Question

Assume the probability of a pessimistic, most likely and optimistic state of nature is .25, .45 and .30, and the returns associated with those states of nature are 10%, 12%, and 16% for asset X. Based on the information, the expected return and standard deviation of return are: (MUST SHOW ALL WORK FOR CREDIT)

A) 12.0% and 4.0%
B) 12.7% and 2.3%
C)12.7% and 4.0%
D) 12.0% and 2.3%
E) none of the above

Answer 1

E) none of the above

12.70% and 2.49% standard deviation

Step-by-step explanation:

We multiply probability by the outcome to get the weighted amount, we add them and get the expected return.

probability outcome weighted

0.25 0.10 0.0250

0.45 0.12 0.0540

0.30 0.16 0.0480

expected return 0.1270

Now that we got the expected return at 12.7%

We now subtract the possible outcome with the expected return and square them:

(0.127-0.1)^2

(0.127-0.12)^2

(0.127-0.16)^2

Then we add them and divide by the sample which is 3

0.000622

²√ 0.000622 = 0.024944383

Final step, will be the square root which gives the standard deviation

of 2.49% = 0.024947