Explanation:
The cost of liquidation for a position under a stressed market scenario at a given confidence level is calculated using the proportional bid-offer spread:
Cost of Liquidation = 0.5 × Σ [Position_i × (μ_p,i + Z × σ_p,i)]
Given the mid-market positions (the options units imply the positions are in millions):
$1,235 million$627 millionFor a 99% confidence level in a normal distribution, the Z-score is approximately 2.326.
For Shares:
$1,235 million × 0.059931 = $37.0076 millionFor the Commodity:
$627 million × 0.018885 = $5.9205 millionTotal Cost of Liquidation = $37.0076 million + $5.9205 million = $42.9281 million.
This closely matches option C ($42.93 million).
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Q.2 Suppose that a bank invests in shares and a commodity whose mid-market position is 1,235, and 627 respectively, the mean and standard deviation for the bid-offer spread for the shares is $1.2 and $1.4. Given that the mean and standard deviation for the bid-offer spread of the commodity are both $0.14, and the mean and standard deviation for the proportional bid-offer spread for the shares are 0.02346 and 0.01568, respectively. Furthermore, the mean and standard deviation for the proportional bid-offer spread for the commodity are both 0.005678. Assuming the distribution of the spreads is normal, calculate the cost of liquidation in a stressed market at a 99% confidence level.
A
$32.45 million
B
$50.23 million
C
$42.93 million
D
$54.86 million