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##### FINA 471 Problem Set 1 Assignment

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Question;FINA 471Problem Set 11. The price of a stock is $36 and the price of a three-month call option on the stock with a strike price of $36 is $3.60. Suppose a trader has $3,600 to invest and is trying to choose between buying 1,000 options and 100 shares of stock. How high does the stock price have to rise for an investment in options to be more profitable than an investment in the stock?2. On Aug 26, you sold 10 gold futures contracts at a price of $1298/oz. Each contract represents gold 100 oz.. The initial margin is USD 5,000 per contract, and the maintenance margin is USD 4,000 per contract. You deposited the initial margin on Aug 26. The subsequent settlement prices are shown in the table below:Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Aug 311297 1284 1283 1304 1307 13151) Compute the daily loss/gain, and cumulative loss/gain for each date.2) Suppose you did not withdraw any money from your account during this period, when would you receive a margin call and how much would you have to deposit to meet the margin call?3) Suppose you withdrew money from your account whenever it was possible and as much as possible, when would you receive your first margin call and how much would you have to deposit? If you just put in minimum amount of money that was sufficient to meet that margin call, would you get a second call during this period?If yes, when and how much?3. You manage a $13.5 million portfolio, currently all invested in equities, and has a beta of 1.2. You believe that the market is on the verge of a big but short-lived downturn, you would move your portfolio temporarily into T-bills, but you do not want to incur the transaction costs of liquidating and reestablishing your equity position. Instead,you decide to temporarily hedge your equity holding with S&P 500 index futures contracts.1) Should you be long or short the contracts? Why?2) How many contracts should you enter into? The S&P 500 index futures price is now at 1286 and the contract multiplier is $250.3) Suppose instead of reducing your portfolio beta all the way down to zero, you decide to maintain a beta of 0.5 during the hedging period, how many index futures contracts should you enter into?4. The following table gives data on monthly changes in the spot price and the futures price for a certain commodity. Use the data to calculate the optimal hedge ratio.Hints: 1) for a sample of N observations, x1, x2, ?, xN, the formula for the sample standard deviation is:? 1????????? 1?(?????????????????????????)2????????????????=12) for two samples of N observations, x1, x2, ?, xN, y1, y2, ?, yN, the formula for thecorrelation coefficient is:?????????????????????????????????????????????????????????=1? (?????????????????????????????????=1)(?????????????????????????????????=1)?[?????????????????????????2? (?????????????????????????????????=1)???????? 2????????=1 ][?????????????????????????2? (?????????????????????????????????=1)???????? 2????????=1 ]Spot Price Change +. 0 50 +. 0 61?. 0 22?. 0 35 +. 0 79Futures Price Change +. 0 56 +. 0 63?. 0 12?. 0 44 +. 0 60Spot Price Change +. 0 04 +. 0 15 +. 0 70?. 0 51?. 0 41Futures Price Change?. 0 06 +. 0 01 +. 0 80?. 0 56?. 0 46

Paper#48856 | Written in 18-Jul-2015

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