Problem $4$: A mutual fund portfolio manager manages $$5$ Billion in stocks. The entire portfolio is highly correlated with the SProblem $4$: A mutual fund portfolio manager manages $$5$ Billion in stocks. The entire portfolio is highly correlated with the SProblem $4$: A mutual fund portfolio manager manages $$5$ Billion in stocks. The entire portfolio is highly correlated with the SProblem $4$: A mutual fund portfolio manager manages $$5$ Billion in stocks. The entire portfolio is highly correlated with the S

Problem $4$: A mutual fund portfolio manager manages $$5$ Billion in stocks. The entire portfolio is highly correlated with the S&P$500.$ The ETF SPY which follows the S&P$500$ is priced at $$550$ a share. The manager is worried that Trumps tariffs will cause the S&P$500$ to fall by $20\%$ as a worst case scenario and wants to limit his loss on the portfolio to about $10\%$ if possible. A call option on the SPY is available with a strike price of $$600$ and a cost of $$12$ a share with an expiration in six months. A put option is available with a strike price of $$500$ and a price of $$12$ a share.

A$.$ Would the fund manager us a "call" option or a "put" option to hedge his risk?

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b$.$ Each option contract is for $100$ shares. How many option contacts would the manager need to hedge his risk of keeping his losses to about $10\%?$ Round your answer to the nearest integer. What is the total dollar cost of this hedge?

Ans. $$ ans. $q,$

c$.$ Now assume in six months the S&P$500$ falls $18\%$ and his portfolio falls by $18\%.$ Further, the SPY falls by $18\%.$ What is the ending value of his portfolio?

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d$.$ What is the amount of money the manager made on his option hedge after subtracting the cost of the options?

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e$.$ What is the ending value of the portfolio after the drop in the market by $18\%$ when including the gain or loss on the option hedge.?

Ans. $q,$