Question

Stocks X and Y have the following probability distributions of expected future returns:

Probability      X      Y     

      0.3      2%      25%
      0.4      12%      20%
      0.3      20%      0%
     
One investor invests 40% in stock X and 60% in stock Y. Calculate the expected return, standard deviation, and coefficient of variation Stocks X and Y. Compute the expected rate of return for the portfolio.

Answer 1

Following formulas will be used;

Expected Return: Pi * Return on Stock

where Pi= Probability

Standard Deviation=

Now,

Expected Return on Stock X E[R_x] = Pi * R_x

   = (0.3* 2) + (0.4 * 12) + (0.3 * 20)

= 0.6 + 4.8 + 6

= 11.4%

Expected Return on Stock Y E[R_y] = Pi * R_y

= (0.3* 25) + (0.4 * 20) + (0.3 * 0)

= 7.5 + 8 + 0

= 15.5%

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Standard Deviation of Stock X and Stock Y

Probabilty (Pi)	Return on Stock X ( Rx)	[ Rx - E[Rx] ] 2	[ Rx - E[Rx ] 2 * Pi
0.3	2	[ 2 - 11.4] 2	26.508
0.4	12	[12 - 11.4] 2	0.144
0.3	20	[ 20 - 11.4] 2	22.188
			48.84

Standard Deviation of Stock X =

=6.98%

Probabilty (Pi)	Return on Stock Y ( Ry)	[ Ry - E[Ry] ] 2	[ Ry - E[Ry ] 2 * Pi
0.3	25	[ 25 - 15.5] 2	27.075
0.4	20	[ 20 - 15.5] 2	8.1
0.3	0	[ 0 - 15.5] 2	72.075
			107.25

Standard Deviation of Stock Y =

=10.35%

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Coefficient of Variation:

where,

= Standard deviation

E[R] = expected return of stock

Now,

Coefficient of Variation of Stock X:

=

= 61.22%

Coefficient of Variation of Stock Y:

=

= 66.77%

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Weight of X is 40% or 0.4
Weight of Y is 60% or 0.6

Expected Return of Portfolio= Rx * Wx + Ry * Wy

= 11.4 * 0.4 + 15.5 * 0.6

= 4.56 + 9.3

= 13.86%