# Expected Return and Standard Deviation of Return

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).

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#### Solution Preview

Please see the attached excel file for answers:

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

Answer: Expected return= 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

Answer: Expected return= 0.0880

What is the standard deviation for Security A?

Security A

Condition Probability Return return x Probability Difference from mean, i.e.0.066 Difference 2 Prob x Difference 2

Economy Sluggish 0.30 0.16 0.0480 0.0940 0.008836 0.0026508

Economy Normal 0.40 0.06 0.0240 -0.0060 ...

#### Solution Summary

Questions on expected return and standard deviation of securities and portfolios have been answered.