This article presents empirical evidence that European stock markets independently determine the values of their listed common stocks. It shows that European common stocks establish their own discount rates, which in turn determine their equity values. The study models mean reversion in continuous time and demonstrates its minimal impact on prediction accuracy, indicating the efficiency of self-valuation. Mean reversion of current stock prices is an activity where investors assess the values of common stocks listed on an exchange. The speed of mean reversion of a current stock price determines the discount rate. The continuous-time first-order autoregressive model captures both the mean reversion of a current stock price and the volatility due to mean reversion, describing the dynamics of mean reversion in pricing. The closing prices of European common stocks are shown to be volatile, indicating the inherent risks of investing in common stocks.
References
[1]
Lee, M.H. (2023) Equity Value and Volatility. JournalofMathematicalFinance, 13, 394-407. https://doi.org/10.4236/jmf.2023.133025
Poterba, J.M. and Summers, L.H. (1988) Mean Reversion in Stock Prices: Evidence and Implications. JournalofFinancialEconomics, 22, 27-59. https://doi.org/10.1016/0304-405x(88)90021-9
[4]
Fama, E.F. (1970) Efficient Capital Markets: A Review of Theory and Empirical Work. TheJournalofFinance, 25, 383-417. https://doi.org/10.1111/j.1540-6261.1970.tb00518.x
[5]
Fama, E.F. (1991) Efficient Capital Markets: II. TheJournalofFinance, 46, 1575-1617. https://doi.org/10.1111/j.1540-6261.1991.tb04636.x
[6]
Fama, E.F. and French, K.R. (2015) A Five-Factor Asset Pricing Model. JournalofFinancialEconomics, 116, 1-22. https://doi.org/10.1016/j.jfineco.2014.10.010
[7]
Sharpe, W.F. (1964) Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. TheJournalofFinance, 19, 425-442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x
[8]
Black, F. (1972) Capital Market Equilibrium with Restricted Borrowing. TheJournalofBusiness, 45, 444-455. https://doi.org/10.1086/295472
[9]
Ross, S.A. (1976) The Arbitrage Theory of Capital Asset Pricing. JournalofEconomicTheory, 13, 341-360. https://doi.org/10.1016/0022-0531(76)90046-6
[10]
Breeden, D.T. (1979) An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities. JournalofFinancialEconomics, 7, 265-296. https://doi.org/10.1016/0304-405x(79)90016-3
[11]
Dessaint, O., Olivier, J., Otto, C.A. and Thesmar, D. (2021) CAPM-Based Company (Mis)valuations. TheReviewofFinancialStudies, 34, 1-66. https://doi.org/10.1093/rfs/hhaa049
[12]
Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus. Springer.
[13]
Gauss 25 (2025) Aptech Systems, Inc., Maple Valley, WA.
[14]
Maxlik (2025) Aptech Systems, Inc., Maple Valley, WA.
[15]
Shiller, R.J. (1981) Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends? American Economic Review, 71, 421-436. https://doi.org/10.3386/w0456
[16]
LeRoy, S.F. and Porter, R.D. (1981) The Present-Value Relation: Tests Based on Implied Variance Bounds. Econometrica, 49, 555-574. https://doi.org/10.2307/1911512