Question

Complete showing all work (formulas, calc key strokes) for question #2

Part 2 2. Your portfolio consists of three stocks: Stock Investment Beta Expected Return A $45,000 $50,000 $55,000 1.3 9.5% B 0.8 6.7 % C 1.6 9.9% Find the beta and expected return on the portfolio.

Answer 1

Stock	Investment	Beta	Expected return
A	45000	1.3	9.5%
B	50000	0.8	6.7%
C	55000	1.6	9.9%

Total amount invested in the portfolio = $45000 + 50000 + 55000 = $150000

Stock A

Weight of A = W_A = Amount invested in A/Total amount invested in portfolio = 45000/150000 = 0.3

Beta of A = β_A = 1.3

Return on A = R_A = 9.5%

Stock B

Weight of B = W_B = Amount invested in B/Total amount invested in portfolio = 50000/150000 = 10/30

Beta of B = β_B = 0.8

Return on B = R_B = 6.7%

Stock C

Weight of C = W_C = Amount invested in C/Total amount invested in portfolio = 55000/150000 = 11/30

Beta of C = β_C = 1.6

Return on C = R_C = 9.9%

Portfolio

Beta of the portfolio is calculated using the formula:

Beta of portfolio = β_P = W_A*β_A+W_B*β_B+W_C*β_C = 0.3*1.3 + ((10/30)*0.8) + ((11/30)*1.6) = 1.2433333

Expected return on the portfolio is calculated using the formula:

E[R_P] = W_A*R_A+W_B*R_B+W_C*R_C​​​​​​​ = (0.3*9.5%) + ((10/30)*6.7%) + ((11/30)*9.9%) = 8.71333333%

Answers

Beta of the portfolio = 1.243333

Expected return on the portfolio = 8.713333%