Empirical Finance Spring II 2024 Assignment 2

Q1. (30pts) Portfolio choice

Suppose that the  S&P  500  index has mean  of E(rM  )  =  0. 16  and  standard  deviation  of σ(rM ) = 0. 10. The risk-free rate is rf = 0.08.

1.  (10pts) What is the expected return and standard deviation of a portfolio that is totally invested in the risk-free  rate

2.  (10pts) What is the expected return and standard deviation of a portfolio that has weight ω = 0.5 on the risk-free rate and 1 − ω = 0.5 in the S&P 500index?

3.  (10pts) What are the weights on a portfolio, ω for investing in the risk-free rateand 1 − ω for investing in the S&P 500 index, that produce a standard deviation that is  0.04? What is the expected return on that portfolio?

Q2. (20pts) Read Fama  and French  (2004) carefully and summarize the paper in one page (at least four paragraphs).

Q3. (80pts) Portfolio choice (coding  exercise)

Download “stocks.xlsx.” You will find 3 stock prices (labeled “market, A, B”) and 3 factors (labeled “riskfree, smb, hml”) in the range of 2011:M12 to 2021:M2.

1.  (20pts) Let the log return for stock i be ri,t at time t. Provide the sample mean and standard deviation for rM,t, rA,t,rB,t where 2012:M1 ≤t≤ 2021:M2. Forconvenience, “M” refers to “market.”

2.  (20pts)  Estimate the  CAPM  equation  and report the  estimated β  and R2   from  the regression. Here the estimation sample ranges from 2012:M1 to 2021:M2. Note that you are estimating the CAPM equation for A and B stocks separately (so, twice in total).

3.  Similarly  estimate  the  Fama-French  3  factor  model  for  A  and  B  stocks.  Here  the estimation sample ranges from 2012:M1 to 2021:M2.

(a)  (20pts) Compare the estimates of β with those from the CAPM equation.

(b)  (20pts) Based on the coefficient estimates for “smb” and “hml” factors, discuss the characteristics of A and B stocks.

Q4a. (15 pts) Read the paper “The Pollution Premium (2023)”  carefully and summarize the paper in one page (at least four paragraphs).

Q4b. (15 pts.)  Look at the TRI database (https://www.epa.gov/toxics-release-inventory-tri-program/tri-data-and-tools) and form portfolios based on the pollution factor as formed in the “Pollution Premium” paper. Read the appendix of the paper for more details on TRI data.