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50. A savings bank has the following balance sheet ($ millions, market values). Assets Liabilities Treasuries:$200 Deposits:$900 Floating rate mortgage loans:$300 Equity:$100 Fixed rate mortgage loans:$500 Total: $1,000 Total: $1,000 Fall 2008 Page 22 of 66 Durations are as follows: Treasuries 6 months Floating rate mortgage loans 1 year Fixed rate mortgage loans 5 years Deposits 1 year (a) What is the duration of the banks equity? Briefly explain what this duration means for the banks stockholders. (b) Suppose interest rates move from 3% to 4% (flat term structure). Use duration to calculate the change in the value of the banks equity. Will the actual change be more or less than your calculated value? Explain briefly. 51. Fixed Income Management: A pension fund has the following liability: A 20-yr annuity, that will pay coupons of 7% at the end of each year. (t=1...t=20). The pension fund's liability has a face value of 100. The yield curve is flat at 5%. (a) Calculate the PV and duration of this liability. (b) The same pension fund has the following assets: a 1-yr discount bond with face value 100, and a 20-yr discount bond which also has a face value of 100. Calculate the PV and duration of the portfolio of assets. (c) How would you change the portfolio composition of assets (keeping the PV of assets the same), so that the NPV of the firm, defined as PVA - PV, that is Present Value of assets minus the Present Value of liabilities, is unaffected by interest rate changes? (d) After making the change above in (c), what is the change in the NPV of the firm if interest rates increase by 10 basis points. 52. Three bonds trade in London and pay annual coupons Bond Coupon Maturity Price 5% 100.96% 6.5% 106.29% 09 09 2% 93.84% Prices are in decimals, not 32nds. (a) What is each bond's yield to maturity? (b) What are the 1, 2 and 3-year spot rates? What are the forward rates?K 91 92 93) (94) 95 (96) (97) (98 (99) 100 This Question: 1 pt This Test: 100 pts Time Remaining: 09:08:55 Consider an economy characterized by the following equations: C =75 + 0.50Y + 0.10W Aggregate Expenditure and Equilibrium I = 25 1,000- where C is desired consumption, I is desired investment, W is household wealth, and Y is national income. 800- a. Suppose wealth is constant at W = 1,000. Use the line drawing tool to draw and label the aggregate expenditure function on a scale diagram along with the 450 line to the right. Make sure that 800- the line starts at y-axis and extends to the right Desired Aggregate Expenditures Carefully follow the instructions above, and only draw the required objects. 100- b. The marginal propensity to spend in this economy is. 200- c. What is the value of the simple multiplier? The value of the multiplier is . (Round your response to two decimal places.) 200 400 800 800 1,000 Actual National Income d. Using your answer from part (b), what would be the change in equilibrium national income if desired investment increased to $125? (0,0) The change in equilibrium national income would be $ . (Round your response to the nearest dollar) e. Assuming investment is $25, if household wealth increased from $1,000 to $3,500, the AE function would by s . (Round your response to the nearest dollar) By how much does national income change? Equilibrium national income would change by $ . (Round your response to the nearest dollar.)
