Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article

Degree

Master of Science

Program

Statistics and Actuarial Sciences

Supervisor

Sendova, Kristina

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.

Summary for Lay Audience

This research is about helping everyday Canadians with their investments and retirement savings. Many people in Canada invest their money in different ways to make sure they have enough for retirement. To make things easier for investors, we have come up with a way to simulate how different types of investments, like stocks and mutual funds, might perform, especially during tough times like market crashes. We used some math and statistics to create a new way to understand these investments and their risks.

We looked at different patterns and found that some of the usual ways of predicting how investments will do did not work so well. So, we came up with a new way to understand these patterns and make better predictions.

We also studied sudden jumps in security prices. To understand this better, we used a model that includes a "jump diffusion" to see how these big jumps happen and how they affect investments.

Lastly, we know that big market crashes can happen unexpectedly and really shake up the investment world. We studied what defines a market crash and how often it happens. We used this information to create a way to understand and prepare for these market crashes when planning our investments.

Erratum

Inclusion of the reference to a graph from Wikipedia

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