1. An insurance company must make a payment of $19,487 in seven years. The market interest rate is 6%. The company's portfolio manager wishes to fund the obligation using three-year, 8% annual coupon bonds and perpetuities paying $100 annual coupons. To fully fund the obligation, how much (in dollars) should be invested in three-year bonds?
2. Consider a convertible bond with 5-year maturity, $1,000 par value, and 6% coupon, paid annually. This bond can be converted only at the end of third year (t=3) with the conversion ratio of 30. The current stock price is $15 per share but you forecast the stock price at the end of third year to be either $20 (with 40% probability) or $34.50 (with 60% probability). The current yield to maturity is 6 percent but you believe that the market interest rate at the end of third year will be either 4% (with 50% probability) or 6% (with 50% probability). What will be the maximum price that you are willing to pay for this convertible bond?
3. Whizzkid Inc. is experiencing a period of rapid growth. Dividend is expected to grow at a rate of 15 percent during the next two years, 13 percent in the third year, 10 percent in the fourth year, and at a constant rate of 6 percent thereafter. The firm just provided $2.00 cash dividend. If the required rate of return on the stock is 17 percent, what is the price of a share of the stock today?
4. Assuming that the yield on a 5 year security is 2.35% the one year yield is .29%, and your expectations for the next 4 year one year yields are .85%, 1.35%, 2.45%, and 2.95%, determine whether you should invest in the five year security or five consecutive one year securities according to the un-bias expectations theory.
5. If the yield on a 6 year security is 2.30% and the yield on a 7 year security is 2.35%, determine the implied forward rate of the market. If your expectations for the short term yield in year 7 is 2.45%, determine whether you should long or short the bond market.
6. Discuss the development of exchange traded funds (ETFs) in the United States. How do these ETFs differ from conventional equity mutual funds? Please discuss what is meant by the Sharpe Ratio, the Treynor Ratio, theSortino Ratios, and Jensen's alpha.