Problem Set 2, FIN 206
Spring 2025
Problem 1
Download from Yahoo finance, or from your favorite data provider, the monthly time series of the adjusted close prices for Bitcoin-USD (tracker ID: BTC-USD), General Motors (tracker ID: GM) and Coca Cola (tracker ID: KO) for the period 09/2014 to 12/2024. Moreover, from Ken French’s data library, download the monthly time series of the Fama-French 3 factors returns for the same time period, and combine the two datasets in Excel.
1. Calculate the time-series of monthly returns for the 3 assets, and construct the monthly returns of the Market (MKT) from Fama-French factors
2. Estimate the expected returns and standard deviation of returns for both the 3 assets and the 3 Fama-French factors
3. Construct the variance covariance matrix Σ, and the vector of expected excess returns µe. Note: conceptually, it makes sense to use only the last RF in the data, not the historical. Do you see why?
4. Use these vectors and matrices to solve for the Minimum Variance Portfolio of the 3 assets, and comment on your findings
5. Now, use the same information to solve for the Mean-Variance Efficient portfolio (MVE), and comment on its differences/similarities with the MVP
6. Estimate the CAPM beta of each of the 3 assets. What do you observe?
7. Plot on a standard diagram the Security Market Line (SML) and include all of the information you have about these assets. What can we learn about the validity of the CAPM from this exercise? How do these findings relate to the stylized facts about the empirical SML?
8. Estimate the One-Factor (or market) model for each asset. Comment on your findings.
9. Construct the residuals of the regressions and test whether the 1 factor model is a ‘good’ model, or if it is likely to miss additional important factors. Explain in details your reasoning
10. Estimate the 2-Factor model (with MKT and SMB) for each asset. Comment on your findings.
11. Construct the residuals of the regressions and test whether the 2 factor model is a ‘good’ model, or if it is likely to miss additional important factors
12. Estimate the 3-Factor model (with MKT, SMB and HML) for each asset. Comment on your findings.
13. Now, assume that the right model of the world is a two-factor model with MKT and SMB as factors. Use the available assets to construct the two pure factor portfolios, as well as the risk-free portfolio.
14. Suppose we want to track an asset with beta of 3 on MKT and 2 on SMB. What are the portfolio weights on the assets? Explain how you can derive these weights in at least two ways.