Question

You have just invested in a portfolio of three stocks. The amount of money that you invested in each stock and its beta are summarized below.

Stock		Investment			Beta
A		$208,000			1.54
B		312,000			0.56
C		520,000			1.15

Calculate the beta of the portfolio and use the Capital Asset Pricing Model (CAPM) to compute the expected rate of return for the portfolio. Assume that the expected rate of return on the market is 15percent and that the risk-free rate is 9percent. (Round beta answer to 3 decimal places, e.g. 52.750 and expected rate of return answer to 2 decimal places, e.g. 52.75%.)

Beta of the portfolio:
Expected rate of return:

Answer 1

Total investment in the portfolio = 208000 + 312000 + 520000 = 1040000

Weight of A in the portfolio = w_A = 208000/1040000 = 0.2

Weight of B in the portfolio = w_B = 312000/1040000 = 0.3

Weight of C in the portfolio = w_C = 520000/1040000 = 0.5

Stock	Investment	Beta	Weights
A	208000	1.54	0.2
B	312000	0.56	0.3
C	520000	1.15	0.5

Beta of the portfolio is calculated using the formula:

β_P = w_A*β_A + w_B*β_B + w_c*β_C = 0.2*1.54 + 0.3*0.56 + 0.5*1.15 = 1.051

Expected return on portfolio is calculated using the CAPM equation

E[R_P] = R_F + β_P*(R_M - R_F)

Risk-free rate = R_F = 9%, Expected return on market = R_M = 15%

E[R_P] = 9% + 1.051*(15% - 9%) = 15.306%

Answers

Beta of the portfolio = 1.051

Expected rate of return = 15.31%