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.
What is the probability distribution of your dollar return at the
end of the year? (Round your answers to 2 decimal
places.)
|
The cost of one share of the index fund plus a put option is $112. The probability distribution of the HPR on the portfolio is:
| State of economy | Probability | Endig price+Put+Dividend | HPR |
| Excellent | 0.25 | $131.00 | 17% = (131-112)/112 |
| Good | 0.45 | $114.00 | 1.8% = (114 -112)/112 |
| Poor | 0.25 | $113.50 | 1.3% = (113.50- 112)/112 |
| Crash | 0.05 | $112.00 | 0.0% = (112 -112)/112 |
The probability distribution of the dollar return on CD plus call option is:
| State of economy | Probability | Endig value of CD | Ending Value of call | Combined Value |
| Excellent | 0.25 | $107.55(1+6%) = $114.00 | $16.5 | $130.50 |
| Good | 0.45 | $114.00 | $0.00 | $114.00 |
| Poor | 0.25 | $114.00 | $0.00 | $114.00 |
| Crash | 0.05 | $114.00 | $0.00 | $114.00 |
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