FRM Part II · FRM Exam Part II · VaR Mapping
A bank holds a 3-year zero-coupon bond with present value of USD 10 million. The risk system has vertices at 2 years and 5 years only. Using duration mapping, what share of the position is allocated to the 2-year vertex? Assume the 2-year and 5-year vertices have durations of 2 and 5, and the allocation matches the bond's duration.
About 66.7% goes to the 2-year vertex. Duration mapping chooses weights so the combined duration equals the bond's duration of 3: 2w + 5(1-w) = 3 gives w = 2/3, leaving 33.3% at the 5-year vertex.
- A33.3%
- B66.7%Correct
- C60.0%
- D40.0%
Explanation
Let w be the weight at 2 years: 2w + 5(1-w) = 3, so 5 - 3w = 3, w = 2/3 = 66.7%. Check: 0.667*2 + 0.333*5 = 1.333+1.667 = 3. The 33.3% distractor is the weight at the 5-year vertex.
Did you get it right without looking?
One question tells you little. A timed set on VaR Mapping shows your real accuracy, how long you take and where you lose marks.
More VaR Mapping questions
- A bank's options book is hedged so that its net delta is zero. The risk manager reports a delta-normal VaR that is close to zero, even thoug…
- A $10 million equity position has a beta of 1.2 to an index whose daily volatility is 1.0%. The position's residual (specific) daily return …
- A risk team maps a large equity portfolio to a single market index using each stock's beta. The portfolio is concentrated in a few stocks of…
- A bank maps its equity options book to the underlying stocks using delta-normal mapping and measures VaR only from the underlying price move…
- A risk manager at a bank must compute VaR for a portfolio holding thousands of bonds, equities and derivatives. Instead of modelling each po…
- A portfolio holds USD 10 million of stock A with beta 1.2 and USD 5 million of stock B with beta 0.8. The market index has annual volatility…