Equity Risk Premiums and Risk Free Rates in Modelling and Prediction of Financial Markets

Authors: Mohammad Ghavami, Reza S. Dilmaghani

Abstract:

This paper presents an adaptive framework for modelling financial markets using equity risk premiums, risk free rates and volatilities. The recorded economic factors are initially used to train four adaptive filters for a certain limited period of time in the past. Once the systems are trained, the adjusted coefficients are used for modelling and prediction of an important financial market index. Two different approaches based on least mean squares (LMS) and recursive least squares (RLS) algorithms are investigated. Performance analysis of each method in terms of the mean squared error (MSE) is presented and the results are discussed. Computer simulations carried out using recorded data show MSEs of 4% and 3.4% for the next month prediction using LMS and RLS adaptive algorithms, respectively. In terms of twelve months prediction, RLS method shows a better tendency estimation compared to the LMS algorithm.

Keywords: Prediction of financial markets, Adaptive methods, MSE, LSE.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1131359

References:

[1] X. Zheng and B. Chen, “Modelling and analysis of financial markets using system adaptation and frequency domain approach,” at the IEEE Int. Conf. Control and Automation, Christchurch, New Zealand, 2009, pp. 1068-1073.
[2] E. Andersson, “Turning point detection using non-parametric statistical surveillance: Influence of some turning point characteristics,” at the Int. Workshop on Intelligent Statistical Quality Control, Warsaw, Poland, 2004.
[3] K. Adam, J. Beutel and A. Marcet “Stock price booms and expected capital gains,” CEPR Discussion Paper No.9988, 2014.
[4] K. Adam and A. Marcet, “Internal Rationality, Imperfect Market Knowledge and Asset Prices,” Journal of Economic Theory, vol. 146, pp. 1224-1252, 2014.
[5] J. Wesen, V. Vermehren and H. M. de Oliveira, “Adaptive Filter Design for Stock Market Prediction Using a Correlation-based Criterion,” arXiv preprint arXiv:1501.07504, 2015.
[6] M. Labonte, “Monetary Policy and the Federal Reserve: Current Policy and Conditions,” US Congressional Research Service, Jan 2016.
[7] The ECB’s forward guidance, 2015.
[8] A. Damodaran, “Equity Risk Premiums (ERP): Determinants, Estimation and Implications,” New York University, Stern Business School, 2012.
[9] L. Booth, “Estimating the Equity Risk Premium and Equity Costs: New Way of Looking at Old Data,” Journal of Applied Corporate Finance, v12(1), pp. 100-112, 1999.
[10] CBOE, “The COBE Volatility Index VIX”, white-paper, available at CBOE website.
[11] B. Widrow and S. D. Stearns. Adaptive Signal Processing, Prentice-Hall, Englewood Cliffs, N.J., 1985.