Table 9 summarizes the size, frequency, and length of E-minis ex-post boundary v i o l a t i o n s b e f o r e ( p a n e l A ) a n d a f t e r ( p a n e l B ) t h e d e c i m a l i z a t i o n . Boundary violations are identified according to Equation 3 for various levels of two-way transaction costs ranging from 0.20 to 0.40% of the theoretical futures price.
Column 6 through 8 reports the average number of subsequent violations occurring within a 20-min interval after the first mispricing signal. For example, in the pre-decimalization period with the 0.2% transaction costs category, there is an average of 5.69 subsequent violations following a new occurrence of boundary violation, 5.69 penetrating the upper bound, and 0.60 violating the lower bond.
TABLE 9
Ex-Post Violations of S&P 500 E- mini Price Boundaries Using S&P 500 Index as a Cash-Market Proxy
Note. The ex-post tests focus on the frequency and persistence of boundary violation. No-arbitrage bands are constructed on the basis of the spot index
Transaction costs are measured in percentages of the theoretical futures value. An occurrence of boundary violation is defined as a series of same-side violations such that any two adjacent violations are apart by less than 20 min. Average number of subsequent violations and time span of violations measure the frequency of observed mispricing in an occurrence of violation and the time length of the occurrence, respectively.
Columns 9 through 11 present the average time span of boundary violations. Results suggest that the subsequent violations usually diminish within a short time period. For instance, for violations in the 0.2% transaction costs category in the pre-decimalization period last an average of 1 min and 36 s. The upper boundaryviolations (1 min and 36 s) persist longer then the lower boundary violations (0 min and 9 s). The short duration of each cluster of violations indicates that the S&P 500 E- mini price is closely linked to the underlying index. More important, arbitrage with transaction lags longer than the time span of violations is subject to uncertainty and may not be profitable, as the ex-ante analysis shows.
In the pre-decimalization period, mispricings are asymmetric for the upper and lower bounds. When transaction costs exceed 0.2%, there are no lower bound violations, but there are upper bound ones, suggesting that the market tends to overprice E- minis’ prices in this period. Moreover, the larger upper bound violations tend to persist for longer periods of time and are followed by more subsequence violations as the result of the difference between ETF & index in Table 1.
Table 10 generating the result of ex-post analysis on NASDAQ 100 index also shows the same pattern with S&P 500 index. We also can find that after decimalization, occurrence of boundary violations, subsequent violations, and time span all decreased at any cost level, different with the result using ETFs as cash-market proxy. It seems to that after decimalization, the smaller bid-ask spread improve to trade at the true values of the component stocks form the index. Therefore, we can conjecture that decimalization strengthen the pricing efficiency between E-minis and ETFs. On the other hand, this study here doesn’t consider the true bid and ask price of every component stock and we can’t see the true arbitrage opportunities.
TABLE 10
Ex-Post Violations of NASDAQ 100 E- mini Price Boundaries Using NASDAQ 100 Index as a Cash-Market Proxy
Note. The ex-post tests focus on the frequency and persistence of boundary violation. No-arbitrage bands are constructed on the basis of the spot index
Transaction costs are measured in percentages of the theoretical futures value. An occurrence of boundary violation is defined as a series of same-side violations such that any two adjacent violations are apart by less than 20 min. Average number of subsequent violations and time span of violations measure the frequency of observed mispricing in an occurrence of violation and the time length of the occurrence, respectively.
A.2. Ex-Ante Arbitrage Profit
Table 11 summarizes results for ex-ante arbitrage profit assuming a 5-min transaction lag for a trading spot portfolio. Panel A reports negative mean arbitrage profit for the various levels of transaction costs in the pre-decimalization period. For example, although traders in the 0.20% transaction costs category face 4,427 arbitrage opportunities, executing these arbitrage opportunities results in an average losses of 0.139 index points.
The mean arbitrage losses are even greater for higher transaction cost traders, with -0.345 at 0.30% and -0.916 at 0.40% transaction costs. Further investigation shows that neither long nor short arbitrage is profitable at any cost level, as shown in columns 4 through 9.
Comparison of the two subperiods provides one insight. We found that index arbitrage using program trading results in negative mean profits in both subperiods, indicating that the market is ex-ante efficient.
TABLE 11
Ex-Ante Arbitrage Profit Using Program Trading (Reported Index with Time Lag)
All Arbitrage Long Arbitrage Short Arbitrage
Transaction Note. The ex-ante test imposes a 5-min execution lag for trading underlying stocks (program trading) against futures. A long arbitrage, triggered by futures overpricing, buys a basket of S&P 500 stocks and shorts futures after observing an upper-boundary violation, whereas a short arbitrage, triggered by futures underpricing, performs the reverse transactions. Profits for long and short arbitrage are measured as follows
]
Ex-ante mean profit measures the profit/loss after considering transaction lag. Signal size stands for the ex-post pro fit. “NA” stands for not available.
“STD” in parentheses means standard deviation.
TABLE 12
Ex-ante Arbitrages by Type and Profitability of Arbitrages Using Program Trading Against S&P 500 E- mini
Long Arbitrage Short Arbitrage
Profitable Unprofitable Profitable Unprofitable
Note. The ex-ante tests impose a 5-min execution lag for trading underlying stocks (program trading) against S&P 500 E-mini. A long arbitrage buys a basket of S&P 500 stocks and short S&P 500 E-mini after observing an upper-boundary violation. A short arbitrage performs opposite transactions.
“NA” stands for not available.
TABLE 13
Ex-Ante Arbitrage Profit Using Program Trading (Reported Index with Time Lag)
All Arbitrage Long Arbitrage Short Arbitrage
Transaction Note. The ex-ante test imposes a 5-min execution lag for trading underlying stocks (program trading) against futures. A long arbitrage, triggered by futures overpricing, buys a basket of NASDAQ 100 stocks and shorts futures after observing an upper-boundary violation, whereas a short arbitrage, triggered by futures underpricing, performs the reverse transactions. Profits for long and short arbitrage are measured as follows
]
Ex-ante mean profit measures the profit/loss after considering transaction lag. Signal size stands for the ex-post profit. “NA” stands for not available.
“STD” in parentheses means standard deviation.
TABLE 14
Ex-ante Arbitrages by Type and Profitability of Arbitrages Using Program Trading Against NASDAQ 100 E- mini
Long Arbitrage Short Arbitrage
Profitable Unprofitable Profitable Unprofitable
Note. The ex-ante tests impose a 5-min execution lag for trading underlying stocks (program trading) against NASDAQ 100 E-mini. A long arbitrage buys a basket of NASDAQ 100 stocks and short NASDAQ 100 E-mini after observing an upper-boundary violation. A short arbitrage performs opposite transactions. “NA” stands for not available.
Table 12 analyzes the arbitrage outcomes by dividing long and short arbitrage further into profitable and unprofitable transactions. For both types of arbitrage, unprofitable arbitrage consistently dominates profitable arbitrage in both subperiods.
For NASDAQ 100, we can see similar result in Table 13 and 14 and find that the performance of NASDAQ 100 is more significant than S&P 500.
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