Data for this homework is given in the Excel file “Homework Assignment 2.xlsx”, which can be downloaded from QMplus. In sheet “Stock Data” of the Excel file, you will find excess returns data for 20 of the largest stocks listed on the London Stock Ex- change, excess returns on the FTSE 100 Index (our proxy for the market portfolio), and one-month GBP LIBOR interest rates (our risk-free rate proxy), covering the period from January 2000 to December 2019. The data are expressed on a monthly (that is, not annualised) basis. This dataset is identical to the dataset in your “Class 01 Spread-

sheet”Excel file.

Using this data, complete the following six tasks:

1. Conduct one time series CAPM regression for each stock. That is, estimate the following model for each stock:

Ri,t − rf,t − 1  = αi + βi [Rm,t − rf,t − 1] + ϵi,t

Use the full sample to estimate the regression. Your answer to this item will be a vector of alphas for the 20 stocks and a vector of betas for the 20 stocks (ignore the statistical significance, or otherwise, of the alpha and beta estimates).

2. Noting that in a regression framework, the Mean Square Error provides an un- biased estimate of the error term’s variance, estimate the monthly idiosyncratic variance of each stock’s excess return. Your answer to this item will be a vector containing the monthly idiosyncratic variance estimates for the 20 stocks.

3. Using the Single Index Model (SIM) framework, and without adjusting your beta estimates, compute the annualised expected excess returns and covariance ma- trix of the 20 stocks. When calculating expected excess returns, ignore the alpha parameter (i.e. calculate the CAPM expected excess return for each stock). Your answer to this item will be the vector of annualised expected excess returns and annualised covariance matrix of excess returns.

Now consider an investor whose utility function is given by U = µ − σ 2, where µ is the portfolio mean return, σ 2is the variance of portfolio returns and λ is the investor’s coefficient of risk aversion. Assume there are no short sales constraints; asset weights are allowed to be negative. Also assume that the investor is free to borrow and lend at the risk-free interest rate (take this to be the LIBOR that applies to the month of January 2020). Using your results in Item 3:

4. Determine the magnitude of the investor’s risk aversion parameter λ that would result in the investor’s optimal complete portfolio being fully invested in risky assets (i.e. the investor’s utility-maximising portfolio is the tangency portfolio)