Zura Kakushadze

Correspondence: Zura Kakushadze , zura@quantigic.com

Quantigic Solutions LLC, USA

pdf (296.81 Kb) | doi:

Abstract

We discuss – in what is intended to be a pedagogical fashion – a criterion, which is a lower bound on a certain ratio, for when a stock (or a similar instrument) is not a good investment in the long term, which can happen even if the expected return is positive. The root cause is that prices are positive and have skewed, long-tailed distributions, which coupled with volatility results in a long-run asymmetry. This relates to bubbles in stock prices, which we discuss using a simple binomial tree model, without resorting to the stochastic calculus machinery. We illustrate empirical properties of the aforesaid ratio. Log of market cap and sectors appear to be relevant explanatory variables for this ratio, while price-to-book ratio (or its log) is not. We also discuss a short-term effect of volatility, to wit, the analog of Heisenberg’s uncertainty principle in finance and a simple derivation thereof using a binary tree.

Keywords:

  Bubble, Skewed Distribution, Stock Price, Volatility, Return, Dividends, Buybacks, Binomial Tree, Brownian Motion, Uncertainty Principle, Market Cap, Price-To-Book, Sectors, Time Ordering.

References

Baaquie, B.E. (2007) Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge, UK: Cambridge University Press, pp. 99-101.

Biane, P. (2010) Itˆo’s stochastic calculus and Heisenberg commutation relations. Stochastic Processes and their Applications 120(5) (2010) 698-720.

Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81(3): 637-659.

Heisenberg, W. (1927) ¨Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift fu¨r Physik 43(3-4): 172-198.

Kakushadze, Z. (2015a) On Origins of Alpha. The Hedge Fund Journal 108: 47-50. Available online: http://ssrn.com/abstract=2575007.

Kakushadze, Z. (2015b) Path Integral and Asset Pricing. Quantitative Finance 15(11): 1759-1771. Available online: http://ssrn.com/abstract=2506430.

Kennard, E.H. (1927) Zur Quantenmechanik einfacher Bewegungstypen. Zeitschrift fu¨r Physik 44(4-5): 326-352.

Miller, M.H. and Modigliani, F. (1961) Dividend Policy, Growth and the Valuation of Shares. Journal of Business 34(4): 411-433.

Powers, M.R. (2010) Uncertainty principles in risk finance. The Journal of Risk Finance 11(3): 245-248.

Protter, P. (2013) A Mathematical Theory of Financial Bubbles. ParisPrinceton Lectures on Mathematical Finance (Springer Lecture Notes in Mathematics) 2081: 1-108.

Sharpe, W.F. (1966) Mutual Fund Performance. Journal of Business 39(1): 119-138.

Sharpe, W.F. (1994) The Sharpe Ratio. The Journal of Portfolio Management 21(1): 49-58.

Soloviev, V. and Saptsin, V. (2011) Heisenberg uncertainty principle and economic analogues of basic physical quantities. Computer Modelling and New Technologies 15(3): 21-26.

Sornette, D. and Cauwels, P. (2014) Financial Bubbles: Mechanisms and Diagnostics. Swiss Finance Institute Research Paper, No. 14-28.

Taleb, N.N. The Black Swan: The Impact of the Highly Improbable. New York, NY: Random House (expanded 2nd edition).

Weyl, H. (1928) Gruppentheorie und Quantenmechanik. Leipzig, Germany: Hirzel.

Wick, G.C. (1954) Properties of Bethe-Salpeter Wave Functions. Phys. Rev. 96(4): 1124-1134.