Beauty contest, bounded rationality, and sentiment pricing dynamics

- Price volatility decreases by sentiment precision and percentage of second-order investors.
- Higher-order investors are more rational and attentive to the strategies of other participants rather than private signals.
- Bounded rationality results in mispricing on date 1 and reduces it on date 2.
- Investor sentiment produces more significant effects than private signals.
- Optimistic investor sentiment increases hedging demand, thus causing prices to soar.

We present a dynamic asset pricing model that incorporates investor sentiment, bounded rationality and higher-order expectations to study how these factors affect asset pricing equilibrium. In the model, we utilize a two-period trading market and investors make decisions based on the heterogeneous expectations principle and the “sparsity-based bounded rational” sentiment. We find that bounded rationality results in mispricing and reduces it in next period. Investor sentiment produces more significant effects than private signals, optimistic investor sentiment increases hedging demand, thus causing prices to soar. Higher-order investors are more rational and attentive to the strategies of other participants rather than private signals. This model also derives the dampening effect of higher-order expectations to price volatility and the heterogeneity expectation depicts inconsistent investor behavior in financial markets. In the model, investors' expectations about future price is distorted by their sentiment and bounded rationality, so they obtain a biased mean from the signal extraction.