In the trading market, since the birth of Bitcoin, people have been disputing gold and bitcoin. How to seek an appropriate and optimal investment portfolio has become a problem that people pay close attention to. In this case, we need to build a model and give an optimal trading strategy to maximize the profit of their portfolio. We used time series analysis to predict the price and AHP to quantify the investment risk, so as to give the best investment strategy and prove its rationality. Firstly, in order to get the optimal investment strategy, we had to predict future price movements of investment products, determined whether to sell, held or bought investment products, we adopted the method of time series analysis, with the aid of XGBoost machine learning algorithms, using some existing data as a training set, using the day before the data as a test set, to forecast movements in the price of the second day of investment products, to use the ideas of hedging. Through the analysis of gold, Bitcoin investment risk, we came up with the optimal ratio between cash, Bitcoin, and gold. Through the study of the classification of all kinds of possible situations, with the help of the has to predict prices, the best investment strategy was given. With the help of the optimal strategy given in this paper, the initial investment of $1000 was put into the debugged model, and the final total investment reached about $250,000.Secondly, in order to justify our model, in this paper established on the basis of the optimal strategy and design of three other different schemes, analyzed four different schemes, we used the analytic hierarchy process (AHP) 1-9 scale of four different schemes of risk quantitative analysis, it was concluded that the risk of four plans relative size, The final returns of the three other schemes were calculated by using the dynamic programming model, and the rationality of the proposed strategy was proved by the combination of risk and return. Thirdly, in order to determine the sensitivity of the trading strategy of transaction cost, by changing the transaction cost rate of gold and Bitcoin, we observed the change of the total asset amount, and concluded that there is a non-linear relationship between the transaction cost rate of gold or Bitcoin and the total asset amount, and the transaction cost of gold or Bitcoin affects the total asset amount by affecting the frequency of total asset allocation conversion. Finally, we conducted sensitivity analysis and model improvement, and analyzed the triality of the strategy presented in this paper in real life, and wrote a two-page memo to convey our strategy, model and results to traders.
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