In: Finance
1. Find the mean and standard deviation for option 1 and option 2
Option 1:
Year Return
1 15 %
2 -12 %
3 8 %
4 11 %
Option 2:
Prob. Return
0.05 16 %
0.40 8 %
0.25 -6 %
0.30 7 %
Calculation of Mean & Standard Deviation for Option1:
Formula:
Mean = Sum of all the returns / total number of returns
Sum of all the returns = 15% + (-12%) + 8% + 11% = 22%
Total number of returns = 4
therefore, Mean of returns = 22% / 4 = 5.5%
Now, Standard deviation:
Formula: (xi - )^2 / N
where, xi = returns = 15%, -12%, 8%, 11%
= mean of returns = 5.5%
N = number of returns = 4
therefore, standard deviation = [(15% - 5.5%)^2 + (-12% - 5.5%)^2 + (8% - 5.5%)^2 + (11% - 5.5%)^2 ] / 4
= [(9.5)^2 + (-17.5)^2 + (2.5)^2 + (5.5)^2 ] / 4 = 108.25 = 10.40
Hence, the Mean return is 5.5% and standard deviation is 10.40%.
Option2:
Probability | returns | returns with probabilities |
0.05 | 16% | 0.8% |
0.40 | 8% | 3.2% |
0.25 | -6% | -1.5% |
0.30 | 7% | 2.1% |
Total returns = 0.8% + 3.2% + -1.5% + 2.1% = 4.6%
Mean returns = total or sum of returns / number of returns = 4.6% / 4 = 1.15%
Standard deviation of returns:
Formula: (xi - )^2 / N
where, xi = returns = 0.8%, 3.2%, -1.5%, 2.1%
= mean of returns = 1.15%
N = number of returns = 4
therefore, standard deviation = [(0.8% - 1.15.%)^2 + (3.2% - 1.15%)^2 + (-1.5% - 1.15%)^2 + (2.1% - 1.15%)^2 ] / 4
= [(-0.35)^2 + (2.05)^2 + (-0.35)^2 + (0.95)^2 ] / 4 = 1.3375 = 1.157%
Hence, the mean return is 1.15% and standard deviation is 1.157%