3. You want to build a portfolio. You have a few stocks that you want to put in

Question

3. You want to build a portfolio. You have a few stocks that you want to put in your US Market Portfolio portfolio. Their payoffs are: States Probability Return 15% 10% -5% Stock A Stock B Stock CT-Bill | 24.60% | 11.40%|-11.40%| 3% 2% 1090 | | 80 % | 16.40%| 7.60%|-7.60%| 2 10% 1% Expected Payoff 14.60% | 6.90% | -6.40% | 72.13%-12.62%24.97%2 Variance You decide to put these three stocks into your portfolio, with portions of 30% (Stock A), 40% (Stock B), and 30% (Stock C). Calculate the expected return and variance of the portfolio. Comment on the expected payoff and variance of the portfolio comparing to the expected payoffs and variances of each stock. What is the beta of this portfolio?

Explanation / Answer

Portfolio Return = Sum of (weights x Stock return)

Portfolio return (State 1) = .30 x 24.60% + .40 x 11.4% + .30 x -11.40% = 8.52%

Portfolio return (State 2) = .30 x 16.40% + .40 x 7.60% + .30 x -7.60%= 5.68%

Portfolio return (State 3) = .30 x -9.80% + .40 x -3.20% + .30 x 8.20% = -1.78%

Expected portfolio return = sum of (Probability x Return)

State

P

R

P x R

1

10%

8.52%

0.85200%

2

80%

5.68%

4.54400%

3

10%

-1.78%

-0.17800%

5.21800%

Therefore, Expected portfolio return (Er) would be 5.218%.

State

P

R

R- ER

P x (R-ER)^2

1

10%

8.52%

3.30200%

0.01090320400%

2

80%

5.68%

0.46200%

0.00170755200%

3

10%

-1.78%

-6.99800%

0.04897200400%

0.06158276000%

Variance = Sum of P x (R-ER)^2

                = 0.06158276000%

= 6.16%^2

Beta of the portfolio is 0.5109

Comparison with Stock A

The portfolio has lower expected portfolio and lower variance.

Comparison with Stock B

The portfolio has lower expected portfolio and lower variance. The difference between expected payoff is very low whereas the difference between their variance is huge.

Comparison with Stock C

The poftfolio has higher return with lower risk.

State

P

R

P x R

1

10%

8.52%

0.85200%

2

80%

5.68%

4.54400%

3

10%

-1.78%

-0.17800%

5.21800%

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.