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Extra Problems 5 - compounded continuously calculate the 6...

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ACTSC 231 Extra Problems 5 1. Investor A buys a zero growth stock, which pays annual dividends of $8, at a price to yield i = 7% . After receiving the 10th dividend investor A sells the stock to investor B to yield i = 8% . (a) Find the IRR for investor A. (b) Find the e/ective annual yield rate earned by investor A if each of the dividends earned i = 5% in a saving account. (c) Repeat part b) assuming an annual growth rate of 1% (e.g. D 0 = 8 ; D 1 = 8 : 08 ; ::: ). 2. A 1-year forward contract on a non dividend paying stock is entered into when the stock price is $35. If the risk free rate of interest is 10% com- pounded continuously calculate: (a) the forward price and the initial value of the long position in the forward contract. (b) the forward price and value of the long position in the forward con- tract at the end of 6 months assuming that the stock is now worth $40. 3. For a stock index with current value of $200 and a dividend yield of 3%
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Unformatted text preview: compounded continuously, calculate the 6 month forward price assuming a risk free force of interest of 8%. 4. You are given (the face amount in each case is $100): 6-month T-bills sell for $95 1-year T-bills sell for $90 1.5-year bonds with 8% coupons paid semiannually sell for $95.80 2-year bonds with 10% coupons paid semiannually sell for $97.55 Calculate the 6-month, 1-year, 1.5-year and 2-year annual e/ective spot rates. 5. Consider a 2-year $1000 bond with 7% coupons paid semiannually. (a) Calculate the volatility and convexity of the bond at an interest rate of 10% compounded semiannually. (b) Using part a) calculate the approximate relative change in the price of the bond if interest rates increased from10% to 11% compounded semiannually. (c) Compare your answer in b) to the actual relative price change. 1...
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