Portfolio Optimization for US. Stock with Mean-variance Model, CAPM, Fama French Three-factor Model

Abstract

Applying modern investment theories to construct investment portfolios is a crucial way for investors to reduce risks and obtain high returns in the investment market. This paper selects eight stocks from eight industries of the US stock market and constructs a portfolio based on their historical return data over the past five years. This study uses the CAPM model and the Fama French three-factor model to estimate the expected returns of these eight stocks, and then applies the mean-variance model to construct the optimal risky portfolio under both expectations. Under the CAPM model, the expected monthly returns for these eight stocks are BKNG (1.05%), EQR (0.80%), MPC (1.38%), NTDOY (0.64%), ON (1.44%), PFE (0.68%), SBUX (0.86%) and FCX (1.60%) respectively. Under Fama-French three factor model, the expected monthly returns for these eight stocks are BKNG (1.21%), EQR (0.90%), MPC (2.06%), NTDOY (0.55%), ON (1.82%), PFE (0.60%), SBUX (0.82%) and FCX (1.96%) respectively. The optimal portfolio weights obtained by using CAPM model estimation results are BKNG (7.97%), EQR (23.72%), MPC (6.02%), NTDOY (11.61%), ON (8.24%), PFE (18.66%), SBUX (10.61%) and FCX (13.16%) respectively. Under Fama French three factor model, the weight distribution of the portfolio is as follows BKNG (3.01%), EQR (27.04%), MPC (33.89%), NTDOY (2.40%), ON (15.85%), PFE (4.98%), SBUX (0.00%) and FCX (12.83%). These results can provide a reference for investors who are willing to invest in US stock market, which will help them reduce investment risks and increase returns.