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FIN3702A
AY 2024/2025 Semester 1
Group Project – Case C

Objectives:

1. Parts 1, 2 and 4 test whether you have understood the Excel exercises done in class.

Most of what is required are similar to the exercises.

What is different is the number of funds used for the analyses.

2. Part 3 tests whether you can independently read instructions to apply them and also tests your resourcefulness to search for online/offline materials to aid your understanding.

This is an important skill that you must learn as you prepare to enter the workforce.

Oftentimes at work, you will be given tasks with little guidance and expected to figure things out. I intend to leave this part to the groups to work through completely on their own. In other words, I will not entertain questions about how to perform the style analysis. Figuring it out is very much part of the task!

Not everyone enjoys working in groups. Yet, it is critical to learn skills of teamwork because that is largely how the workplace functions. The more experience you get, the more you’ll learn. This includes the good and the bad. I hope you will enjoy working in your group and learn much from each other!

Instructions:

a. Excel spreadsheet containing all original fund data, the mathematical results you have generated and all the diagrams/charts.

Please include a cover sheet that states your Section, Group and Case (A#_Group#_CaseC), as well as the names and matric numbers of all members of your group.

4. Please upload your required documents as listed above in one zip folder with the following filename: “A#_Group#_CaseC” to the “Group Project Submission” folder in Canvas.

5. Presentations will be done in class on Week 13. Each group is given 15 minutes to present.

TOTAL - 100%

Case C

1. Collect monthly adjusted closing prices of the 10 funds in Appendix A from May 2019 to May 2024. Calculate the monthly returns from June 2019 to May 2024.

Produce the minimum variance frontier.

The risk-free rate is 2% and the risk aversion parameter of the client, A = 4.

Finally, assume a front-end load of 1.5% and a management fee of 0.3%.

What was the expected return after fees and standard deviation of the optimal complete portfolio?

Perform regressions using the Single Index Model and the Fama French 3-Factor Model.

Discuss the results of your output tables.

3. Perform Style Analysis (refer to Appendix B) on only the top 2 funds that make up the optimal risky portfolio from Question 1. If the ORP only has 2 funds, then use these. If the ORP has more than 2 funds, only use the 2 funds with greatest weights.

Use a 100% stacked-area chart (refer to Appendix B exhibit 1) to illustrate the Rolling 36-month periods returns-based style analysis of the funds for May 2022 to May 2024.

Comment on the consistency of the style of the fund over this period.

4. Recreate the final minimum variance frontier diagram using the original 10 funds in Appendix A and also the 4 funds in Appendix C.

The risk-free rate is 2% and the risk aversion parameter of the client, A = 4.

On the same graph, plot three indifference curves and clearly label the minimum variance portfolio, the optimum risky portfolio and the optimal complete portfolio.

Finally, assume a front-end load of 1.5% and a management fee of 0.3%.

What was the expected return after fees and standard deviation of the final optimal complete portfolio?

Suggest reasons to support the addition of any new funds from Appendix C to the final portfolio combination. 

APPENDIX A – 10 Equity Funds

APPENDIX B – Style Analysis (extracted from Section 24.2 of the textbook)

Sharpe’s idea was to regress fund returns on indexes representing a range of asset classes. The regression coefficient on each index would then measure the fund’s implicit allocation to that “style.” Because funds are barred from short positions, the regression coefficients are constrained to be either zero or positive and to sum to 100%, so as to represent a complete asset allocation. The Rsquare of the regression would then measure the percentage of return variability attributable to style choice rather than security selection. The intercept measures the average return from security selection of the fund portfolio. It therefore tracks the average success of security selection over the sample period.

To illustrate Sharpe’s approach, we use monthly returns on Fidelity Magellan’s Fund during the famous manager Peter Lynch’s tenure between October 1986 and September 1991, with results shown in Table 24.4. While seven asset classes are included in this analysis (of which six are represented by stock indexes and one is the T-bill alternative), the regression coefficients are positive for only three, namely, large capitalization stocks, medium cap stocks, and high P/E (growth) stocks. These portfolios alone explain 97.5% of the variance of Magellan’s returns. In other words, a tracking portfolio made up of the three style portfolios, with weights as given in Table 24.4, would explain the vast majority of Magellan’s variation in monthly performance. We conclude that the fund returns are well represented by three style portfolios.

Style analysis provides an alternative to performance evaluation based on the security market line (SML) of the CAPM. The SML uses only one comparison portfolio, the broad market index, whereas style analysis more freely constructs a tracking portfolio from a number of specialized indexes. Style analysis reveals the strategy that most closely tracks the fund’s activity and measures performance relative to this strategy. If the strategy revealed by the style analysis method is consistent with the one stated in the fund prospectus, then the performance relative to this strategy is the correct measure of the fund’s success.

Style Analysis in Excel

You can do style analysis with Excel’s Solver. The strategy is to regress a fund’s rate of return on those of a number of style portfolios (as in Table 24.4). The style portfolios are passive (index) funds that represent a style alternative to asset allocation. Suppose you choose three style portfolios, labeled 1–3. Then the coefficients in your style regression are alpha (the intercept that measures abnormal performance) and three slope coefficients, one for each style index. The slope coefficients reveal how sensitively the performance of the fund follows the return of each passive style portfolio.

The residuals from this regression, e(t), represent “noise,” that is, fund performance at each date, t, that is independent of any of the style portfolios. We cannot use a standard regression package in this analysis, however, because we wish to constrain each coefficient to be nonnegative and sum to 1.0, representing a portfolio of styles.

To do style analysis using Solver, start with arbitrary coefficients (e.g., you can set α = 0 and set each β = ⅓). Use these to compute the time series of residuals from the style regression according to

 (24.8)

R(t) = Excess return on the measured fund for date t

Equation 24.8 yields the time series of residuals from your “regression equation” with those arbitrary coefficients. Now square each residual and sum the squares. At this point, you call on the Solver to minimize the sum of squares by changing the value of the four coefficients. You also add four constraints to the optimization: three that force the betas to be nonnegative and one that forces them to sum to 1. Solver’s output will give you the three style coefficients, as well as the estimate of the fund’s unique, abnormal performance as measured by the intercept. The sum of squares also allows you to calculate the R-square of the regression.

Style Drift

Exhibits 1 and 2 show the style analysis for Provident and Ariel over a seven-year period, 1995 to 2002. Exhibit 1 shows that Provident has consistently maintained a heavy style tilt towards large cap growth, whereas Exhibit 2 shows that Ariel has recently picked up a higher small cap value exposure.

APPENDIX C – 4 Other Funds