Modelling long-term security returns
Abstract
This research focuses on the concerns of Canadian investors regarding portfolio diversification and preparedness for unexpected risks in retirement planning. It models market crashes and two main financial instruments as independent components to simulate clients’ portfolios. Initially exploring single distributions on mutual funds such as Laplace and t distributions, the research finds limited success. Instead, a normal-Weibull spliced distribution is introduced to model log returns. The Geometric Brownian Motion (GBM) model is employed to predict and evaluate returns on common stocks using the Maximum Likelihood Estimator (MLE), assuming that daily log returns follow a normal distribution. Additionally, the Merton Jump Diffusion (MJD) model is considered to account for jumps in stock trajectories with an independent Poisson process term based on the GBM model. Market crashes, defined as a decline of at least 10% in the S&P500 over a maximum of 252 trading days, are modelled using a homogeneous Poisson process. The combined simulation results show that the model is effective in most portfolio predictions.