FINA 6332: Financial Math and Financial Markets. HOMEWORK 3.
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FINA 6332: Financial Math and Financial Markets.
HOMEWORK 3.
Fall 2023
Deadline: November 20, 2023 (11:59 PM) Total Points: 40
Instructions: Please mark all the questions properly to make the assignment readable. You are supposed to show your work to get full credit. Each student is supposed to pick two industry portfolios for this assignment, and your choice should be confidential. Thus, this is an independent assignment, and due to the nature of the assigned problems, student are expected to submit quite unique estimations, coding output, and interpretation. Any overlapping results will be subject to additional scrutiny, according to the university policies. The assignment has to be submitted as a single pdf file (MATLAB pdf output file that includes all calculations and graphs, followed by your comments and interpretations) plus a single Excel file (data sets). Both files must be submitted through Canvas (exclusively, not via email) by the deadline. The assignment will not be graded if both files (the MATLAB pdf output file with your comments and interpretations, and the Excel file) are not submitted (separately). Late assignments and assignment submitted via email will receive zero points without any consideration.
PART A: The Fama-French-Carhart Model (10 pts.)
Problem A1.
Download data for 30 industry portfolios from Keneth R. French data library (Online Data Library), and corre- sponding factors and risk-free rate (you will need to download the momentum factor, as well as all five factors for this assignment). Data set should include at least 252 observation, but there is no upper limit for the number of observation. Pick any two industry portfolios from the data set (out of those 30 portfolios, but different from the portfolios you used for HW2), calculate the descriptive statistics for these two industry portfolios (mean, variance, standard deviation, skewness, kurtosis), and comment on the differences between respective statistical indicators for each portfolio.
Problem A2.
Plot the original returns for the two industry portfolios, and their respective moving averages (30-day window). Comment on the difference between these two time series for each industry portfolio. Also, propose an optimal trading strategy for each portfolio, having in mind the moving-average dynamics.
Problem A3.
Plot the distribution of the industry portfolio returns using histogram and kernel density plot. Comment on the shape of the distribution for each portfolio, and compare the two distributions.
Problem A4.
Estimate the Fama-French-Carhart Model model for each industry portfolio (two models), and interpret the results (goodness-of-fit, significance, the meaning of the estimated coefficients, etc.).
PART B: The Fama French 5-Factor Model (15 pts.)
Problem B1.
Pick the other two industry portfolios (out of those 30 industry portfolios, but different than the portfolios you use in Part A) from the data set. Then, calculate the descriptive statistics for these two industry portfolios (mean, variance, standard deviation, skewness, kurtosis), and comment on the differences between respective statistical indicators for each portfolio.
Problem B2.
Plot the distribution of returns using histogram and kernel density plot. Comment on the shape of the distribution, and compare the distribution of returns for the two industry portfolio of your choice.
Problem B3.
Estimate the five-factor French-Fama model for each industry portfolio (you need to estimate two regression mod- els), and interpret the results (goodness-of-fit, significance, the meaning of the estimated coefficients, etc.).
PART C: The Mean-Variance Optimization (15 pts.)
Problem C1.
Download daily prices for any five stocks from (YahooFinance). Data set has to include at least 252 observation, but there is no upper limit for the observation period. Calculate the simple returns for each stock, and provide the descriptive statistics (the mean, variance, standard deviation, skewness, and kurtosis) for each asset. Then, comment on the differences between respective statistical indicators for each asset.
Problem C2.
Your investment portfolio should include all five stocks, but you do not know apriori in what proportions. Since your goal is to minimize portfolio risk for a given level of portfolio return, you can find these proportions (optimal portfolio weights) by finding optimal solution to the minimum-variance portfolio. Thus, use MATLAB to optimize the Markowitz mean-variance model and to find the optimal portfolio weights. Feel free to include any constraint(s) in the optimization procedure, and comment on these constraints when interpreting the results. Finally, plot these optimal portfolio weights on a bar plot.
Problem C3.
Use the estimated optimal portfolio weights in C2 to compute optimal portfolio returns. Then, derive standard descriptive statistics indicators (mean, variance, standard deviation, skewness, kurtosis), and plot the distribution of the optimal portfolio weights (histogram and kernel density plot). Finally, comment on the descriptive statistics and the distribution of the optimal portfolio returns.
2023-11-20