Chapter 6 The Gaussian White Noise Return Model

Updated: May 4, 2021

Copyright © Eric Zivot 2015, 2016

The first model of asset returns we consider is the very simple Gaussian white noise (GWN) model for asset returns . This model is motivated by the stylized facts for monthly asset returns discussed in the previous chapter. The GWN model assumes that an asset’s return (simple or continuously compounded) over time is independent and identically normally distributed. The model allows for the returns on different assets to be contemporaneously correlated but does not allow for any lead-lag cross correlations. The GWN model is widely used in finance. For example, it is used in risk analysis (e.g., for computing Value-at-Risk) for assets and portfolios, in mean-variance portfolio analysis, in the Capital Asset Pricing Model (CAPM), and in the Black-Scholes option pricing model. Although this model is very simple, it provides important intuition about the statistical behavior of asset returns and prices and serves as a benchmark against which more complicated models can be compared and evaluated. It allows us to discuss and develop several important econometric topics such as Monte Carlo simulation, estimation, bootstrapping, hypothesis testing, forecasting, and model evaluation that are discussed in later chapters.

The outline of this chapter is as follows. Section 6.1 reviews the assumptions of the GWN model and presents several equivalent specifications of the model. Application of the model to continuously compounded returns, simple returns, and portfolios is also discussed. Section 6.2 illustrates Monte Carlo simulation of the GWN model as a first-step reality check of the model.

The R packages used in this chapter are IntroCompFinR, mvtnorm, and PerformanceAnalytics. Make sure these packages are installed and loaded before running the R examples in the chapter.