Using two different methods of intertemporal arbitrage strategy, it is applied to the study of intertemporal arbitrage during the month-changing period. First, an introduction to cost-of-carry strategies. In this strategy, we borrow the method of spot arbitrage and use the holding cost strategy to predict the theoretical price difference between the current month and the next month's contract, and consider the relevant costs to determine the arbitrage space. This strategy can be used in conjunction with the futures arbitrage strategy, and it is also a strategy that is easily accepted by many investors. Secondly, the statistical arbitrage strategy is introduced. This strategy was researched by Morgan Stanley's R&D team in 1985. After being widely disseminated, it gradually became the most commonly used investment strategy by foreign hedge funds and investment banks. In foreign countries, statistical arbitrage strategies have achieved good results, especially during the bear market stage.
1. Holding cost strategy
Usually in futures arbitrage, the reasonable price of futures will be calculated based on the holding cost pricing model, and various costs will be considered to determine the upper and lower arbitrage. boundary, in intertemporal arbitrage, we learn from this method and calculate the reasonable prices of the contract of the current month and the contract of the next month during the month-to-month transfer period, and obtain the reasonable price difference accordingly. The so-called holding cost refers to the net cost that investors must pay to hold spot assets until the maturity date of the futures contract, that is, the financing cost paid for financing the purchase of spot assets minus the income obtained from holding spot assets.
This article only introduces the basic principles and conclusions of reasonable spread calculations. The theoretical spread of intertemporal arbitrage is the theoretical price of the next month's contract minus the theoretical price of the current month's contract. Let F represent the theoretical price of stock index futures, S represent the market price of spot assets, r represents the risk-free interest rate, y represents the annual rate of return obtained by holding spot assets, △t represents the number of days until the expiration of the contract, in simple interest calculation The theoretical price of stock index futures can be expressed as:
F=S×[1+(r-y)×△t/360]
Based on the theoretical price difference, Taking into account various costs, including transaction fees, taxes, market impact costs, etc., the upper and lower bounds of intertemporal arbitrage can be determined.
Theoretical price of futures contract: F=S×[1+(r-y)×△t/360]
Theoretical price difference of intertemporal arbitrage:
Among them, the subscripts f and n represent the contracts of the next month and the current month of the month-to-month transfer period respectively. Assuming that C1 is the cost involved in bear market arbitrage, and C2 is the cost involved in bull market arbitrage, then the upper bound of intertemporal arbitrage is Ff- Fn+C1, and the lower bound of intertemporal arbitrage is Ff-Fn-C2. Investors can calculate the upper and lower bounds of intertemporal arbitrage based on their actual situation, and execute bear market arbitrage when the price difference exceeds the upper bound, that is, sell the next month's contract and buy the current month's contract; execute bull market arbitrage when the price difference is below the lower bound. Arbitrage, sell the current month's contract and buy the next month's contract.
Considering that the current month contract during the month-to-month transfer period is close to delivery, under normal circumstances, the price of the current month contract during this period will be very close to the spot index, that is, the absolute value of the basis difference of the current month contract will be very small. Qualified investors can consider combining intertemporal arbitrage during the month-to-month transfer period with futures arbitrage. If the price difference returns to a reasonable area before the delivery of the current month's contract, the position can be closed to make a profit. If the price difference fails to return to a reasonable area before delivery, , you can consider establishing the corresponding spot position on the last trading day of the current month's contract. Of course, in this case, more factors including market impact costs need to be considered.
IF1008 and IF1007 price difference chart
Using the 1-minute data when the IF1007 contract and IF1008 contract move to the next month as a sample for analysis. In the calculation process, we did not consider dividends and impact costs, and took the risk-free interest rate as the one-year financial institution RMB loan benchmark interest rate of 5.31%, and set the handling fee to one ten thousandth. At the same time, technical adjustments were made to the arbitrage boundary using data lagged one period. As can be seen from the figure, there are discontinuities in the upper and lower boundaries obtained based on this strategy. The reason is that the futures contract and the Shanghai and Shenzhen 300 Index trading hours are inconsistent. In fact, intertemporal arbitrage itself should not have such a discontinuity. This is also a flaw of this method when applied to intertemporal arbitrage. The arbitrage opportunities during the discontinuity period will be lost. According to this strategy, *** there are 33 arbitrage opportunities. If the margin rate is 25%, the cumulative income of 33 arbitrages reaches 6.1449%.
2. Statistical arbitrage strategy
Statistical arbitrage strategy is a market-neutral strategy that obtains stable returns independent of the market by hedging related securities. The basic idea behind the statistical arbitrage strategy is mean reversion, which means that if there is a certain stable relationship between the prices of two highly correlated investment targets, then arbitrage will exist when their prices deviate. Opportunities, because this divergent trend will be corrected in the future. In actual investment, when prices deviate from the trend, if you buy stocks that perform relatively poorly and sell stocks that perform relatively well, you can expect to obtain relatively stable returns in the future when this divergence trend is corrected.
We still select the 1-minute data during the month-to-month transfer period (July 13-July 15) of the IF1007 and IF1008 contracts as a sample. When conducting a cointegration test, first logarithmize the price of the object under investigation. This has two advantages: first, the time series after logarithmization is more stable; second, the change in the logarithmic spread corresponds to the income, which is convenient Determine the weights of each security in the arbitrage portfolio to construct a fully hedged portfolio.
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- We use the deviation of the logarithmic price difference between each contract from its historical mean as a signaling mechanism for arbitrage. When the deviation of the logarithmic price difference from its mean exceeds the set The arbitrage strategy is executed when the price reaches the range, and the position is closed when it returns to the equilibrium area (between the upper and lower bounds). If the price difference not only does not return to the mean but expands further after executing the arbitrage strategy, the loss will be stopped immediately when the loss reaches a certain level. We set up the following arbitrage strategy: when the logarithmic spread deviates from its mean value by more than 2 standard deviations, the arbitrage strategy is executed, and the undervalued contract is bought and the overvalued contract is sold; after the arbitrage is executed, when the logarithmic spread returns to Immediately close the position after the equilibrium area and take profits; if the logarithmic spread continues to diverge after executing the arbitrage strategy, stop the loss immediately when the loss reaches more than 5% of the total investment.
By examining the relationship between the 1-minute logarithmic prices of contracts IF1008 and IF1007 from July 13th to July 15th, it was found that there is a stable cointegration relationship between the two: LNY= -0.5451052502+1.069838949×LNX. It can be seen that when the return rate of IF1007 changes by 1%, the return rate of the next month's contract IF1008 changes in the same direction by 1.069838949%. Therefore, if you want to achieve complete hedging, for every 1 million of current-month contract IF1007 purchased (short-selling), you have to short-sell (purchase) 934,600 of next-month contract IF1008, and the margin ratio is calculated at 25%.
Based on the cointegration relationship between the two, we found that 10 arbitrage opportunities appeared during the period from July 13 to July 15, 2010. The arbitrage results of each time were as follows:
The above table of CSI 300 intertemporal arbitrage strategy table *** lists 10 arbitrage trading opportunities and their arbitrage results. The total return of 10 arbitrage is 4.2768%. It should be noted that the calculation in the above table does not take into account the transaction fee. If the handling fee is set to 0.01%, the total handling fee for each arbitrage will be approximately 0.04%, and the 7th and 9th arbitrage will be a failure. arbitrage. When the handling fee is one ten thousandth and the margin rate is 25%, the total arbitrage income is 3.8768%. In actual investment, the corresponding handling rate can be specifically considered to adjust the arbitrage boundary.
Compared with the holding cost strategy, under the same handling rate and margin rate, the arbitrage opportunities and cumulative return rate of the statistical arbitrage strategy are relatively low. The main reason is that only statistical methods are used To determine the arbitrage boundary, the holding cost strategy calculates the arbitrage boundary based on actual transaction conditions, with higher accuracy.
In addition, the setting of the statistical arbitrage strategy in this article is: when the logarithmic spread deviates from its mean value by more than 2 standard deviations, the arbitrage strategy is executed, and the undervalued contract is bought and the overvalued contract is sold. In actual operation, the standard deviation multiple of the deviation can be adjusted accordingly. If the investor has a low risk preference (more inclined to avoid risks), a higher standard deviation multiple of the deviation can be set. Of course, this will also result in the loss of some arbitrage opportunities.
In the holding cost strategy, we mainly consider the connection with spot arbitrage to minimize risks. If we only consider the use of intertemporal arbitrage strategies without involving the spot market, then the statistical arbitrage strategy is a A simple and easy-to-implement strategy that can be well utilized by programmatic trading.