# Expected Returns, Standard Deviations, Covariance and Correlation Coefficient

You are considering investing in two stocks with the unimaginative names stock X and stock Y. You believe that there are only three scenarios possible for the future and they can be labeled "bear market," "normal market," and "bull market." The table below shows the returns for the two stocks for these three scenarios and also shows the probability of each scenario occurring.

Bear Market Normal Market Bull Market

Probability .2 .5 .3

Stock X -20% 15% 50%

Stock Y -15% 10% 20%

4. What is the expected return for Stock X and Stock Y?

5. What is the standard deviation of returns for Stock X and Stock Y?

6. What is the covariance of Stock X and Stock Y?

7. What is the correlation coefficient of Stock X and Stock Y?

8. What is the expected rate of return on your portfolio if you invest $6,000 in Stock X and $4,000 in stock Y?

9. What is the variance in the returns of your portfolio with the 60%/40% proportion of question 8? What is the standard deviation?

10. Suppose that there is a safe asset that offers a return of 2% in all states of the world. What would be the expected rate of return and standard deviation of a portfolio that initially invested $5,000 in the safe asset, $3,000 is Stock X and $2,000 in Stock Y?

11. What is the slope of the Capital Asset Line (CAL) connecting the safe asset and the risky portfolio with 60% in Stock X and 40% in stock Y?

https://brainmass.com/economics/investments/expected-returns-standard-deviations-covariance-and-correlation-coefficient-124924

#### Solution Summary

Expected Returns, Standard Deviations, Covariance and Correlation Coefficient are determined.

Average Return, Std Deviation, Coefficient, Co-variance

The annual returns of three stocks during the last eight years are presented.

STOCK A: 1%, 6%, 10%, 18%, 20%, 7%, -10%, -2%

STOCK B: 12%, 9%, 16%, 11%, -5%, -2%, -2%, 6%

STOCK C: 20%, -2%, 33%, 10%, -8%, -10%, 8%, 30%

1) Using Excel, Determine the average return, and the standard deviation of returns for each stock. Which stock has the highest expected return and which one has the highest risk?

2) Using Excel, Determine the correlation coefficient and the covariance between each pair of stocks.

3) Using Excel, Determine the expected return, and the standard deviation of returns of equally weighted portfolios consisting of two stocks (AB, BC, and AC) and three (ABC) stocks.

4) Create charts showing how the standard deviation of the two-stock (AB and AC) portfolios' returns changes as the weight of one stock (A) changes.

5) Use the Solver to determine the minimum variance portfolio composed of three stocks (ABC).