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. (5p)

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

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

3.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"). (1p)

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

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)

5.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? (1p)

b.Which funds have the highest and lowest standard deviation? (1p)

c.Which funds look most and least normally distributed? (1p)

6.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? (1p)

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:

oEuropean stock fund: Fidelity Europe (FIEUX)

oLatin America Fund: Fidelity Latin America (FLATX)

oSmall 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.

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

8.Step 2. Estimate the sensitivities of the stock to each of those factors. (1p)

9.Step 3. The expected returns can be calculated by combining the results of the previous steps. (1p)

10.Which fund has the highest and lowest expected return? (1p)

Now, use the Fama-French 3-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 3 simple steps:

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

12.Step 2. Estimate the sensitivities of the stock to each of those factors.(1p)

13.Step 3. The expected returns can be calculated by combining the results of the previous steps. (1p)

14.Which fund has the highest and lowest expected return? (1p)