Question

A stock can earn a return of 2%, 20%, or 8%. The stock’s distribution is known, and states that there is a 30% probability of the stock earning a return of 2%, a 36% probability of the stock earning a return of 20%, and a 34% probability of stock earning a return of 8%. What is the variance of the stock’s return?Select one: a. .0056 b. .0923 c. .0061 d. .078 e. .0748

Answer 1

option (a) 0.0056

Step-by-step explanation:

Data provided in the question:

Return that can be earned : 2% 20% 8%

Probability of returns : 30% 36% 34%

Now,

Average return, m =
`(2\% + 20\% + 8\%)/(3)` = 10%

Return (X) P(X) X - m ( X - m )² ( X - m )² × P(X)

2% 30% -8% = -0.08 0.0064 0.00192

20% 36% 10% = -0.10 0.01 0.0036

8% 34% -2% = -0.02 0.0004 0.000136

Thus,

Variance of the stock’s return = ∑ ( ( X - m )² × P(X) )

= 0.00192 + 0.0036 + 0.000136

= 0.005656 ≈ 0.0056

Hence,

The correct answer is option (a) 0.0056