The probability that this bank will go bankrupt if it has a leverage of 10 to 1 (l = 10) is 0.05
How the probability is determined.
Given asset value = 10
Leverage = 10
Equity, E = Asset value/Leverage = 10/10 = 1
Debt = asset value-equity = 10-1 = 9
The ftable shows the different values of equity next period for different asset values:
Asset Probability Debt (D) Equity (E)
7 5% 9. -2
9 20%. 9. 0
11 50% 9. 2
13 20% 9 4
15 5.00% 9 6
Equity is calculated as: Equity = Asset-Debt
From the above table
the bank's equity is negative or 0 at asset value is 7 or 9.
Therefore, probability of bankruptcy = Probabiity of asset value is 7 + Probabiity of asset value is 9 = 5/100 + 20/100 = 25%
For leverage, L = 5
Equity, E = Asset value/Leverage = 10/5 = 2
Debt = asset value-equity = 10-2 = 8
The table shows the different values of equity next period for different asset values:
Asset Probability Debt (D) Equity €
7 5% 8 -1
9 20% 8 1
11 50% 8 3
13 20% 8 5
15 5.00% 8. 7
Equity is calculated as: Equity = Asset-Debt
From the above table,
the bank's equity is negative or 0 at asset value 7.
Therefore, probability of bankruptcy = Probabiity of asset value is 7 = 5%
Complete question