Question 13.S-TP.2: Portfolio Risk and Return Using the information in the previ...
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?
The portfolio weights are $15,000/$20,000 = .75 and $5,000/$20,000 = .25. The expected return is thus:
E(R_{P}) = .75 × E(R_{A}) + .25 × E(R_{B})
= (.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(R_{P}) = (.20 × −.0625) + (.50 × .2250) + (.30 × .5500) = .265, or 26.5%
This is the same as we had before.
The portfolio’s variance is:
\sigma ^{2}_{P} = .20 × (−.0625 − .265)² + .50 × (.225 − .265)²
+ .30 × (.55 − .265)²
= .0466
So the standard deviation is\sqrt{.0466}=.2159,\text{or }21.59\%.