Portfolio Risk and Return Using the information in the previous problem, suppose you have $20,000 total. If you put $15,000 in Stock A and the remainder in Stock B, what will be the expected return and standard deviation of your portfolio?

Question

Accepted Answer

The portfolio weights are $15,000/$20,000 = .75 and $5,000/$20,000 = .25. The expected return is thus:

E([latex]R_{P}[/latex]) = .75 × E([latex]R_{A}[/latex]) + .25 × E([latex]R_{B}[/latex])
= (.75 × .25) + (.25 × .31)

= .265, or 26.5%

Alternatively, we could calculate the portfolio’s return in each of the states:

State of Economy	Probability of State of Economy	Portfolio Return If State Occurs
Recession	.20	(.75 × −.15) + (.25 × .20) = −.0625
Normal	.50	(.75 × .20) + (.25 × .30) = .2250
Boom	.30	(.75 × .60) + (.25 × .40) = .5500

The portfolio’s expected return is:

E([latex]R_{P}[/latex]) = (.20 × −.0625) + (.50 × .2250) + (.30 × .5500) = .265, or 26.5%

This is the same as we had before.
The portfolio’s variance is:

[latex]\sigma ^{2}_{P}[/latex] = .20 × (−.0625 − .265)² + .50 × (.225 − .265)²

+ .30 × (.55 − .265)²

= .0466

So the standard deviation is[latex]\sqrt{.0466}=.2159, ext{or }21.59\%. [/latex]

Question 13.S-TP.2: Portfolio Risk and Return Using the information in the previ...

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