A Mathematical Research on the Long-term Rate of Return of Holding Risk Assets

In the field of risk management, people usually focus on the distribution of the return on assets. The formula of long-term yield is often used to calculate the average growth rate, the bank rate and the actuarial pricing for rates. People who invest in risk assets make investment decisions based on the average rate of return and the risk of the assets (standard deviation of return on investment). This paper uses the theory of probability theory, the convolution theorem and continuous random variable density function theorem to derive the probability density function of the long-term return on risk assets. On the basis of the general formula, this paper chooses the normal distribution to discuss and gets some of the theoretical results which will provide reference for the investment decisions of investors and provide investors with quantifiable operational guidance, reducing investment risk and increase return on investment