Why pessimism leads to higher Equity Risk Premium?
The abundant financial literature covering several fields, such as the quantitative analysis/forecast of the Equity Risk Premium or the literature related to the field of Decision Theory or also Behavioral Finance, came majorly to the consensus conclusion that pessimism in financial markets leads to a higher Equity Risk Premium. If we take for example financial crashes, periods where pessimism is exacerbated, it has been underlined that these periods are associated with an increase of the Equity Risk premium and we generally observe the following relations (as stated in Financial Market Bubbles and Crashes from H.L.Vogel):
We cover here the reasons explaining such a relationship (i.e. Pessimism -> High Equity Risk Premium) from the perspectives of 2 separate theoretical frameworks: Firstly, departing from the asset pricing model under the assumption of heterogeneous beliefs constructed by Jouini & Napp (2003), we underline that when the consensus belief in financial markets tends to pessimism, the Equity Risk premium increases. Secondly, we highlight this same result from the perspective of behavioral finance, precisely based on the work of Tversky & Kahneman (1979).
1. Asset pricing model under the assumption of heterogeneous beliefs assumption by Jouini & Napp (2003):
The innovative idea presented by Jouini & Napp in 2003 consists in presenting an asset-pricing model where investors have “heterogeneous” beliefs with regard to the asset fundamental value. While, the classic framework of asset pricing models, such as the Capital Asset Pricing Model (CAPM), are indeed based on the assumption that all investors do have the same belief with regard to the asset fundamental value, Jouini & Napp introduced the pragmatic assumption of the heterogeneity of investors’ belief. This is a pragmatic assumption in the sense that the basic observation of the divergent recommendations of analysts with regard to a unique and same asset leads to think that their analysis are based on different views that they have on the strength of the future cash flows generated by this asset. And as the price is theoretically defined as the future cash flows of the asset discounted by an interest rate, divergence is assessing the variability of the future cash flows generates various values for this same asset. This heterogeneity can be seen as an additional source of risk as it increases uncertainty with regard to the fair value at which the trade should take place. This uncertainty generates a higher risk premium as a compensation of the additional risk is requested by investors.
For more detailed explanations on the Jouini & Napp model, we quickly cover here one of the most important results underlined by this latter that is the existence of a “consensus” belief, i.e. economy reacts as if there existed a unique representative agent whose belief represented the consensus belief. The belief of the representative agent is hence given by the average of the individual beliefs weighted by the individual risk tolerances.
For more details, the mathematical formulation of the model is the following:
Basically, the representative agent maximizes his utility function that is the following:
Now, if we apply this very generalist result to the class of Hyperbolic Absolute Risk Aversion (HARA) utility functions (HARA is the most generalist class of utility function used in practice), we arrive to this property of the discounting factor:
For more details on how this result is obtained, please refer to the articles Aggregation of Heterogeneous Beliefs and Hétérogénéité des Croyances, Prix du Risque et Volatilité des Marchés from Jouini & Napp.
Based on this last result, we can see that u < 0 (i.e. the aggregate sentiment is pessimism) iif n>1 (i.e. investors are risk-takers). So, pessimism leads to a higher risk premium.
Note:
§ u < 0 means that the discounting factor is negative, so individuals privilege the use of their wealth in savings rather than present consumption--> Overall situation of uncertainty and pessimism.
§ n>1 means that the cautiousness parameter is higher than 1--> individuals have a risk-taking attitude.
2. Prospect Theory:
Now from the perspective of Prospect Theory, an important principal on which the theory is built relies on the fact that individuals are more risk-averse when gains are realized and in the opposite, tend to be risk-taker when important losses are realized. So, for instance, in the context of lotteries where individuals need to take decisions among risky options with different gain schema, majorly the attitude of the participants will tend to be risk-aversion, i.e. the sure gain -even lower- seems most attractive. By contrast, in a lottery with loss schema options, the participants will be risk-takers as per the following example extracted from the article “Aspects of investor psychology” by Kahneman and Riepe (1998):
So, based on this observation, the conclusion is that in loss situations (obviously, situations where investors are pessimists), investors tend to be more risk-takers and hence the price of a unit of risk increases as the demand on risky assets increases (simple offer-demand law applied to risk).
References
[1] Jouini, E., and C. Napp, Hétérogénéité des Croyances, Prix du Risque et Volatilité des Marchés.
[2] Jouini, E., and C. Napp, Are More Risk Averse Agents More Optimistic?
Insights From a Rational Expectations Model, Economics Letters, Volume 101, Issue 1, October 2008, Pages 73-76.
[3] Kahneman, D., and M. Riepe, Aspects of Investor Psychology: Beliefs, preferences, and biases investment advisors should know about, Journal of Portfolio Management, Vol. 24 No. 4, 1998.
[4] Vogel, Harold L., Financial Market Bubbles and crashes, 2010.
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