### Anchoring Heuristic And The Equity Premium Puzzle

University of Queensland

November 1, 2015

**Abstract: **

We model a scenario in which investors face Knightian uncertainty in relatively newer stocks and use the payoff distribution of similar well-established stocks as starting points for forming judgments about the payoff distributions of newer stocks. Anchoring bias (Kahneman and Tversky (1974)) implies that such adjustments typically fall short. We show that adjusting consumption CAPM for anchoring provides a unified explanation for 9 asset pricing puzzles including the equity premium puzzle. The anchoring approach achieves these explanations while maintaining the tractable framework of a representative agent with time additive preferences in a complete market.

### Anchoring Heuristic And The Equity Premium Puzzle – Introduction

In the simplest version of consumption based asset pricing model (CCAPM), the price of an asset is equal to the present value of expected payoff plus an adjustment term for risk. The adjustment term for risk is usually (almost always) negative and depends both on the quantity of risk as well as the price of risk. It is equal to the covariance of the assetâ€™s payoffs with the stochastic discount factor (SDF) or equivalently with the inter-temporal marginal rate of substitution (IMRS) of the representative investor. Intuitively, the risk term depends on how badly an asset is expected to perform in bad times. An asset that performs worse in bad times is riskier (with a negative risk adjustment term of a larger magnitude) and gets a lower price when compared with an asset that performs better.

In a standard CCAPM (Rubinstein (1976), Lucas (1978), Grossman and Shiller (1981), Hansen and Singleton (1983) among others), the price of risk is the coefficient of relative risk aversion, and the quantity of risk depends on the covariance of payoffs with consumption growth. Mehra and Prescott (1985) show that in order to justify the historically observed high equity premium, an implausibly large price of risk is needed. This is because the quantity of risk seems small as historical consumption growth has little volatility. Mehra and Prescott (1985) show that the historical data implies a risk aversion coefficient of around 30 whereas a value of around 1 to 3 seems reasonable. If one accepts that the price of risk is indeed that high, then this acceptance gives rise to, what is known as, the low risk-free rate puzzle put forward in Weil (1989): As consumption tends to grow with time, the high price of risk should increase the demand for borrowing causing the risk-free rate to rise; however, inconsistent with this prediction, the historically observed risk-free rate is too low. Apart from high equity premium and low risk-free rate, the strongly countercyclical nature of the equity premium is also a related puzzle along with high stock price volatility given the considerably smaller volatility in fundamentals.

In standard CCAPM, the first order condition yields:

In (1.1), q is an indicator of bad times, so the risk adjustment term is equal to the judgment of the representative investor regarding the covariance of an assetâ€™s future payoffs with the state of the economy. CCAPM requires that such risk judgments are correctly formed for every asset in the economy. This is a strong assumption especially given the fact that such covariances are not only just difficult to estimate but are also unknowable in many cases. Firms differ in terms of history, data availability, and how much media and analyst attention they get. Some stocks have been around for decades and belong to well-known and well-established companies while others are relative new comers. In standard CCAPM, no allowance has been made for the fact that some firms have lived through a series of good and bad times, so forming risk judgments about them is easier when compared with firms that have just started operating. In other words, standard CCAPM views every firm with the same lens of omniscience. Differences of information availability across firms are simply brushed away by assuming that correct risk judgments are formed. Of course, omniscience is a convenient assumption. However, this convenience comes at a great cost. We argue, in this article, that the inability of standard CCAPM to explain the equity premium and related puzzles is the price paid for assuming omniscience.

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