Comparing Stock Portfolio Strategies Using Stochastic Volatility Models

Abstract

This thesis uses stochastic volatility models for volatility prediction and comparison of different portfolio strategies, where data will be pulled from the Center for Research in Security Prices (CRSP) and the Trade and Quote database (TAQ). The preliminary research is based on “Derivatives in Financial Markets with Stochastic Volatility” by Fouque, Papanicolaou, and Sircar (2000a). Throughout this work, primarily, Hull-White (HW) and Scott (SC) models will be used, which are characterized as follows: HW : σt = p Yt , dYt = c1Ytdt + c2YtdZt (1) SC : σt = e Yt , dYt = α (m − Yt) dt + βdZt (2) where Zt is a standard Brownian motion. Seeing as common stocks are the most popular and widely accessible financial instruments for small individual investors, this thesis will discuss stock portfolio strategies using only historic volatility, expected volatility in the future, and the variance of volatility in the future. The decision making process will be simplified as such with the aim of creating efficient tools of guidance for such investors. The historic volatility data inferred from CRSP and TAQ is used to estimate the parameters of the driving processes. These estimates are then used to compute optimal weights for the assets in the portfolio, suggesting a new framework that depends on the aforementioned three metrics and the risk specific risk affinity of the investor. Using constant weight allocation, their performances are compared to each other and to the S&P 500 index. Historic volatility data is separated into train and test sets which are also used in error measurement for each model. For each volatility metric, their effects are further examined in controlled experiments where everything else is fixed. The risk affinity parameters are tested mostly between −1 and 1 and under a varying set of assumptions for each model.