FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging

A portfolio has key rate 01s of $4,000 at the 5-year point and $10,000 at the 10-year point. It is to be hedged by shorting two bonds. Bond A (5-year) has key rate 01s per $1 million face of $400 at 5 years and $0 at 10 years. Bond B (10-year) has $40 at 5 years and $800 at 10 years per $1 million face. To neutralize both key rate exposures, what face amount of Bond A must be shorted?

Short $8.75 million of Bond A. First the 10-year exposure fixes Bond B at $12.5 million, which already offsets $500 of the 5-year exposure. The remaining $3,500 at 5 years divided by $400 per million gives the Bond A amount.

A$8.75 millionCorrect
B$10.00 million
C$11.25 million
D$12.50 million

Explanation

Only Bond B has 10-year exposure, so 800b = 10,000 gives b = $12.5 million. Bond B contributes 40 x 12.5 = $500 at 5 years, leaving 4,000 - 500 = 3,500 for Bond A: a = 3,500/400 = $8.75 million. Ignoring Bond B's 5-year exposure gives $10 million, and adding it instead of subtracting gives $11.25 million.

Did you get it right without looking?

One question tells you little. A timed set on Modeling Non-Parallel Term Structure Shifts and Hedging shows your real accuracy, how long you take and where you lose marks.

Practise Modeling Non-Parallel Term Structure Shifts and Hedging Free diagnostic mock

More Modeling Non-Parallel Term Structure Shifts and Hedging questions