Question

You are faced with the probability distribution of the HPR on the stock market index fund given in Spreadsheet 5.1 of the text. Suppose the price of a put option on a share of the index fund with exercise price of $110 and time to expiration of 1 year is $12, and suppose the risk-free interest rate is 6% per year. You are contemplating investing $107.55 in a 1-year CD and simultaneously buying a call option on the stock market index fund with an exercise price of $110 and expiration of 1 year.

Answer 1

Answer = $114

Step-by-step explanation:

We are investing $107.55 in CD for 1 year with the risk free rate of 6% per annum.

So, at the end of 1 year we will receive the face value as well as the interest on the same.

So, ending value of CD = 107.55*1.06 (6% interest) = $114.003

= $114

Now, in case of the excellent economic conditions, the ending price of stock is $131. So, here instead of buying the stock from market we will exercise our call option at the rate of $110.

So, value of our call will be:-

Probability * Ending value of CD - cost of call option

= 0.25*114 - 12

= $16.5

So, combined value will be $130.5 (114 + 16.5) which is less than the market price of $131.

In all the other three cases, the end price of stock is less than the ending value of CD. So, instead of exercising the call option, we will purchase the stock from market at less price to make profits.

So, combined value in the other three cases will be the ending value of CD = $114.