Modelling Asset Returns in a Portfolio Using Ornstein-Uhlenbeck Stochastic Process

Abstract

The study explores the modelling of asset returns in portfolio as a stochastic process which exhibits mean reversion towards the long-term stationary mean. This can be thought of as if an asset return is connected to its long-run mean with a spring which pulls the asset return towards the long-run mean. The study investigates the stochastic nature of two assets returns by use of autoregressive and Ornstein-Uhlenbeck (OU) processes to illustrate the features of the assets weekly return series in Ghana from January 2011 to December 2017. The assets in the portfolio are assumed to include two major classes of investment: three-month Treasury bill and equity. The study elucidated from using the OU process to examine the mean reversion speed that the accumulated interest rate of equity approaches its long-run mean more quickly than the Treasury bill. The bivariate model revealed that the interest rate of each asset depends moderately on its interest rate of the past week and on a small portion of the interest rate of the other asset. For an investor to achieve an optimum portfolio of these assets, the investor should consider to invest in about 60% of equity and 40% of Treasury bill. One key recommendation is that the Ghana Stock Exchange should encourage the investing public to invest in stocks listed on the exchange because the rates of return are more stable.