Broadly diversified portfolio

Jack O’Boyle and David O’Brien are district managers for C&M Inc., a leading supplier of construction equipment. Over the years as they moved through the firm’s sales organization they became, and still remain, close friends. Jack, who is 33 years old, currently lives in Newark, New Jersey; David, who is 35 years, lives in Houston, Texas. Recently at the national sales meeting they were discussing various company matters, as well as bringing each other up to date on their families, when the subject of investment came up. Each of them had always been fascinated by the stock market and now they have achieved some financial success, they have begun actively investing. As they discussed their investments, Jack indicated that he felt that only way an individual who did not have hundreds of thousands of dollars to invest can safely is buy mutual funds shares, since they contain a large number of securities representing the stocks of the leading firms in a broad cross-section of industries. Jack emphasized that in order to be safe, a person need to hold a broadly diversified portfolio and that only those with a lot of money and time can achieve the needed diversification that can be readily obtained by purchasing mutual fund shares.

David totally disagreed. He said, “Diversification! Who needs it?” He felt that what one must do is to look carefully at each stock possessing desired risk-return characteristics and then invest all one’s money in that stock. Jack told him he was crazy. He said, “There is no way to conveniently measure risk- You are just gambling.” David disagreed. He explained how his stockbroker has acquainted him with beta, which is a measure of risk. David said that higher the beta, the more risky the stock, and therefore higher will be its return. By looking up the betas for potential stock investments in his broker’s beta book, he can pick socks having an acceptable risk level for him. David explained that with beta, one does not need to diversify; one merely need to be willing to accept the risk reflected by beta and then hope for the best. The conversation continued, with Jack indicating that although he knew nothing about beta, he did not believe one could safely invest in a single stock. David continued to argue that his broker had explained to him that beta can be calculated not just for a single stock, but also for a portfolio of stocks such as a mutual fund. He said, “What’s the difference between a stock with beta of say, 1.20 and mutual fund with beta of 1.20? They both have the same risk and should therefore provide a similar return.”

As Jack and David continued to discuss their differing opinions relative to investment strategy, they began to get angry with each other. Neither was able to convince the other that he was right. The level of their voice now raised, they attracted the attention of the company vice-president of finance, Jordan Katz, who was standing nearby. He came over to Jack and David and indicated he had overheard their argument about investments and thought that, given his expertise in financial matters, he might be able to resolve their disagreement. He asked them to explain the crux of their disagreement, and each reviewed his viewpoint. After hearing their views, Jordan responded, “I have some good news and some bad news for each of you. There is some validity to what each of you said, but there also are some errors in each of your explanations. Jack tends to support the traditional approach to portfolio management; David’s view is more supportive of modern portfolio theory.” Just then, the company president interrupted them, indicating that he must talk to Jordan immediately. Jordan apologized for having to leave and made an arrangement to continue their discussion over a drink later that evening.

a) Analyze Jack’s argument and explain to him why a mutual fund investment may be over- diversified and that one does not necessarily have to have hundreds of thousands of dollars in order to diversify adequately.
b) Analyze David’s argument and explain the major error in his logic relative to the use of beta as substitute for diversification. Explain the key assumption underlying the use of beta as a risk measure.
c) Briefly describe the traditional approach to portfolio management and relate it to the approaches supported by Jack and David.

d) Briefly describe modern portfolio theory and relate it to the approaches supported by Jack and David. Be sure to mention diversifiable, non-diversifiable, and total risk along with the role of beta
e) Explain how the traditional approach and modern portfolio theory can be blended into an approach to portfolio management that might prove useful to the individual investor. Relate this to reconciling Jack’s and David’s differing points of view.

2)

a) Define and discuss different forms of efficient market hypothesis. Explain why in an efficient market it is difficult or impossible to consistently outperform the market.

b) You have been following the stock price of Lee Inc., for the past 16 consecutive days in an attempt to determine whether you can outperform the buy and hold strategy by employing a filter rule. The simple filter rule states that your buy or sell decision is dictated by the level of the filter. If the price of the stock increases by at least the level of the filter, you will buy and hold the stock until it reaches a peak and then drops at least by the level of the filter. In this exercise, you will refrain from short selling. As a result, when the stock price drops from the peak by the level of the filter, you will liquidate the position and hold on to cash until the next buying opportunity arises.

Day
Security Prices ($)
1 100
2 99.2
3 98.59
4 97.11
5 94.33
6 96.09
7 95.57
8 95.59
9 94.64
10 94.47
11 94.99
12 95.43
13 93.22
14 92.7
15 94.7
16 93.36

i) Compute the return on $100.00 invested in the security by a 0.3% filter rule (without short sales) and compare this strategy to a buy and hold policy. Note that investors wait until the price increases by more than 0.3% for the first time. In addition, note that a fraction of a share can be purchased or sold. (Carry out calculations to 4 decimal points).
ii) Perform the autocorrelation of price movement over the 16 day period. Explain your finding.

iii) What do the results obtained in (i) and (ii) imply for weak form market efficiency? Based on the limited data that you have analyzed, what is your conclusion about the weak form market efficiency? Justify your conclusion.
3) Please refer to the attached Excel spreadsheet, QUESTION 3 tab. The data set contains monthly closing prices for the period of December 2013 to October 2018 for four stock indices. They stock indices are the DJIA, S&P500, Russell 2000 and Nikkei 225.

Based on the data provided, you are asked to do the following:

a) Compute the monthly holding period returns for each index;
b) Compute the mean, variance and standard deviation of returns for each index. Provide a comparative analysis of their performance.
c) Compute the variance-covariance matrix of returns for the above indices. What information is contained in the variance-covariance matrix? Why is variance-covariance matrix important for portfolio analysis? Explain.
d) Compute the correlation matrix for the above indices. What additional information provided by the correlation matrix that is not provided by the variance-covariance matrix? Explain in detail.
e) Calculate equally weighted two asset portfolios of the following combinations:

i. DJIA –S&P500
ii. S&P500 – Russell 2000
iii. S&P500 – Nikkei 225
iv. Russell 2000 – Nikkei 225

f. Rank the portfolios based on their risk-return performance. Explain and justify your response.

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