Question

You have been provided the following data on the securities of three firms, the market portfolio, and the risk-free asset:

a. Fill in the missing values in the table. (Leave no cells blank - be certain to enter 0 wherever required. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Security	Expected Return	Standard Deviation	Correlation*	Beta
Firm A	.105	.36		.80
Firm B	.145		.55	1.35
Firm C	.165	.60	.40
The market portfolio	.12	.20
The risk-free asset	.05

*With the market portfolio.

b-1. According to the CAPM, what is the expected return of Firm A's stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return             

b-2. What is your investment recommendation for someone with a well-diversified portfolio?

Sell

Buy

b-3. According to the CAPM, what is the expected return of Firm B's stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return             

b-4. What is your investment recommendation for someone with a well-diversified portfolio?

Sell

Buy

b-5. According to the CAPM, what is the expected return of Firm C's stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return             

b-6. What is your investment recommendation for someone with a well-diversified portfolio?

Sell

Buy

Answer 1

Part 1

Solution (a) - Calculation of Missing figures

Formula to be used for calculation

Beta = (Correlation* Standard deviation of security)/Standard deviation of Market portfolio.

Security	Expected Return	Standard Deviation	Correlation	Beta
Firm A	0.105	0.36	0.44 (Note 2)	0.8
Firm B	0.145	0.49 (Note 1)	0.55	1.35
Firm C	0.165	0.6	0.4	1.2 (Note 3)
Market Portfolio	0.12	0.2	1 (Correlation of market portfolio with iteself is always 1)	1 (Beta of market with iteself is always 1)
The Risk free asset	0.05	0 (Risk of risk free asset is always zero)	0 (correlation of risk free asset when combine with risky asset is always zero)	0 (beta of risk free asset is always zero)

Note 1 - Standard deviation of Firm B (let 'x')

Beta = (Correlation * Standard deviation of security)*standard deviation of market portfolio

1.35 = (0.55*x)/0.20

0.55x = 0.27

x = 0.49

Note 2 - Correlation of firm A

0.8 = (x*0.36)/0.2

0.36x = 0.16

x = 0.44

Note 3 - Beta of Firm 3

x = (0.4*0.6)/0.2

x = 1.2

Part 2 - Calculation of return as per CAPM model (Capital asset pricing model)

R_s = R_f + B_i * (R_m - R_f)

R_s = CAPM return

R_f = Risk free return

R_m = Market return

B_i = Beta of Firm

Concept of Buy/sell = In case valuation of return of security, CAPM model is used to calculate the return. In case the return as per CAPM model is greater than the expected return then such stock is overpriced and should be sell (go short). And if Return calculated as per CAPM Model is less than expected return then stock is undervalued and should be bought (go long)

Solution to question from b-1 to b-6 is in this single table

Security	Question Part	CAPM return	Question Part	Decision of Buy/sell
Firm A	(b-1)	0.106 or 10.6% (Note 4)	(b-2)	Expected Return= 0.105 CAPM return = 0.106 Since return as per CAPM model is greater such stock is overpriced and should be sell (go short)
Firm B	(b-3)	0.1445 or 14.45% (Note 5)	(b-4)	Expected return = 0.145 CAPM return = 0.1445 Since return as per CAPM mod is less than the expected return such stock is underpriced and should be bought (go long)
Firm C	(b-5)	0.134 or 13.4% (Note 6)	(b-6)	Expected return = 0.165 CAPM return = 0.134 Since return as per CAPM model is less than the expected return such stock is underpriced and should be bought (go long)

Note 4

Calculation of CAPM return

let CAPM return (R_s) = 'x'

x = 0.05 + 0.8*(0.12 - 0.05)

x = 0.106

Note 5-

x = 0.05 + 1.35*(0.12-0.05)

x = 0.1445

Note 6 -

x = 0.05 + 1.2*(0.12-0.05)

x = 0.134