1. Most important objective: Construct a portfolio using stocks (from market index components, for example, S&P 500 has 500 companies, we can use the 500 companies’ data, i.e., monthly stock returns, to compute the optimal weights of the stocks…with the goal of building a portfolio with either highest return, or with the lowest standard deviation.)
2. Reasoning to compare the 2 methods: mutual funds, pension funds, and insurance companies have restrictions on short positions. They cannot have short positions.
3. Two methods:
Ø Method 1: mean-variance method, using the method in the notes. But this method has some drawbacks: high turnover ratio, short positions.
Ø Method 2: Principal Component Analysis (PCA), by computing the eigenvalues of the covariance/correlation matrix of the stock returns, standardized eigenvalues are the weights of the stocks.
4. Objective is to compare method 1 and 2, using the following measures:
Ø Turnover ratio
Ø Sharpe ratio: risk-adjusted return (
Ø Largest short position
Ø Construct portfolios based on methods 1 and 2 every month using previous 60-month returns: for example, now is January 1st, 2015, portfolio is built using data from January 2010 to December 2014, next month, Feb 1st, 2015, portfolio is built using data from February 2010 to January 2015.
Ø Construct portfolios for at least 5-10 years