Question

Risk, Return, and the Capital Asset Pricing ModelAs a first day intern at Tri-Star Management Incorporated the CEO asks you to analyze the following in-formation pertaining to two common stock investments, Tech.com Incorporated and Sam’s Grocery Cor-poration. You are told that a one-year Treasury Bill will have a rate of return of 5% over the next year. Also, information from an investment advising service lists the current beta for Tech.com as 1.68 and for Sam’s Grocery as 0.52. You are provided a series of questions to guide your analysis.

Estimated Rate of Return

Economy             Probability          Tech.com            Sam’s Grocery                   S&P 500

Recession            30%                        –20%                                     5%                          – 4%

Average               20%                        15%                                        6%                          11%

Expansion            35%                        30%                                        8%                          17%       

Boom                    15%                        50%                                        10%                        27%

1. Which of these two-stock portfolios do you prefer? Why

Answer 1

Economy	Probability	Tech. com	E(r) of Tech.com	Sam’s Grocery	E(r) of Sam’s Grocery	S&P 500 (market)	E(r) of S&P 500
Recession	30%	-20%	-6.00%	5%	1.50%	-4%	-1.20%
Average	20%	15%	3.00%	6%	1.20%	11%	2.20%
Expansion	35%	30%	10.50%	8%	2.80%	17%	5.95%
Boom	15%	50%	7.50%	10%	1.50%	27%	4.05%
E(r)			15.00%		7.00%		11.00%

E(r) = Sum of (Probability*Return)
Risk free rate= 5%
Beta of Tech.com= 1.68
Beta of Sam's grocery = 0.52
Required Return as per CAPM = Risk free rate + (Beta*(market return - Risk free rate))
required return of Tech.com =
5% + (1.68 * (11% - 5%))
15.08%
Expected return of Tech.com = 15.00%
Required return of Sam's grocery=
5% + (0.52 * (11% - 5%))
8.12%
Expected return of Sam's grocery is 7.00%
If a security provides Expected return more than required return, stock portfolio will be selected.
If expected return is less than required return, stock portfolio will not be selected.
On the above calculation Sam's grocery expected return is more than required return.
So Sam's grocery portfolio would be preferred.

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