An exhaustive financial analysis has produced the following returns on two inves

Question

An exhaustive financial analysis has produced the following returns on two investments (Stock X and Stock Y) under three different scenarios (Si):

                                                                        Expected Returns

Scenario

Probability

Stock X

Stock Y

S1

0.3

10%

8%

S2

0.4

16%

15%

S3

0.3

12%

20%

           

a. Calculate the expected return on each investment.

b. Calculate the standard deviations (?) for both X and Y.

c. Calculate the coefficient of variation (CV) for both X and Y.

d. If you were to create a portfolio consisting of 67% of Stock X and 33% of Stock Y, what will be the expected return (rP) and the standard deviation (?P) for your portfolio?

Scenario

Probability

Stock X

Stock Y

S1

0.3

10%

8%

S2

0.4

16%

15%

S3

0.3

12%

20%

Explanation / Answer

a) The formula to calculate expected return is = Sum of the individual probabilities multiplies by their expected returns.

Hence, we have = Expected value of stock X = (.3 * .10) + (.4 * .16) + (.3 * .12) = 13 %

Expected value of stock Y = (.3 * .08) + (.4 * .15) + (.3 * .20) = 14.40 %

b) Standard deviation = under root of Variance. Or Variance = square of Standard Deviation.

Variance = Sum of the probabilities multiplied by the squared differences of the observations.

Variance of stock X = .3(.10 - .13)2 + .4(.16 - .13)2 + .3(.12 - .13)2 = .0007 or Standard Deviation = 2.57 %

Variance of stock Y = .3(.08 - .144)2 + .4(.15 - .144)2 + .3(.20 - .144)2 = 0.0022 or Standard Deviation = 4.67 %

c) Co-efficient of Variation = Standard Deviation / Mean (Expected Return in this case)

CV of X = 0.0257 / 0.13 = 0.1976

CV of Y = 0.0467 / 0.144 = 0.3243

d) If a portfolio has 67% of X and 33% of Y then its expected return would be = (.67 * .13) + (.33 * .144) = 13.46 %

The Variance will be = .67(.13 - .1346)2 + .33(.144 - .1346)2 = .000043

Standard deviation will be = 0.6557

Hope my detailed solution solves your query.

Regards.

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