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AD685 – Term Paper Project

Part 1. Univariate Statistics.

The data below was obtained from Professor Kenneth French's data library website:

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

The table below contains monthly returns of the “Fama/French 5 Factors” and the monthly returns of the “Momentum factor” for the period from July 1963-December 2017 (654 months)

(Double click on the window to access the data on the excel spreadsheet)

· RM-RF The return spread between the capitalization weighted stock market and cash.

· SMB The return spread of small minus large stocks (i.e., the size effect).

· HML The return spread of cheap minus expensive stocks (i.e., the value effect).

· RMW The return spread of the most profitable firms minus the least profitable.

· CMA The return spread of firms that invest conservatively minus aggressively.

· MOM   The retun spread of firms with high prior return minus low prior return.

1. Split the sample in 3 equal periods and compute the average, SD, skew, and kurtosis for each of the six “risk factors” for the full sample and the three different periods. Arrange these values in a table similar to the one shown below. (5p)

2. Do the statistics suggest to you that returns for those risk factors come from the same distribution over the entire period? (5p)

3. Make a plot showing the growth of $1 in each of the six “risk factors (portfolios)” over the full sample.  (Recall, this is called an "equity curve"). (5p)

4. Which factor portfolio gives the lowest and highest future value (full sample)? (5p)

5. Make a plot showing the growth of $1 in each of the six “risk factors (portfolios)” over the five-year period (Jan 2013 – Dec 2017).  (Recall, this is called an "equity curve"). (5p)

6. Which factor portfolio gives the lowest and highest future value (over the five-year period (Jan 2013 – Dec 2017).  )? (5p)

7. Give a brief explanation of what are the real, macroeconomic, aggregate, nondiversifiable risk that are proxied by the returns of the [RM-RF], SMB, HML, RMW, CMA and MOM risk portfolios. For example, why are investors so concerned about holding stocks that do badly at the times that the HML (value less growth) and SMB (small-cap less large-cap) portfolios do badly, even though the market [RM-RF] does not fall? (5p)

Part 2.

Go to Yahoo! finance site. Please download monthly adj. close prices from 12/1/2012 to 12/1/2017 for S&P 500 index (^SP500TR) and the following funds:

· European stock fund: Fidelity Europe (FIEUX)

· Latin America Fund: Fidelity Latin America (FLATX)

· Long-term bond fund: Fidelity Corporate Bond (FCBFX)

· Real Estate fund: T. Rowe Price Real Estate (TRREX)

· Small Cap Stock Fund: Fidelity Small Cap Stock (FSLCX)

1. Describe briefly the goal of each fund (5p)

2. Compute time plots of monthly prices and continuously compounded returns and comment. (5p)

a. Are there any unusually large or small returns? (5p)

b. Can you identify any news events that may explain these unusual values? (5p) 

3. Make a plot showing the growth of $1 in each of the funds over the five-year period. (5p)

a. Which fund gives the highest future value? (5p)

b. Are you surprised? (5p) 

4. Compute univariate descriptive statistics (mean, variance, standard deviation, skewness, kurtosis) for each return series and comment. (5p)

a. Which funds have the highest and lowest average return? (5p)

b. Which funds have the highest and lowest standard deviation? (5p)

c. Which funds look most and least normally distributed? (5p)

5. Using a monthly risk free rate equal to 0.04167% per month (which corresponds to a continuously compounded annual rate of 0.5%), compute Sharpe's slope/ratio for each fund. Arrange these values in a table from highest to lowest. Which asset has the highest Sharpe ratios? (5p)

6. Compute estimated standard errors and form 95% confidence intervals for the estimates of the mean and standard deviation. Arrange these values in a table. (5p)

a. Are these means and standard deviations estimated very precisely? (5p)

b. Which estimates are more precise: the estimated means or standard deviations? (5p)

7. Convert the monthly sample means into annual estimates by multiplying by 12 and convert the monthly sample SDs into annual estimates by multiplying by the square root of 12. Comment on the values of these annual numbers. (5p)

a. Using these values, compute annualized Sharpe ratios. (5p)

b. Are the asset rankings the same as with the monthly Sharpe ratios? (5p)

8. Compute and plot all pair-wise scatterplots between these 5 funds. Briefly comment on any relationships you see. (5p)

9. Compute the sample covariance matrix of the returns on these 5 funds and comment on the direction of linear association between the asset returns. (5p)

10. Compute the sample correlation matrix of the returns on these 5 funds. (5p)

a. Which funda are most highly correlated?  (5p)

b. Which are least correlated?  (5p)

c. Based on the estimated correlation values do you think diversification will reduce risk with these assets? (5p)

Part 3. Estimating expected returns

In this section, you need to use information from Part 1 and Part 2.

Use the Fama-French Three-Factor model augmented by “Momentum”(MOM) to estimate the  expected returns of each of the funds from part 2:

o European stock fund: Fidelity Europe (FIEUX)

o Latin America Fund: Fidelity Latin America (FLATX)

o Long-term bond fund: Fidelity Corporate Bond (FCBFX)

o Real Estate fund: T. Rowe Price Real Estate (TRREX)

o Small Cap Stock Fund: Fidelity Small Cap Stock (FSLCX)

 

To simplify notation in the regression notice that = is stock or portfolio  excess return and  = is the excess return on a “stock market portfolio”

In order to do this follow 3 simple steps:

1. Step 1. Estimate the risk premia for each factor (5p)

 

2. Step 2. Estimate the sensitivities of the  stock to each of those factors.  (5p)

 

3. Step 3. The expected returns can be calculated by combining the results of the previous steps. (5p)

 

4. Which fund has the highest and lowest expected return? (5p)

5. Compare the factor betas and provide some comparisons between the two funds. (5p)

Now, use the Fama-French 5-Factor model below to estimate each of these funds’ expected returns

 

To simplify notation in the regression notice that = is stock or portfolio  excess return and  = is the excess return on a “stock market portfolio”

In order to do this follow the same procedure as before.

6. Step 1. Estimate the risk premia for each factor (5p)

7. Step 2. Estimate the sensitivities of the  stock to each of those factors.  (5p)

8. Step 3. The expected returns can be calculated by combining the results of the previous steps. (5p)

9. Which fund has the highest and lowest expected return? (5p)

10. Compare the factor betas and provide some comparisons between the two funds. (5p)

11. Which model is better to calculate the factor betas? (5p)

Part 4. Portfolio

Please download monthly adj. close prices from 12/1/2012 to 12/1/2017 for the following individuals stocks:

· Alphabet Inc. (GOOG)

· Boeing (BA)

· Costco Wholesale Corporation (COST)

· Wells Fargo & Company (WFC)

· Tesla, Inc. (TSLA)

Information on these stocks is available on the Yahoo! finance site. After typing in the sticker symbol and retrieving the quote data, choose Profile to get a summary of the stock. Please review each stock before doing any of the analysis below.

1. Compute monthly returns for each individual stock. (5p)

2. Compute univariate descriptive statistics (mean, standard deviation) for each return series and comment. Arrange these values in a table. (5p)

a. Which stocks have the highest and lowest average return? (5p)

b. Which stocks have the highest and lowest standard deviation? (5p) 

3. Compute the sample covariance matrix of the returns on the five stocks and comment on the direction of linear association between the asset returns. (5p)

4. Compute the sample correlation matrix of the returns on the 5 stocks. (5p)

a. Which assets are most highly correlated? (5p)

b. Which are least correlated? (5p)

c. Based on the estimated correlation values do you think diversification will reduce risk with these assets? (5p)

5. Convert the monthly sample means into annual estimates by multiplying by 12. Monthly variances and covariances can be annualized by multiplying by 12. Standard deviations are annualized by multiplying monthly standard deviations by the square root of 12. (5p)

6. Using the annualized estimated means, variances and covariances computed earlier. Suppose, an investor currently owns a portfolio consisting of two stocks, COST and WFC, with 60% invested in COST. (5p)

a. Calculate the expected value of the portfolio returns. (5p)

b. Calculate the risk (standard deviation) of the portfolio returns. (5p)

7. Suppose the previous investor wants to keep her stake in Costco Wholesale Corporation (COST) and would like other asset to substitute for WFC. Which of the remaining three stocks will give her the maximum benefit of diversification, assuming she still keeps 60% invested in COST? (5p)

a. Calculate the expected value of returns of this new portfolio. (5p)

b. Calculate the risk (standard deviation) of this new portfolio. (5p)