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A stock market investor has $500 to spend and is considering pur- chasing an option contract on 1,000 shares of Apricot Computer
A stock market investor has $500 to spend and is considering pur- chasing an option contract on 1,000 shares of Apricot Computer. The shares themselves are currently selling for $28.50 per share. Apricot is involved in a lawsuit, the outcome of which will be known within a month. If the outcome is in Apricot's favor, analysts expect Apricot's stock price to increase by $5 per share. If the outcome is unfavorable, the price is expected to drop by $2.75 per share. The option costs $500, and owning the option would allow the investor to purchase 1,000 shares of Apricot stock for $30 per share. Thus, if the investor buys the option and Apricot prevails in the lawsuit, the investor would make an immediate profit. Aside from purchasing the option, the investor could (1) do nothing and earn about 8% on his money, or (2) purchase $500 worth of Apricot shares. a) Construct cumulative risk profiles for the three alternatives, assum- ing Apricot has a 25% chance of winning the lawsuit. Can you draw any conclusions? b) If the investor believes that Apricot stands a 25% chance of win- ning the lawsuit, should he purchase the option? What if he believes the chance is only 10%? How large does the probability have to be for the option to be worthwhile?
Expert Solution
(a)
Decision Tree:
| Purchase Option | Do nothing | Purchase shares | |
| ($500) | =500*8%=40 | =17*$28.50=-$484.0 | |
| Favourable (0.25) | =1000*(33.50-$30) | =(17*$33.50)+(15.5*8%) | |
| $3,500.00 | $570.74 | ||
| =$3500+(-$500) | =$570.74+(-484.50) | ||
| $3,000.00 | $40 | $86.24 | |
| Unfavourable (0.75) | =$0 | =(17*$25.75)+(15.5*8%) | |
| =$0 | $438.99 | ||
| =$0+(-$500) | =$438.99+(-484.50) | ||
| $(500.00) | $(45.51) |
| =28.5+5 | |||
| $33.50 | |||
| =28.5-2.75 | |||
| $25.75 |
Decision Strategies:
| Purchase Option | ROI (return on investment) | Probabilities | Payoffs |
| Favourable (0.25) | $3,000.00 | $0.25 | $3,000.00 |
| Unfavourable (0.75) | $(500.00) | $0.75 | $(500.00) |
| Do nothing | Probabilities | Payoffs | |
| $40.00 | $1.00 | $40.00 | |
| Purchase shares | Probabilities | Payoffs | |
| Favourable (0.25) | $86.24 | $0.25 | $86.24 |
| Unfavourable (0.75) | $(45.51) | $0.75 | $(45.51) |
Risk profile-Return on investment and Probabilities
- Black-line = Purchase Option
- Blue-line =Purchase shares
- Red-line = Do nothing
As no alternative gives a feasible return or no one alternative dominates another, no conclusion can be drawn.
(b)
Assuming 8% is the monthly interest rate and let p be the probability that Apricot will win the lawsuit:
| Purchase Option | Do nothing | Purchase shares | |
| Expected monetary value | =3,000p-500(1-p) | $40.00 | =86.24p-45.51(1-p) |
| =3,000p-500+500p | =86.24p-45.51+45.51p | ||
| =3,500p-500 | =131.75p-45.51 | ||
When Apricot has a 25% chance of winning the lawsuit:
| When p=0.25 | |||
| Purchase Option | Do nothing | Purchase shares | |
| Expected monetary value | =3,500p-500 | $40.00 | =131.75p-45.51 |
| =3500*.25-500 | =(131.75*.25)-45.51 | ||
| $375.00 | $(12.57) |
So here Apricot should go with "purchase option".
If he believes the chance is only 10%:
| When p=0.10 | |||
| Purchase Option | Do nothing | Purchase shares | |
| Expected monetary value | =3,500p-500 | $40.00 | =131.75p-45.51 |
| =(3500*.1)-500 | =(131.75*.1)-45.51 | ||
| $(150.00) | $(32.34) |
So here Apricot should go with "Do nothing".
As per the above, we can derive that:
- EMV(Purchase Option) > EMV(Do Nothing), So 3,500p-500 > 40, so p > 0.1543, so the probability should be larger than 0.1543.
- EMV(Purchase Option) > EMV(Purchase shares ), So 3,500p-500 >131.75p-45.51, so p > 0.1349, so the probability should be larger than 0.1349.
Workings:
| 3500p-500=40 | 3,500p-500=131.75p-45.51 |
| 3500p=540 | 3368.25p = 454.49 |
| p=540/3500 | p=454.49/3368.25 |
| 0.1543 | 0.1349 |
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