Therefore, Salomon Brothers should purchase $1,500,000 of the market index portfolio in order to hedge its position so that a 1% change in the index would result in a $15,000 change in the value of the portfolio. b. The delta of a put option is: 0.8 – 1 = –0.2 Therefore, for every 1% the market increases, the index will rise by 10 points and the value of the put option contract will change by: delta ×10 ×contract multiplier = –0.2 ×10 ×100 = –$200 Therefore, Salomon should write: $12,000/$200 = 60 put contracts 47. If the stock market index increases 1%, the 1 million shares of stock on which the options are written would be expected to increase by: 0.75% ×$5 ×1 million = $37,500 The options would increase by: delta ×$37,500 = 0.8 ×$37,500 = $30,000 In order to hedge your market exposure, you must sell $3,000,000 of the market index portfolio so that a 1% change in the index would result in a $30,000 change in the value of the portfolio. 21-18
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