Question

TThe following data are available to you as a financial analyst: Security Expected Return Beta Standard Deviation A 0.32 1.70 0.50 B 0.30 1.40 0.35 C 0.25 1.10 0.40 D 0.22 0.95 0.24 E 0.20 1.05 0.28 F 0.14 0.70 0.18 Market 0.12 1.00 0.20 Treasury Bills 0.08 0 0 Required: a) Assuming that a portfolio is constructed using equal portions of the A, B and C stocks listed above: i) What is the expected return on and risk of such a portfolio?[4] b) Now suppose a portfolio is constructed with D and E stocks calculate the risk of a minimum variance portfolio. [4]

Answer 1

Answer: Putting information in a tabular form

Portfolio	Security Expected Return	Beta	Standard Deviation
A	0.32	1.70	0.50
B	0.30	1.40	0.35
C	0.25	1.10	0.40
D	0.22	0.95	0.24
E	0.20	1.05	0.28
F	0.14	0.70	0.18
MARKET	0.12	1.00	0.20
TREASURY BILLS	0.08	0	0

a) Assuming that a portfolio is constructed using equal portions of the A, B and C stocks listed above

i) Expected return of the total portfolios A, B, C is

Expected return_portfolioA = β_portfolioA * (Expected Return_market - Rate_risk-free) + Rate_risk-free

= 1.70 * (0.12 - 0.08) + 0.08

= 0.068 + 0.08

= 0.148 = 14.8%

Expected return_portfolioB = β_portfolioB * (Expected Return_market - Rate_risk-free) + Rate_risk-free

= 1.40 * (0.12 - 0.08) + 0.08

= 0.056 + 0.08

= 0.136 = 13.6%

Expected return_portfolioC = β_portfolioC * (Expected Return_market - Rate_risk-free) + Rate_risk-free

= 1.10 * (0.12 - 0.08) + 0.08

= 0.044 +0.08

= 0.124 = 12.4%

All the three A,B and C portfolios are giving expected returns above market return which is 12%.

Higher the risk higher the returns from above calculations we can see that portfolio A gives highest returns among all having its standard deviation 0.50.

b)