Equity Risk Premiums and Risk Free Rates in Modelling and Prediction of Financial Markets
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
 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.
 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.
 K. Adam, J. Beutel and A. Marcet “Stock price booms and expected
capital gains,” CEPR Discussion Paper No.9988, 2014.
 K. Adam and A. Marcet, “Internal Rationality, Imperfect Market
Knowledge and Asset Prices,” Journal of Economic Theory, vol. 146, pp.
 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.
 M. Labonte, “Monetary Policy and the Federal Reserve: Current Policy
and Conditions,” US Congressional Research Service, Jan 2016.
 The ECB’s forward guidance, 2015.
 A. Damodaran, “Equity Risk Premiums (ERP): Determinants, Estimation
and Implications,” New York University, Stern Business School, 2012.
 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.
 CBOE, “The COBE Volatility Index VIX”, white-paper, available at
 B. Widrow and S. D. Stearns. Adaptive Signal Processing, Prentice-Hall,
Englewood Cliffs, N.J., 1985.