Homework 4_Bank Management

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Jan 9, 2024

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1 4th Set of Homework (Due Date: November 8, 2023) Ch15 9. Bank Alpha has an inventory of AAA-rated, 15-year zero-coupon bonds with a face value of $400 million. The bonds currently are yielding 9.5 percent in the over-the-counter market. a. What is the modified duration of these bonds? 15/(1.095) = -13.6986. b. What is the price volatility if the potential adverse move in yields is 25 basis points? = (-13.6986) x (.0025) = -0.03425 or -3.425 percent. c. What is the DEAR? = 400/(1 + 0.095) 15 = $102.5293million. DEAR = $102.5293499 million x -0.03425 = -$3.5116 million d. If the price volatility is based on a 90 percent confidence limit and a mean historical change in daily yields of 0.0 percent, what is the implied standard deviation of daily yield changes? s = .0025/1.65 = .001515 or 15.15 basis points. 11. Bank Two has a portfolio of bonds with a market value of $200 million. The bonds have an estimated price volatility of 0.95 percent. What are the DEAR and the 10-day VAR for these bonds? $200 million x .0095 = $1.9million = $1,900,000 x Ö 10 = $1,900,000 x 3.1623 = $6,008,327.55

2 12. Bank of Southern Vermont has determined that its inventory of 20 million euros (€) and 25 million British pounds (£) is subject to market risk. The spot exchange rates are $0.40/€ and $1.28/£, respectively. The s ’s of the spot exchange rates of the € and £, based on the daily changes of spot rates over the past six months, are 65 bp and 45 bp, respectively. Determine the bank’s 10-day VAR for both currencies. Use adverse rate changes in the 90 th percentile. FX position of € = 20m x 0.40 = $8 million FX position of £ = 25m x 1.28 = $32 million FX volatility € = 1.65 x 65bp = 107.25, or 1.0725% FX volatility £ = 1.65 x 45bp = 74.25, or 0.7425% DEAR = ($ Value of position) x (Price volatility) DEAR of € = $8m x .010725 = $0.0860m, or $85,800 DEAR of £ = $32m x .007425 = $0.2376m, or $237,600 VAR of € = $138,000 x Ö 10 = $85,800 x 3.1623 = $271,323.42 VAR of £ = $237,600 x Ö 10 = $237,600 x 3.1623 = $751,357.17 14. Bank of Alaska’s stock portfolio has a market value of $10 million. The beta of the portfolio approximates the market portfolio, whose standard deviation ( s m ) has been estimated at 1.5 percent. What is the five-day VAR of this portfolio using adverse rate changes in the 99 th percentile? DEAR= $10m x (2.33 x .015) = $10m x .03495 = $0.3495m or $349,500 VAR = $349,500 x Ö 5 = $349,500 x 2.2361 = $781,505.76 15. Jeff Resnick, vice president of operations at Choice Bank, is estimating the aggregate DEAR of the bank’s portfolio of assets consisting of loans (L), foreign currencies (FX), and common stock (EQ). The individual DEARs are $300,700, $274,000, and $126,700 respectively. If the correlation coefficients ( r ij ) between L and FX, L and EQ, and FX and EQ are 0.3, 0.7, and 0.0, respectively, what is the DEAR of the aggregate portfolio?

3 19. Export Bank has a trading position in euros yen and Australian dollars. At the close of business on October 20, the bank had €20 million and A$30 million. The exchange rates for the most recent six days are given below: Exchange Rates per U.S. Dollar at the Close of Business 10/20 10/19 10/18 10/17 10/16 10/15 Euros 1.3900 1.3870 1.3675 1.3775 1.3850 1.4015 Australian $s 0.7800 0.7650 0.7900 0.7755 0.7605 0.7560 a. What is the foreign exchange (FX) position in dollar equivalents using the FX rates on October 20? Euros: 20,000,000/1.3900= $14,388,489.21 Australian: 30,000,000/.788= $38,461,538.46 b. What is the sensitivity of each FX position; that is, what is the value of delta for each currency on October 20? Euros: 1.01 * 1.39= 1.4039 20,000,000/1.4039= $14,246,028.92 = $14,246,028.92-$14,388,389.21 = $-142,460.29 Australian: 1.01 * .7800 = .7878 30,000,000/.7878= $38,080,731.15 =$38,080,731.15- 308,461,538.46 = $-380,807.31 [ ] 219 , 533 $ 000 , 626 , 322 , 284 $ ) 700 , 126 )($ 000 , 274 )($ 0 . 0 ( 2 ) 700 , 126 )($ 700 , 300 )($ 7 . 0 ( 2 ) 000 , 274 )($ 700 , 300 )($ 3 . 0 ( 2 700 , 126 $ 000 , 274 $ 700 , 300 $ ) 2 ( ) 2 ( ) 2 ( ) ( ) ( ) ( 5 . 0 5 . 0 2 2 2 5 . 0 , , , 2 2 2 = = ú û ù ê ë é + + + + + = ú ú ú ú ú û ù ê ê ê ê ê ë é + + + + + = EQ FX EQ FX EQ L EQ L FX L FX L EQ FX L DEAR x DEAR x DEAR x DEAR x DEAR x DEAR x DEAR DEAR DEAR portfolio DEAR r r r

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4 c. What is the daily percentage change in exchange rates for each currency over the five- day period? Euro: Australian: 10/20 10/19 10/18 10/17 10/16 d. What is the total risk faced by the bank on each day? What is the worst-case day? What is the best-case day? 10/20 -$142,460 0.21629% -$308.13 -$380,807 1.96078% -$7,466.79 -$7,774.92 10/19 -$142,460 1.42596% -$2,031.43 -$380,807 -3.16456% $12,050.88 $10,019.45 10/18 -$142,460 -0.72595% $1,034.19 -$380,807 1.86976% -$7,120.18 -$6,085.99 10/17 -$142,460 -0.54152% $771.45 -$380,807 1.97239% -$7,511.01 $6,739.56 10/16 -$142,460 -1.17731% $1,677.20 -$380,807 0.59524% -$2,266.72 -$589.52 0.21629% 1.42596% -0.72595% -0.54152% -1.17731% 1.96078% -3.16456% 1.86976% 1.97239% 0.59524%