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%

Respond to this discussion board:

After doing my calculations I decided that the best option in my opinion would be choosing the second portfolio where $70,000 is invested in tech.com and $30,000 is invested in Sams Grocery Competition. I think this is the best option because it gives a higher return than the first option. I also think that the amount of risk someone is willing to take can play a part in which one is the best option as well because if I was afraid of risk then I would go with the first portfolio. If we don't just look at the numbers and we let risk make the decisions for us then they would probably not make us to choose differently. In this case I could choose either or depending on how much of a risk I am willing to take after examining all of the numbers needed. If I am being risky though then I would stick with the higher returns. In this case for higher returns the second portfolio will be the best option because I can handle the risk

Answer 1

1. Calculation of Expected return (ER )

Expected return = Return Of The security * probability of each case

ER tech.com = -20%*0.3 + 15%*0.2 + 30%*0.35 + 50%*0.15

= 15%

ER Sam Grocery = 5%*0.3 + 6%*0.2 + 8%*0.35 + 10%*0.15

= 7%

ER S&P = -4%*0.3 + 11%*0.2 + 17%*0.35 + 27%*0.15

= 11%

2. Calculation of Standard deviation

²tech.com = [(-20%-15%)² *0.3 + (15% - 15%)² *0.2 + (30%-15%)² * 0.35 + (50% - 15%)² * 0.15]

= 630

= 25.0998%

² Sam Grocery =[(5% - 7%)² * 0.3 + (6% - 7%)² * 0.2 + (8% - 7%)² * 0.35 + (10% - 7%)² * 0.15]

= 2.95

= 1.7176%

² S&P 500= [(-4%-11%)² * 0.3 + (11% - 11%)² * 0.2 + (17% - 11%)² * 0.35 + (27% - 11%)² * 0.15]

= 118.5

= 10.8858%

3. Beta is a better measure of risk than the standard deviation. Beta is the measure of systematic risk whereas the standard deviation is the measure of total risk consisting of systematic risk and unsyatematic risk. The unsyatematic risk is diversifiable and can also be eliminated so systematic risk which is non diversifiable is the only relevant risk.

4. Calculation of ER based on beta

ER = R_F + * (ER_M - R_F)

R_F is the risk free rate

ER_M is the Expected return from market

ER tech.com = 5% + 1.68*(10.8858% - 5%)

= 14.8881%

ER sam grocery = 5% + 0.52*(10.8858% - 5%)

= 8.0606%