:Solve the following questions.
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?35. Valerie Smith is attempting to construct a bond portfolio with a duration of 9 years. She has $500,000 to invest and is considering allocating it between two zero coupon bonds. The first zero coupon bond matures in exactly 6 years, and the second zero coupon bond matures in exactly 16 years. Both of these bonds are currently selling for a market price of $100. Suppose that the yield curve is flat at 7.5%. Is it possible for Valerie to construct a bond portfolio having a duration of 9 years using these two types of zero coupon bonds? If so, how? (Describe the actual portfolio.) If not, why not? 36. Given the bond prices in the question above, you plan to borrow $15 million one year from now (end of year 1). It will be a two-year loan (from year 1 to year 3) with interest paid at the ends of year 2 and 3. The cash flow is as follows: Year 1 Year 2 Year 3 Borrow $15M Pay interest Pay interest plus principal of 15M/ Explain how you could arrange this loan today and "lock in" the interest rate on the loan. What transactions today would be required? What would the interest rate be? You can buy or sell any of the bonds listed above (in the previous question). 37. You purchased a 3 year coupon bond one year ago. Its par value is $1,000 and coupon rate is 6%, paid annually. At the time you purchased the bond, its yield to maturity was 6.5%. Suppose you sell the bond after receiving the first interest payment. Fall 2008 Page 18 of 66 (a) What is the total rate of return from holding the bond for the year if the yield to maturity remains at 6.5% when you sell it? (b) What if the yield to maturity becomes 6.0% when you sell it? 38. You manage a pension fund, which provides retired workers with lifetime annuities. The fund must pay out $1 million per year to cover these annuities. Assume for simplicity that these payments continue for 20 years and then cease. The interest rate is 4% (flat term structure). You plan to cover this obligation by investing in 5- and 20-year maturity Treasury strips. (a) What is the duration of the funds 20-year payout obligation? (b) You decide to minimize the funds exposure to changes in interest rates. How much should you invest in the 5- and 20- year strips? What will be the par value of your holdings of each strip? (c) After three months, you reexamine the pension funds investment strategy. Interest rates have increased. You still want to minimize exposure to interest rate risk. Will you invest more in 20-year strips and less in 5-year strips? Explain briefly. 39. Duration and Convexity. Consider a 10 year bond with a face value of $100 that pays an annual coupon of 8%. Assume spot rates are flat at 5%. (a) Find the bond's price and duration. (b) Suppose that 10yr yields increase by 10bps. Calculate the change in the bond's price using your bond pricing formula and then using the duration approximation. How big is the difference? (c) Suppose now that 10yr yields increase by 200bps. Repeat your calculations for part (b). (d) Given that the bond has a convexity of 33.8, use the convexity adjustment and repeat parts (b) and (c). Has anything changed? 40. The yield to maturity of a 10-year zero-coupon bond is 4%. (a) Suppose that you buy the bond today and hold it for 10 years. What is your return? (Express this return as an annual rate.) (b) Given only the information provided, can you compute the return on the bond if you hold the bond only for 5 years? If you answered yes, compute the return. If you answered no, explain why.NAME SECTION# PRINT LAST NAME, FIRST NAME DEMAND AND SUPPLY SHIFTS Match the graph showing a demand or supply shift with the event that would cause the shift. Graph 1 Graph 2 P P PI Dz DI DI Q1 Q2 Q1 Q2 Q Graph 3 Graph 4 P Sz. SI P2 P P2 D DI Q1 Q2 Q Q1 Q2 Q + Graph # Events: 1. A decrease in the price of a good considered a substitute by consumers 2. An increase in the price of a good considered a substitute by consumers 3. An increase in the costs of production 4. A decrease in the costs of production 5 . A decrease in the price of a good considered a complement by consumers 6. An increase in the price of a good considered a complement by consumers 7. Improved production technology 8. A decrease in consumer income, assuming the product is a normal good A decrease in consumer income, assuming the product is an inferior good 9. An increase in consumer income, assuming the product is a normal good 10.NAME SECTION# PRINT LAST NAME, FIRST NAME DEMAND AND SUPPLY Assume there is an increase in the price of a cereal. According to the law of demand, what happens in the market for cereal when the price of a cereal increases, ceteris paribus? Now assume cereal and milk are complements. What happens in the market for milk when the price of cereal increases, ceteris paribus? Starting from equilibrium in the market for milk, explain how an increase in the price of cereal affects equilibrium price and quantity in the market for milk, ceteris paribus. 12 Draw a graph of the market for milk, labeling both axes and the demand and supply curves. Show any shift(s) that occurred as a result of the increase in the price of cereal.b. Answer the following questions: Explain how Islamic economic system ensures the distribution of goods and services in the economy is just and fair. (4 marks) (ii) Discuss whether the goal of efficiency is in line with Islamic principles. (4 marks) c. The table below shows a daily data on the market demand for lobsters and individual supply of lobsters by three sellers in Kuala Selangor. Assume that seller A. B and C are the only suppliers of lobsters in the market. Price/kg Quantity demanded Quantity Supplied (kg) (RM) (kg) Seller A Seller B Seller C 20 180 8 10 12 40 160 11 13 16 60 130 20 24 26 80 90 24 30 36 100 50 32 44 54 120 20 52 58 60 (1) Plot the market demand and market supply curves for lobsters in a single diagram and identify the market equilibrium price and quantity in the diagram. (3 marks) (ii) Due to a technological improvement in fishing equipment, the total daily catch of lobsters by the three sellers increased by 60kg at every price level. Plot this new market supply curve in the same diagram you have drawn in part (i) above. Identify the new market equilibrium price and quantity for lobsters. (2 marks) (ili) Using midpoint formula, calculate the price elasticity of demand for lobsters if the price increases from RM80 to RM100. Explain the meaning of the coefficient and determine what type of product lobster is. (3 marks) (iv) Suppose that the price of meat in the market increases from RM30 to RM40, and as a consequent of that, demand for lobsters increased from 70kg to 100kg. Using this information, calculate the cross-elasticity of demand for lobsters in relation to the 10 change in the price of meat. Based on your answer, what can you conclude on the relationship between meat and lobsters? Explain
