving to laddered structure, Wharton - heretofore barbelled - will give up some of the convexity as he moves towards a laddered portfolio. Recall that barbelled portfolio has the most convexity, followed by laddered, and then bulleted as the portfolio with the least convexity among all three.

All statements are correct --> A is your answer.