This study investigates the impact of the introduction of new tick size on the pricing efficiency and the long-run and short-run price dynamics between futures and
spot markets. The non-linear VECM can evidently characterize the arbitrageurs’
behavior. When the futures and spot prices deviate from no-arbitrage boundary settled by the transaction costs mainly composed of spread costs, arbitrageurs would trigger the buy or sell program to make arbitrage immediately. The smaller tick size settled by the Taiwan Stock Exchange Corporation (TSEC) after March 1, 2005 can effectively lower the spread costs between best bid and ask prices according to past researches. The lower transaction costs make the arbitrageurs trigger the arbitrage program more easily, which lead mispricing error to shrink and improve the pricing efficiency after the reduction of tick size.
For the Linear VECM, our results show that the long-run co-movement extent between these two financial markets turn stronger and the two price series tend to approximate to each other after the reduction of tick size. This result is caused by the lower transaction costs after the reduction of tick size, which reduces the obstacles for the two prices to return to long-run equilibrium. The dynamic coefficients show the futures clearly lead the spot in both sub-sample periods and the feedback relation which means the impacts of spot on futures in the second period.
For the threshold VECM model, the results show the presence of threshold cointegration, and nonlinear dynamic coefficients in both sub-sample periods. This implies the threshold VECM model fits the price dynamics between futures and spot markets superior to the linear VECM model. Furthermore, the threshold value (γ) decreases from 0.347891 to 0.307617 after the reduction of tick size, because the decrease of tick size reduces the spread cost which comprises the main transaction cost and lower the arbitrage threshold for arbitrageurs, which is consistent with our expectation.
In the first sample period, the error-correction phenomena in futures and spot equations are more significant in the extreme regime, since the triggers of arbitrage
trades enhance the co-movement extent across two price series. The coefficients of error correction terms in the extreme regime of threshold VECM appear to be larger than those in the linear VECM, which indicates that two price series have a faster convergence or mean-reversion to the long-run equilibrium in the extreme regime of nonlinear VECM than that in linear VECM model. This result is consistent with Dwyer, Locke, and Yu’s (1996).
In the second sample period, the error-correction phenomenon is only significant in the futures price equation in the typical regime, which indicates that there exists mean reversion only in the futures price. However, as contrary to typical regime, the error-correction effect is not significant both in the futures (ΔF) and spot (ΔS) equations, which means that there does not evidence any long-run equilibrium relationship between futures market and spot market in the extreme regime. In other words, the two series behave like a random walk and free from the cointegration constraint (Tsay, 1998) probability due to the decrease of market depth at the best-quoted prices (Harris(1994, 1997) and Furfine (2003)) after the reduction of tick size. Equilibrium relationship between futures market and spot market in the extreme regime becomes insignificant. The decrease of arbitrage trade numbers might result from stronger co-movement between the two financial markets discovered in linear VECM after reduction of tick size.
For the short-term dynamics, all the coefficients of the lagged futures prices on the spot equation are statistically significant in both periods. These results confirm again that futures market leads the spot market, which is consistent with those in the linear VECM. Nevertheless, we find some feedback relation which means the impact of spot on futures in the second period as the result in the linear VECM.
Finally, while conditioning the change for volatility and buy and sell programs effects, we find the reduction of tick size can lower the mispricing error and improve
the pricing efficiency. However, we use the arbitrage data drawn from the second regime of threshold VECM model instead to run the OLS regression again. We find the mispricing error increases and pricing efficiency deteriorates for the arbitrage data after the reduction of tick size. Because the market depth might reduce after the reduction of tick size, the error-correction terms of the second regime of threshold VECM model are insignificant which means long-term equilibrium relationship of futures and spot does not exist after the reduction of tick size. Hence, mispricing error of arbitrage data does not reduce for the arbitrage data after the reduction of tick size.
In the future, we can improve the threshold VECM by considering ARCH-effect into its error term and estimating the optimal lag time for arbitrage threshold, because financial markets in Taiwan usually have ARCH-effect and arbitrage time might not be just at lag one period. We believe this improved model can fit the price dynamics more precisely. In the meantime, we can do more research in all different futures contracts and even longer empirical period to confirm the impact of the new policy more robustly.
References
Aggarwal .Raj and Young S. Park, 1994, “The relationship between daily U.S. and Japanese equity prices: Evidence from spot versus futures markets,” Journal
of Banking & Finance, 18, 757-773.
Balke, N.S., and T.B. Fomby, 1997, “Threshold cointegration,” International Economic Review 38, 627-645.
Bessembinder, Hendrik, 2003, “Trade execution costs and market quality after decimalization,” Journal of Financial and Quantitative Analysis, 38, 747-777.
Bollen, Nicolas P. B. and Jeffrey A. Busse, 2003, “Tick Size and Institutional Trading Costs: Evidence from Mutual Funds,” Journal of Financial and Quantitative
Analysis, forthcoming.
Bollen, Nicolas P.B., and Robert E. Whaley, 1998, “Are teenies better?” Journal of
Portfolio Management, 25, 10-24.
Chakravarty, Sugato, Bonnie F. Van Ness, and Robert A. Van Ness, 2005, “The effect of decimalization on trade size and adverse selection costs,” Journal of
Business Finance & Accounting, 32, 1063-1081.
Chakravarty, Sugato, Robert A. Wood, and Robert A. Van Ness, 2004, “Decimals and Liquidity: A study of the NYSE,” Journal of Financial Research, 27, 75-94.
Chakravarty, Sugato, Venkatesh Panchapagesan, and Robert A. Wood, 2003, “Has decimalization hurt institutional investors? An investigation into trading costs and order routing practices of buy-side institutions,” Working Paper, Purdue University.
Chung, Huimin, Tsung-Wu Ho, and Ling-Ju Wei, 2005, “The dynamic relationship between the prices of ADRs and their underlying stocks: evidence from the threshold vector error correction model,” Applied Economics, 37, 2387-2394.
Dwyer, Jr., G.P., Locke, P., Yu, W., 1996. “Index arbitrage and nonlinear dynamics between the S&P 500 futures and cash,” Review of Financial Studies, 9, 301–
332.
Enders, W. and P. L. Siklos, 2001, “Cointegration and Threshold Adjustment,”
Journal of Business and Economic Statistics, 19, 166-176.
Furfine, Craig H., 2003, “Decimalization and market liquidity,” Economic
Perspectives of Federal Reserve Bank of Chicago, 4, 2-12.
Goldstein, M.A., K.A. Kavajecz, 2000. “Eighths, sixteenths and market depth:
changes in tick size and liquidity provisions on the NYSE,” Journal of
Financial Economics, 56, 125-149.
Hansen, Bruce. E. and Byeongseon Seo, 2002, “Testing for two-regime threshold cointegration in vector error-correction models,” Journal of Econometrics, 110, 293-318.
Harris, Lawrence E., 1994, “Minimum price variations, discrete bid-ask spreads, and quotation sizes,” Review of Financial Studies, 7, 149-178.
Harris, Lawrence E., 1997, “Decimalization: A review of the arguments and evidence,” Working Paper, University of Southern California.
Henker, Thomas and Martin Martens, 2005, “Index futures arbitrage before and after the introduction of sixteenths on the NYSE,” Journal of Empirical Finance, 12, 353-373
Jones, C.M., and M.L. Lipson, 2001. “Sixteenths: direct evidence on institutional execution costs,” Journal of Financial Economics, 59, 253-278.
Mackinlay, A. C. and K. Ramaswamy, 1988, “Index-Futures Arbitrage and the Behavior of Stock Index Futures Prices,” The Review of Financial Studies, 1, 137-158.
Martens, M., P. Kofman, and T.C.F. Vorst, 1998. “A threshold error-correction model for intraday futures and index returns,” Journal of Applied Econometrics, 13, 245-263.
Michael, P., A. R. Nobay, and D. A. Peel, 1997, “Transactions costs and nonlinear adjustment in real exchange rates: an empirical investigation,” Journal of
Political Economy, 105, 862-879.
Neal, R., 1996. “Direct tests of index arbitrage models,” Journal of Financial and
Quantitative Analysis, 31, 541-562.
Stoll, H. R. and R. E. Whaley, 1990, “The Dynamics of Stock Index and Stock Index and Stock Index Futures Returns,” Journal of financial and Quantitative
Analysis, 25, 441-468.
Tsay, R. S., 1998, “Testing and modeling multivariate threshold models,” Journal of
the American Statistical Association, 93, 1188-1202.
Table 1 Comparison of Old and New Tick Size Policy
The table presents the minimum price increment comparison prior to and posterior to the reduction for every price interval on March 1, 2005.
Old policy Before March 1, 2005
New policy After March 1, 2005 Minimum
stock price
Maximum stock price
Tick
Size Minimum
stock price
Maximum stock price
$5 and below $0.01 $10 and below
$5 $15 $0.05 $10 $50
$15 $50 $0.1 $50 $100
$50 $150 $0.5 $100 $500
$150 $1000 $1 $500 $1000
$1000 and above $5 $1000 and above
Table 2 Properties of Index and Futures Returns and the MPE
Sample statistics includes sample mean, standard deviation (S.D.), and autocorrelation (ρ) of index returns, futures returns, and the absolute value of mispricing error (MPE). The data frequency is 5-minute intervals, with the first 30 and the last 10 min of each trading day excluded, leaving 47 observations per day (eliminating January 13, 2005due to TEJ data recording problems). Overnight price changes are excluded. The index and futures are the last index value and futures transaction price prior to or on the 5-minute mark. The MPE is based on the cost-of-carry model using the annualized one-month post office deposit rate as the risk-free rate of interest.
Series Mean(%) S.D.(%) ρ1 ρ2 ρ3 ρ4
Panel A: Before the Reduction of Tick Size (May 3, 2004 - February 25, 2005) index -0.00002 0.00120 0.17254 *** -0.12231 *** -0.09679 *** 0.00576 return (<.0001) (<.0001) (<.0001) (0.5739) futures -0.00001 0.00135 0.03519 *** -0.04222 *** -0.00923 0.01485 return (0.0006) (<.0001) (0.3673) (0.1470) MPE 0.00484 0.00497 0.97477 *** 0.96450 *** 0.95971 *** 0.95530 ***
(<.0001) (<.0001) (<.0001) (<.0001) Panel B: After the Reduction of Tick Size (March 1, 2005 - December 30, 2005) index -0.00002 0.00071 a 0.31747 *** -0.09959 *** -0.14862 *** -0.04110 ***
return (<.0001) (<.0001) (<.0001) (<.0001) futures -0.00001 0.00081 a 0.00867 -0.05246 *** -0.02859 *** -0.00854
return (0.3855) (<.0001) (0.0042) (0.3930)
MPE 0.00333a 0.00318 a 0.98032 *** 0.97002 *** 0.96350 *** 0.95861 ***
(<.0001) (<.0001) (<.0001) (<.0001)
The p-value is showed in the parentheses below each coefficient estimate.
*: the coefficient estimate is statistically significant at 10% level.
**: the coefficient estimate is statistically significant at 5% level.
***: the coefficient estimate is statistically significant at 1% level.
a Indicates that mean or standard deviation in panel (B) is significantly smaller than the corresponding mean or standard deviation in panel (A) at the 1% significance level, respectively.
Table 3 Unit Root Test for Log-Prices of Futures and Underlying Spot
Panel A and Panel B present the results of the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests of futures and spot during two sample periods. Spot represents Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), Futures stands for TAIEX Futures, and *** denotes significance at the 1% level.
Panel A: Before the Reduction of Tick Size (May 3, 2004 - February 25, 2005) Augmented Dickey-Fuller test Phillips-Perron test k=4 Level First Difference Level First difference
Futures -2.2407 -42.8296 *** -2.2742 -94.6834 ***
Spot -2.0284 -44.8171 *** -2.0771 -82.4279 ***
Panel B: After the Reduction of Tick Size (March 1, 2005 - December 30, 2005) Augmented Dickey-Fuller test Phillips-Perron test k=3 Level First Difference Level First difference
Futures -0.9243 -52.2905 *** -0.9587 -99.0363 ***
Spot -1.0257 -51.8933 *** -1.0345 -71.1728 ***
Note: k is the lag length and is chosen by minimum Schwarz Bayesian Information Criterion (SBIC).
Critical values: 1%= -3.434 5%= -2.862 10%= -2.567.
Table 4 Johansen Cointegration Test for Log-Prices of Futures and Underlying Spot
Panel A and Panel B present the results of trace test (Trace) and maximum eigenvalue test (Max-Eign) used to evaluate whether the variables in each respective period are cointegrated during two sample periods. r is the number of cointegrating vectors, * denotes rejection of the hypothesis at the 5% level.
Max-Eigen and Trace are two test statistics under Johansen’s approach, that is,
λ
max andλ
tracerespectively.
Null Hypothesis
Trace Statistic
5 Percent Critical Value
Max-Eigen Statistic
5 Percent Critical Value Panel A: Before the Reduction of Tick Size (May 3, 2004 - February 25, 2005)
r=0 38.6766
* 15.4947 34.4722 * 14.2646r=1
4.2044 * 3.8415 4.2044 * 3.8415Panel B: After the Reduction of Tick Size (March 1, 2005 - December 30, 2005)
r=0 39.0463
* 15.4947 37.8830 * 14.2646r=1
1.1634 3.8415 1.1634 3.8415Table 5 Linear VECM Estimations for Log-Prices of Futures and Underlying Spot
The linear VECM is applied to determine the long-run equilibrium and short-run dynamics between two markets for two periods. Std error indicates Eicker-White standard errors. Schwarz Bayesian Information Criterion (SBIC) determines the optimal lag length. S represents Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), F stands for TAIEX Futures, and EC is the error correction term. *, **, and *** denotes significant rejection of the hypothesis at the 10%, 5%, and 1%
significance level, respectively.
Panel A: Before the Reduction of Tick Size (May 3, 2004 - February 25, 2005)
Dep. ΔFt ΔSt
Ind. Estimate Std error Estimate Std error
EC(wt-1) -0.006095 0.005771 0.005433 0.004407
Constant -0.002067 0.001948 0.001846 0.001489
ΔFt-1 0.013459 0.024874 0.344751 *** 0.024350 ΔFt-2 -0.024618 0.026965 -0.297760 *** 0.022986 ΔFt-3 0.002089 0.024441 0.178521 *** 0.020433 ΔFt-4 -0.043311 0.027151 -0.211223 *** 0.021827 ΔSt-1 0.035073 0.023905 0.102990 *** 0.019846 ΔSt-2 -0.040734 0.026881 -0.117381 *** 0.022092 ΔSt-3 -0.000317 0.023815 0.039103 ** 0.017639 ΔSt-4 0.009781 0.025218 -0.038580 ** 0.019510
AIC --125,002 SBIC -124,962
Cointegrating Vector 1.038860***
Panel B: After the Reduction of Tick Size (March 1, 2005 - December 30, 2005)
Dep. ΔFt ΔSt
Ind. Estimate Std error Estimate Std error
EC(wt-1) -0.007258 *** 0.002382 0.002652 0.002144 Constant -0.002336 *** 0.000770 0.000860 0.000693 ΔFt-1 -0.020466 0.017044 0.262395 *** 0.023332 ΔFt-2 0.040090 ** 0.018470 -0.100863 *** 0.025669 ΔFt-3 0.030867 * 0.018577 0.163832 *** 0.022777 ΔSt-1 -0.081018 *** 0.020520 -0.159828 *** 0.023789 ΔSt-2 0.024244 0.015823 0.082322 *** 0.016841 ΔSt-3 -0.023990 0.016719 -0.074518 *** 0.016144
AIC --141,562 SBIC -141,530
Cointegrating Vector 1.03697***
Table 6 Threshold VECM Estimations for Log-Prices of Futures and Underlying Spot before the Reduction of Tick Size at TSE(May 3, 2004-February 25, 2005)
The threshold VECM is applied to determine threshold effect on the long-run equilibrium and short-run dynamics between two markets before the reduction of tick size. Std error indicates Eicker-White standard errors. Schwarz Bayesian Information Criterion (SBIC) determines the optimal lag length.
S represents Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), F stands for TAIEX Futures, and EC is the error correction term. *, **, and *** denotes significant rejection of the hypothesis at the 10%, 5%, and 1% significance level, respectively.
First Regime: |wt-1| 0.34≦ 7891 Percentage of Obs = 0.159396
Dep. ΔFt ΔSt
Ind. Estimate Std error Estimate Std error
EC(wt-1) -0.061548 0.048113 -0.030680 0.035392
Constant 0.021325 0.016565 0.010539 0.012185
ΔFt-1 0.116192 ** 0.056808 0.336968 *** 0.051529 ΔFt-2 -0.155923 ** 0.066102 -0.306816 *** 0.058421 ΔFt-3 0.029596 0.051302 0.171139 *** 0.038922 ΔFt-4 -0.118747 * 0.069930 -0.280836 *** 0.050378
ΔSt-1 0.069487 0.049682 0.078356 ** 0.037725
ΔSt-2 -0.067445 0.066867 -0.121951 ** 0.050034
ΔSt-3 0.021720 0.053655 0.006932 0.036526
ΔSt-4 0.015154 0.073989 0.028471 0.053958
Second Regime: |wt-1|＞0.347891 Percentage of Obs = 0.840604
Dep. ΔFt ΔSt
Ind. Estimate Std error Estimate Std error
EC(wt-1) 0.008166 *** 0.005789 0.011112 ** 0.004722 Constant -0.002951 *** 0.002082 -0.003981 ** 0.001697 ΔFt-1 -0.022832 0.025150 0.366853 *** 0.022536 ΔFt-2 0.018898 ** 0.027715 -0.310540 *** 0.022479 ΔFt-3 0.013230 * 0.028275 0.212948 *** 0.022476 ΔFt-4 -0.030822 0.028101 -0.210293 *** 0.022738 ΔSt-1 0.030769 *** 0.027363 0.135923 *** 0.022851 ΔSt-2 -0.035558 0.028087 -0.135454 *** 0.024011 ΔSt-3 -0.011124 0.023957 0.059589 *** 0.020041 ΔSt-4 0.011075 0.023196 -0.067512 *** 0.019063
Threshold estimate = 0.347891 Cointegrating Vector = 0.958673;
AIC = -125,042 SBIC = -124,963 Lagrange Multiplier threshold test
Fixed regressor (asymptotic) bootstrap = 44.0753*** (p-value < 0.0001).
Residual bootstrap = 38.4376*** (p-value < 0.0001).
Wald test
Equality of dynamic coefficients = 68.0757*** (p-value < 0.0001).
Equality of EC coefficients = 2.35093 (p-value = 0.308675).
Table 7 Threshold VECM Estimations for Log-Prices of Futures and Underlying Spot after the Reduction of Tick Size at TSE(March 1, 2005-December 30, 2005)
The threshold VECM is applied to determine threshold effect on the long-run equilibrium and short-run dynamics between two markets after the reduction of tick size. Std error indicates Eicker-White standard errors. Schwarz Bayesian Information Criterion (SBIC) determines the optimal lag length.
S represents Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), F stands for TAIEX Futures, and EC is the error correction term. *, **, and *** denotes significant rejection of the hypothesis at the 10%, 5%, and 1% significance level, respectively.
First Regime: |wt-1|≦0.307617 Percentage of Obs = 0.754272
Dep. ΔFt ΔSt
Ind. Estimate Std error Estimate Std error
EC(wt-1) -0.009054 ** 0.003709 -0.001640 0.003281 Constant 0.002767 ** 0.001125 0.000495 0.000994 ΔFt-1 -0.014178 0.018843 0.260894 *** 0.027508 ΔFt-2 0.021899 0.022373 -0.127880 *** 0.030391 ΔFt-3 0.044826 ** 0.019836 0.183949 *** 0.026573 ΔSt-1 -0.101275 *** 0.021890 -0.190072 *** 0.025869 ΔSt-2 0.035083 * 0.018046 0.096491 *** 0.020684 ΔSt-3 -0.026505 0.019338 -0.074313 *** 0.020506
Second Regime: |wt-1|＞0.307617 Percentage of Obs = 0.245728
Dep. ΔFt ΔSt
Ind. Estimate Std error Estimate Std error
EC(wt-1) 0.000008 0.006032 -0.000662 0.005474
Constant -0.000040 0.001881 0.000230 0.001706
ΔFt-1 -0.026894 0.040385 0.288709 *** 0.040929 ΔFt-2 0.085844 *** 0.032192 -0.032528 0.042143 ΔFt-3 -0.005057 0.041419 0.110046 *** 0.039256 ΔSt-1 -0.027249 0.043015 -0.082448 ** 0.043974
ΔSt-2 -0.015277 0.035868 0.023320 0.030155
ΔSt-3 -0.021268 0.034245 -0.084224 *** 0.024544 Threshold estimate = 0.307617 Cointegrating Vector = 0.964937 AIC = -141,557 SBIC = -141,493
Lagrange Multiplier threshold test
Fixed regressor (asymptotic) bootstrap = 42.4844* (p-value = 0.066667).
Residual bootstrap = 37.5842*** (p-value < 0.0001).
Wald test
Equality of dynamic coefficients = 21.9461** (p-value = 0.0381278).
Equality of EC coefficients = 3.13770 (p-value = 0.208284).
Table 8 GARCH Model
The table shows the result of the following GARCH model.
1 table stands for the futures market lagged volatility and the variable stands for the spot market volatility. is the event dummy taking the value one for the period before the reduction of tick size and the value zero for the period after the reduction of tick size.
t
RF, RS,t εF2,t−1
2,t−1
εS
D1
Mean Equation Variance Equation
t
RF, RS,t hF,t hS,t
Constant 0.000007 -0.000008 Constant 0.00000002 *** 0.00000004 ***
(0.1749) (0.1243) (<.0001) (<.0001)
The p-value is showed in the parentheses below each coefficient estimate.
*: the coefficient estimate is statistically significant at 10% level.
**: the coefficient estimate is statistically significant at 5% level.
***: the coefficient estimate is statistically significant at 1% level.
Table 9 Ordinary Least Square (OLS) for Mispricing Errors in the Pre-Reduction of Tick Size Period
reduction
where MPEi,t is the absolute value of percentage mispricing error on day t and intraday period i, while the superscript indicates the minimum price increment at the period, VOLAi,t is the futures volatility in the 30 min prior to every trade at time i in the first regression and GARCH conditional futures volatility at time i in the second regression, BUYi,t is an indicator variable with value one if the arbitrage trade is a buy program and zero otherwise, and SHORTi,t is an indicator variable with value one if the arbitrage trade involved short selling and zero otherwise.
MPE MPE
30-minute futures VOLA 0.72477 (<.0001)
***
Conditional VOLA 1.44625
(<.0001)
The p-value is showed in the parentheses below each coefficient estimate.
*: the coefficient estimate is statistically significant at 10% level.
**: the coefficient estimate is statistically significant at 5% level.
***: the coefficient estimate is statistically significant at 1% level.