Asset Price Dynamics: Shocks and Regimes

Security prices changes are known to have a non-normal distribution, with heavy tails. There are modifications to the standard geometric Brownian motion model which accomodate heavy tails, most notably (1) adding point processes to the Brownian motion or (2) classifying time into regimes. With regimes the prices follow Brownian motion dynamics within regime, but the parameters vary by regime. The unconditional distribution of returns is a mixture of normals, with the mixing coefficients being Markov transition probabilities. The contrasting approaches have a common link—risk factors. In the case of the point processes, the intensity of “shocks” depends on a set of factors, eg. bond-stock yield differential, credit spread, implied volatility, exchange rates. The factors drive shocks, which are a component of the returns. With regimes, the economic state is hidden (latent) and is determined by the period by period observations on factors. The characterization of regimes follows from description in terms of the set of risk factors. In this paper the link between the shocks and regimes is explored. The shocks times defined by risk factors are an alternative method of determining regimes and the classifications by shocks and by the Expectation-Maximization algorithm are examined. The connections factors → regimes → shocks further justifies a classifiaction of financial markets into homogeneous epochs. The regime structure leads to improved estimates for distribution parameters. The methods are applied to the prediction of returns on Sector Exchange Traded Funds (ETFs).The allocation of investment capital to funds based on predicted returns generates favorable wealth accumulation over a planning horizon.