Reference no: EM132443386

Case: A&G Services, Inc.

You work as the assistant to Mark Bates, a CFP with A&G Services, Inc., an Atlanta based medium-sized financial services firm.  One of Mark's clients, Mr. Willey, recently inherited $250,000.  Mr. Willey is a real estate developer whose current projects are fully funded; so, he considers investing the inheritance money in stocks.  Nevertheless, he will need the money in slightly more than a year from now when he initiates a new real estate project.  Furthermore, Mr. Willey has expressed a keen interest in three U.S. stocks.  The first one, ALG, is a manufacturer of high-end leather goods. The second one, CCS, specializes in the collection of past-due credit card and medical bills.  The third one, AF, is a furniture manufacturer.  The three companies do business nationwide and are traded on major U.S. stock exchanges.  In about a week Mark plans to meet with and suggest a portfolio to Mr. Willey for his one year investment horizon.

Using several economic reports, Mark has developed probability estimates for the five states of the economy over the coming year.  In addition, the security analysts at A&G Services have provided estimates of the rate of return on each of the three stocks under each state of the economy.  Upon Mark's request, the analysts have also provided estimates of the rate of return under each state of the economy on the computer-run, market-weighted "Index Fund" A&G Services uses in-house to gauge the performance of the stock market as a whole.  Finally, the security analysts have provided estimates of the return on T-Bills over the coming year.  The following table summarizes the above information.

Estimated Rate of Return on Alternative Investments

Economy State	Probability	T-Bills	ALG	CCS	AF	Index Fund
Recession	0.10	3.0%	(20.0%)	26.5%	10.0%	(13.0%)
Below average	0.15	3.0	(2.0)	13.0	(10.0)	1.0
Average	0.50	3.0	23.3	(2.7)	7.0	15.0
Above average	0.15	3.0	37.3	(12.0)	45.0	25.0
Expansion	0.10	3.0	48.0	(20.0)	30.0	40.0

In preparation for his meeting with Mr. Willey, Mark wants you to work on providing him within the next two days with a substantial amount of information which he has sorted into four different groups.

First, to gain a better understanding of the three stocks and the stock market as a whole, Mark asked you to:

• Calculate the expected rate of return, variance and standard deviation of the rate of return of each of the three stock and the Index Fund; (ALG)
• Calculate the expected beta of each of the three stocks and intuitively explain to Mr. Willey the difference between a stock's standard deviation and beta; (ALG)
• Calculate the covariance and the correlation between ALG and CCS, between ALG and AF, as well as between CCS and AF.

Second, Mark wants to assess the benefits of investing in portfolios as opposed to individual stocks.  He is interested in combining the three stocks to create three two-stock portfolios; portfolio P1 includes ALG and CCS, portfolio P2 includes ALG and AF, while portfolio P3 includes CCS and AF.  (Note: ALG is the first stock in P1 and P2, while CCS is the first stock in P3.)  Mark is also interested in portfolio P4 which includes all three securities. Hence, Mark asked you to:

• Calculate the standard deviation of each of the three portfolios P1, P2, and P3 assuming its expected rate of return is 8%;
• Calculate the expected return and the standard deviation of each of the three portfolios P1, P2, and P3 assuming the weight assigned to the first stock of each portfolio takes values between 30% and 60% in steps of 1% (in other words, the weight assigned to the first stock of each portfolio is 30%, 31%, 32%, ......, 59%, 60%; you should use Excel to expedite your calculations);
• Intuitively explain which one of the three portfolios is more effective in reducing total risk (Hint: To answer this you should rely on your findings in the previous two bullets);
• Calculate the expected return and standard deviation for P1 (with 1/2 weight for each of the stocks) and P4 (with 1/3 weight for each stock);
• Perform any additional calculations you deem appropriate to explain/rationalize/justify the change in expected return and standard deviation as investment shifts from 100% in CCS, to an equally weighted portfolio of ALG and CCS, to finally an equally-weighted portfolio of ALG, CCS, and AF;
• Based on this part of your analysis, advise whether it is best to invest only in CCS, the equally-weighted portfolio P1, or the equally-weighted portfolio P4.

Third, to assess whether the three stocks, as well as the equally-weighted portfolios P1, P2, P3, and P4 are valued properly, Mark asked you to:

• Prepare a table in which you report the expected rate of return, beta, and required rate of return for each of the three securities, each of the four equally-weighted portfolios, and the Index Fund;
• Perform any additional calculations you deem appropriate to explain whether each of the three securities and the four equally-weighted portfolios is overvalued or undervalued;
• Based on this part of your analysis, advise which of the above eight alternatives (the three stocks, the four portfolios, and the Index Fund) is the best investment option.

Fourth, Mark is concerned that due to the strengthening of the economy inflation may turn and remain higher and, as a result, force the Fed to raise the T-Bills rate from its current level of 3% to 3.25% or even 3.5% over Mr. Willey's one-year investment horizon.  Therefore, Mark asked you to:

• Demonstrate how, all else the same, such a change in the T-Bills rate will impact your previous findings;
• Prepare a brief report explaining which of the investment alternatives discussed above is most appropriate for Mr. Willey overall, given his interest in ALG, CCS, and AF.

Note: Your reports must show explicitly the calculations for the items indicated parenthetically in bold letters at the RHS margin of several bullets throughout the case.