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 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 gross stock returns, lower interest rates, and lower modified stock volatilities if the ownership concentration is sufficiently high. More importantly, by establishing an approximation scheme for good (bad) memory of investors on the historical market information, we conclude that good (bad) memory would increase (decrease) aforementioned dynamics and reveal that good (bad) memory strengthens (weakens) investor protection for minority shareholder when the ownership concentration is sufficiently high, while good (bad) memory inversely weakens (strengthens) investor protection for minority shareholder when the ownership concentration is sufficiently low. Our models implications are consistent with a number of interesting facts documented in the recent literature.
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