Covariance of random stock prices in the Stochastic Dividend Discount Model

TL;DR

This paper derives a formula for the covariance of random stock prices in the stochastic dividend discount model, considering correlated dividend growth rates, and applies it to real market data.

Contribution

It extends previous deterministic dividend discount models by providing a covariance formula for correlated stochastic dividend growth rates.

Findings

Derived a closed-form covariance formula for stock prices

Applied the formula to real market data

Enhanced understanding of stock price variability

Abstract

Dividend discount models have been developed in a deterministic setting. Some authors (Hurley and Johnson, 1994 and 1998; Yao, 1997) have introduced randomness in terms of stochastic growth rates, delivering closed-form expressions for the expected value of stock prices. This paper extends such previous results by determining a formula for the covariance between random stock prices when the dividends' rates of growth are correlated. The formula is eventually applied to real market data.