Answer:
None of the above. The correct answer is 1.47%, 1.10%.
Step-by-step explanation:
The first thing to do is to calculate the Expected return of Stock A and Stock B.
For A;
Probability. Return.
0.1.= 0.1 × 10% = 1.00%
0.2= 0.2 × 13% = 2.60%
0.2= 0.2× 12% = 2.40%.
0.3= 0.3 × 14% = 4.20%
0.2= 0.2 × 15% = 3.00%
Total = 13.20%.
For B;
Probability. Return.
0.1= 0.1 × 8% = 0.80%
0.2= 0.2 × 7% = 1.40%
0.2.= 0.2 × 6% = 1.20%
0.3.= 0.3 × 9% =2.70%
0.2.= 0.2 × 8%= 1.60%
Total = 7.70%.
Hence, the Expected return of Stock A and B = 13.20% and 7.70%. respectively.
Now, let us find the Standard deviation of Stock A and the Standard deviation of Stock B.
For A
For individual value of A, we use the following formula;
(A - Expected return of Stock A)^2 × probability.
For instance,
(10% - 13.20%)^2 × 0.1 =0.000102.
(13% - 13.20%)^2 × 0.2= 0.000001.
(12% - 13.20%)^2 × 0.2 = 0.000029.
(14% - 13.20%)^2 × 0.3 =0.000019.
(15% - 13.20%)^2 × 0.2 = 0.000065.
Which gives us the following values;
0.000102, 0.000001, 0.000029, 0.000019, 0.000065.
The next thing to do is to find the variance (that is the addition of all the values above) and the value for the square root of variance which is the standard deviation.
√( 0.000102 + 0.000001 + 0.000029 + 0.000019 + 0.000065) = 0.000216.
Thus, variance = 0.000216, square root of variance= 0.014697(1.47%).
For B;
We follow as the one above.
(B - Expected return of Stock A)^2 × probability.
We have values as;
0.000001, 0.000010, 0.000058, 0.000051, 0.000002.
√ ( 0.000001 + 0.000010 + 0.000058 +0.000051 + 0.000002).
= 0.011( 1.10%).
