2. Suppose you want to construct a portfolio of five stocks: BAC, MKR, HPQ, IBM, and AAPL and hold it for one month. Suppose you apply Markowitz portfolio selection theory (without risk-free asset) on the data during 2014- 2018 to estimate the parameters and construct your portfolio with expected return target 2%. You then use the data in 2019 for testing. The historical data of the monthly returns of these five stocks in 2014-2019 are provided in "HistoricalData.xlsx." (a) Calculate the sample mean and covariance matrix of the monthly returns of the five stocks from year 2014-2018 (60 returns for each stock). (Hint: In Excel, one can use COVARIANCE.S function to calculate the sample covariance between two arrays of returns. Repeat this for every pairs of stocks to get the sample covariance matrix. One can also calculate the sample covariance by definition.) (b) Suppose you estimate the model parameters by the sample mean and co- variance matrix calculated in (a). Calculate the weight w of your optimal portfolio. (Hint: In Excel, one can calculate the inverse of a matrix by MINVERSE function, and the matrix multiplication by MMULT func- tion.) (c) Using the monthly returns of the 5 stocks in 2019, you can obtain the 12 monthly returns of the optimal portfolio with weight calculated in (b). Calculate the sample mean and sample variance of these 12 monthly re- turns of this optimal portfolio in 2019, and compare them with those of an equal weighted portfolio (i.e. w = (0.2, 0.2,0.2,0.2,0.2)). 2. Suppose you want to construct a portfolio of five stocks: BAC, MKR, HPQ, IBM, and AAPL and hold it for one month. Suppose you apply Markowitz portfolio selection theory (without risk-free asset) on the data during 2014- 2018 to estimate the parameters and construct your portfolio with expected return target 2%. You then use the data in 2019 for testing. The historical data of the monthly returns of these five stocks in 2014-2019 are provided in "HistoricalData.xlsx." (a) Calculate the sample mean and covariance matrix of the monthly returns of the five stocks from year 2014-2018 (60 returns for each stock). (Hint: In Excel, one can use COVARIANCE.S function to calculate the sample covariance between two arrays of returns. Repeat this for every pairs of stocks to get the sample covariance matrix. One can also calculate the sample covariance by definition.) (b) Suppose you estimate the model parameters by the sample mean and co- variance matrix calculated in (a). Calculate the weight w of your optimal portfolio. (Hint: In Excel, one can calculate the inverse of a matrix by MINVERSE function, and the matrix multiplication by MMULT func- tion.) (c) Using the monthly returns of the 5 stocks in 2019, you can obtain the 12 monthly returns of the optimal portfolio with weight calculated in (b). Calculate the sample mean and sample variance of these 12 monthly re- turns of this optimal portfolio in 2019, and compare them with those of an equal weighted portfolio (i.e. w = (0.2, 0.2,0.2,0.2,0.2))
