Measuring Irrationality in Financial Markets
DOI:
https://doi.org/10.14738/abr.612.5876Keywords:
irrationality, volatility, risk, speculative behavior, Fourier transformAbstract
This paper presents the measurement of irrationality contained in the continuous pricing of individual stocks. Irrationality is used to extend the concept of historical volatility by decomposing historical stock quotes into frequencies via Fourier transformation. The analysis in the frequency domain enables clustering of the contributions of short and long-term fluctuations to the overall price changes. With the resulting ratio it is possible to rank stocks within an index according to their specific fluctuation profile. The analysis is performed on daily stock quotes over a period of 20 years (1997-01-02 until 2016-12-30). Although the analysis presented here focuses on the stock market, the concept of irrationality is transferable to other financial markets as for bonds, housing prices or derivatives as well as to different time periods.References
Mandelbrot, B. The Variation of Certain Speculative Prices. The Journal of Business 1963, 36, 394–419.
Fama, E.F. Random Walks in Stock Market Prices. Financial Analysts Journal 1965, 21, 55–59.
_______. Efficient Capital Markets: A Review of Theory and Empirical Work. The Journal of Finance 1970, 25,
–417, doi:10.2307/2325486.
Shiller, R.J. Irrational exuberance, Revised and expanded third edition; Princeton University Press: Princeton, 2016.
Summers, L.H. Does the Stock Market Rationally Reflect Fundamental Values? The Journal of Finance 1986, 41, 591–601, doi:10.2307/2328487.
Shiller, R.J. Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends? American Economic Review 1981, 71, 421–436.
Appel, D.; Grabinski M. The origin of financial crisis: A wrong definition of value. Portuguese Journal of Quantitative Methods 2011, 3, 33–51.
Lomb, N.R. Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science 1976, 39,
–462, doi:10.1007/BF00648343.
Scargle, J.D. Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly
spaced data. Astrophysical Journal 1982, 263, 835–853.
Hill, M. The uncertainty principle for Fourier transforms on the real line. University of Chicago 2013.
