In this paper, we consider a dynamic asset pricing model in an approximate fractional economy to address empirical regularities related to both investor protection and past information. Our newly developed model features not only in terms with a controlling shareholder who diverts a fraction of the output, but also the good (or bad) memory in his budget dynamics which can be well-calibrated by a pathwise way from the historical data. We find that poorer investor protection leads to higher stock holdings of controlling holders, lower stock returns, lower interest rates, and lower stock volatilities if the ownership concentration is sufficiently high. More importantly, by establishing an approximation scheme for the good (or bad) memory of investors on the historical market information, we conclude that the good/bad memory would increase/decrease both real stock returns and interest rates while the equilibrium balances the economy by preventing investors from benefiting the memory. Our model's implications are consistent with a number of interesting facts documented in the recent literature.
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