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# Calculating expected return of a portfolio

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Problem:

Rate of Return if State Occurs
State of Economy Probability of State of Econ Stock A Stock B Stock C
Boom 0.30 0.30 0.45 0.33
Good 0.40 0.12 0.10 0.15
Poor 0.25 0.01 -0.15 -0.05
Bust 0.05 -0.06 -0.30 -0.09

1. How do I calculate the expected return on this portfolio if it invested 30% each in Stocks A and C and 40% in Stock B?

2. Also, please help me find the variance of the portfolio as well as the standard deviation. Thank you so much!

#### Solution Preview

Please refer attached file for better clarity of tables and formulas.

Solution:

State of Economy Rate of Return if State ccurs Potrfolio's
Probability Stock A % allocation Stock B % allocation Stock C % allocation Weighted return

Boom 0.30 0.30 30% 0.45 40% 0.33 30% 0.369
Good 0.40 0.12 30% 0.10 ...

#### Solution Summary

The following solution describes the steps for calculating expected returns and standard deviation of a portfolio.

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