Spring 2018 Homework Assignment 3 For this assignment, you will use the data in the spreadsheet Assignement3_Data.xlsx. 1. Worksheet “Returns” contains monthly returns over the 20—year period for three

stocks, F, IBM, XOM, as well as monthly returns on RF (risk—free), MKTRF

(excess return on market portfolio), and Fama—French factors SMB and HML.

Estimate the factor loadings (betas) for the excess returns on F, IBM, and XOM

using Fama-French 3-factor model. For the three stocks, compute predicted excess

returns and residuals. For F, IBM, and XOM, compute t-statistics for the OLS regression and highlight

statistically significant coefficients. Compute the factor covariance matrix V and the residuals covariance matrix (for

speciﬁc risks of the three stocks) Delta. Next, compute the covariance matrix for

the three stocks Sigma in two ways: (1) using historical excess returns, Sigma = Sigma(historical), and (2) using the estimates from the 3-factor model, Sigma = BVB’ + Delta. Verify that the two approaches produce the same matrices. Is matrix Delta close to

diagonal? Please report all covariance matrices in annualized form. Now replace Delta with a diagonal matrix diag(De1ta), where the main diagonal of

diag(Delta) is the same as that for Delta and all other elements are set to zero.

Deﬁne matrix Sigmal = BVB’ + diag(Delta). For covariance matrix Sigma, compute the minimum-variance portfolio (MVP) of

the three stocks. Similarly, for covariance matrix Sigmal, also compute the

minimum-variance portfolio (MVPl). Are MVP and MVP] similar? Worksheet “Characteristics” contains monthly returns for December, 2003 on six

stocks (BUD, DELL, DIS, IBM, INTC, XOM) along with their Market Cap, Price—

Earnings ratio, and Price—Book ratio. Run a cross—sectional regression on constant,

Size, PE ratio, and BP ratio to estimate factor returns for December, 2003.

(Remember to first normalize raw values for Size, PE ratio, and BP ratio.) For the

six stocks, compute predicted excess returns and residuals for December, 2003.

Finally, using the sensitivity matrix B, compute the factor-mimicking portfolios

(matrix W).