Consider the following information Rate of Return If State Occurs State of Econo

Question

Consider the following information Rate of Return If State Occurs State of Economy Boom Bust Probability of State of Economy Stock B 15 06 Stock A Stock C 58 42 07 16 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return b. What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) Variance

Explanation / Answer

Return if State occurs P A B C D=P*A E=P*B F=P*C State of Probability Stock A Stock B Stock C Expected Expected Expected Economy of state Retuen of A Retuen of B Retuen of C Boom 0.58 0.07 0.15 0.33 0.0406 0.087 0.1914 Bust 0.42 0.16 0.06 -0.06 0.0672 0.0252 -0.0252 TOTAL 0.1078 0.1122 0.1662 Expected return of stock 0.1078 0.1122 0.1662 Expected Return of Portfolio having equal weight of Stocks A, B and C=(1/3)*0.1078+(1/3)*0.1122+(1/3)*0.1662= 0.128733 Expected Return 12.87% CALCULATION OF PORTFOLIO VARIANCE VARIANCE OF STOCK A Expected Return of A= 0.1078= 10.78% P A B=A-10.78 C=B^2 Probability Return of A Deviation Deviation Deviation square* (percentage) from expected Squared Probability 0.58 7 -3.78 14.2884 8.287272 0.42 16 5.22 27.2484 11.444328 TOTAL 19.7316 VARIANCE OF STOCK A 19.7316 VARIANCE OF STOCK B Expected Return of B= 0.1122 11.22% P A B=A-11.22 C=B^2 Probability Return of B Deviation Deviation Deviation square* (Percentage) from expected Squared Probability 0.58 15 3.78 14.2884 8.287272 0.42 6 -5.22 27.2484 11.444328 TOTAL 19.7316 VARIANCE OF STOCK B 19.7316 VARIANCE OF STOCK C Expected Return of C= 0.1662 16.62% P A B=A-16.62 C=B^2 Probability Return of C Deviation Deviation Deviation square* from expected Squared Probability 0.58 33 16.38 268.3044 155.616552 0.42 6 -10.62 112.7844 47.369448 TOTAL 202.986 VARIANCE OF STOCK C 202.986 W V (W^2)*(V^2) Wa Weight of A 0.2 Va Variance of A 19.7316 15.57344154 Wb Weight of B 0.2 Vb Variance of B 19.7316 15.57344154 Wc Weight of C 0.6 Vc Variance of C 202.986 14833.19383 Total 14864.340714 Portfolio Variance=(Wa^2)(Va^2)+(Wb^2)(Vb^2)+(Wc^2)(Vc^2) Portfolio Variance=(0.2^2)(19.7316^2)+(0.2^2)(19.7316^2)+(0.6^2)(202.986^2)= 14864.340714 VARIANCE 14864.340714

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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