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Informed traders in the stock index futures market cannot directly know the public value of stock index futures; however, they can calculate the theoretical value of the stock index futures as follows Footnote 4 :. The variables a i , b i , and c i , which represent the weights, are randomly chosen from [0,1].
The forecast price of the technical investor for the asset is as follows:. If the transaction can be completed in real time, the order is considered a market order; otherwise, it is considered a limit order.
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Regarding arbitrage investors, they pursue real-time trading and therefore only submit market orders. Following Chiarella et al. This study mainly evaluates trading strategies for stock index futures based on cost-benefit analysis. High-frequency data were obtained through simulation experiments by modeling the stock market and the stock index futures market.
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This study attempts to establish an evaluation framework for trading strategies—including wealth growth rate, volatility of wealth growth rate, capital occupancy, and impact cost—to explore the effectiveness, risks, and costs of these trading strategies. Footnote 5 Each group of experiments in the study was carried out 30 times to ensure that the experimental results were statistically significant. To ensure there were enough arbitrage opportunities in the market, we set the number of arbitrage investors to be smaller than that of other types of investors.
At the same time, since arbitrageurs need to trade in both markets, we set arbitrageurs to have more initial wealth. Table 1 shows the detailed parameters. Intuitively, only the wealth of informed traders increases. Other investors are subject to wealth losses. Earnings from technical trading strategies tend to be more volatile, and earnings volatility is similar among the other three types trading strategies. The evaluation of a trading strategy involves the costs, benefits, and risks. A strategy is considered a good strategy if it has higher earnings, lower costs, and lower risks.
Next, we analyze the effectiveness, risk, capital occupancy, and impact cost of trading strategies in detail. Analyzing the effectiveness of trading strategies aims to determine whether the strategy can bring benefits to investors. Then, we calculated the daily wealth growth rate for all of them; Fig. Wealth growth rate of investors. Blue line: informed traders; Red line: technical traders; Black line: noise traders; Green line: arbitrage traders. Arbitrage is theoretically risk free, but risks still exist in actual transactions.
For example, the index tracks risks.
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We purchase the index by buying a spot portfolio; this process will have index-tracking bias. For another example, the market affects risk. When investors purchase a large number of assets, they generally cannot deal in fixed prices. Therefore, arbitrage investors are likely to have negative returns.
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This is also in line with the real market. ANOVA was used to better observe the differences between the wealth growth rates of the four types of investors. Table 3 shows the experimental results. This means the wealth growth rate differs among the four types of investors, and the effectiveness of the four trading strategies is therefore different.
The second is the technical trading strategy, which ultimately does not increase investor wealth; it did, however, offer opportunities for profit in the simulation experiment. The third is the arbitrage trading strategy; its average wealth growth rate is negative, but it offers a chance for profit through arbitrage. The last is the noise trading strategy. Noise traders suffered huge losses in the experiment, indicating that investors who are not informed and do not study do not successfully invest.
When evaluating trading strategies for stock index futures, we should consider not only profitability but also risk to seek a balance between the two. Then, we analyze the wealth growth rate volatility of the four kinds of investors to evaluate the risk level of each trading strategy. Volatility is measured by standard deviation. Figure 6 and Table 2 show the results. Wealth growth volatility of investors. ANOVA was used to better observe the differences in wealth growth rate volatility.
Table 3 shows the detailed values. We can see that there are significant differences between the wealth growth standard deviations of the four types of investors; the risks of all types of trading strategies show great differences. The technical trading strategy faces the biggest risks. The average standard deviations of the wealth growth rates of informed traders and arbitrage traders are similar. Accordingly, the risks of those strategies are similar, although the risk of the arbitrage trading strategy is slightly higher.
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In addition to the profitability and risk analysis, cost is also an important factor used to evaluate trading strategies for stock index futures. Cost can directly affect the effectiveness of trading strategies and the results of the execution. The cost of the trading strategy includes the occupation of capital and impact cost.
Occupation of capital refers to the capital investors need to pay for the transaction in unit order. A high degree of occupied capital means the trading strategy has greater risk. Informed traders, technical traders, and noise traders only invest in the stock index futures market while arbitrage traders invest in both.
Thus, the capital requirement of arbitrage traders is greater than that of the other three types. We obtain 60, period data for the occupation of capital among all trading strategies. Then, we calculate the occupation of capital for each trading strategy in each day. Figure 7 and Table 4 show the experimental results. Occupation of capital for the arbitrage strategy and other strategies.
Red line: arbitrager strategy; Blue line: other strategies, include informed strategy, technical strategy and noise strategy. Figure 7 shows that the occupation of capital for the arbitrage strategy is greater than that for the other strategies. The variance in the occupation of capital is also greater for the arbitrage strategy than for the others, meaning the arbitrage strategy is more volatile.
As shown in Table 4 , the average capital occupation of the arbitrage strategy is 3. Thus, the capital occupation of arbitrage traders is nearly 6. Trading strategies can affect market trends, which might in turn affect the execution of trading strategies and transactions at optimal prices.
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The loss caused by this situation is known as the market impact cost, which is another type of cost. This study uses the number of deals in the optimal price to measure the impact costs of the trading strategies. Footnote 7 The larger the number of deals, the smaller the impact cost. The informed, technical, and noise trading strategies are only used in the stock index futures market; they only affect that market and thus suffer impact costs from only one market.
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Meanwhile, since the arbitrage trading strategy operates in both markets simultaneously, it suffers impact costs from two markets. Thus, the impact cost of the arbitrage trading strategy is greater than that of the other three types. We obtain high-frequency data for the number of deals at the optimal price in the stock market and the stock index futures market. We calculate the average value of the number of deals at the optimal price for the trading strategies to measure the daily average impact costs.
Figure 8 and Table 4 show the experimental results. Average impact costs of the arbitrage strategy and the other strategies. We can see in Fig. This means the impact cost of the arbitrage trading strategy is higher than that of the others. Evaluating trading strategies for the stock index futures market mainly involves analyzing benefits, costs, and risks. Cost analysis includes occupation-of-capital analysis and impact cost analysis.
Each aspect i.