讲解 AD 685 Project – Spring 2024讲解 Python编程

Full Sample: 1963M07 - 2023M12
	MKT_RF	SMB	HML	RMW	CMA
Mean
Std. Dev.
Skewness
Kurtosis
Observations
First sub-sample: 1963M07 - 1983M08
Mean
Std. Dev.
Skewness
Kurtosis
Observations
Second sub-sample: 1983M09 - 2003M10
	MKT_RF	SMB	HML	RMW	CMA
Mean
Std. Dev.
Skewness
Kurtosis
Observations
Third sub-sample: 2003M10 - 2023M12
	MKT_RF	SMB	HML	RMW	CMA
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? (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 full sample period.  (Recall, this is called an "equity curve"). (5p)

6. Which factor portfolio gives the lowest and highest future value over the full sample period? (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, and CMA 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)

Section B. Funds Univariate Statistics

Go to Yahoo! finance site. Please download monthly adj. close prices from 12/1/2003 to 12/1/2023 for S&P 500 index (^SP500TR) and the following funds:

· European stock fund: Fidelity Europe (FIEUX)

· Asian Fund: Fidelity Emerging Asia (FSEAX)

· 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 whole sample 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 0.115% per month (which corresponds to a continuously compounded annual rate of 1.38%), 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 correlation matrix of the returns on these 5 funds. (5p)

a. Which funds 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)

Section C. Estimating expected returns

In this section, you need to use information from Section A and B.

Use the Fama-French Three-Factor model to estimate the expected returns of each of the funds from part 2:

o European stock fund: Fidelity Europe (FIEUX)

o Asian Fund: Fidelity Emerging Asia (FSEAX)

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)