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# Expected Return and Standard Deviation of Return

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1) You are interested in investing, and are considering a portfolio comprised of the following two stocks. Their estimated returns under varying market conditions are provided:

Condition Probability of condition Return on security A Return on security B
Economy Sluggish 0.3 0.16 -0.05
Economy Normal 0.4 0.06 0.1
Economy Booms 0.3 -0.02 0.21

a) What is the expected return for security A?
b) What is the expected return for security B?
c) What is the standard deviation for Security A?
d) What is the standard deviation for Security B?

2) Now that you have calculated the standard deviations of A and B, assuming an equally weighted portfolio of each, calculate the correlation coefficient of the two stocks and use that calculation to discuss the appropriateness of holding the stocks together in a single portfolio. (hint: you must use your answers above to first calculate the covariance).
Now that you have calculated the standard deviations of A and B, assuming an equally weighted portfolio of each, calculate the correlation coefficient of the two stocks and use that calculation to discuss the appropriateness of holding the stocks together in a single portfolio. (hint: you must use your answers above to first calculate the covariance).

https://brainmass.com/statistics/probability/expected-return-and-standard-deviation-of-return-241681

#### Solution Preview

You are interested in investing, and are considering a portfolio comprised of the following two stocks. Their estimated returns under varying market conditions are provided:

Condition Probability of condition Return on security A Return on security B
Economy Sluggish 0.3 0.16 -0.05
Economy Normal 0.4 0.06 0.1
Economy Booms 0.3 -0.02 0.21

What is the expected return for security A?

Security A
Condition Probability Return return x Probability
Economy Sluggish 0.30 0.16 0.0480
Economy Normal 0.40 0.06 0.0240
Economy Booms 0.30 -0.02 -0.0060

1.00 0.0660

What is the expected return for security B?

Security B
Condition Probability Return return x Probability
Economy Sluggish 0.30 -0.05 -0.0150
Economy Normal 0.40 0.10 0.0400
Economy Booms 0.30 0.21 0.0630

1.00 0.0880