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On Kernels and Sentiment


The paper analyzes the manner in which sentiment affects the pricing kernel. Sentiment is another term for traders’ errors. The central question of the paper is: How can the concept of sentiment be formally defined so as to identify the manner in which traders’ errors are manifest in the pricing kernel? The subsidiary question in the paper is as follows.

Because the pricing kernel underlies the pricing of all assets, how do traders’ errors impact the pricing of major asset classes such as fixed income securities, options, mean-variance portfolios, and the market portfolio? The central result in the paper is that the log-pricing kernel can be decomposed into two stochastic processes, one pertaining to fundamentals and the other to sentiment. Hence, prices are efficient if and only sentiment is uniformly zero.

In the model, investors differ from each other in respect to beliefs, risk tolerance, and time preference. This heterogeneity has far reaching implications for asset pricing theory. When sentiment is nonzero, I demonstrate that heterogeneity can lead to “smile” effects both in the graph of the kernel and in option prices, and “frown” effects in mean-variance returns. In this respect, heterogeneity can prevent the conditions necessary for equilbrium option prices to be given by Black-Scholes. As a result, the smile effect for call options can differ from the smile effect for put options.

Nonzero sentiment distorts the mean-variance frontier from its “efficient” position, thereby giving rise to behavioral betas. In addition, nonzero sentiment interferes with the expectations hypothesis of the term structure, and can affect the volatility of the return to the market portfolio, depending on traders’ risk tolerance spectrum.

Prof. Hersh Shefrin

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