You have recently joined a Bank, a large systemically important financial institution

Use this information to answer questions 1-5

You have recently joined a Bank, a large systemically important financial institution that has two business units, Division 1 and Division 2. Important financial characteristics of the two divisions appear in the table below where all figures are reported in billions of dollars. Note for clarity operational costs reflect operating expenses to run the business.

In addition you are provided with the variance-covariance matrix for Division 1 and 2 losses as shown below where variances are reported on the diagonal and covariances are off diagonal. The bank faces only two risks for which it needs to measure its risk exposure against the Board tolerance; credit and operational. You may assume that the matrix below is the same to apply for credit losses as it is for total (credit plus operational) losses of each division.

Variance-Covariance Matrix

The bank has established a hurdle rate of 15% and the Board of Directors requires the bank to maintain its risk positions within a 97.5% level of confidence. You know that a value of plus or minus 1.96 standard deviations accounts for about 5% of all outcomes under the standard normal distribution while a value of plus or minus 1.65 standard deviations accounts for about 10% of all outcomes. The bank as a regulated entity must comply with Basel capital standards and faces a required capital charge of 4% of assets in each division.

In addition, Division 1 and 2’s operational risk capital are estimated to be $3B and $7B, respectively. You also determine that expected operational losses are $1B and $2B for Division 1 and 2, respectively. Along with that you find that the correlation between credit and operational losses for Division 1 is .833 and the correlation between credit and operational losses for Division 2 is .75.

1)
What is the highest credit loss the bank would be willing to take for each division given the information above? Full credit requires a numeric and verbal answer with specific terms used in risk management to convey understanding and you must show all work

2)

What amount would you need to put aside for each division for credit risk based on the information above?

3)

How do the two divisions compare in terms of financial performance unadjustedfor risk? Specifically which division is better? A quantitative response is required.

4)

Provide 2 measures for each division adjusting for risk and describe the performance differences between the divisions and state what these measures are.

5)

What is the total risk capital that should be assigned to Division 1 separately and to Division 2 separately? What inference can you make with respect to any diversification benefit?