Equilibrium Driven by Discounted Dividend Volatility
We derive representations for the stock price drift and volatility in the equilibrium of agents with arbitrary, heterogeneous utility functions and with the aggregate dividend following an arbitrary Markov diffusion. We introduce a new, intrinsic characteristic of the aggregate dividend process that we call the ”rate of discounting volatility” and show that, in equilibrium, the size of market price of risk is determined by the market price of discounted dividend volatility (DDV), discounted at that rate, and multiplied by the aggregate risk aversion. The stock price volatility is equal to the market price of DDV plus a volatility risk premium. In particular, stock price volatility is larger than the dividend volatility if the aggregate risk aversion is decreasing, dividend volatility is countercylical and the rate of discounting volatility is procyclical. We also obtain a representation for the optimal portfolios. Under the above cyclicality conditions, we show that the non-myopic (hedging) component of an agent’s portfolio is positive (negative) if the product of agent’s prudence and risk tolerance is below (above) two, and the sign is reversed for the reversed cyclicality conditions.