AD685 – Experiential Learning – Hand out #1

AD685 – Experiential Learning – Hand out #1

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Part 1. Univariate Statistics.

Please go to Professor Kenneth French’s data library website and obtained monthly returns data on the “Fama/French 3 Factors” and the risk free rate for the period from July 1963-December 2017 (654 months):

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

  1. Split the sample in 3 equal periods and compute the average, SD, skew, and kurtosis for each of the three “risk factors” for the full sample and the three different periods. Arrange these values in a table similar to the one shown below.
Full Sample: 1963M07 – 2017M12
  MKT_RF SMB HML      
 Mean            
 Std. Dev.            
 Skewness            
 Kurtosis            
 Observations            
First sub-sample: 1963M07 – 1981M08
  MKT_RF SMB HML      
 Mean            
 Std. Dev.            
 Skewness            
 Kurtosis            
 Observations            
     
Second sub-sample: 1981M09 – 1999M10
  MKT_RF SMB HML      
 Mean            
 Std. Dev.            
 Skewness            
 Kurtosis            
 Observations            
Third sub-sample: 1999M11 – 2017M12
  MKT_RF SMB HML      
 Mean            
 Std. Dev.            
 Skewness            
 Kurtosis            
 Observations            

 

  1. Do the statistics suggest to you that returns for those risk factors come from the same distribution over the entire period?

 

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

 

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

 

 

 

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

 

 

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

 

  1. Which funds have the highest and lowest average return?
  2. Which funds have the highest and lowest standard deviation?
  3. Which funds look most and least normally distributed?

 

 

  1. 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?

 

  1. Compute and plot all pair-wise scatterplots between these 3 funds. Briefly comment on any relationships you see.

 

  1. Compute the sample covariance matrix of the returns on these 3 funds and comment on the direction of linear association between the asset returns.

 

  1. Compute the sample correlation matrix of the returns on these 3 funds.
    1. Which funds are most highly correlated?
    2. Which are least correlated?
    3. Based on the estimated correlation values do you think diversification will reduce risk with these assets?

 

Part 3. Estimating expected returns

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

Use the CAPM to estimate the  expected returns of each of the funds from part 2:

 

  • European stock fund: Fidelity Europe (FIEUX)
  • Latin America Fund: Fidelity Latin America (FLATX)
  • 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 three 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. 
  3. Step 3. The expected returns can be calculated by combining the results of the previous steps.
  4. Which fund has the highest and lowest expected return?
  5. Compare the factor betas and provide some comparisons between the two funds.

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