An option to buy a stock is priced at $300. If the stock closes above 30 on May

Question

An option to buy a stock is priced at $300. If the stock closes above 30 on May 15, the option will be worth $400. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $300. A trader thinks there is a 40% chance that the stock will close in the 20-30 range, a 50% chance that it will close above 30, and a 10% chance that it will fall below 20 on May 15. Complete parts (a) through (c).

a) How much does she expect to gain? $----------- (Round to the nearest dollar as needed.)

b) What is the standard deviation of her gain? $----------- (Round to the nearest dollar as needed.)

c) Should she buy the stock option? Discuss the pros and cons in terms of your answers to (a) and (b).

The expected gain is

a. positive, b. negative,

which means the trader can expect a. a net gain. b. a net loss.

The standard deviation is a.smaller

b.much smaller c. larger than the expected gain.

That means a net loss is

a.nearly certain. b. almost impossible. c. a real possibility.

The trader should balance the risk of a net loss against her tolerance for loss to make the decision.

Explanation / Answer

(a) expected gain=sum(x*p(x))=20

(b) var(x)=E(x2)-(E(x))2=14000-20*20=13600

standard deviation=sd(x)=sqrt(13600)=116.6

(c) based on (a) and (b), she should avoid the stock

The expected gain is (a) positive

which means the trader can expect a. a net gain.

The standard deviation is c. larger than the expected gain.

That means a net loss is

. c. a real possibility.

x -300 0 100 sum p(x) 0.1 0.4 0.5 1 x*p(x) -30 0 50 20 x2*p(x) 9000 0 5000 14000

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