Asset Pricing: What happens to the Risk-Free rate and the Equity Premium?

What would a standard asset pricing model predict for the risk-free rate and the equity premium, if the volatility of consumption growth fell?

My gut feel is that the equity premium should fall, but I cannot justify why this would be the case.

Note: By 'standard asset pricing model' the question is implying one with the following intuition:

• Assets are priced according to their covariance with consumption growth. Assets which pay off when consumption growth is high (in good times) are risky, hence they will need to have high expected returns for investors to want to hold them

2 Answers

When investors make decisions in the market, they maximize utility. The utility in turn depends on consumption volatility. An overall goal of the investors is to smooth consumption, so they can consume in each point in time roughly the same amount.

It is clear, the more volatile consumption growth the more uncertain is future consumption. Investors want to hedge this risk by saving money today to have extra money tomorrow to keep their level. The saving is done by putting more money in the bank account and less money into stocks. Therefore, stock (bond) prices go down (up) and thus expected returns (interest rates) go up (down). This increases the Equity Risk Premium. In the simplest case of a Lucas Tree model the Equity premium is given by $$ERP = \gamma \sigma_C^2$$ Where $\sigma_C$ is consumption growth volatility and $\gamma$ the risk aversion. The consumption process is defined via $$dC_t = C_t(\mu_C dt + \sigma_C dW_t^C)$$

Edit: Just to be clear. The above explanations hold the other way around as well. So, if consumption volatility goes down, investors don't wish to save as much as before. Therfore the interest rate goes up and, since they invest more in stocks, stocks get more expensive and subsequent expected stock returns go down. This results in a lower ERP.

Short answer: Individuals have a preference for smooth consumption streams. To be able to smooth consumption if consumption is more volatile, individuals save more driving down risk-free rates.

• Thank you for this, but what in the scenario where consumption is less volatile? – Curious Student May 16 '16 at 16:10