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# P1.T4.920. Economic capital relative to credit risk (Schroeck)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
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Learning objectives: Evaluate a bank’s economic capital relative to its level of credit risk. Identify and describe important factors used to calculate economic capital for credit risk: probability of default, exposure, and loss rate.

Questions:

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:
• Deposits: $29.0 billion • Senior debt:$17.0 billion
• Junior debt: $20.0 billion • Shareholder's equity:$13.0 billion
Importantly, 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

920.2. Consider a credit portfolio that includes many loans. In order to derive economic capital (EC) for credit risk, we need to quantify four measures: expected losses (EL), unexpected losses, unexpected loss contribution (ULC), and economic capital (EC). In regard to these four measures, each of the following definitions or descriptions is true EXCEPT which is inaccurate?

a. Expected losses (EL) can be viewed as payments to an insurance pool, does not itself constitute risk, and is reimbursed through adequate loan pricing
b. Unexpected losses (UL) is the standard deviation of credit losses around the expected loss average
c. Unexpected loss contribution (ULC) is the first partial derivative of the portfolio's unexpected loss (portfolio UL) with respect to the position's weight, w(i)
d. Economic capital (EC) for credit risk is the difference between the expected outcome and the unexpected, negative outcome at a certain confidence level

920.3. Which distribution is most appropriate to generate the variance of the loss rate (LR)?

a. Binomial or Poisson
b. Uniform or exponential
c. Chi-squared or gamma
d. Normal or beta distribution

As total asset of bank is $79 and critical thresh hold capital is$ 46, so S is 79 and K is 46. The answer given in (B) is d2 calculation. As d2 is the negative Z score of $46, n(d2) provides only the probability of total asset value($79) falling below d2($46), given a mean of .15 and SD of .28. To find economic capital at 99 pc confidence level ,I think more working needs to be done. The calculation is 79*(.15)+79*(.28)*2.32=$ 63, which provides the extent to which the total asset value can fall with 99 pc confidence level. Thus the asset value at that extreme low becomes 16 (79-63). So economic capital of \$30(46-16) should be required for 99 pc confidence level. Since Bionic turtle comprises experts of financial engineering, so I thought of sharing my idea.