The effect of futures trading activity on the distribution of spot market returns

Transcription

1 The effect of futures trading activity on the distribution of spot market returns Manuel Illueca Juan Angel Lafuente Universitat Jaume I INSTITUTO MEFF RISKLAB UAM Madrid, 6 de noviembre de 003

2 Introduction Motivation Objective of the paper Review of the literature Our contribution to the extant literature Data Matching spot and futures volume with spot prices Rolling-over futures contract Trading volume variables Expected and Unexpected components

3 Methodology Estimating spot market volatility conditional to trading volume Empirical results Summary and Concluding Remarks

4 Introduction: motivating the paper Since their introduction, stock index futures markets have experienced a substantial increase in trading activity Financial futures contracts are key instruments in portfolio management as they allow for risk transference (to hedge risky portfolios) The existence of mispricing in traded futures prices relative to the cost-of-carry valuation has been well documented in the literature (see Mackinlay and Ramaswamy 988, Miller et al., (994), Yadav and Pope (990, 994), Bühler and Kempf (995) and Fund and Draper (999), among others)

5 Introduction: motivating the paper However, mispricing generally occurs with spot and futures prices inside the non-profitable arbitrage bounds (see, for example, Lim, 99), and the adjustment in response to pricing error takes place rapidly (see Taylor et al. (000), Dwyer et al. (996), Tse (00) and Chu and Hsieh (00)) Given that spot and futures prices are linked by arbitrage operations, one popular perception is that arbitrage trading activities involving index futures and underlying equities tend to increase stock volatility in the short-run Recent episodes of market crash and volatility contagion among countries did not contribute to mitigate such perception

6 Introduction: motivating the paper Moreover, criticisms of derivative markets argue that lower transaction costs in futures markets attract uninformed speculative order flow, introducing noisy information in the price discovery process (see Cox (976) and Stein (987))

7 Introduction: motivating the paper Transmission of volatility could raise the required rate of return of investors in the market, leading to a misallocation of resources in the economy The alleged increase in volatility has led to many proposals for closer regulation of the derivatives markets Empirical work providing additional insights on the destabilizing hypothesis can be useful in designing regulations

8 Introduction: aim of the paper The main objective of the paper is to analyze the foregoing topic in the Spanish stock index futures market

9 Introduction: literature review Empirical work concerning the relationship between spot volatility and futures trading activity is performed by following two approaches: Event studies: the behavior of spot volatility is analyzed before and after the introduction of the derivative market (Rahman, 00, Chan et al, 999, Antoniou et al., 998, Pericli and Koutmos, 997, and Lee and Ohk, 99, among many others) However, as pointed out by Bessembinder and Seguin (99, Journal of Finance), the potential volatility change ''need not be solely attributable to the introduction of futures'', but also to other changes in the financial environment during the period examined.

10 Introduction: literature review Following those authors, other studies only focus on the behavior of spot volatility after the introduction of the futures market. What about the identification of the potential source of instability in futures trading activity? There is no case for regulating financial futures on the basis of price discovery (William J. Rainer, Chairman of the Commodity Futures Trading Commision, October 8, 999, nd Annual Chicago-Kent College of Law Derivatives) Bessembinder and Seguin (99) suggest to break down total trading volume into expected (informationless) and unexpected components using an ARIMA filter.

11 Introduction: literature review To test the effect of futures trading on spot volatility, empirical work is generally performed using parametric techniques. In particular, two approaches are considered: ) Two-steps procedure: a) Estimation of spot market volatility (Garman- Klass statistic, 987 and related) b) Using VAR methodology to test whether futures trading significantly affects spot volatility ) One-step procedure: GARCH models for spot market volatility that incorporate a variable capturing futures activity

12 Introduction: : literature review Problems related to the extant literature can be summarized as follows: ) Two-steps procedure: empirical results are known to be significantly sensitive to the volatility proxy chosen (see, for example, Kyriacou and Sarno (999) and Board and Sutcliffe (99)) ) One-step procedure: as initially suggested by Lamoureaux and Lastrapes (990), GARCH models adding futures volume to spot variance equation may suffer from simultaneity bias

13 Introduction: : literature review Recently Board et al. (00) illustrate this point with the following example: Assuming that the true generating process of volume and volatility is affected by a latent variable (information arrival, sequential arrival hypothesis) σ = α l + ε t t, t V = β l + ε t t, t α σ = V + ε ε β β t t, t, t

14 Introduction: : literature review Assuming without loss of generality that spot return (R s ) has zero mean, parametric approaches seek to test whether if in: ( ) ( ) E R Volume,R ; j >0 =Φ R ; j >0 +γvolume + ε st ft st-j st- j ft t the coefficient γ is not significant at conventional levels.

15 Introduction : our contribution Rather than just focussing on a single moment of spot return distribution, this paper contributes to the literature by analyzing the effect of futures trading activity on the overall distribution. In particular, a non-parametric approach is considered to: ) estimate the distribution of spot returns conditional to trading volume ) test whether the conditional distribution of spot returns depends on futures trading activity

16 Introduction : our contribution Once the density function of spot returns conditional to trading activity is estimated, the implied moments of spot returns can be computed. This paper provides additional evidence on the destabilizing hypothesis by focussing on spot price volatility.

17 Data Data on the Ibex 35 spot and futures market are provided by MEFF, RV for the period December, 999 to December, 00 5-minute matched spot and futures trading volume from 9:00 to 7:30 hours are considered (futures trading volume refers to the next-to-maturity futures contract) Overall, the data set contains more than 4,000 observations for each variable Spot returns for each 5-minute interval is also computed Overnight returns are removed

18 Rolling over futures contract Ma et al, 99 show that conclusions drawn from empirical tests are not robust to the choice of methods for rolling over When the current contract is roll to the next? 00 Average intraday futures trading volume within time to maturity :5 9:45 0:5 0:45 :5 next maturity :45 :5 :45 3:5 3:45 4:5 4:45 nearest to maturity 5:5 5:45 6:5 6:45 7:5

19 Data: Trading volume variables Constructing volume variables: Spot and futures trading volume are I() variables. Intraday trading interval is partitioned as follows: [9:00-0:00],..., [5:00-6:00], [6:00-7:30] For each hourly interval, a centered moving average with observations is considered to detrend both variables (Fung and Patterson, 999 and Campbell et al., 993) V = t, t N N N j= Trading Volume t, t Trading Volume t + j, t+ j

20 Data: Trading volume variables For each trading hourly interval we decompose the detrended volume into predictable and unpredictable components by using a bivariate Vector Autoregression: Vspot Vspot P t t j = C + Ψ j + Vfutt j= Vfutt j U t Fitted values are interpreted as the informationless trading, while the residuals of the model are interpreted as the innovation in trading activity in each market

21 Data: Trading volume variables Fraudulent financial reporting is detected

22 Methodology: estimating the conditional distribution of spot market returns Conditional spot volatility is computed from the estimated density function of spot returns conditional to trading volume. Two steps are required: ) the joint probability distribution of the bivariate (Returns, Volume) vector is estimated using a kernel estimator (Silverman, 986). T ( ; ) = ( ) f X H K X X where T is the sample size, X i denotes the i-th sample observation and K H is a function involving the Kernel function, K, and the smoothing matrix, H, with the following general form: i= K ( Z ) H = K H Z H H i

23 Methodology: estimating conditional spot market distribution The Epanechnikov kernel function (Epanechnikov, 969), and the plug-in-solve-the-equation estimator suggested by Wand and Jones (994) are used. ) The implied marginal density function of volume is obtained from the bivariate density. 3)The density function of spot returns conditional to spot volume is then computed as the ratio of the bivariate density and the implied marginal density.

24 Methodology: estimating conditional spot market volatility The spot volatility conditional to trading volume (TV) is computed as the conditional variance of spot returns (SR) : + ( ) ( ) [ SV TV ] = SR - E SR TV f SR TV dsr

25 Empirical results THE DISTRIBUTION OF SPOT RETURNS CONDITIONAL TO SPOT TRADING ACTIVITY

26 Density function of spot returns conditional to total spot trading volume 3 pd f spot volume spot return m e u v o l po t s spot return

27 Testing the stochastic independence between spot returns distribution and spot volume distribution Null Hypothesis of stochastic independence between Empirical value P value r Spot Return and Total Spot Volume r r ( Nij Ni N j ).. ~ χ ( r ) NN i.. j = NN i= j= i.. j Sample Size r

28 Empirical results THE DISTRIBUTION OF SPOT RETURNS CONDITIONAL TO SPOT AND FUTURES TRADING ACTIVITY

29 Density function of spot returns conditional to both total spot trading volume and [0-0]-th quantile of total futures trading activity.5 pd f spot volume spot re turn

30 Density function of spot returns conditional to both total spot trading volume and [40-60]-th quantile of total futures trading activity.5 pd f spot volume spot re turn

31 Density function of spot returns conditional to both total spot trading volume and [80-00]-th quantile of total futures trading activity.5 pd f spot volume spot re turn

32 Testing the stochastic independence between conditional spot returns distribution and TOTAL futures volume distribution Null Hypothesis of equality between Empirical value P value r SR STV and SR STV,FTV SR STV and SR STV,FTV SR STV and SR STV,FTV SR STV and SR STV,FTV SR STV and SR STV,FTV r r ( FTV f ) ik TEOik i= k= ik j TEO ~ χ ( r ) TEO ik Nik Sample _ Size = N 5 r i ik

33 Spot Market Volatility conditional to spot volume under different levels of TOTAL futures trading activity spot volatility spot volume percentiles [0-0]-th quantile of TFTV [0-40]-th quantile of TFTV [40-60]-th quantile of TFTV [60-80]-th quantile of TFTV [80-00]-th quantile of TFTV

34 Spot Market Volatility conditional to spot volume under different levels of TOTAL futures trading activity Kolmogorov-Smirnov test: H 0 : F(SR STV,FTV j ) = G(SR STV,FTV j+ ) H : F(SR STV,FTV j )>G(SR STV,FTV j+ ) KS statistic FTV vs FTV *** FTV vs FTV *** FTV 3 vs FTV *** FTV 4 vs FTV * ***,**,* refers to rejection of the null hypothesis at %, 5% or 0% significance level, respectively

35 Density function of spot returns conditional to both total spot trading volume and [0-0]-th quantile of expected total futures trading activity 0.8 pd f spot volume spot re turn

36 Density function of spot returns conditional to both total spot trading volume and [40-60]-th quantile of expected total futures trading activity 0.8 pd f spot volume spot re turn

37 Density function of spot returns conditional to both total spot trading volume and [80-00]-th quantile of expected total futures trading activity 0.8 pd f spot volume spot re turn

38 Testing the stochastic independence between conditional spot returns distribution and EXPECTED futures volume distribution Null Hypothesis of equality between Empirical value P value r SR STV and SR STV,FEV SR STV and SR STV,FEV SR STV and SR STV,FEV SR STV and SR STV,FEV SR STV and SR STV,FEV r r ( FTV f ) ik TEOik i= k= ik j TEO ~ χ ( r ) TEO ik Nik Sample _ Size = N 5 r i ik

39 Spot Market Volatility conditional to spot volume under different levels of EXPECTED futures trading activity spot volatility spot volume percentiles [0-0]-th quantile of EFTV [0-40]-th quantile of EFTV [40-60]-th quantile of EFTV [60-80]-th quantile of EFTV [80-00]-th quantile of EFTV

40 Spot Market Volatility conditional to spot volume under different levels of EXPECTED futures trading activity Kolmogorov-Smirnov test: H 0 : F(SR STV,FEV j ) = G(SR STV,FEV j+ ) H : F(SR STV,FEV j )>G(SR STV,FEV j+ ) KS statistic FEV vs FEV 0.63 FEV vs FEV FEV 3 vs FEV FEV 4 vs FEV Note: in all cases the null hypothesis is not rejected at % significance level

41 Density function of spot returns conditional to both total spot trading volume and [0-0]-th quantile of unexpected total futures trading activity.5 pd f spot volume spot re turn

42 Density function of spot returns conditional to both total spot trading volume and [40-60]-th quantile of unexpected total futures trading activity.5 pd f spot volume spot re turn

43 Density function of spot returns conditional to both total spot trading volume and [80-00]-th quantile of unexpected total futures trading activity.5 pd f spot volume spot re turn

44 Testing the stochastic independence between conditional spot returns distribution and UNEXPECTED futures volume distribution Null Hypothesis of equality between Empirical value P value r SR STV and SR STV,FUV SR STV and SR STV,FUV SR STV and SR STV,FUV SR STV and SR STV,FUV SR STV and SR STV,FUV r r ( FTV f ) ik TEOik i= k= ik j TEO ~ χ ( r ) TEO ik Nik Sample _ Size = N 5 r i ik

45 Spot Market Volatility conditional to spot volume under different levels of UNEXPECTED futures trading activity 6 5 spot volatility [0-0]-th quantile of UFTV [40-60]-th quantile of UFTV [80-00]-th quantile of UFTV spot volume percentiles [0-40]-th quantile of UFTV [60-80]-th quantile of UFTV

46 Spot Market Volatility conditional to spot volume under different levels of UNEXPECTED futures trading activity Kolmogorov-Smirnov test: H 0 : F(SR STV,UTV j ) = G(SR STV,UTV j+ ) H : F(SR STV,UTV j )>G(SR STV,UTV j+ ) KS statistic FUV vs FUV *** FUV vs FUV *** FUV 3 vs FUV *** FUV 4 vs FUV * ***,**,* refers to rejection of the null hypothesis at %, 5% or 0% significance level, respectively

47 Conclusions A positive correlation between spot volatility and spot trading volume is detected This finding is due to the arrival of information (unexpected component) Futures trading is also positively related to conditional spot market volatility However, this transmission of volatility is due to the price discovery role of the futures market Moreover, no significant relationship arises between time to maturity and spot price fluctuations

48 Conclusions Contrary to the traditional view of futures trading, this research provides no empirical support for futures market being a force behind jump spot volatility. The paper suggests that regulatory initiatives to limit futures trading premised on the assumption that futures trading tends to destabilize spot market prices are not justified, at least in the Spanish stock index futures market.

49 Methodology: hypothesis testing To corroborate whether spot volume is a significant variable to explain the distribution of spot returns, we formally test the hypothesis of stochastic independence between both distributions. To do this, each univariate support is partitioned into r equally sized groups, and then joint frequencies are computed. Then, the following non-parametric test is carried out to test the null of independence: ( ) r r Nij Ni N j.. ~ χ i j NN = = i.. j ( r ) with NN = Sample Size r i.. j

50 Methodology: hypothesis testing Note: in this case the support of spot return is partitioned according to the overall sample, while the partition of spot volume is based on the corresponding 0.0 quantile subsample To corroborate whether futures volume is a significant variable to explain the distribution of spot returns conditional to spot volume, the following non-parametric test is applied to each futures volume subsample (FTV j ). r r ( FTV f ) ik TEOik i= k= ik j TEO ~ χ ( r ) with TEO ik Nik Sample _ Size = Nik 5 r i

51 The effect of mini futures contract on the distribution of spot market returns Manuel Illueca Juan Angel Lafuente Universitat Jaume I INSTITUTO MEFF RISKLAB UAM Madrid, 6 de noviembre de 003

52 Data: Trading volume variables For each trading hourly interval we decompose the detrended volume into predictable and unpredictable components by using a trivariate Vector Autoregression: Vspott Vspot P t j Vfut = C + Ψ Vfut + U Vmfut t j t j t j= t Vmfutt j Fitted values are interpreted as the informationless trading, while the residuals of the model are interpreted as the innovation in trading activity in each market

53 Density function of spot returns conditional to both total spot trading volume and [0-5]-th quantile of expected total mini futures trading activity

54 Density function of spot returns conditional to both total spot trading volume and [5-50]-th quantile of expected total mini futures trading activity

55 Density function of spot returns conditional to both total spot trading volume and [50-75]-th quantile of expected total mini futures trading activity

56 Density function of spot returns conditional to both total spot trading volume and [75-00]-th quantile of expected total mini futures trading activity

57 Density function of spot returns conditional to both total spot trading volume and [0-5]-th quantile of unexpected total mini futures trading activity

58 Density function of spot returns conditional to both total spot trading volume and [5-50]-th quantile of unexpected total mini futures trading activity

59 Density function of spot returns conditional to both total spot trading volume and [50-75]-th quantile of unexpected total mini futures trading activity

60 Density function of spot returns conditional to both total spot trading volume and [75-00]-th quantile of unexpected total mini futures trading activity

61 Density function of spot returns conditional to total spot trading volume, unexpected futures trading activity ([0-5]-th quantile) and unexpected mini futures trading activity ([0-50]-th quantile)

62 Density function of spot returns conditional to total spot trading volume, unexpected futures trading activity ([0-5]-th quantile) and unexpected mini futures trading activity ([50-00]-th quantile)

63 Density function of spot returns conditional to total spot trading volume, unexpected futures trading activity ([50-00]-th quantile) and unexpected mini futures trading activity ([0-50]-th quantile)

64 Density function of spot returns conditional to total spot trading volume, unexpected futures trading activity ([50-00]-th quantile) and unexpected mini futures trading activity ([50-00]-th quantile)