Question 1 A company has a $35 million stock portfolio with a beta of 1.2. The S

Question

Question 1

A company has a $35 million stock portfolio with a beta of 1.2. The S&P index futures price is currently standing at 800. Futures contracts on $250 times the index can be traded. How many contacts is needed to reduce the beta to 1? If a short position is needed, report a negative number (margin of error = +/- 1).

Question 2

The spot price of an investment asset is $27 and the risk-free rate for all maturities (with continuous compounding) is 7%. The asset provides $2 income at the end of the second year. What is the three-year forward price? (margin of error = +/- $0.10).

Question 3

The price of a stock is $36 and the price of a three-month call option on the stock with a $36 strike is $3.60. Suppose a trader has $3,600 to invest and is trying to choose between buying 1,000 options (10 contracts) or 100 shares of stock. How high does the stock price have to rise for an investment in options to be as profitable as an investment in the stock?

Explanation / Answer

Current Beta = 35 * 1.2 = 42 million

1 trade costs 800 * 250 = 200,000

Now,

1 * ( 35,000,000 + 200,000 * x ) = 35,000,000 * 1.2 - 200,000 * x

400,000 * x = 7,000,000

x = 17.5 contracts

2) value is 27 * e^0.07 * 3 + 2 * e^0.07 = $35.45

3)

Let the stock price be x

100 * ( x - 36 ) = 1000 * ( x - 36 - 3.6 )

x-36 = 10x - 396

9x = 360

x = 40. The stock price should rise to 40

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