Chapter Seven Risks of Financial Intermediation

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1 Chapter Seven Risks of Financial Intermediation Selected Solutions for End-of-Chapter Questions and Problems: Chapter Seven. What is refinancing risk? How is refinancing risk part of interest rate risk? If an FI funds long-term fixed-rate assets with short-term liabilities, what will be the impact on earnings of an increase in the rate of interest? A decrease in the rate of interest? Refinancing risk is the uncertainty of the cost of a new source of funds that are being used to finance a long-term fixed-rate asset. This risk occurs when an FI is holding assets with maturities greater than the maturities of its liabilities. For example, if a bank has a ten-year fixed-rate loan funded by a -year time deposit, the bank faces a risk of borrowing new deposits, or refinancing, at a higher rate in two years. Thus, interest rate increases would reduce net interest income. The bank would benefit if the rates fall as the cost of renewing the deposits would decrease, while the earning rate on the assets would not change. In this case, net interest income would increase. 3. What is reinvestment risk? How is reinvestment risk part of interest rate risk? If an FI funds short-term assets with long-term liabilities, what will be the impact on earnings of a decrease in the rate of interest? An increase in the rate of interest? Reinvestment risk is the uncertainty of the earning rate on the redeployment of assets that have matured. This risk occurs when an FI holds assets with maturities that are less than the maturities of its liabilities. For example, if a bank has a two-year loan funded by a ten-year fixed-rate time deposit, the bank faces the risk that it might be forced to lend or reinvest the money at lower rates after two years, perhaps even below the deposit rates. Also, if the bank receives periodic cash flows, such as coupon payments from a bond or monthly payments on a loan, these periodic cash flows will also be reinvested at the new lower (or higher) interest rates. Besides the effect on the income statement, this reinvestment risk may cause the realized yields on the assets to differ from the a priori expected yields. 6. A financial institution has the following balance sheet structure: Assets Liabilities and Equity Cash $1,000 Certificate of Deposit $10,000 Bond $10,000 Equity $1,000 Total Assets $11,000 Total Liabilities and Equity $11,000 The bond has a 10-year maturity and a fixed-rate coupon of 10 percent. The certificate of deposit has a 1-year maturity and a 6 percent fixed rate of interest. The FI expects no additional asset growth. a. What will be the net interest income (NII) at the end of the first year? Note: Net interest income equals interest income minus interest expense. Interest income $1,000 $10,000 x 0.10

2 Interest expense 600 $10,000 x 0.06 Net interest income (NII) $400 b. If at the end of year 1 market interest rates have increased 100 basis points (1 percent), what will be the net interest income for the second year? Is the change in NII caused by reinvestment risk or refinancing risk? Interest income $1,000 $10,000 x 0.10 Interest expense 700 $10,000 x 0.07 Net interest income (NII) $300 The decrease in net interest income is caused by the increase in financing cost without a corresponding increase in the earnings rate. Thus, the change in NII is caused by refinancing risk. The increase in market interest rates does not affect the interest income because the bond has a fixed-rate coupon for ten years. Note: this answer makes no assumption about reinvesting the first year s interest income at the new higher rate. c. Assuming that market interest rates increase 1 percent, the bond will have a value of $9,446 at the end of year 1. What will be the market value of the equity for the FI? Assume that all of the NII in part (a) is used to cover operating expenses or is distributed as dividends. Cash $1,000 Certificate of deposit $10,000 Bond $9,446 Equity $ 446 Total assets $10,446 Total liabilities and equity $10,446 $10,599.5 d. If market interest rates had decreased 100 basis points by the end of year 1, would the market value of equity be higher or lower than $1,000? Why? The market value of the equity would be higher ($1,600) because the value of the bond would be higher ($10,600) and the value of the CD would remain unchanged. e. What factors have caused the change in operating performance and market value for this firm? The operating performance has been affected by the changes in the market interest rates that have caused the corresponding changes in interest income, interest expense, and net interest income. These specific changes have occurred because of the unique maturities of the fixed-rate assets and fixed-rate liabilities. Similarly, the economic market value of the firm has changed because of the effect of the changing rates on the market value of the bond. 1. A bank invested $50 million in a two-year asset paying 10 percent interest per annum and simultaneously issued a $50 million, one-year liability paying 8 percent interest per annum. What will be the bank s net interest income each year if at the end of the first year all interest rates have increased by 1 percent (100 basis points)?

3 Net interest income is not affected in the first year, but NII will decrease in the second year. Year 1 Year Interest income $5,000,000 $5,000,000 Interest expense $4,000,000 $4,500,000 Net interest income $1,000,000 $500,000 Chapter Eight Interest Rate Risk I Selected Solutions for End-of-Chapter Questions and Problems: Chapter Eight 3. What is the repricing gap? In using this model to evaluate interest rate risk, what is meant by rate sensitivity? On what financial performance variable does the repricing model focus? Explain. The repricing gap is a measure of the difference between the dollar value of assets that will reprice and the dollar value of liabilities that will reprice within a specific time period, where reprice means the potential to receive a new interest rate. Rate sensitivity represents the time interval where repricing can occur. The model focuses on the potential changes in the net interest income variable. In effect, if interest rates change, interest income and interest expense will change as the various assets and liabilities are repriced, that is, receive new interest rates. 5. Calculate the repricing gap and the impact on net interest income of a 1 percent increase in interest rates for each of the following positions: Rate-sensitive assets = $00 million. Rate-sensitive liabilities = $100 million. Repricing gap = RSA - RSL = $00 - $100 million = +$100 million. ΔNII = ($100 million)(.01) = +$1.0 million, or $1,000,000. Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million. Repricing gap = RSA - RSL = $100 - $150 million = -$50 million. ΔNII = (-$50 million)(.01) = -$0.5 million, or -$500,000. Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million. million. Repricing gap = RSA - RSL = $150 - $140 million = +$10 ΔNII = ($10 million)(.01) = +$0.1 million, or $100,000. a. Calculate the impact on net interest income on each of the above situations assuming a 1 percent decrease in interest rates.

4 ΔNII = ($100 million)(-.01) = -$1.0 million, or -$1,000,000. ΔNII = (-$50 million)(-.01) = +$0.5 million, or $500,000. ΔNII = ($10 million)(-.01) = -$0.1 million, or -$100,000. b. What conclusion can you draw about the repricing model from these results? The FIs in parts (1) and (3) are exposed to interest rate declines (positive repricing gap) while the FI in part () is exposed to interest rate increases. The FI in part (3) has the lowest interest rate risk exposure since the absolute value of the repricing gap is the lowest, while the opposite is true for part (1). 8. Which of the following assets or liabilities fit the one-year rate or repricing sensitivity test? 91-day U.S. Treasury bills 1-year U.S. Treasury notes 0-year U.S. Treasury bonds 0-year floating-rate corporate bonds with annual repricing 30-year floating-rate mortgages with repricing every two years 30-year floating-rate mortgages with repricing every six months Overnight fed funds 9-month fixed rate CDs 1-year fixed-rate CDs 5-year floating-rate CDs with annual repricing Common stock No No No 11. Use the following information about a hypothetical government security dealer named M.P. Jorgan. Market yields are in parenthesis, and amounts are in millions. Assets Liabilities and Equity Cash $10 Overnight Repos $170 1 month T-bills (7.05%) 75 Subordinated debt 3 month T-bills (7.5%) 75 7-year fixed rate (8.55% 150 year T-notes (7.50%) 50 8 year T-notes (8.96%) year munis (floating rate) (8.0% reset every 6 months) 5 Equity 15 Total Assets $335 Total Liabilities & Equity $335 a. What is the funding or repricing gap if the planning period is 30 days? 91 days? years? Recall that cash is a noninterest-earning asset. Funding or repricing gap using a 30-day planning period = = -$95 million. Funding gap using a 91-day planning period = ( ) = -$0 million.

5 Funding gap using a two-year planning period = ( ) = +$55 million. b. What is the impact over the next 30 days on net interest income if all interest rates rise 50 basis points? Decrease 75 basis points? Net interest income will decline by $475,000. ΔNII = FG(ΔR) = -95(.005) = $0.475m. Net interest income will increase by $71,500. ΔNII = FG(ΔR) = -95(.0075) = $0.715m. c. The following one-year runoffs are expected: $10 million for two-year T- notes, and $0 million for eight-year T-notes. What is the one-year repricing gap? Funding or repricing gap over the 1-year planning period = ( ) = +$35 million. d. If runoffs are considered, what is the effect on net interest income at year-end if interest rates rise 50 basis points? Decrease 75 basis points? Net interest income will increase by $175,000. ΔNII = FG(ΔR) = 35(0.005) = $0.175m. Net interest income will decrease by $6,500, ΔNII = FG(ΔR) = 35( ) = -$0.65m. 6. Gunnison Insurance has reported the following balance sheet (in thousands): Assets Liabilities and Equity -year Treasury note $175 1-year commercial paper $ year munis $165 5-year note $160 Equity $45 Total Assets $340 Total Liabilities & Equity $340 All securities are selling at par equal to book value. The two-year notes are yielding 5 percent, and the 15-year munis are yielding 9 percent. The one-year commercial paper pays 4.5 percent, and the five-year notes pay 8 percent. All instruments pay interest annually. a. What is the weighted-average maturity of the assets for Gunnison? M A = [*$ *$165]/$340 = 8.31 years b. What is the weighted-average maturity of the liabilities for Gunnison? M L = [1*$ *$160]/$95 = 3.17 years c. What is the maturity gap for Gunnison?

6 MGAP = = 5.14 years d. What does your answer to part (c) imply about the interest rate exposure of Gunnison Insurance? Gunnison Insurance is exposed to interest rate risk. If interest rates rise, net worth will decline because the average maturity of the assets is higher than the average maturity of the liabilities. The opposite holds true if interest rates fall (That is, net worth will increase.) Selling at par => C=YTM= 5% => CF =.05*175 e. Calculate the values of all four securities of Gunnison Insurance s balance sheet assuming that all interest rates increase percent. What is the dollar change in the total asset and total liability values? What is the percentage change in these values? F=175 T-notes: PV = 8.75*PVIFA i=7%,n= + 175*PVIF i=7%,n= = $ Munis: PV = 14.85*PVIFA i=11%,n= *PVIF i=11%,n=15 = $141.7 Commercial Paper: PV = 6.075*PVIFA i=6.5%,n= *PVIF i=6.5%,n=1 = $13.46 Note: PV = 1.80*PVIFA i=10%,n= *PVIF i=10%,n=5 = $ Total assets = $ $141.7 = $ ΔA = -$30.06 or percent change Total liabilities = $ $ = $80.33 ΔL = -$14.67 or percent change f. What is the dollar impact on the market value of equity for Gunnison? What is the percentage change in the value of the equity? ΔE = ΔA - ΔL = -$30.06 (-$14.67) = -$ percent g. What would be the impact on Gunnison s market value of equity if the liabilities paid interest semiannually instead of annually? The value of liabilities will be lower with semi-annual compounding, increasing the value of net worth. The one-year CP will decline in value to $ The five-year note will decline in value to $ The value of equity will increase to $9.869 = ($ $141.7) - ($ $ ). Chapter Nine Interest Rate Risk II Solutions for End-of-Chapter Questions and Problems: Chapter Nine 1. What are the two different general interpretations of the concept of duration, and what is the technical definition of this term? How does duration differ from maturity?

7 Duration measures the average life of an asset or liability in economic terms. As such, duration has economic meaning as the interest sensitivity (or interest elasticity) of an asset s value to changes in the interest rate. Duration differs from maturity as a measure of interest rate sensitivity because duration takes into account the time of arrival and the rate of reinvestment of all cash flows during the assets life. Technically, duration is the weighted-average time to maturity using the relative present values of the cash flows as the weights.. Two bonds are available for purchase in the financial markets. The first bond is a -year, $1,000 bond that pays an annual coupon of 10 percent. The second bond is a -year, $1,000, zero-coupon bond. a. What is the duration of the coupon bond if the current yield-to-maturity (YTM) is 8 percent? 10 percent? 1 percent? (Hint: You may wish to create a spreadsheet program to assist in the calculations.) Coupon Bond Par value = $1,000 Coupon = 0.10 Annual payments YTM = 0.08 Maturity = 1 $ $9.59 $9.59 $1, $ $1, Price = $1, Numerator = $1, Duration = = Numerator/Price YTM = $ $90.91 $90.91 $1, $ $1, Price = $1, Numerator = $1, Duration = = Numerator/Price YTM = $ $89.9 $89.9 $1, $ $1, Price = $966.0 Numerator = $1, Duration = = Numerator/Price b. How does the change in the current YTM affect the duration of this coupon bond? Increasing the yield-to-maturity decreases the duration of the bond. c. Calculate the duration of the zero-coupon bond with a YTM of 8 percent, 10 percent, and 1 percent.

8 Zero Coupon Bond Par value = $1,000 Coupon = 0.00 YTM = 0.08 Maturity = 1 $ $0.00 $0.00 $1, $ $1, Price = $ Numerator = $1, Duration =.0000 = Numerator/Price YTM = $ $0.00 $0.00 $1, $86.45 $1,65.89 Price = $86.45 Numerator = $1,65.89 Duration =.0000 = Numerator/Price YTM = $ $0.00 $0.00 $1, $ $1, Price = $ Numerator = $1, Duration =.0000 = Numerator/Price d. How does the change in the current YTM affect the duration of the zerocoupon bond? Changing the yield-to-maturity does not affect the duration of the zero coupon bond. e. Why does the change in the YTM affect the coupon bond differently than the zero-coupon bond? Increasing the YTM on the coupon bond allows for a higher reinvestment income that more quickly recovers the initial investment. The zero-coupon bond has no cash flow until maturity. 3. A one-year, $100,000 loan carries a market interest rate of 1 percent. The loan requires payment of accrued interest and one-half of the principal at the end of six months. The remaining principal and accrued interest are due at the end of the year. a. What is the duration of this loan? Cash flow in 6 months = $100,000 x.1 x.5 + $50,000 = $56,000 interest and principal. Cash flow in 1 year = $50,000 x 1.06 = $53,000 interest and principal.

9 Time Cash Flow PVIF CF*PVIF T*CF*CVIF 1 $56, $5, $5, $53, $47, $94,339.6 Price = $100, $147, = Numerator D $147, = x $100, = years b. What will be the cash flows at the end of 6 months and at the end of the year? Cash flow in 6 months = $100,000 x.1 x.5 + $50,000 = $56,000 interest and principal. Cash flow in 1 year = $50,000 x 1.06 = $53,000 interest and principal. c. What is the present value of each cash flow discounted at the market rate? What is the total present value? $56, = $5, = PVCF 1 $53,000 (1.06) = $47, = PVCF =$100, = PV Total CF d. What proportion of the total present value of cash flows occurs at the end of 6 months? What proportion occurs at the end of the year? Proportion t=.5 = $5, $100,000 x 100 = percent. Proportion t=1 = $47, $100,000 x 100 = percent. e. What is the weighted-average life of the cash flows on the loan? D = x 0.5 years x 1.0 years = = years. f. How does this weighted-average life compare to the duration calculated in part (a) above? The two values are the same. 19. Financial Institution XY has assets of $1 million invested in a 30-year, 10 percent semiannual coupon Treasury bond selling at par. The duration of this bond has been estimated at 9.94 years. The assets are financed with equity and a $900,000, -year, 7.5 percent semiannual coupon capital note selling at par. a. What is the leverage-adjusted duration gap of Financial Institution XY? The duration of the capital note is years.

10 Two-year Capital Note Par value = $900 Coupon = Semiannual payments YTM = Maturity = 0.5 $ $31.48 $15.74 PVIF = 1/(1+YTM/)^(Time*) 1 $ $30.38 $ $ $9.3 $43.98 $ $ $1, Price = $ Numerator = $1, Duration = = Numerator/Price The leverage-adjusted duration gap can be found as follows: Leverage adjusted duration gap = $900,000 $1,000,000 [ D D k] = = 8. years A L 3 b. What is the impact on equity value if the relative change in all market interest rates is a decrease of 0 basis points? Note, the relative change in interest rates is ΔR/(1+R/) = The change in net worth using leverage adjusted duration gap is given by: ΔE = ΔR R 1 + [ D D k] * A * = [ 9.94 (1.8975) 9 ](.00)(1,000,000) = $16, 464 A L c. Using the information that you calculated in parts (a) and (b), infer a general statement about the desired duration gap for a financial institution if interest rates are expected to increase or decrease. If the FI wishes to be immune from the effects of interest rate risk, that is, either positive or negative changes in interest rates, a desirable leverage-adjusted duration gap (LADG) is zero. If the FI is confident that interest rates will fall, a positive LADG will provide the greatest benefit. If the FI is confident that rates will increase, then negative LADG would be beneficial. d. Verify your inference by calculating the change in market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points. ΔR ΔE = [ DA DLk] * A * = [ 8.35 ](1,000,000)(.003) = $4, 697 R 1 + e. What would the duration of the assets need to be to immunize the equity from changes in market interest rates? 10

11 Immunizing the equity from changes in interest rates requires that the LADG be 0. Thus, (D A -D L k) = 0 D A = D L k, or D A = 0.9* = years.. The following balance sheet information is available (amounts in $ thousands and duration in years) for a financial institution: Amount Duration T-bills $ T-notes T-bonds 176 x Loans, Deposits, Federal funds Equity 715 Treasury bonds are 5-year maturities paying 6 percent semiannually and selling at par. a. What is the duration of the T-bond portfolio? years as shown below. Treasury Bond Par value = $176 Coupon = 0.06 Semiannual payments YTM = 0.06 Maturity = $ $5.13 $.56 1 $ $4.98 $ $ $4.83 $7.5 $ $4.69 $ $ $4.55 $ $ $4.4 $ $ $4.9 $ $ $4.17 $ $ $4.05 $ $ $ $ Price = $ Numerator = $ Duration = = Numerator/Price b. What is the average duration of all the assets? [(.5)(90) + (.9)(55) + (4.393)(176) + (7)(74)]/3045 = 6.55 years c. What is the average duration of all the liabilities? [(1)(09) + (0.01)(38)]/330 = 0.90 years d. What is the leverage-adjusted duration gap? What is the interest rate risk exposure? DG = D A - kd L = (330/3045)(0.90) = 5.86 years

12 The duration gap is positive, indicating that an increase in interest rates will lead to a decline in net worth. e. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 0.5 percent [i.e., ΔR/(1+R) = ]? The market value of the equity will change by the following: MV E = -DG * (A) * R/(1 + R) = -5.86(3045)(0.0050) = -$89.. The loss in equity of $89,0 will reduce the equity (net worth) to $65,780. f. If the yield curve shifted downward by 0.5 percent (i.e., ΔR/(1+R) = ), what is the forecasted impact on the market value of equity? The change in the value of equity is MV E = -5.86(3045)(-0.005) = $44,610. Thus, the market value of equity (net worth) will increase by $44,610, to $759,610. g. What variables are available to the financial institution to immunize the balance sheet? How much would each variable need to change to get DGAP equal to 0? Immunization requires the bank to have a leverage-adjusted duration gap of 0.0. Therefore, the FI could reduce the duration of its assets to years by using more T-bills and floating rate loans. Or the FI could try to increase the duration of its deposits possibly by using fixed-rate CDs with a maturity of 3 or 4 years. Finally, the FI could use a combination of reducing asset duration and increasing liability duration in such a manner that LADG is 0.0. This duration gap of 5.86 years is quite large and it is not likely that the FI will be able to reduce it to zero by using only balance sheet adjustments. For example, even if the FI moved all of its loans into T-bills, the duration of the assets still would exceed the duration of the liabilities after adjusting for leverage. This adjustment in asset mix would imply foregoing a large yield advantage from the loan portfolio relative to the T-bill yields in most economic environments.

13 Exercise on Market Risk Revised list of exercises Exercise II Chapter 10 1,, 3, 4, 5, 6, 7, 9, 11, 1, 13, 14, 16 Solutions to Bolded numbers. Chapter What is meant by market risk? Market risk is the uncertainty of the effects of changes in economy-wide systematic factors that affect earnings and stock prices of different firms in a similar manner. Some of these market-wide risk factors include volatility, liquidity, interest-rate and inflationary expectation changes.. Why is the measurement of market risk important to the manager of a financial institution? Measurement of market risk can help an FI manager in the following ways: a. Provide information on the risk positions taken by individual traders. b. Establish limit positions on each trader based on the market risk of their portfolios. c. Help allocate resources to departments with lower market risks and appropriate returns. d. Evaluate performance based on risks undertaken by traders in determining optimal bonuses. e. Help develop more efficient internal models so as to avoid using standardized regulatory models. 3. What is meant by daily earnings at risk (DEAR)? What are the three measurable components? What is the price volatility component? DEAR or Daily Earnings at Risk is defined as the estimated potential loss of a portfolio's value over a one-day unwind period as a result of adverse moves in market conditions, such as changes in interest rates, foreign exchange rates, and market volatility. DEAR is comprised of (a) the dollar value of the position, (b) the price sensitivity of the assets to changes in the risk factor, and (c) the adverse move in the yield. The product of the price sensitivity of the asset and the adverse move in the yield provides the price volatility component. 4. Follow Bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,40,55. The bond is trading at a yield to maturity of 7.00 percent. The historical mean change in daily yields is 0.0 percent, and the standard deviation is 1 basis points. a. What is the modified duration of the bond?

14 MD = 5 (1.07) = years b. What is the maximum adverse daily yield move given that we desire no more than a 5 percent chance that yield changes will be greater than this maximum? Potential adverse move in yield at 5 percent = 1.65σ = 1.65 x = c. What is the price volatility of this bond? Price volatility = -MD x potential adverse move in yield = x = or percent d. What is the daily earnings at risk for this bond? DEAR = ($ value of position) x (price volatility) = $1,000,000 x = $9,5 5. What is meant by value at risk (VAR)? How is VAR related to DEAR in J.P. Morgan s RiskMetrics model? What would be the VAR for the bond in problem (4) for a 10-day period? With what statistical assumption is our analysis taking liberties? Could this treatment be critical? Value at Risk or VAR is the cumulative DEARs over a specified period of time and is given by the formula VAR = DEAR x [N] ½. VAR is a more realistic measure if it requires a longer period to unwind a position, that is, if markets are less liquid. The value for VAR in problem four above is $9,5 x = $9, The relationship according to the above formula assumes that the yield changes are independent. This means that losses incurred on one day are not related to the losses incurred the next day. However, recent studies have indicated that this is not the case, but that shocks are autocorrelated in many markets over long periods of time. 6. The DEAR for a bank is $8,500. What is the VAR for a 10-day period? A 0- day period? Why is the VAR for a 0-day period not twice as much as that for a 10-day period? For the 10-day period: VAR = 8,500 x [10] ½ = 8,500 x = $6, For the 0-day period: VAR = 8,500 x [0] ½ = 8,500 x = $38, The reason that VAR 0 ( x VAR 10 ) is because [0] ½ ( x [10] ½ ). The interpretation is that the daily effects of an adverse event become less as time moves farther away from the event. 11. Bank of Southern Vermont has determined that its inventory of 0 million euros ( ) and 5 million British pounds ( ) is subject to market risk. The spot exchange rates are $0.40/ and $1.8/, respectively. The σ 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 95 th percentile.

15 FX position of FX position of = 0m x 0.40 = $8 million = 5m x 1.8 = $3 million FX volatility = 1.65 x 65bp = 107.5, or 1.075% FX volatility = 1.65 x 45bp = 74.5, or 0.745% DEAR = ($ Value of position) x (Price volatility) DEAR of = $8m x = $0.0860m, or $85,800 DEAR of = $3m x = $0.376m, or $37,600 VAR of = $138,000 x 10 = $85,800 x = $71,33.4 VAR of = $37,600 x 10 = $37,600 x = $751, Jeff Resnick, vice president of operations of 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, $74,000, and $16,700 respectively. If the correlation coefficients ρ 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? ( DEARL ) + (ρ L, DEAR portfolio = + (ρ L, + (ρ FX + ( DEAR FX EQ, EQ x DEAR x DEAR FX L L x DEAR ) FX + ( DEAR x DEAR x DEAR FX EQ x DEAR ) ) EQ EQ ) ) 0.5 $300,700 + $74,000 + $16,700 + (0.3)($300,700)($74,000) = + (0.7)($300,700)($16,700) + (0.0)($74,000)($16,700) 0.5 = 0.5 [ $84,3,66,000] = $533, 19