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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
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 0.530994 0.202997 0.353150
Std. Dev. 4.388029 3.059458 2.807876
Skewness -0.541296 0.434001 0.157583
Kurtosis 5.023339 7.911291 4.964970
Observations 654 654 654

First sub-sample: 1963M07 – 1981M08
MKT_RF SMB HML
Mean 0.217615 0.487890 0.437294
Std. Dev. 4.418737 3.152686 2.605497
Skewness -0.106940 0.099146 -0.171608
Kurtosis 4.121000 3.812049 4.776249
Observations 218 218 218

Second sub-sample: 1981M09 – 1999M10
MKT_RF SMB HML
Mean 0.895367 -0.195138 0.343945
Std. Dev. 4.380985 2.596309 2.548630
Skewness -0.922516 0.022054 0.249475
Kurtosis 7.275274 3.604591 2.902502
Observations 218 218 218

Third sub-sample: 1999M11 – 2017M12
MKT_RF SMB HML
Mean 0.480000 0.316239 0.278211
Std. Dev. 4.357630 3.351598 3.229272
Skewness -0.613636 0.789770 0.303814
Kurtosis 3.978512 12.07127 5.449277
Observations 218 218 218

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

No, it did not show those risk factors came from the same distribution over the entire period.

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"). 



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)

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

Which funds have the highest and lowest average return? 

FIEUX has highest average return and FSLCX has average lowest return
Which funds have the highest and lowest standard deviation?
FLATS has the highest standard deviation and FSLCX has the lowest standard deviation

Which funds look most and least normally distributed? 


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? 

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

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

Compute the sample correlation matrix of the returns on these 3 funds. 
Which funds are most highly correlated?  
Which are least correlated?  
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)

R_(i,t)^e=αi+β(i,M) R_MKT^e+e_(i,t)

To simplify notation in the regression notice that R_(i,t)^e=R_(i,t)-R_(F,t)= is stock or portfolio i^th excess return and R_MKT^e=R_Mt-R_(F,t) = is the excess return on a “stock market portfolio”
In order to do this follow three simple steps.
Step 1. Estimate the risk premia for each factor (5p)
λMKT=1/T ∑(t=1)^T▒(R_Mt-R_(F,t) )
Step 2. Estimate the sensitivities of the i^th stock to each of those factors.
R_(i,t)^e=αi+β_iM R_MKT^e+e_it Step 3. The expected returns can be calculated by combining the results of the previous steps. E(R_i^e )=β ̂(i,M) λ_MKT
Which fund has the highest and lowest expected return?
Compare the factor betas and provide some comparisons between the two funds.