The effects of risk aversion and money illusion on the components of dividend growth rate

ABSTRACT

We evaluate the impact of risk aversion and money illusion in the equity and options markets when the expected dividend growth rate is endogenously determined as a function of the dividend-price ratio and expected inflation. The closed-form equilibrium expressions for the dividend-price ratio, expected inflation, and dividend growth rate allow us to perform comparative statics to understand their sensitivity relative to the agent's preference parameters. Our calibration exercise indicates that the sensitivity of the dividend-price ratio relative to risk aversion depends critically on the sign of the exposure of the expected dividend growth rate to the divided yield, while an increase in the degree of money illusion always raises the dividend-price ratio, irrespective of its exposure to the dividend yield. In addition, we show that expected inflation is much less sensitive to variations in risk aversion and money illusion than these parameters, while the price of a zero-coupon caplet is affected in the opposite direction by these parameters.

KEYWORDS:

• Endogenous dividend growth rate
• asset pricing
• money illusion
• CPI derivatives

JEL CLASSIFICATIONS:

• G12
• G13
• G41

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Diogo Duarte http://orcid.org/0000-0002-0984-6833

Notes

1 While this result follows immediately in the case studied by Modigliani and Cohn (1979), the analysis is more subtle in our setting because the illusioned investor could mistakenly expect higher future cash flows (given that money illusion affects the expected dividend growth rate in our model). Consequently, the error in cash flow projections could, in theory, overweight the error caused by discounting those cash flows with a higher nominal rate, resulting in a higher stock price. In this case, the dividend-price ratio would be lower. While this outcome is feasible in our setting, it is not the observed result when we calibrate the model with financial market data, as explained in Section 4.

2 We opt to follow (Basak and Gallmeyer 1999) and model the price of money instead of the consumer price index (CPI). Since the CPI is the inverse of the price of money, once $p_t$ is determined, the CPI is obtained simply by calculating the money price inverse (i.e. $CP{I}_t=1/p_t$).

3 We refer the readers to Basak and Yan (2010) and references therein for an extensive discussion on the microfoundations of money illusion as a belief distortion phenomenon. Other recent papers investigating the effects of money illusion for asset prices are Miao and Xie (2013), David and Veronesi (2013), and Duarte and Saporito 2019.

4 While the standard procedure is to state the dynamic programing problem and show its equivalence to the static variational problem, we opt to directly state the latter to save space. The equivalence between these problems is derived following the exact same steps as in Proposition 2.1 of Basak and Gallmeyer (1999).

5 Our results are robust with respect to the series proxying the dividend process. All results remain qualitatively the same if we use the earnings series to proxy $({\delta }_t{)}_{t\ge 0}$.

6 Note this no-arbitrage condition is exactly the same as in Basak and Gallmeyer (1999), equation (2.12), Lemma 2.1.