QUESTIONS 43-48 RELATE TO FIXED INCOME PORTFOLIO MANAGEMENT. QUESTIONS...

6.32 is the modified duration. If the portfolio is fully funded with GBP12 million to match the

present value of the liabilities, what is the effect on the surplus (asset PV - liability PV) of an

immediate 1.5 percentage point decrease in all yields?

A) There will be no change in the surplus.

B) The surplus will turn positive.

C) The surplus will turn negative.

Percent change in value can be estimated as:

[-MD × ∆Yield] + [½ × Convexity × (∆Yield)

²

]

Where MD is modified duration.

We know the initial surplus is zero (PVA = PVL).

We can calculate the estimated % change in value to the assets and liabilities to determine the

change in value of the surplus.

For a 1.5% decline in yields:

%∆Liabilities = [-6.34 × -0.015] + [½ × 47.75 × (-0.015)

²

] = +10.05%

%∆Portfolio S = [-6.32 × -0.015] + [½ × 68.34 × (-0.015)

²

] = +10.25%

Portfolio S's value rises by more than the liability, so the surplus turns from zero to positive.

For Further Reference:

Study Session 10, LOS 22.c, d, e

SchweserNotes: Book 3 p.253, 259, 265

CFA Program Curriculum: Vol.4 p.64, 78, 88

Question #46 of 60

How many long gilt futures contracts must be purchased to eliminate the duration gap in the

immunized group 2 liabilities?

A) 18.

B) 21.

C) 24.

Asset BPV is now below liability BPV, and therefore, bond contracts must be purchased. The

duration gap is: 31,207 - 29,324 = GBP1,883.

We will need the BPV of the contract, which is: BPV of CTD / CF of CTD: