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# fe535hw6 - RAROC, Economic Capital & Basel Accords 1....

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RAROC, Economic Capital & Basel Accords 1. Consider the following data for a particular sample period: Calculate the following performance measures for portfolio P and the market: Sharpe, Jensen (alpha), Treynor and Appraisal ratio. The T-bill rate during the period was 6%. By which measures did portfolio P outperform the market? a. Sharpe, Treynor, Appraisal b. Sharpe, Jensen, Treynor c. Sharpe, Jensen, Appraisal d. Jensen, Treynor, Appraisal Note: Appraisal ratio: Solution: d Sharpe: Formula = (35-6)/42 = 0.69 SM = (28-6)/30= 0.733 Treynor: Formula = (35-6)/1.2 = 24.2 TM = (28-6)/1 = 22 Jensen: Formula = 35 - (6+ 1.2 (28-6)) = 2.6 Appraisal: Formula = 2.6/18 = 0.144 2.A bond trader deals in \$100 million in a market with very high volatility of 20% per annum. He yields \$10 million profit. The risk capital (RC) is computed as a value-at-risk (VAR) measure at the 99% level over a year. Assuming a normal distribution of returns, calculate the risk- adjusted performance measure (RAPM). a. 15.35% b. 19.13% c. 21.46% d. 25.02% Solution:c) VAR is \$100 , 000 , 000 × 0 . 2 × 2 . 33 = \$46 , 600 , 000. Hence RAPM is \$10 / \$46 = 21 . 46% .

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3.Tim Brown and Steve Parker undertake trades that generate profits of \$5 million and USD 6 million, respectively. Both trades have face amounts of \$100 million. Brown trades mortgage- backed securities, with a volatility of 14%. Parker trades asset-backed securities, with a volatility of 16%. Based on a 99% confidence level RAROC (risk-adjusted return on capital), whose investment is superior? a. Brown b. Parker c. Same d. Cannot be determined from the information given Solution: b) The 99% one-year VAR, assuming a normal distribution, is 2 . 33 × \$100 ×14% = 32 . 6 and 37.3, for Brown and Parker, respectively. This gives a RAPM of 5 / 32 . 6 = 15 . 3% and 6 / 37 . 3 = 16 . 1%, respectively. Parker is better. Note that the choice of the horizon and confidence level is arbitrary in this case. 4. Suppose that a business line of a bank has a loan book of \$100 million. The average interest rate is 10%. The book is funded at a cost of \$5.5 million. The economic capital against these loans is \$7.5 million (7.5% of the loan value) and is invested in low-risk securities earning 5.5% per annum. Operating costs are \$1.5 million per annum, and the expected loss on this portfolio is assumed to be 1% per annum (i.e., \$1 million). The risk-adjusted return of the business line used in the computation of RAROC is: a. \$2.4125 million b. \$3 million c. \$1.5875 million d. \$2 million Solution: a) Revenues are, in millions, 10% × \$100 + 5 . 5% × \$7 . 5. Costs and expected losses are 5 . 5% × \$100 + \$1 . 5 + \$1. The difference is \$2.4125 million. 5. Following up on the previous question, the RAROC for this business line is:
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## This note was uploaded on 02/27/2010 for the course MA 535 taught by Professor Prasad during the Spring '10 term at Stevens.

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fe535hw6 - RAROC, Economic Capital & Basel Accords 1....

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