The Relationship between Portfolio Size and Risk Based on Investors Utility

In actual investment activities, rational investors always allocate their funds to different assets in order to diversify their investment. From the perspective of investor's utility, this paper studies the relationship between portfolio size and risk under different risk aversion levels by repeating stochastic simulations on the components of CSI 300 index in Chinese stock market. Empirical studies show that: Compared with the equal-weighted method, the idea based on the maximization of the investor's utility function can diversify most of the unsystematic risk with fewer assets. The lower limit of the optimal portfolio risk of the risk seeker is higher, and is lower for the risk averter.