1. Calculate the risk-adjusted asset base for a bank under the following:
a. Cash of $20 million, 0%
b. General Obligation municipal security of $100 million, 20%
c. Singe family home mortgages of $500 million, 50%
d. Commercial loans of $300 million, 100%.
- If the bank has no off-balance sheet activity what is the banks minimum required level of Tier1 and Tier 2 capital?
- If the bank has Tier 1 capital of $25 million and Tier 2 capital of $15 million does the bank comply with its capital requirement?
- Also, explain how the addition of off-balance sheet activities might impact the capital requirement of the bank.
2. If the rate on a one-year T-bill is currently 6% what is the probability of repayment and the risk premium on the following two securities. Assume that if the loan is defaulted, no payments are expected.
A. 1 year AA-rated loan yielding 9 percent
B. 1 year BB rated loan yielding 13 percent. 15 points
3. Calculate the FI's annual rate of return on a loan if:
a. Fees are 0.25%, the base loan rate is 10% annually, the borrower's risk premium is 2%, compensating balances are 5% and the reserve requirements are 10%?
b. Explain what is meant by compensating balances and collateral.
4. Calculate the term structure of default probabilities from the following information. Calculate annual marginal default probability for year one and two. Also, estimate the cumulative probability of default for time period 2, cp02?
Spot Spot Spot
1 year 2 year 3 year
Treasury Bonds 5.0% 5.0% 5.0%
BBB rated Bonds 7.0% 8.2% 9.3%
In general, what happens to the probability of repayment as the yield curve increases in slope?
5. A bank is planning to make a loan of $3,000,000 to a firm in the steel industry. It expects to charge an up-front fee of 1.25% and a servicing fee of 100 basis points. The loan has a maturity of 12 years with duration of 8.5 years. The cost of funds (the RAROC benchmark) for the bank is 8 percent. Assume the bank has estimated the risk premium on the steel manufacturing sector to be 2%, based on two years historical data. The current market interest rate for loans in this sector is 10%. Estimate the RAROC for the loan.
Would you accept or reject the loan based upon RAROC 20?
Risk-Adjusted Asset Base
The calculation of the risk-adjusted asset base for a bank is as below-
Risk-adjusted asset = (Cash × 0%) + (municipal security × 20%) + (home mortgages × 50%) + (Commercial loans × 100%)
= (20 × 0%) + (100 × 20%) + (500 × 50%) + (300$ × 100%)
= 0 + 20 + 250 + 300
= $570 million
The outcome shows that the risk-adjusted or weighted asset based for the bank will be $570 million.
Tier1 and Tier 2 Capital:
If the bank has no off-balance sheet activity then minimum required level of Tier 1 and Tier 2 capital will be-
Tier 1 capital = Risk-weighted asset × 4%
= $570 × 4%
= $22.8 million
Tier 2 capital = Maximum of 1.25% of risk-weighted asset
= $570 × 1.25%
= $7.125 million
Total capital = $22.8 + $7.125 => $29.925 million
The outcomes indicate that the minimum required level of Tier1 and Tier 2 capital is $22.8 million and $7.125 million for the bank.
Bank Comply with Capital Requirements:
If the bank has Tier 1 capital of $25 million and Tier 2 capital of $15 million then it will comply with its capital requirements of $29.925 million. It is because in this situation, total capital of bank is $37 million that is higher than the above calculated capital of $29.925 million.
Impact of off-Balance Sheet Activities on Capital Requirements
The addition of off-balance sheet activities might increase the capital requirement of the bank. It is because an off-balance sheet items is a financial contract that can create credit loss for the company due to credit risk. So, in case of adding off-balance sheet activities, a bank will require more capital to cover credit loss. Along with this, it can also increase the minimum ratio of capital to risk-weighted assets from 8% and in that situation; the bank will need more capital (Carmichael & Graham, 2012).
Probability of Repayment and Risk Premium
If the rate on a one-year treasury bill is 6% and in case of loan default, no payments are expected on financial securities then the probability of repayment and the risk premium on 1 year AA-rated loan yielding 9 percent will be-
Probability of Repayment:
The following formula can be useful to determine probability of repayment.
P = (1 + I) / (1 + k)
I = 6%
k = 9%
The expert calculates the risk-adjusted asset based for a bank. The general obligation municipal security is determined. The commercial loans are analyzed.