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A financial risk consultant assumes that the joint distribution of returns is multivariate normal and calculates the
following risk measures for a twoasset portfolio managed by a midsize insurance company:
Asset Position (JPY) Individual VaR (JPY) Marginal VaR
Financial 20,000,000 4,787,400 0.316
RealEstate 20,000,000 7,299,300 0.562
Portfolio 40,000,000 11,562,450
Question: What is the closest to the correct estimate for the component VaR of the financial asset?
A. JPY 4,787,000
B. JPY 6,322,000
C. JPY 7,299,000
D. JPY 11,240,000
Official explanation:
Firstly, if you punch all the numbers into the calculator, you get 6,320,000, so there is a 2000 calculation error.
Secondly, why are they bothering with the beta????? Marginal var is the measure of how much component var will increase for a unit of asset value increase. So the answer, by definition of marginal VaR is as simple as:
CVaR=MVaR*AssetValue=0.316*20,000,000=6,320,000 (1)
In fact, if you write out the two "official" formulas above on a piece of paper, you will see that (Portfolio VaR) cancels out, and you are left with:
(Marginal VaRf*Portfolio Value)*(Asset Weight) (2)
Asset weight is nothing but AssetValue/(Portfolio Value), so (Portfolio Value) also cancels out in (2), and you are left with (1).
Why are they taking the scenic route? Am I missing something?
following risk measures for a twoasset portfolio managed by a midsize insurance company:
Asset Position (JPY) Individual VaR (JPY) Marginal VaR
Financial 20,000,000 4,787,400 0.316
RealEstate 20,000,000 7,299,300 0.562
Portfolio 40,000,000 11,562,450
Question: What is the closest to the correct estimate for the component VaR of the financial asset?
A. JPY 4,787,000
B. JPY 6,322,000
C. JPY 7,299,000
D. JPY 11,240,000
Official explanation:
Firstly, if you punch all the numbers into the calculator, you get 6,320,000, so there is a 2000 calculation error.
Secondly, why are they bothering with the beta????? Marginal var is the measure of how much component var will increase for a unit of asset value increase. So the answer, by definition of marginal VaR is as simple as:
CVaR=MVaR*AssetValue=0.316*20,000,000=6,320,000 (1)
In fact, if you write out the two "official" formulas above on a piece of paper, you will see that (Portfolio VaR) cancels out, and you are left with:
(Marginal VaRf*Portfolio Value)*(Asset Weight) (2)
Asset weight is nothing but AssetValue/(Portfolio Value), so (Portfolio Value) also cancels out in (2), and you are left with (1).
Why are they taking the scenic route? Am I missing something?
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