Behavioral Economics & Finance

Assignment #5 1. According to the Two-Fund Separation Theorem, should investors of different levels of risk aversion hold the same relative proportions of risky assets in their portfolios? Briefly explain. 2. The table below shows the annual expected rates 𝐸(𝑟) and standard deviations 𝐸(𝜎) of returns of two stocks. Assume that you decide to form an equal-weighted portfolio including only those two stocks. ▪ ▪ ▪ ▪ Stock A Stock B Expected annual rate of return 8% 12% Expected annual standard deviation 24% 30% Calculate the expected standard deviation of your portfolio, corresponding to each scenario with regard to the correlation coefficient between stock A and stock B, i.e. when 𝜌12 = -1, -0.5, 0, 0.5, or 1. If 𝜌12 = 0.5, what is the standard deviation of the portfolio which invests 1/3 in stock A, 1/3 in stock B, and 1/3 in a risk-free asset? If 𝜌12 = 0.5, given that 50% of the total investment is financed by borrowing at the risk-free rate, what is the standard deviation of the portfolio which invests equally in stock A and B? If 𝜌12 = 0.5, what combination of stock A and stock B offers the minimum risk? 3. (Test EMH) First, download the Fama-French three factors (daily, monthly, and annual from 2014 to 2023) from Kenneth French’s data library (https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). To get market returns, simply add up ‘Mkt-RF’ and ‘RF’, For market returns of each frequency, estimate an autoregression model of order 1, i.e. AR(1) as follows 𝑟𝑡 = 𝛼0 + 𝛼1 𝑟𝑡−1 + 𝜀𝑡 Based on the results of estimation, do you reject or not reject the Efficient Market Hypothesis?