Timing Profits to Realize Gains with $1,000: Evidence from Five-Year Prices of Bitcoin and Gold

Abstract

Quantitative investment methods use mathematical models to estimate the price trends of financial assets based on their historical movements and to accurately choose the best time to trade, enhancing returns and their stability. In this paper, we construct quantitative investment models and strategies and practice them in a five-year portfolio of cash, gold and bitcoin, achieving considerable returns. To form a complete investment strategy, two main models are required, namely, one to forecast prices of gold and bitcoin, and one to decide on specific trading operations. To forecast prices, ARIMA-GARCH models group is firstly built. In the method of price forecasting using time series analysis, the ARIMA time series model can grasp the dynamic pattern and trend of prices. However, according to the empirical data, it is found that it is difficult to reflect the price volatility characteristics using ARIMA model forecasting. Therefore, we consider the conditional heteroskedasticity GARCH model to reflect the volatility of the time series in practice. In this section, we use the data given in the topic to construct a hybrid model ARIMA (4,1,4)-GARCH (1,1) by combining the ARIMA model with the GARCH model to forecast the price of gold and the price of bitcoin. After forecasting of the future prices of gold and bitcoin, we apply a dynamic program model to design the specific daily investment strategies based on the prediction. We divide the investment strategies into whether to trade a certain asset and how much to trade. In the specific discussion of each case, we introduce qualifying conditions from the perspective of risk and trading rules, and determine the amount of trading by solving the objective function under the qualifying conditions to form a complete investment strategy. Setting a 10% cap on our gold position and a 90% cap on our bitcoin position without changing transaction fees, our portfolio ends up at $37370.91 after 5 years, with an ideal ROI of 3637.09%, an IRR of 205.19%. For complementary, we conduct sensitivity analysis. To study the impact of transaction costs on total returns, we change the transaction costs of gold and bitcoin 1% at a time simultaneously and calculate the change in expected returns, while using two models, the normalized coefficient method and the shapley value decomposition method, to determine the sensitivity of the transaction costs of both to total returns. It is finally shown that the higher the transaction cost, the lower the return; bitcoin’s transaction cost is more sensitive and contributes more. At the end of the paper, we present evidence that our model provides a better strategy by proving the ARIMA-GARCH model has the ability to forecast prices more accurately.