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?

2. What is dollar duration? How is dollar duration different from duration?

3. Financial Institution XY has assets of $1 million invested in a 30-year, 10 per cent semi-annual 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, two-year, 7.25 per cent semi-annual coupon capital note selling at par. (a) What is the leverage adjusted duration gap of Financial Institution XY? (b) What is the impact on equity value if the relative change in all market interest rates is a decrease of 20 basis points? Note: The relative change in interest rates is ?R/(1+R/2) = -0.0020. (c) Using the information calculated in parts (a) and (b), what can be said about the desired duration gap for a financial institution if interest rates are expected to increase or decrease. (d) Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points. (e) What would the duration of the assets need to be to immunise the equity from changes in market interest rates?

4. The duration of an 11-year, $1000 Treasury Bond paying a 10 per cent semiannual coupon and selling at par has been estimated at 6.763 years. (a) What is the modified duration of the bond? What is the dollar duration of the bond? (b) What will be the estimated price change on the bond if interest rates increase 0.10 per cent (10 basis points)? If rates decrease 0.20 per cent (20 basis points)? (c) What would the actual price of the bond be under each rate change situation in part (b) using the traditional present value bond pricing techniques? What is the amount of error in each case?

5. The following balance sheet information is available (amounts in thousands of dollars and duration in years) for a financial institution: Amount Duration T-notes $90 0.50 T-notes $55 0.90 T-notes (5 year) $176 x Loans $2724 7.00 Deposits $2092 1.00 Interbank borrowings $238 0.01 Equity $715 Treasury Bonds are five-year maturities paying 6 per cent semi-annually and selling at par. (a) What is the duration of the T-Bond portfolio? (b) What is the average duration of all the assets? (c) What is the average duration of all the liabilities? (d) What is the leverage adjusted duration gap? What is the interest rate risk exposure? (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 per cent [that is, ?R/(1+R) = 0.0050]? (f) If the yield curve shifts downward by 0.25 per cent [that is, ?R/(1+R) = -0.0025], what is the forecasted impact on the market value of equity? (g) What variables are available to the financial institution to immunise the balance sheet? How much would each variable need to change to get DGAP equal to 0?

BEA705, Semester 2, 2017 BEA705 Workshop 4 W5 Problem Set 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? 2. What is dollar duration? How is dollar duration different from duration? 3. Financial Institution XY has assets of $1 million invested in a 30-year, 10 per cent semi-annual 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, two-year, 7.25 per cent semi-annual coupon capital note selling at par. (a) What is the leverage adjusted duration gap of Financial Institution XY? (b) What is the impact on equity value if the relative change in all market interest rates is a decrease of 20 basis points? Note: The relative change in interest rates is R/(1+R/2) = -0.0020. (c) Using the information calculated in parts (a) and (b), what can be said about the desired duration gap for a financial institution if interest rates are expected to increase or decrease. (d) Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points. (e) What would the duration of the assets need to be to immunise the equity from changes in market interest rates? 4. The duration of an 11-year, $1000 Treasury Bond paying a 10 per cent semiannual coupon and selling at par has been estimated at 6.763 years. (a) What is the modified duration of the bond? What is the dollar duration of the bond? (b) What will be the estimated price change on the bond if interest rates increase 0.10 per cent (10 basis points)? If rates decrease 0.20 per cent (20 basis points)? (c) What would the actual price of the bond be under each rate change situation in part (b) using the traditional present value bond pricing techniques? What is the amount of error in each case? 1 BEA705, Semester 2, 2017 5. The following balance sheet information is available (amounts in thousands of dollars and duration in years) for a financial institution: T-notes T-notes T-notes (5 year) Loans Deposits Interbank borrowings Equity Amount Duration $90 0.50 $55 0.90 $176 x $2724 $2092 $238 7.00 1.00 0.01 $715 Treasury Bonds are five-year maturities paying 6 per cent semi-annually and selling at par. (a) What is the duration of the T-Bond portfolio? (b) What is the average duration of all the assets? (c) What is the average duration of all the liabilities? (d) What is the leverage adjusted duration gap? What is the interest rate risk exposure? (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 per cent [that is, R/(1+R) = 0.0050]? (f) If the yield curve shifts downward by 0.25 per cent [that is, R/(1+R) = -0.0025], what is the forecasted impact on the market value of equity? (g) What variables are available to the financial institution to immunise the balance sheet? How much would each variable need to change to get DGAP equal to 0? 2