## 3 Design of This Study
### Measuring the Rate of Return Following the VMA Trading Rule  
Initially, by adhering to the VMA trading strategy for ETH index futures, we can calculate the return on ETH futures, denoted by \"R,\" using the following expression:  
\[\text{Ri}=(\alpha\text{i}/\beta\text{i})\,-1 \tag{1}\]  
In Equation (1), \(\alpha\)i represents the closing price of ETH futures at the i-th trade on the selling day, while \(\beta\)i stands for the closing price of ETH futures at the i-th trade on the buying day.  
Then, we proceed to compute the cumulative returns of ETH futures prices, hereafter referred to as \"CR\", employing Equation (2) as delineated below:  
\[\text{CR}=\sum_{i=1}^{n}(1+R_{1})(1+R_{2})........(1+R_{n}) \tag{2}\]  
In Equation (2), CR signifies the cumulative product of adding 1 to each value in the series \(R_{1}\) through \(R_{n}\), encompassing the entire range from 1 to n. Each \(R_{i}\) denotes the return associated with ETH futures, spanning from the first trade (\(i\) = 1) to the last trade (\(i\) = \(n\)), and is generated by one of the VMA trading regulations.  
Following that, we use Equation (3) to calculate the geometric average of the returns associated with ETH futures, designated as \"GAR\".  
\[\text{GAR}=\sqrt[n]{CR}\,-1 \tag{3}\]  
Here, GAR denotes the geometric average return of ETH futures. The parameter \"n\" represents the total number of trades executed by one of the VMA trading regulations.  
In this research framework, following the completion of the first round-trip trading, investors then process the second round-trip transaction. This sequence spans the entire data period, beginning with the first trade and ending with the last transaction. As a result, since we can examine the subsequent return after identifying the first return, we believe that the GAR is appropriate for our research.  
Nonetheless, when engaging in ETH futures round-trip trading, investors must consider transaction expenses. These costs are normally limited to 1%, and in many circumstances, they are significantly lower, perhaps as low as 0.3%. Based on the geometric average returns (GARs) shown in Table 3, which represent the results of the traditional method, we see a range from 37.45% to 2.81%. Given this context, it is evident that, while the transaction costs are not insignificant, they may not be the main concern of this study. Moreover, we can establish a benchmark for the ETH index futures trading performance. The 10-year treasury bond rate is the lower benchmark for ETH investment since it presents the opportunity cost of investments, and the performance of the S&P 500 index would be used as another benchmark because it can represent the performance of stock market trading.  
In summary, this study is directly related to big data analysis and modeling applications since it includes the VMA trading rule and heatmap visualization to derive and display diverse results. The study employed big data analytics approaches to observe and assess the effectiveness of various VMA trading strategies by applying various combinations of short-term and long-term moving averages. This approach allows investors to choose acceptable strategies for trading ETH index futures, which may result in higher returns than the standard design and benchmark performance. The emphasis on the average geometric mean as a measure of returns reflects the evaluation of many round-trip trades, and the research analyzed transaction costs and established acceptable benchmarks, adding to the importance of big data analytics in investment decision making.