Original practice · fully worked
Original variant: convexity test for a conservation fund
A conservation fund's liabilities have present value 10,000, Macaulay duration 6, and Macaulay convexity 40. It allocates current values 5,000 to a two-year zero and 5,000 to a ten-year zero. Determine whether the Redington conditions hold.
- A
They fail because present value differs. - B
They fail because duration differs. - C
They hold: value and duration match, and asset convexity is larger. - D
They fail because asset convexity is larger. - E
The information is insufficient.
Answer and calculation
Asset value is 10,000, duration is 6, and convexity is 52, which exceeds 40; choice C.
Setup
Setup
For zero-coupon positions, duration equals maturity and Macaulay convexity equals squared maturity.
PVA=5000+5000=10000 Model
Model
Current values supply the weights for both risk measures.
DA=100002(5000)+10(5000)=6 Compute
Compute
The two equal investments average to duration six and convexity 52 while preserving the required present value.
CA=1000022(5000)+102(5000)=52>40 Answer
Answer
Since value and duration match and asset convexity is higher, choice C is correct.
Redington conditions hold(C) 