
Explanation:
The total asset value () of the bank is the sum of its liabilities and equity: 29.0 + 17.0 + 20.0 + 13.0 = $79.0 billion.
To find the required debt level () that results in a 1% probability of default (a 99.0% confidence level for economic capital), we use the distance to default (DD) formula:
For a 99.0% confidence level (1-tailed normal distribution), the critical value (or DD) is approximately 2.33.
Plugging in the values:
Solving for gives K \approx \`46.0$ billion. The Economic Capital (EC) is the difference between the current total asset value and this threshold $K$: $EC = V_0 - K = 79.0 - 46.0 = \ billion.
This matches option B perfectly.
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920.1. A bank's asset value has an expected return (ROA) of 15.0% with volatility of 28.0% per annum. Further, here are the market values of the right-hand side of its balance sheet; i.e., liabilities and equity:
$29.0 billion$17.0 billion$20.0 billion$13.0 billionImportantly, and to keep things unrealistically simple, we will assume the bank's asset price has a lognormal distribution. Assuming the displayed calculations are correct (which they are), which of the following represents the bank's 99.0% one-year economic capital (EC)?
A
$12.0 billion because [LN($41.1/$29.0) + 0.150 - 0.280^2/2]/0.28 = 1.65
B
$33.0 billion because [LN($79.0/$46.0) + 0.150 - 0.280^2/2]/0.28 = 2.33
C
$47.3 billion because [LN($127.3/$80.0) + 0.150 - 0.280^2/2]/0.28 = 2.06
D
$56.4 billion because [LN($123.4/$67.0) + 0.150 - 0.280^2/2]/0.28 = 2.58
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