Question

Using the following returns, calculate the expected returns, the variance, standard deviations and coefficient of variation for X and Y.

Prob	Rx	Ry
0.35	12.2	9.65
0.3	0	-2
0.35	6.5	12.5

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Answer 1

Below is the calculation of expected return, standard deviation, variance and coefficient of variation:

Asset X:

States	Probability	X	Probability Weighted Return	P(X - Expected return of X)^2
A	0.35	12.20%	0.35x12.2%=4.27%	0.35(0.122-0.06545)^2=0.1119265875%
B	0.3	0.00%	0.3x0%=0%	0.3(0-0.06545)^2=0.128511075%
C	0.35	6.50%	0.35x6.5%=2.275%	0.35(0.065-0.06545)^2=0
Expected Return = sum of Probability Weighted Return	4.27+0+2.275 = 6.545%
Variance= sum of P(X - Expected return of X)^2	0.1119265875 +0.128511075 +0 = 0.240%
Standard deviation = Square root of variance
Coefficient of variation = Standard deviation/Expected return

Excel screenshot is as follows:

Asset Y:

States	Probability	Y	Probability Weighted Return	P(X - Expected return of X)^2
A	0.35	9.65%	0.35x9.65%=3.3775%	0.35(0.0965-0.071525)^2=0.021831271875%
B	0.3	-2.00%	0.3x-2%=-0.6%	0.3(-0.02-0.071525)^2=0.2513%
C	0.35	12.50%	0.35x12.5%=4.375%	0.35(0.125-0.071525)^2=0.100085146875%
Expected Return = sum of Probability Weighted Return	3.3775-0.6+4.375 = 7.153%
Variance= sum of P(X - Expected return of Y)^2	0.021831271875+0.2513+0.100085146875= 0.373%
Standard deviation = Square root of variance
Coefficient of variation = Standard deviation/Expected return