Study on the Risk-Return Mathematical Model Based on LSTM Time-Series Model and Monte Carlo Simulations

As the returns and risks of stocks are uncertain, decisions are particularly important when investing. For transactions in risky assets, it is difficult for investors to make investment decisions at prices known in the past.Both gold and bitcoin stocks in the U. S. market are high-risk products. Given the initial funding, it is a problem that our team requires to solve. In this paper, we establish the stock time series prediction model and the portfolio strategy model, find the equilibrium point between risk and return, and then obtain the best investment strategy. For problem 1: first, the price of the next trading day is predicted through the LSTM time-series model, and a preliminary qualitative judgment is made by comparing the relationship between the forecast price and the current price. Then, through simulation and the Sharp ratio of Monte Carlo simulation, the best investment ratio is obtained when considering risks and returns to solve this problem. For problem 2: by comparing the cumulative yield and dollar value obtained from the best portfolio, minimum risk portfolio and equal divided weight combination, the strategy obtained in this paper is the best, and proved from two aspects of theory and practice. For problem 3: Based on the reality and development trend of transaction expenses, this paper obtains the sensitivity analysis of transaction expenses to yield and investment holding shares by using derivatives.According to the analysis, the built model is relatively stable and is suitable for most transaction expenses to change.Also, we note that transaction frequency affects how sensitive a commission is to earnings. For question 4: we give the market trader suggestions from the developed model and the optimal strategy. It can be summarized as: following our best daily investment strategy, $1,000 will be added after a 5-year investment and trade period to $74,521.3; proving that this optimal investment strategy takes full consideration of risks and benefits. Reduce the risk through investment portfolio and ensuring the maximum return at this risk level; transaction expenses have less impact on investment decisions under certain transaction frequency. The model established in this paper fully considers the risk and return balance relationship. The LSTM time-series prediction model has the advantages of long-term memory, and the Monte Carlo simulation has an iterative function, which can save the tedious mathematical calculus and derivation process. However, the application of this model is limited due to the existence of assumed conditions. Moreover, we extended the model to predict further data than this five-year period to give market investors more favorable decisions.