5. A portfolio is currently worth $600,000 and has a beta of 1.0. A stock index

Question

5. A portfolio is currently worth $600,000 and has a beta of 1.0. A stock index is currently at 1200. Put options with a strike price of 1100 will be used to provide portfolio insurance. You may assume the dividend yield of the portfolio equals the dividend yield on the index.

a. The put options will provide protection against a drop in the value of the portfolio below what amount? [Hint: An equivalent question is, if the index drops to 1100, the value of the portfolio can be expected to drop to what?]

b. How many put option contracts are required to provide this protection? Show work.

c. Suppose that the market falls by 20%, such that the portfolio has a value of $480,000 and the stock index falls to 960. How do the put options work as portfolio insurance in this case? Show specific numerical steps.

6. A U.S. company knows that it will have to make a loan payment of €5 million in six months. The current exchange rate is $1.28 to €1. (Meaning the loan payment is currently equivalent to $6.4 million)

a. What option position could be used to protect the company from having to make a payment of more than $6.4 million? Be as specific as possible.

b. Suppose that the exchange rate in six months turns out to be $1.35 to €1. How does the option position you described in part (a) work in this case? Show specific numerical steps.

Explanation / Answer

Answer:

a) As the beta is 1, the value of the portfolio will drop to : $600,000*1100/1200 = $550,000, when index drops to 1,100 (ans).

b)

Number of put contracts required = $550,000/$1,100 = 500 put contracts

c)

Even if the market falls by 20%, exercising the put options will realise 500*$1100 = $550,000

Profit = $550,000 - $480,000 = $70,000 (ans)

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