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Stochastic dividend discount model: covariance of random stock prices

  • Arianna Agosto
  • Alessandra Mainini
  • Enrico Moretto
Article

Abstract

The price of common stocks, defined as the sum of all future discounted dividends, is at the heart of both the dividend discount models (DDM) and the stochastic DDM (SDDM). Gordon and Shapiro (Manag Sci 3:102–110 1956) assume a deterministic and constant dividends’ growth rate, whereas Hurley and Johnson (Financ Anal J 4:50–54 1994, J Portf Manag 25(1)27–31 1998) and Yao (J Portf Manag 23(4)99–103 1997) introduce randomness by letting the growth rate be a finite-state random variable and random dividends behave in a Markovian fashion. In this second case expected stock price is determined, but what if higher-order moments are needed? In order to address a number of financial topics, the present contribution presents an explicit formula for the covariance between (possibly) correlated stock prices.

Keywords

Stock valuation Dividend discount model Markov chain Financial risk management 

JEL Classification

G11 G12 G32 

References

  1. Agosto A, Moretto E (2015) Variance matters (in stochastic dividend discount models). Ann Finance 11:283–295CrossRefGoogle Scholar
  2. D’Amico G (2013) A semi-Markov approach to the stock valuation problem. Ann Finance 9(4):589–610CrossRefGoogle Scholar
  3. D’Amico G (2017) Stochastic Dividend Discount Model: Risk and Return. Markov Processes and Related Fields 23:349–376Google Scholar
  4. Gordon M (1962) The investment, financing, and valuation of the corporation. Irwin, HomewoodGoogle Scholar
  5. Gordon MJ, Shapiro E (1956) Capital equipment analysis: the required rate of profit. Manag Sci 3:102–110CrossRefGoogle Scholar
  6. Hurley W.J. (2013) Calculating first moments and confidence intervals for generalized stochastic dividend discount models. Journal of Mathematical Finance 3:275–279CrossRefGoogle Scholar
  7. Hurley WJ, Johnson LD (1994) A realistic dividend valuation model. Financ Anal J 50(4):50–54CrossRefGoogle Scholar
  8. Hurley WJ, Johnson LD (1998) Generalized Markov dividend discount models. J Portf Manag 25(1):27–31CrossRefGoogle Scholar
  9. Ingersoll JE (1987) Theory of financial decision making. Rowman and Littlefield Publishers, LanhamGoogle Scholar
  10. Koutmos D (2015) Is there a positive risk-return trade-off? a forward-looking approach to measuring the equity premium. European Financial Management 21(5):974–1013CrossRefGoogle Scholar
  11. Polk C, Thomson S, Vuolteenaho T (2006) Cross-sectional forecasts of the equity premium. J Financ Econ 81(1):101–141CrossRefGoogle Scholar
  12. Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91Google Scholar
  13. Williams JB (1938) The theory of investment value. Harvard University Press, CambridgeGoogle Scholar
  14. Yao YF (1997) A trinomial dividend valuation model. J Portf Manag 23(4):99–103CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Banca Carige SpAGenovaItaly
  2. 2.Dipartimento di Discipline matematiche, Finanza matematica ed EconometriaUniversitá Cattolica del Sacro CuoreMilanoItaly
  3. 3.Dipartimento di EconomiaUniversitá degli Studi dell’InsubriaVareseItaly
  4. 4.CNR-IMATIMilanoItaly

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