You work as the assistant to Michael Brown, a CFP with Securities Services, Inc., an Akron, Ohio based medium-sized financial services firm. One of Michaels clients, Mr. Williamson, has $500,000 in a money market account in a local bank. Mr. Williamson is the owner of a mediumsize bottling company whose current projects are fully funded. Unhappy with the extremely low rate he earns on the money market account, he considers investing the $500,000 in stocks. Nevertheless, he will need the money in slightly more than a year from now to finance a major expansion of his company. Furthermore, Mr. Williamson has expressed a keen interest in three U.S. stocks. The first one, ALW, is a manufacturer of luxury watches. The second one, RCA, specializes in the collection of past-due accounts receivable. The third one, ACM, is a carpet manufacturer. The three companies do business nationwide and are traded on major U.S. stock exchanges. In about a week Michael plans to meet with and suggest a portfolio to Mr. Williamson for his one year investment horizon. Using several economic reports, Michael has developed probability estimates for the five states of the economy over the coming year. In addition, the security analysts at Securities Services have provided estimates of the rate of return on each of the three stocks under each state of the economy. Upon Michaels request, these analysts have also provided estimates of the rate of return under each state of the economy on the computer-run, market-weighted Index Fund Securities 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 ALW RCA ACM 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. Williamson, Michael wants you to provide within the next two days 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, Michael asked you to: Calculate the rate of return and total risk expected from investment in each of the three stock and the Index Fund; (ALW) Calculate the expected beta of each of the three stocks and intuitively explain to Mr. Willey the difference between a stocks standard deviation and beta; (ALW) Calculate the covariance and the correlation between ALW and RCA, between ALW and ACM, as well as between RCA and ACM. Second, Michael 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 ALW and RCA, portfolio P2 includes ALW and ACM, while portfolio P3 includes RCA and ACM. (Note: ALW is the first stock in P1 and P2, while RCA is the first stock in P3.) Michael is also interested in portfolio P4 which includes all three securities. Hence, Michael asked you to: Calculate and tabulate the standard deviation of return of each of the three portfolios P1, P2, and P3 assuming its expected return is 6%, 7%, 8%, or 9%, respectively; (P1) Calculate and tabulate 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); (P1, 50%) 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 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); (P4) Calculate the covariance and the correlation between ACM and portfolio P1; Explain/rationalize/justify the change in expected return and standard deviation as investment shifts from 100% in RCA, to an equally weighted portfolio of ALW and RCA, to finally an equally-weighted portfolio of ALW, RCA, and ACM; Based on this part of your analysis, advise whether it is best to invest only in RCA, 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, Michael 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, Michael wants to assess the impact of possible Fed actions on your calculations. Michael has come across several economic reports some of which predict the Fed may lower the T-Bills rate to 2.5%, while other reports predict the Fed to raise the T-Bills rate to 3.5% over Mr. Williamsons one-year investment horizon. Therefore, Michael asked you to: Demonstrate how, all else the same, such changes 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. Williamson overall, given his interest in ALW, RCA, and ACM.

Economy State	Probability	T bills	ALW	RCA	ACM	Index Fund
Recession	0.1	3.00%	-20.00%	26.50%	10.00%	-13.00%
Below Average	0.15	3.00%	2	13	-10	1
Average	0.5	3.00%	23.3	-2.7	7	15
Above average	0.15	3.00%	37.3	-12	45	25
Expansion	0.1	3.00%	48	-20	30	40