Investment Advisor Comparative Analysis: Mutual Funds & CAPM Alpha Calculation

Task:

When answering the questions on this assignment, please adhere to the following instructions:

Students are encouraged to work together on the homework assignments to obtain a better understanding of material.  However, written responses MUST be original (i.e. in each student's own words) and reflects one's own thoughts.  Assignments submitted that are identical to another student's work will not receive credit.

Answer questions directly and then provide an explanation if/when called for.  For example, if the question asks... "Would you buy the book? Why or why not?" Your response should begin with either "Yes, I would buy the book..." or "No, I would not buy the book..." which should then be followed by "because...".   

Do not provide extraneous information hoping the right answer is buried within the response. Points will be deducted if students submit a "data dump" of extraneous information.  Points will also be deducted for false statements contained in responses even if a correct response was provided.

Questions requiring a discussion or explanation can usually be answered in just a few clearly and concisely written sentences.  Brevity AND thoroughness  are strong indications of mastery and ability to apply the course concepts. 
Students are strongly urged to proof-read responses several times to ensure the requirements outlined above are met. Typos, grammatical errors, poor word usage and sentences that did not make sense are not acceptable. 
Calculations performed in Excel must use either absolute or relative cell references.  Do not hard-code variables as that is not proper form in business (finance or any other business discipline).

1)  An investment advisor is comparing performance of two mutual funds each of which is designed to outperform the S&P 500.
The Freedelity Fund returned 19%
The JPStanley Fund returned 16%.
Based on the information above, which is the better fund in terms of the manager’s ability to select stocks?
Group of answer choices

a. Freedelity Fund has better stock selection
b. JP Stanley Fund has better stock selection
c. S&P 500 Index Fund has better stock selection
d. Freedelity & JP Stanley Funds have the same level of stock selection
e. Cannot tell from information provided

2) An investment advisor is comparing performance of two mutual funds each of which is designed to outperform the S&P 500.
The Freedelity Fund returned 19%
The JPStanley Fund returned 16%.
The betas of the Freedelity & JPStanley funds are 1.5 & 1.0 respectively.
T-Bill rate = 6%; and the S&P 500 returned 14%.
Which fund was the superior performer?  Why?

3)  You are evaluating a stock mutual fund that is among your employer’s 401k fund electives.  The fund is actively managed and seeks to outperform the S&P 500. Over the past 10 years, the fund returned 10.25% per year and had a beta = 0.8.
Over the same period, the S&P 500 returned 10% and the risk-free rate was 3%.
Calculate the fund’s CAPM alpha.

4)  You are evaluating a stock mutual fund that is among your employer’s 401k fund electives.  The fund is actively managed and seeks to outperform the S&P 500. Over the past 10 years, the fund returned 10.25% per year and had a beta = 0.8.
Over the same period, the S&P 500 returned 10% and the risk-free rate was 3%.
A colleague asked your opinion of the fund. Recalling the principles from FINC 561, you inform the colleague that the fund produced positive alpha – meaning that the fund’s manager was able to find under-priced stocks thereby beating the market. Your colleague (who has not taken FINC 561) challenges your assertion stating:
 “The fund returned 10.25%, barely more than the S&P 500. I wouldn’t call 0.25% meaningful alpha – heck it’s not that much better than a S&P 500 index fund.”
 Comment on your colleague’s assertion. Do you agree? Why or why not? Explain.  (10 points)

5) Assume a fictitious world where there are four stocks:
General Electric (GE)
CitiGroup (C)
British Petroleum (BP)
FaceBook (FB)
The market is in equilibrium where CAPM assumptions hold (e.g. homogeneous expectations, efficient markets, zero transaction costs, etc.)
Express the equilibrium condition for this universe of stocks in terms of each stock’s return contribution and risk contribution. For notation purposes, you can use the symbols rmkt & σmkt to represent the market’s return & risk and rf to represent the risk-free rate. (Note: Students can either type or neatly hand-write the relationship and upload a picture or file containing the expression.)

6) Assume a fictitious world where there are four stocks:
General Electric (GE)
CitiGroup (C)
British Petroleum (BP)
FaceBook (FB)
The market is in equilibrium where CAPM assumptions hold (e.g. homogeneous expectations, efficient markets, zero transaction costs, etc.)
Describe in words, the equilibrium relationship from Question #6 above.
7)  Assume a fictitious world where there are four stocks:
General Electric (GE)
CitiGroup (C)
British Petroleum (BP)
FaceBook (FB).
The market is in equilibrium where CAPM assumptions hold (e.g. homogeneous expectations, efficient markets, zero transaction costs, etc.)

What would be the market’s response if the ratio of the contribution to the market’s risk premium divided by the contribution to the market’s variance is higher for BP and lower for FB vs. the other two stocks?