# Probability Distribution: Expected Return and Standard Deviation

Please assist me in accurately answering the following questions. I am having a difficult time solving the questions.

8-6 Expected returns Stocks X and Y have the following probability distributions of

expected future returns:

Probability X Y

0.1 (10%) (35%)

0.2 2 0

0.4 12 20

0.2 20 25

0.1 38 45

a. Calculate the expected rate of return, r?Y, for Stock Y. (r?X _ 12%.)

b. Calculate the standard deviation of expected returns, _X , for Stock X. (_Y _ 20.35%.)Now calculate the coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than Stock X? Explain.

8-20 Realized rates of return Stocks A and B have the following historical returns:

Year Stock A's Returns, rA Stock B's Returns, rB

2001 (18.00%) (14.50%)

2002 33.00 21.80

2003 15.00 30.50

2004 (0.50) (7.60)

2005 27.00 26.30

a. Calculate the average rate of return for each stock during the period 2001 through 2005.

b. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would the realized rate of return on the portfolio have been in each year? What would the average return on the portfolio have been during this period?

c. Calculate the standard deviation of returns for each stock and for the portfolio.

d. Calculate the coefficient of variation for each stock and for the portfolio.

e. Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

https://brainmass.com/economics/supply-and-demand/probability-distribution-expected-return-standard-deviation-161725

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8-6 Expected returns Stocks X and Y have the following probability distributions of

expected future returns:

Probability X Y

0.1 (10%) (35%)

0.2 2 0

0.4 12 20

0.2 20 25

0.1 38 45

a. Calculate the expected rate of return, r?Y, for Stock Y. (r?X _ 12%.)

.

= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)

= 14% versus 12% for X.

b. Calculate the standard deviation of expected returns, _X , for Stock X. (_Y _ 20.35%.)Now calculate the coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than Stock X? Explain.

 = .

= (-10% - ...

#### Solution Summary

The solution explains how to calculate the expected return and standard deviation for individual stocks and a portfolio

Solve: Expected Mean, Variance and Standard Deviation

In answering the following questions, it is given that the potential investment has the following range of possible outcomes and probabilities: 10% probability of a -20% return, 40% probability of a 15% return, 40% probability of a 25% return, and a 10% probability of a 50% return.

(a) Calculate the weighted mean of the probability distribution;

(b) calculate the variance of the probability distribution;

(c) Calculate the standard deviation of the probability distribution.

(d) Calculate the coefficient of variation of the probability distribution.

(e) Would another investment having a coefficient of variation of .25 appear to offer a higher return per unit of risk?