1. Assume that you sell short 350 shares of a stock when the market price is 32.10-32.15....

Question:

1. Assume that you sell short 350 shares of a stock when the market price is 32.10-32.15. Your demands a 20% haircut for collateral and pays a short rebate of 3%. You borrow all needed cash for the transaction above the short proceeds at an interest rate of 4.8%. One year later, the price is 29.50- 29.55, and you close the position. What is the net profit (in $)?  
2. Assume that you sell short a 3.5% semi-annual bond when the market interest rate is 4% (and you buy on a payment date so that the price is clean). You deposit the short proceeds plus a 15% haircut that you pay out of your own capital. 18 months later, interests rates have raised to 4.3%, and you close the position by buying back the bond. If the repo rate is 2%, what is the net profit from these trades? What is the percent return, based on your out-of-pocket capital investment only? What is the effective annual rate for this investment?  
3. If a non-dividend paying stock is trading today at $52 when the interest rate is 3%, what is the 8- month forward price? If the forward contract is available at a price of $51, what three transactions should you make in order to earn the available arbitrage profit? How much money could you make 8 months from now, and what is the present value of that profit today?  
4. A stock is trading today at $90, and the company is expected to pay quarterly dividends of $0.45. The continuously compounded interest rate is 4.2%. What is the 10-month forward price? What is the price of a prepaid 10-month forward? If the price of the stock in 10 months is $95, what is the profit or loss from the forward contract?  
5. If the is currently $2.10/₤ when the pound interest rate is 3% and the dollar interest rate is 1.5%, what is the correct price for a 1-year forward contract? (All rates are continuously compounded.)  
6. Assume that you have a well-diversified valued at $3 million with a beta of 1.8, but you have a negative outlook on the short-term prospects of the market and want to reduce your market risk using index futures. In particular, you want to reposition your to have a beta to 0.7. Assume that the S&P 500 is trading at a price of 2,800, the futures multiplier is $250, and the futures price is currently 2,770. How many futures contracts would you need to trade long or short in order to alter the beta?  
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