Process. There is a single firm producing the perishable consumption good. At any given time , the firm's output must be less than or equal to which is stochastic and follows . There is only one equity share held by the representative household. We work out the intertemporal choice problem. This leads to: as the fundamental equation. For computing stock returns where gives the result. The derivative of the Lagrangian with respect to the percentage of stock held must equal zero to satisfy necessary conditions for optimality under the assumptions of no arbitrage and the law of one price. Data Much data exists that says that stocks have higher returns. For example, Jeremy Siegel says that stocks in the United States have returned 6.8% per year over a 130-year period. Proponents of the capital asset pricing model say that this is due to the higher beta of stocks, and that higher-beta stocks should return even more. Others have criticized that the period used in Siegel's data is not typical, or the country is not typical. Possible explanations A large number of explanations for the puzzle have been proposed. These include: Rare events hypothesis, Myopic loss aversion, rejection of the Arrow-Debreu model in favor of different models, modifications to the assumed preferences of investors, imperfections in the model of risk aversion, the excess premium for the risky assets equation results when assuming exceedingly low consumption/income ratios, and a contention that the equity premium does not exist: that the puzzle is a statistical illusion. Kocherlakota (1996), Mehra and Prescott (2003) present a detailed analysis of these explanations in financial markets and conclude that the puzzle is real and remains unexplained. Subsequent reviews of the literature have similarly found no agreed resolution. The mystery of stock premiums occupies a special place in financial and economic theories, and more progress is needed to understand the spread of stocks on bonds. Over time, as well as to determine the factors driving equity premium in various countries / regions may still be active research agenda. The equity premium: a deeper puzzle Azeredo (2014) showed that traditional pre-1930 consumption measures understate the extent of serial correlation in the U.S. annual real growth rate of per capita consumption of non-durables and services ("consumption growth"). Under alternative measures proposed in the study, the serial correlation of consumption growth is found to be positive. This new evidence implies that an