# Economics Portfolio Report

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Like the first report, Portfolio Report 2 should be descriptive, opinionated and written in a professional manner. In evaluating your report I will take into account how clearly and concisely your thoughts are articulated with an effective and appropriate use of financial terms. As always, make sure to check for grammar and spelling. Make use of diagrams, (pie) charts, tables, table of contents, etc. Do not provide any raw data such as your security prices and daily returns in your main report but do submit your Excel files containing your data and calculations.

Note: Your PR2 mark will only be assigned upon the receipt of your rough work and calculations contained in your Excel file(s). Failure to provide your Excel file(s) will result in a zero mark for Portfolio Report 2.

Your Portfolio Report 2 should be self-contained in a single MS Word DOC or DOCX (preferred formats) or Adobe PDF file. This is the document that will be used in assessing your assignment. Any reference to Excel file or any other references to outside graphic files or links will be ignored.

1. CAPM (10 marks)

Calculate beta’s for each of the security in your portfolio by fitting a linear regression. You will need a vector of market returns. Please choose appropriate measure of market return (refer to Downloading Data section in Portfolio Report 1). Report your finding in a table, as follows:

Here, estimated beta for stock A is 1.25, it is a significant estimate (significantly different from zero) since its p-value is below 0.05 (using 95% confidence level). Alpha was estimated as 0.00084 and is insignificantly different from 0 (its p-value is above 0.05 threshold). Thus, we cannot guaranty that our estimated alpha is non-zero with 95% confidence. 60% of stock A return fluctuations were explained by the market. See an Example of Excel’s Regression Output with Explanations and review some Basic Concepts of Regression Analysis.

• What can you tell about each of the beta’s? intercepts? Are they significant? Was it a good fit?

Note: Betas are sensitivities of your stock returns to fluctuations in market returns. Stocks with betas greater than 1 are, normally, classified as aggressive and stocks with low betas as defensive stocks. One would expect a beta of lower than 1 for Canada’s largest grocer, providing essentials to customers irrespective of economic boom or financial downturn (we all have to consume food irrespective if it is during good or bad economic times). Adjusted R2 shows what percentage of stocks return fluctuations are explained by fluctuations in the market. The rest is firm-specific risk. If you put this into portfolio perspective, Adjusted R2 will show how diversified your portfolio is – portfolios with higher Adjusted R2 (and thus lower non-systematic risk) are considered more diversified.

If you are getting a poor fit (very low Adjusted R2) or insignificant betas (p-values for betas are greater than 0.05) you might want to try a different market proxy. OR (which is worse and mostl likely the case) is that you haven’t aligned the dates for your securities and market proxy at the start of Portfolio Report 1! However, the misalignment of the security prices will only affect students who pool their data for each stock separately (for example, when using Google Finance or Yahoo Finance and downloading the data from these websites one stock at the time and merging/combining the data into a single sheet).

1. Multi-Factor (Bonus Section – 5 Bonus marks)
• Use a multi-index model and add three or more additional systematic factors of your choice and discuss whether that had improved your CAMP-based model and whether the new factors are significant of not.
• (you can do three-factor model of Fama and French instead)
• The table below is an extended version of the table in the CAPM section of this assignment.
1. Construct a correlation coefficient matrix for your factors (market index included)
2. Make sure the correlation between your factors is close to zero: FACTORS MUST BE UNCORRELATED WITH EACH OTHER TO PROVIDE A SOUND RESULT! (colinearity problem). Include a correlation coefficient matrix for your independent variables. Avoid using in the same regression equation factors with correlation coefficient outside the [-0.3;+0.3] bound.
3. Construct a table to compare your historical returns to returns predicted by the CAPM and MULTI-FACTOR models, to your opinion which model outperformed the other?

Here, historical returns as simply arithmetic averages that you have already estimated in your PR1. CAPM predicted returns are calculated as follows: estimated alpha + estimated beta * average market return or using our previous example from the CAPM section and assuming average market return is 7%, CAPM predicted returns for stock A are 0 + 1.25*7% = 8.75%. You can perform similar calculations for multifactor model.

3.Constructing Portfolio and Efficient Frontiers (25 marks)

Assume short sales are not allowed:

• Find global minimum variance (GMV) portfolio and report its composition.
• Find optimal risky portfolio and report its composition.

In a single (σ, Ε [r]) graph plot the following:

• minimum variance portfolio frontier;
• efficient portfolio frontier;
• global minimum variance portfolio;
• optimal risky portfolio;
• all of the original securities;
• risk-free rate;
• construct CML, (derive and) report CML equation;
• (you will later add the new portfolios to this graph)

The graph must be clear and distinct. Use colors, label, legends, etc… Use a whole page if needed.

• Let the original portfolio be your current portfolio holding; calculate, record and report your security composition along with the weights.
• Let the new portfolio (no risk free) be a portfolio found on the efficient frontier (constructed based on composition of your original portfolio) with the same risk level (that is the same standard deviation) as your original portfolio but with a maximum possible E[r]. Calculate, record and report your new weights. Keep track of those transaction costs! Was it worth rebalancing your portfolio after all if you take transaction costs into account?
• Let the new portfolio (with risk free) be a portfolio found on the efficient frontier (constructed based on composition of your original portfolio and availability of a risk free asset) with the same risk level (that is the same standard deviation) as your original portfolio but with a maximum possible E[r]. Calculate, record and report your new weights. Note that you can now land or borrow money at the risk free rate of return!

In a single (β, Ε [r]) graph:

1. construct SML, derive and report SML equation;
1. plot each of the securities;
3. plot minimum variance portfolio
4. plot two of your new portfolio

Discuss whether any of your securities seem to be under/over valued and using some of the figures and values discussed in the article from Canadian Investment Review – How to Choose Undervalued Stocks discuss if the stocks that appear under or over valued based on your (β, Ε [r]) graph coincide with the predictions from the article.

1. Evaluation of Investment Performance (25 marks)

The following returns must be expressed as annual effective rates:

• Plot cumulative returns for the following 4 portfolios for the last 5 years (one plot) and the last 1 year (second plot):
• Original Portfolio (with the weights you used in PR1)
• New Portfolio without risk-free
• New Portfolio with risk-free
• Market Proxy/other benchmark
• Calculate a simplistic after tax return based on the following formula (make sure you annualize it after calculating!, report your tax calculations, list each of your cash inflows/outflows, assume taxes are paid at the end of the stock game period, note you also pay tax on capital gains!):

$$AfterTaxReturn = \frac{End Value + Cash Inflows – Cash Outflows – Initial Value}{(Initial Value)}$$

• Discuss the difference between Sharpe’s and Treynor’s measures. Which do you think would be more applicable to your portfolio?
• How did your new portfolio perform as compared to the original portfolio?
• Is your new portfolio superior/inferior to the market?
• What would you expect if the market proxy would change?
• Were you satisfied with your investment strategy? Did you change it during the second half of the game? Why?

Be sure to discuss what you have learned from the experience and what improvements are required or desired for next year’s offering.