Econ 309 - portfolio analysis project assignment - security

Question

Portfolio Analysis Project Assignment -

Project Overview - The project is comprised of three deliverables: (1) Security Selection; (2) Portfolio Construction; and, (3) Performance Evaluation. There are two important requirements for this project: (1) you are to establish and actively manage a portfolio of five stocks for the duration of the project to facilitate the portfolio analysis; and, answer the thirty questions listed below, numbered, and in order for each component.

The project will include three parts (as listed below) from the text: Bruce, B. and Greene, J. (2014). Trading and Money Management in a student-Managed Portfolio. Academic Press: Elsevier.

This text is assigned for the course as listed in the course Syllabus. It can be purchased "new" through the Campus Store, or, you might use an alternative source. It is highly recommended that you have access to this book... specifically, chapters 3, 4, and 6 in order to complete the project.

Read in the textbook:

Part I - Security Selection is in Chapter 3, pg. 77-130

Part II - Portfolio Construction is in Chapter 4, pg. 133-173

Part IV - Performance Evaluation is in Chapter 6, pg. 269-334.

Students will find material in these chapters extremely helpful in answering the project questions.

Part I - SECURITY SELECTION

1. What key beliefs must be embedded in an investment philosophy for security analysis to be a valuable part of the investment process? That is, what conditions are necessary to believe that security analysis is a valuable activity?

2. What is the difference between a good company and a good stock?

3. Explain the difference between a firm's earnings and its cash flows.

4. Discuss the meaning of relative value.

5. Review then consider stock valuation models. Using valuation concepts, explain how you would value a firm's bond and how you would value the firm's debt.

6. List all of the assumed or forecasted inputs to the Dividend Discount Model. Please create a table with separate columns for items 6 thru 8. For each input, explain how the resulting calculated intrinsic value of each stock changes when the value of the input is increased.

7. On your list of inputs in item 6, identify each input as either universal or firm-specific. Universal inputs take on the same value for all firms. Firm-specific inputs take on different values for different firms.

8. Again, on your list of inputs in item 6, for each input, explain how the resulting calculated intrinsic value of each stock changes when the value of the input is increased.

9. What conditions must be met (or assumptions made) for the calculated intrinsic value using the Discounted Cash Flow model to be equal to the intrinsic value using the Earnings Model for the same firm? You must discuss your answer in words and show your answer algebraically.

10. Discuss the advantages and disadvantages of each valuation model.

11. Some security analysts utilize price-per-unit valuation heuristics, where examples of units are customer, subscriber, store, mile acre, square foot, or internet number of hits.

a. Relate these heuristics to fundamental valuation models and discuss how each heuristic could be considered equivalent to one of the valuation models.

b. Discuss the implicit or explicit assumptions that make these heuristics useful.

c. Are these heuristics more or less useful relative valuations? Why?

12. Suppose a firm has a negative long-term growth rate of earnings and/or cash flows. Does this firm have a positive intrinsic value? Why or why not?

13. Some people are tempted to claim that the Dividend Discount Model is useless for stocks that do not currently pay dividends. Explain why this claim is not valid.

Part II - PORTFOLIO CONSTRUCTION

14. Suppose that an investment fund is mandated to invest 60% in Large-Cap U.S. Equity, 10% in Small-Cap U.S. Equity, and 30% in U.S. Investment Grade Corporate Bonds. Develop an appropriate benchmark for this portfolio by selecting benchmarks (refer to Exhibit 4.1 in Bruce and Greene) from S&P, Russell, and Barclays. Remember: (1) good benchmarks are those that clearly define the set of securities and weights so that a passive investment in the benchmark is feasible; (2) the benchmark should be consistent with the portfolio's target asset class mix and style; and, (3) the benchmark for any active strategy should be declared in advance so that outcomes can be measured against the benchmark (Bruce and Greene 2014).

15. Select and purchase five (5) stocks, and also create an Excel spreadsheet that has their capitalization (shares outstanding multiplied by price) and returns for each month in the past three (3) years.

a. Create a benchmark of these five stocks by calculating a capitalization-weighted portfolio. From these weights, calculate the monthly returns for the benchmark according to the following equation:

r_b,t = _i=1∑^N w_i,t-1^b xr_i,t

b. Calculate each stock's monthly relative returns using the capitalization-weighted portfolio as a benchmark.

c. Create an equally weighted portfolio of the five stocks. Calculate this portfolio's monthly returns and relative returns according to the following equations, respectively:

r_p,t = _i=1∑^Nw_i,t-1^pxr_i,t

rr_p,t = r_p,t - r_b,t = _i=1∑^Nw_i,t-1^p xrr_i,t

Using the monthly portfolio returns and relative returns, calculate the equally weighted portfolio's average return and average relative return.

d. Calculate the equally weighted portfolio's return standard deviation and tracking error by taking the standard deviation of the monthly returns and relative returns, respectively.

e. Calculate the average returns and average relative returns of the five stocks.

f. Calculate the equally weighted portfolio average return and relative return according to the following equations, respectively:

r^-_p = _i=1∑^N w_i^pxr^-_i

r^-_p - r^-_b = _i=1∑^N w_i^p x(r^-_i - r^-_b)

Check that these match with the averages you calculated in part c.

g. Create a covariance matrix of returns for your five stocks. (Note: this might require adjusting the =COVAR() function to match the =VAR() function in Excel by multiplying Excel's population covariance by N/(N-1), where N is the number of periods in your sample.)

h. Create a covariance matrix of relative returns for these stocks.

i. Calculate the equally weighted portfolio's standard deviation and tracking error according to the following equations:

Var(r_p) = σ²_p = _i=1∑^N_i=1∑^Nw_i^pw_j^pσ_i,j²

Var(r_p-r_b) = τ_p² = _i=1∑^N_j=1∑^N w_i^pw_j^pτ_i,j²

Note that these calculations make use of the covariance matrices in parts g and h. Check that portfolio standard deviation and tracking error match the values you found in part d.

16. Now for the five stocks that you have chosen, create an Excel spreadsheet that has each stock's monthly returns for a ten-year historical period (e.g. 2006 - 2015).

a. Create an equally weighted portfolio of the 5 stocks by calculating the equally weighted portfolio's (EWP) return in each month during the 10-yr period.

b. Create a series of monthly portfolio returns using the Time Series Method in Exhibit 4.6 of the handout. To do this, create a set of weights in one row of the spreadsheet and reference these weights and each month's returns in the =SUMPRODUCTO function to calculate the monthly return. Verify that changing these weights changes the portfolio's monthly returns. Refer to this portfolio as P1.

c. Calculate the average and standard deviation of the monthly returns and the Sharpe Ratio for the stocks and the portfolios (EWP and P1) for the "First Half" of the ten year period (i.e., the first five years). Calculate the average and standard deviation of the monthly returns and the Sharpe Ratio for the stocks and the portfolios (EWP and P1) for the "Last Half" of the ten-year period:

r^-_P-r_f/σ_p

d. Are the stocks with the highest standard deviation in the Last Half the same as the stocks with the highest standard deviations in the First Half? What about the average returns and the Sharp Ratio?

e. Using Excel's Solver as in Exhibit 4.13, find the set of weights that sets the "First Half" standard deviation to its minimum for P1.

f. Examine the P1 weights for the stocks resulting from the Solver in part d. Can you determine why each stock received the weight that it did? That is, which stocks received the most weight? Why?

g. Compare the standard deviation during the "Last Half" for P1 with EW. Which is the lower'? Is this what you would have expected? Why?

h. Redo parts e and g but add constraints that the minimum weight in each stock must be at least 5% and/or that the maximum weight in each stock must be no greater than 15%. How does this change your response to part f?

17. Redo parts e through h of question 3, but use the object to maximize the Sharpe Ratio in the First Half.

18. Theoretically, a constraint always results in a worse solution according to mathematics. Why are constraints important in using optimizers to construct portfolios?

19. In general, which portfolio would you expect to have a lower tracking error against the S&P 500: an equally weighted portfolio of 20 large-cap stocks or an equally weighted portfolio of 40 large- cap stocks? Why?

20. In general, which portfolio would you expect to have a lower tracking error against the S&P 500: an equally weighted portfolio of 40 large-cap stocks or an equally weighted portfolio of 40 mid-cap stocks? Why?

21. In general, which portfolio would you expect to have a lower tracking error against the S&P 500: an equally weighted portfolio of 40 large-cap stocks or a portfolio of 40 large-cap stocks that has the same sector weights as the S&P 500, assuming stocks are equally weighted within sectors? Why?

22. What are some advantages and disadvantages to constraining a portfolio to be sector neutral (i.e., have the same sector weights as the benchmark)?

Part III - PERFORMANCE EVALUATION

23. Use the example in Exhibit 6.3 to answer the following questions.

a. Verify that the portfolio's security weights are approximately the same on Nov. 7, 2012, pre-and post-flow. That is, verify that the cash flow was converted to equities using approximately the same portfolio weights.

b. Verify that the return on the portfolio would have been approximately the same for the entire month of November 2012 if there had been no cash flow. Hint: use the security holdings at the end of October and the security prices at the end of November to calculate a portfolio market value for the end of the month. Also, use a cash amount of $7956.00 on November 30, 2012, which is approximately what the cash would have been if there had been no cash flow.

24. Using the monthly returns below from the first quarter of 2008, calculate the compound return for the entire quarter for the strategy and the benchmark. Also, calculate the relative returns for each month and for the entire quarter. Finally, compound the monthly relative returns to show that they are not equal to the quarterly relative return.

Month	Portfolio Return	Benchmark Return
Jan 2008	17.35%	14.87%
Feb 2008	8.57%	5.85%
Mar 2008	-26.01%	-26.12%

25. Using the annual returns below, calculate the annualized average return for strategy and the benchmark over the 3-year period. Also calculate the annualized average 3-year relative return. Note that the annualized average 3-year relative return is negative, despite the fact that the portfolio beat the benchmark by more than 2% in the first two years and only lagged the benchmark by 2% in the third year. Explain why this happens.

Year	Portfolio Return	Benchmark Return	Relative Return
1	26.97%	24.95%	2.02%
2	16.04%	14.03%	2.01%
3	-41.98%	-39.98%	-2.00%

26. The sector contribution to the relative return in Equation 6.19 can also be calculated using the relative return sector allocation in Equation 6.14. In general, the individual sector contributions will be different when using Equation 6.13 versus Equation 6.14. Prove algebraically that both approaches sum to the same total portfolio relative return. Hint: simply sum each of the two versions of Equations 6.19 across all sectors.

27. Using the Fama-French 3-Factor Model regression results from monthly portfolio returns in the table below, describe the strategies that each fund appears to follow. That Is describe what types of stocks the fund is likely to hold and the types of risks to which it is exposed.

Fund	Alpha	MArket	SMB	HML	R-Sq.
A	-0.0012	0.71	-0.14	0.20	0.78
B	0.0008	1.02	0.10	-0.02	0.93
C	0.0019	1.11	0.34	-0.22	0.73
D	-0.0017	1.59	-0.10	-0.18	0.82
E	0.0012	1.07	0.30	-0.23	0.98

28. Consider the funds in question 27. Funds C and E appear quite similar. Which investment manager outperforms by more? Which manager would you be most confident has skill in generating value? Why?

29. Suppose that the Large Cap 500 Index Fund is the benchmark for the Growth Fund in Exhibit 6.14. Using the information in Exhibit 6.14, attribute the Growth Fund's average relative return of -0.69% per month to the components of the Fama-French 3-Factor Model. Specifically, determine the sources of the average relative return in terms of the alpha and Market, SMB, and HML factors.

30. Suppose that the Total Market Index Fund is the benchmark for the Value Fund in Exhibit 6.14. Using the information in Exhibit 6.14, attribute the Value Fund's average relative return of +0.43% per month to the components of the Fama-French 3-Factor Model. Specifically, determine the sources of the average relative return in terms of the alpha and Market, SMB, and HML factors.

Source: Bruce, Brian and Greene, Jason (2014). Trading and Money Management in a Student-Managed Portfolio. Elsevier: Academic Press.

Project Final Paper Overview -

There are three parts of this semester-long project that conclude with a final paper and in-class presentation that uses certain aspects from each of the three Parts. Hence, the 3+1 reference. In essence, you will illustrate your understanding of what you have learned from those parts and present your own security selection analysis, and evaluation. You will be provided with the opportunity to present a summary of your project to the class. When presenting keep in mind that this is a FINANCE class and delivered in a FINANCE setting. Although you do not have to wear business attire, you need to provide explanations for each of your claims using the vocabulary you have learned.

There are two main requirements:

1. Power Point Presentation lasting of 6 minutes comprised of each section (see below).

2. Final Paper of 3-5 pages writing in detail about your findings that is due upon conclusion of your class presentation. Do not show your work (that has already been submitted in the three Parts), but show your numbers and explain how you arrived at them. I'm not looking for excel pages, but final answers.

Section 1- Introduction to your Fund

Review your original IPS statement and determine if it matches the type of stocks you selected. Did you want a growth portfolio or an income portfolio? Is it large-cap, mid-cap, small-cap, or a blend? Did you utilize the weights you said you would? Did you seek the return you said you would? Did you diversify your stock pick in terms of buying all utilities or a mix of different types? These answers should be explained with the inclusion of a pie chart.

The goal in this section is to see if you did what you originally set out to do. If not, then discuss what made you change your original IPS statement and present the new IPS statement (as an appendix). Another question you must answer is "why"? It is not sufficient to say "I choose a large-cap growth portfolio". You need to explain why, e.g., "we have all seen large-cap growth funds outperform the majority of other funds when coming out of a decline. However, they are also the most volatile of funds since they are exposed to the most amount of risk. Because I wanted a 20% return (and, you must also provide evidence as to why 20%), the best way to fund it was with large-cap a growth fund. A large-cap growth fund is ..."

Section 2 - Security Selection

Explain what stocks you bought and why? If you wanted a fund that beat the market, did you pick stocks with a Beta greater than 1? If you wanted an income fund, did you pick stocks with high dividend yields? Explain why the stocks you picked align with your goals. Did you use any of the models discussed in Chapter 3 of B&G (Bruce and Greene, 2014)? What separates a good Company from a good stock?

Your answers do not have to be based on fundamentals or technical analysis, but could also be based on financial statements or a top-down approach of a sector. Also, don't say "the P/E is 30, so I bought it" What is the P/E compared to other companies in the same industry, is that P/E better than the industry P/E? What is the company's forward P/E for example? Is it undervalued, overvalued? What makes your stocks better than competitors, aka your classmates selected stocks? In your paper you will have to write about each stock in a few sentences, but for your in-class presentation, simply pick one or two that were most intriguing and stand out quantitatively, in your opinion.

The goal of this section is to see if you understand the theme behind investment philosophy for your analysis to be valuable.

Section 3 - Analysis

• Calculate weekly returns from January 22 to April 20, 2018. Remember to include any dividends.
• Calculate each stocks weekly return, then sum them to find the portfolio's return. Remember to use the weights you picked. Note that the portfolio weights change weekly because of price changes. Call this portfolio "RP".
• Now calculate the Equally Weighted Portfolio (EWP). Compare and contrast the two in terms of return, average return per week, and risk.
• Find the Sharpe Ratio and explain what risk-free rate you are using. Use "RP" for this.
• Also, find, the set of weights that would have resulted in the lowest standard deviation. Find the set of weights between 5% and 15% that gave the lowest standard deviation. Why do these constraints matter (refer to page 167 in B&G)? Discuss the returns and average returns in each case.
• Clearly outline your benchmarks. One should be the market-cap created from Part 2 and the other should be something like the S&P or the Russel. Note that the S&P 500 is based on large-cap stocks. If you have a small-cap fund, so it's probably not a good comparison with the S&P 500. Use Exhibit 4.1 in B&G to see a listing of possible alternative indexes and make sure your goals in the IPS statement align with them.
• Now, find the relative return between RP and your market-cap benchmark "BMK", and also the other benchmark "OBMK" that you selected. Report the tracking error. It might also be informative to find the return, average return, and risk of BMK and OBMK.
• Find the Beta for your portfolio with OBMK and the Alpha.

Again, it will be improper to show excel numbers or simply list the weights. Tell us how you found them using the equations in Chapter 4 of B&G. Also, discuss why each weight was assigned with numerical analysis. It is wrong to say "the stock with the lowest weight has the highest standard deviation"... Provide the numbers!

The goal here is to see if you understand the equations portfolio managers use in their analysis to report figures.

Section 4 - Evaluation

Did you do any rebalancing to keep the same proportion of weights? Did it align with your IPS? How well did you feel you did?

Find the compound return of your portfolio. Find the overall return. Find the relative compound return with BMK. Find the annualized average return and the annualized average relative return.

Section 5 - How did you feel you did? Perform well? Do you still want to be a portfolio manager or do you now see why they get paid large sums of money?