Variance matters (in stochastic dividend discount models)

Stochastic dividend discount models (Hurley and Johnson in Financ Anal J 50–54. http://​www.​jstor.​org/​stable/​4479761, 1994, J Portf Manag 27–31. doi:10.​3905/​jpm.​1998.​409658, 1998; Yao in J Portf Manag 99–103. doi:10.​3905/​jpm.​1997.​409618, 1997) present expressions for the expected value of stock prices when future dividends, periodically received by shareholders as a reward for their risky investment, evolve through time in a Markovian setting by the means of a discretely distributed random rate of growth. Such result extends and makes more flexible the classical textbook formula for stock prices known as Gordon model. This paper introduces a closed-form expression for the variance of random stock prices, determines how their variance is affected by the variance of the dividend rate of growth, establishes that, in this framework, the dividend process is non-stationary, and perform a simple econometric analysis applying real market data.