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 ​$800. 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 30​% chance that it will close above​ 30, and a 30​% 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 ______  which means the trader can expect _______ . The standard deviation is _______than the expected gain. That means a net loss is _______ . The trader should balance the risk of a net loss against her tolerance for loss to make the decision

Answer 1

X	P(X)	X*P(X)	X^2*P(X)
-300	0.3	-90	27000
0	0.4	0	0
500	0.3	150	75000
SUM		60	102000

a)Mean

Expected gain = $60

b)Standard deviation

c)

No,she do not buy the stock​ option (avoid)

The expected gain is Positive which means the trader can expect net gain . The standard deviation is larger than the expected gain. That means a net loss is real possibility. The trader should balance the risk of a net loss against her tolerance for loss to make the decision