Skip to main content
SpringerLink
Log in

When noise trading fades, volatility rises

  • Original Research
  • Published:
Review of Quantitative Finance and Accounting Aims and scope Submit manuscript

Abstract

We hypothesize and test an inverse relation between liquidity and price volatility derived from microstructure theory. Two important facets of liquidity trading are examined: volume and noisiness. As represented by the expected turnover rate (volume) and realized average commission cost per share (noisiness) of NYSE equity trading, both facets are found negatively associated with the ex post and ex ante return volatilities of the NYSE stock portfolios and the NYSE composite index futures. Furthermore, the inverse association between noisiness and volatility is amplified in times of market crisis. The negative noisiness–volatility relation is also supported by our analysis on the effects of trade size on price volatility. The overall results demonstrate that volatility increases as noise trading declines.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. Noise in the sense of a large number of small events is often a causal factor much more powerful than a small number of large events can be (Black 1986). The terms “noise trading” and “liquidity trading” are used interchangeably in the market microstructure literature. We use “noise trading” to emphasize the nosiness and “liquidity trading” to emphasize the volume of liquidity.

  2. This view is consistent with the work of Huang and Wang (2009), which postulates that endogenous illiquidity can lead to market crashes in the absence of any aggregate shocks.

  3. Shleifer and Summers (1990) discuss arbitrage limits and conclude that “news alone does not move stock prices; uninformed changes in demand move them too.” Irrational noise traders with erroneous stochastic beliefs may affect prices and earn higher expected returns (De Long et al. 1990). In the presence of heterogeneous beliefs, Daigler and Wiley (1999) and Shalen (1993) have found that uninformed trading may cause price volatility.

  4. Brennan and Subrahmanyam (1996) combine diverse empirical techniques from asset pricing and market microstructure research to study this relation. They find the microstructure parameters of market depth and illiquidity to be related to stock return premia. They relate illiquidity to adverse selection costs, which are costs associated with the discovery of private information that are paid by liquidity traders.

  5. Johnson (2008) provides a model in which the equilibrium price-response measure of liquidity reflects the average risk-bearing capacity of the economy and volume reflects the changing contribution of individuals to that average. In that model, volume and liquidity are unrelated but jointly determined.

  6. By AIC and BIC, an AR(1) process with a time drift is adequate to fit the logarithm quarterly turnover rate.

  7. French et al. (1987) use one lagged cross-variance in Eq. (2) and make no adjustment for the mean return. We also estimate the quarterly volatility following their method. The estimates following French et al. (1987) are all positive and very close to the estimates in Eq. (2). The empirical analysis using the French et al. estimates of quarterly volatility is consistent with the analysis using the estimates in Eq. (2). For brevity, we do not report the analysis using the French et al. estimates.

  8. According to Eq. (3), the association between \(\widetilde{{\Delta {\text{ACR}}_{\text{t}} }}\) and quarterly volatility (variance) can be written as \(\sigma_{\text{t}}^{2} = \exp \left( {2\varphi_{1} \cdot \widetilde{{\Delta {\text{ACR}}_{\text{t}} }} } \right) \cdot \exp \left[ {2\left( {\mu + \sum\nolimits_{{{\text{m}} = 2}}^{\text{M}} {\varphi_{\text{m}} \cdot {\text{f}}_{{{\text{m}},{\text{t}}}} + \frac{{1 - \theta {\text{L}}}}{{1 - \rho {\text{L}}}}\varepsilon_{\text{t}} } } \right)} \right]\), where \({\text{f}}_{{{\text{m}},{\text{t}}}}\) refers to the explanatory variables in addition to \(\widetilde{{\Delta {\text{ACR}}_{\text{t}} }}\). The marginal proportion of the volatility that is explained by \(\widetilde{{\Delta {\text{ACR}}_{\text{t}} }}\) is \(\exp \left( {2\varphi_{1} \cdot \widetilde{{\Delta {\text{ACR}}_{\text{t}} }} } \right) - 1\).

  9. We also run the regressions with restrictions of the GARCH parameters and yield essentially identical results.

  10. In the following reported GARCH regressions, we include the MA term. We also run the GARCH regressions without this MA term, and yield qualitatively similar results.

  11. It is well known that the residual series in the GARCH process is strictly stationary with finite second moment provided α + β < 1 (see Tsay 2005: page 14). Engle and Rangel (2008: page 1191) explicitly point out that when α+β<1 , the conditional variance reverts to its mean value at a geometric rate of α + β.

  12. \(\widetilde{{\Delta {\text{ACR}}_{\text{t}} }}\) is related to the variance of daily stock price returns in the following way: \(\sigma_{i,t}^{2} = \exp \left( {\varphi_{1} \cdot \widetilde{{\Delta {\text{ACR}}_{\text{t}} }} } \right) \cdot \exp \left( {m + \sum\nolimits_{n = 2}^{N} {\varphi_{n} \cdot f_{n,t} } } \right) \cdot h_{i,t}\), where \(\varphi_{n}\) (n = 1 to N) denotes the coefficient of \(\widetilde{{\Delta {\text{ACR}}_{\text{t}} }}\) or other corresponding liquidity variables in the regressions. The marginal (proportional) effect of \(\widetilde{{\Delta {\text{ACR}}_{\text{t}} }}\) on return variance is thus \({ \exp }(\varphi_{1} \cdot \widetilde{{\Delta {\text{ACR}}_{\text{t}} }}) - 1\).

  13. This paper focuses on “micro” liquidity (trading volume and transaction costs), while the government often refers to “macro” liquidity (money supply in general or fund flows between asset sectors).

  14. Jones (2002) reports a similar estimate.

  15. Report that brokers charge a per-share commission to institutional traders as a convenient way of charging a predetermined fixed fee for broker services.

  16. We use the 30 DJIA component companies as of the beginning of 2004. They are 3 M, Alcoa, Altria Group, American Express, AT&T, Boeing, Caterpillar, Citigroup, Du Pont, Eastman Kodak, EXXON Mobil, General Electric, General Motors, Hewlett–Packard, Home Depot, Honeywell International, Intel, IBM, International Paper, Johnson & Johnson, J. P. Morgan Chase, Coca-Cola, McDonald’s, Merck, Microsoft Corporation, Proctor & Gamble, SBC Communications, United Technologies, Wal-Mart Stores, and Walt Disney. AT&T, International Paper, and Eastman Kodak were subsequently replaced by AIG, Pfizer, and Verizon on April 8, 2004. However, AIG was later removed from the index on September 22, 2008.

  17. NYSE TAQ databank traces back to the beginning of 1993.

References

  • Admati AR, Pfleiderer P (1988) A theory of intraday patterns: volume and price variability. Rev Financ Stud 1:3–40

    Article  Google Scholar 

  • Amihud Y (2002) Illiquidity and stock returns: cross-section and time-series effects. J Financ Mark 5:31–56

    Article  Google Scholar 

  • Amihud Y, Mendelson H (1986) Asset pricing and the bid-ask spread. J Financ Econ 17:223–249

    Article  Google Scholar 

  • Amihud Y, Mendelson H, Lauterbach B (1997) Market microstructure and securities values: evidence from the Tel Aviv Stock Exchange. J Financ Econ 45:365–390

    Article  Google Scholar 

  • Andersen TG, Bollerslev T (1997) Heterogeneous information arrivals and return volatility dynamics: uncovering the long run in high-frequency returns. J Finance 52:975–1005

    Article  Google Scholar 

  • Bae K, Karolyi GA, Stulz RM (2003) A new approach to measuring financial contagion. Rev Financ Stud 16:717–763

    Article  Google Scholar 

  • Bailey W, Jagtiani J (1994) Foreign ownership restrictions and stock prices in the Thai capital market. J Financ Econ 36:57–87

    Article  Google Scholar 

  • Barber BM, Odean T (2000) Trading is hazardous to your wealth: the common stock investment performance of individual investors. J Finance 55:773–806

    Article  Google Scholar 

  • Barber BM, Odean T (2008) All that glitters: the effect of attention and news on the buying behavior of individual and institutional investors. Rev Financ Stud 21:785–818

    Article  Google Scholar 

  • Barclay M, Warner J (1993) Stealth trading and volatility: which trades move prices. J Financ Econ 34:281–305

    Article  Google Scholar 

  • Bekaert G, Harvey G, Lundblad C (2007) Liquidity of emerging markets: lessons from emerging markets. Rev Financ Stud 20:1783–1831

    Article  Google Scholar 

  • Berkman H, Eleswarapu V (1998) Short-term traders and liquidity: a test using Bombay Stock Exchange data. J Financ Econ 47:339–355

    Article  Google Scholar 

  • Berkowitz SA, Logue DE, Noser EA (1988) The total cost of transactions on the NYSE. J Finance 43:97–112

    Article  Google Scholar 

  • Bessembinder H, Seguin PJ (1992) Futures trading activity and stock price volatility. J Finance 47:2015–2034

    Article  Google Scholar 

  • Bessembinder H, Seguin PJ (1993) Price volatility, trading volume, and market depth: evidence from futures markets. J Financ Quant Anal 28:21–39

    Article  Google Scholar 

  • Bhar R, Malliaris A (1998) Volume and volatility in foreign currency futures markets. Rev Quant Financ Account 10:285–302

    Article  Google Scholar 

  • Black F (1986) Noise. J Finance 41:529–543

    Article  Google Scholar 

  • Bloomfield R, O’Hara M, Saar G (2009) How noise trading affects markets: an experimental analysis. Rev Financ Stud 22:2275–2302

    Article  Google Scholar 

  • Bollerslev T (1987) A conditionally heteroskedastic time-series model for speculation prices and rates of return. Rev Econ Stat 69:542–547

    Article  Google Scholar 

  • Box GEP, Pierce DA (1970) Distribution of residual autocorrelations in autoregressive-integrated moving average time-series models. J Am Stat Assoc 65:1509–1526

    Article  Google Scholar 

  • Brennan MJ, Subrahmanyam A (1996) Market microstructure and asset pricing: on the compensation for illiquidity in stock returns. J Financ Econ 41:441–464

    Article  Google Scholar 

  • Brennan MJ, Subrahmanyam A (1998) The determinants of average trade size. J Bus 71:1–25

    Article  Google Scholar 

  • Campbell JY, Grossman SJ, Wang J (1993) Trading volume and serial correlation in stock returns. Q J Econ 108:905–939

    Article  Google Scholar 

  • Chakravarty S (2001) Stealth-trading: Which traders’ trades move stock prices? J Financ Econ 61:289–307

    Article  Google Scholar 

  • Chan K, Fong W (2000) Trade size, order imbalance, and the volatility–volume relation. J Financ Econ 57:247–273

    Article  Google Scholar 

  • Chiang TC, Doong S (2001) Empirical analysis of stock returns and volatility: evidence from seven Asian stock markets based on TAR-GARCH model. Rev Quant Financ Account 17:301–318

    Article  Google Scholar 

  • Chordia T, Roll R, Subrahmanyam A (2000) Commonality in liquidity. J Financ Econ 56:3–28

    Article  Google Scholar 

  • Chordia T, Subrahmanyam A, Anshuman VR (2001) Trading activity and expected stock returns. J Financ Econ 59:3–32

    Article  Google Scholar 

  • Chordia T, Sarkar A, Subrahmanyam A (2005) An empirical analysis of stock and bond market liquidity. Rev Financ Stud 18:85–129

    Article  Google Scholar 

  • Daigler RT, Wiley MK (1999) The impact of trader type on the futures volatility–volume relation. J Finance 54:2297–2316

    Article  Google Scholar 

  • Datar VT, Naik NY, Radcliffe R (1998) Liquidity and stock returns: an alternative test. J Financ Mark 1:203–219

    Article  Google Scholar 

  • De Long JB, Shleifer A, Summers LH, Waldmann RJ (1990) Noise trader risk in financial markets. J Polit Econ 98:703–738

    Article  Google Scholar 

  • Duffie D, Pedersen LH, Singleton KJ (2003) Modeling sovereign yield spreads: a case study of Russian debt. J Finance 58:119–159

    Article  Google Scholar 

  • Dungey M, Renée F, González-Hermosillo B, Martin V (2006) Contagion in international bond markets during the Russian and the LTCM crises. J Financ Stab 2:1–27

    Article  Google Scholar 

  • Easley D, Kiefer NM, O’Hara M, Paperman JB (1996) Liquidity, information, and infrequently traded stocks. J Finance 51:1405–1436

    Article  Google Scholar 

  • Easley D, Kiefer NM, O’Hara M (1997) One day in the life of a very common stock. Rev Financ Stud 10:805–835

    Article  Google Scholar 

  • Engle RF, Rangel JG (2008) The spline-GARCH model for low-frequency volatility and its global macroeconomic causes. Rev Financ Stud 21:1187–1222

    Article  Google Scholar 

  • Epps TW, Epps ML (1976) The stochastic dependence of security price changes and transaction volumes: implications for the mixture-of-distributions hypothesis. Econometrica 44:305–321

    Article  Google Scholar 

  • Evans MDD, Lyons RK (2002) Time varying liquidity in foreign exchange. J Monet Econ 49:1025–1051

    Article  Google Scholar 

  • Forbes KJ, Rigobon R (2002) No contagion, only interdependence: measuring stock market comovements. J Finance 57:2223–2261

    Article  Google Scholar 

  • French KR, Schwert GW, Stambaugh RF (1987) Expected stock returns and volatility. J Financ Econ 19:3–29

    Article  Google Scholar 

  • Gallant AG, Rossi PE, Tauchen G (1992) Stock prices and volume. Rev Financ Stud 5:199–242

    Article  Google Scholar 

  • Glosten LR, Milgrom PR (1985) Bid, ask, and transaction prices in a specialist market with heterogeneously informed traders. J Financ Econ 14:71–100

    Article  Google Scholar 

  • Hamao Y, Masulis R, Ng V (1990) Correlations in price changes and volatility across international stock markets. Rev Financ Stud 3:281–307

    Article  Google Scholar 

  • Harris L (1986) A transaction data study of weekly and intradaily patterns in stock returns. J Financ Econ 16:99–117

    Article  Google Scholar 

  • Harris M, Raviv A (1993) Differences of opinion make a horse race. Rev Financ Stud 6:473–506

    Article  Google Scholar 

  • Huang J, Wang J (2009) Liquidity and market crashes. Rev Financ Stud 22:2607–2643

    Article  Google Scholar 

  • Huang C, Lin T, Yu C, Hoe S (2006) Volatility–volume relationships among types of traders considering the investment limitation to foreign investors. Rev Pac Basin Financ Mark Polic 9:575–596

    Article  Google Scholar 

  • Hvidkjaer S (2006) A trade-based analysis of momentum. Rev Financ Stud 19:457–491

    Article  Google Scholar 

  • Hvidkjaer S (2008) Small trades and the cross-section of stock returns. Rev Financ Stud 21:457–491

    Article  Google Scholar 

  • Jain PC, Joh G (1988) The dependence between hourly prices and trading volume. J Financ Quant Anal 23:269–283

    Article  Google Scholar 

  • Johnson TC (2008) Volume, liquidity, and liquidity risk. J Financ Econ 87:388–417

    Article  Google Scholar 

  • Jones CM (2002) A century of stock market liquidity and trading costs. Working paper, Columbia University

  • Jones CM, Lipson ML (2001) Sixteenths: direct evidence on institutional execution costs. J Financ Econ 59:253–278

    Article  Google Scholar 

  • Jones CM, Kaul G, Lipson ML (1994) Transactions, volume and volatility. Rev Financ Stud 7:631–651

    Article  Google Scholar 

  • Karpoff JM (1987) The relation between price changes and trading volume: a survey. J Financ Quant Anal 22:109–126

    Article  Google Scholar 

  • Keim DB, Madhavan A (1997) Transactions costs and investment style: an inter-exchange analysis of institutional equity trades. J Financ Econ 46:293–319

    Article  Google Scholar 

  • King MA, Wadhwani S (1990) Transmission of volatility between stock markets. Rev Financ Stud 3:5–33

    Article  Google Scholar 

  • Kyle AS (1985) Continuous auctions and insider trading. Econometrica 53:1315–1335

    Article  Google Scholar 

  • Lamoureux CG, Lastrapes WD (1990) Heteroskedasticity in stock return data: volume versus GARCH effects. J Finance 45:221–229

    Article  Google Scholar 

  • Lesmond DA (2005) Liquidity of emerging markets. J Financ Econ 77:411–452

    Article  Google Scholar 

  • Levine R, Schmukler SL (2007) Migration, spillovers, and trade diversion: the impact of internationalization on domestic stock market activity. J Bank Finance 31:1595–1612

    Article  Google Scholar 

  • Li J, Wu C (2006) Daily return volatility, bid-ask spreads and information flow: analyzing the information content of volume. J Bus 79:2697–2739

    Article  Google Scholar 

  • Madhavan A (1995) Consolidation, fragmentation, and the disclosure of trading information. Rev Financ Stud 8:579–603

    Article  Google Scholar 

  • O’Hara M (1995) Market microstructure theory. Blackwell Publishers, Cambridge

    Google Scholar 

  • Odean T (1998) Are investors reluctant to realize their losses? J Finance 53:1775–1798

    Article  Google Scholar 

  • Odean T (1999) Do investors trade too much? Am Econ Rev 89:1279–1298

    Article  Google Scholar 

  • Pagano M (1989) Endogenous market thinness and stock price volatility. Rev Econ Stud 56:269–288

    Article  Google Scholar 

  • Pástor L, Stambaugh RF (2003) Liquidity risk and expected stock returns. J Polit Econ 111:642–685

    Article  Google Scholar 

  • Rahman S, Lee CF, Ang KP (2002) Intraday return volatility process: evidence from NASDAQ stocks. Rev Quant Financ Account 19:155–180

    Article  Google Scholar 

  • Roll R (1983) On computing mean returns and the small firm premium. J Financ Econ 12:371–386

    Article  Google Scholar 

  • Rouwenhorst G (1999) Local factors and turnover in emerging markets. J Finance 54:1439–1464

    Article  Google Scholar 

  • Sadka R (2006) Momentum and post-earnings-announcement drift anomalies: the role of liquidity risk. J Financ Econ 80:309–349

    Article  Google Scholar 

  • Schwert GW (1989) Why does stock market volatility change over time? J Finance 44:1115–1153

    Article  Google Scholar 

  • Shalen CT (1993) Volume, volatility and the dispersion of beliefs. Rev Financ Stud 6:405–434

    Article  Google Scholar 

  • Shleifer A, Summers LH (1990) The noise trader approach to finance. J Econ Perspect 4:19–33

    Article  Google Scholar 

  • Tauchen GE, Pitts M (1983) The price variability–volume relation on speculative markets. Econometrica 51:485–505

    Article  Google Scholar 

  • Tsay RS (2005) Analysis of financial time series. Wiley, Hoboken

    Book  Google Scholar 

  • Wu C, Xu EX (2000) Return volatility, trading imbalance and the information content of volume. Rev Quant Financ Account 14:131–153

    Article  Google Scholar 

Download references

Acknowledgments

The author wishes to thank C.F. Lee (Editor) and two anonymous referees for helpful comments, M. Nimalendran, Jeffrey Pontiff, and Jiang Wang for helpful discussions, and Charles Bartlett from SIFMA for providing and explaining part of the data. The financial support from National Science Foundation of China for research project#71,273,150 is gratefully acknowledged.

Author information

Authors and Affiliations

  1. School of Economics and Management, Tsinghua University, Beijing, 100084, China

    Jinliang Li

Authors
  1. Jinliang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinliang Li.

Appendices

Appendix 1: Average commission rate

SIFMA derives the exchange commission revenues of NYSE member brokers from the Security Exchange Commissions’ Financial and Operational Combined Uniform Single (FOCUS) Report regulatory filings. Initiated in 1980, the SIFMA databank is the sole source for quarterly reporting on the US securities industry financials. We track the time-series data of exchange commission revenues, which is the total quarterly commission income of all NYSE member brokers resulting from exchange equity transactions.

Our primary interest is in the average commission rate of NYSE trading. To derive this rate, we need to identify the trading volume that contributes to this commission revenue. Because NYSE members trade for their own accounts, not all NYSE share volume contributes to the exchange commission. On a monthly basis, NYSE discloses share and dollar volumes on the exchange, and total member purchases and sales. Total member volume consists of specialists’ purchases and sales, purchases and sales of non-specialists originating on the floor, and purchases and sales of non-specialists originating off the floor. We aggregate the NYSE member purchases and sales into a quarterly measure. We then subtract the sum of quarterly member purchases and sales from two times the quarterly NYSE share volume. This contributing volume is then used to scale the quarterly equity commission revenue to obtain the one-way average commission rate per share as follows:

$${\text{ACR}}_{\text{t}} = \frac{{{\text{NYSE}}\,\,{\text{Member}}\,\,{\text{Brokers}}'\,\,{\text{Exchange}}\,\,{\text{Equity}}\,\,{\text{Commissions}}}}{{2 \times {\text{NYSE}}\,\,{\text{Share}}\,\,{\text{Volume}} - {\text{NYSE}}\,\,{\text{Member}}\,\,{\text{Purchases}}\,\,{\text{and}}\,\,{\text{Sales}}}} .$$
(10)

Since some previous studies report commission costs relative to price, we estimate the percentage ACRt by scaling ACRt with the average trade price:

$${\text{Percentage ACR}}_{\text{t}} = \frac{{{\text{ACR}}_{\text{t}} }}{\text{Average Trade Price for time t}} \times 100$$
(11)

The average trade price is calculated as the ratio of dollar volume and share volume, which are reported by the NYSE on a quarterly basis.

Appendix 2: Validity check of ACR

Several prior studies have estimated institutional commission rates for sporadic time spots, and these estimates are consistent with ours for matched time spots. For instance, Berkowitz et al. (1988) estimate the institutional commission costs of NYSE trading in 1985 to be 0.18 %, as compared to our average commission rate estimate of 0.31 %. Keim and Madhavan (1997) find an average institutional commission rate of 0.20 % of trades during the period of January 1991 through March 1993, as compared to our estimate of the average commission rate of 0.24 % for the same period. Jones and Lipson (2001) find the average institutional commission rate of NYSE trades to be 0.119 % in the second and third quarters of 1997, which coincides with our estimate of the average commission rate of 0.119 % for the same period.Footnote 14 Note that the aforementioned researchers’ estimates of commission costs are based on their samples of NYSE institutional trades in different time spans, while our estimate of the average commission rate is for all NYSE trades. The above studies together with our research suggest that retail commission rates have declined more than institutional commission rates and that by 1997 both rates became similar in size.

Commissions vary over time and are not a constant proportion of stock price (see Jones 2002 for a complete survey of the history of commission regulation in the US). Per-share commissions are the dominant form of payment between brokers and their institutional clients. The negotiated rate per share charged to institutional investors depends on trade size and the research provided by the broker.Footnote 15 Commission rates charged to retail traders differ across brokers, while discount brokerages allow lower commission with less research service. For instance, per-trade commission is charged for Internet trades by online discount brokers. For both institutional and retail traders, trade size is inversely related to the realized commission rate. The latter reflects the composition of small trades in total trading volume. A higher realized commission per share reflects the presence of more small trades.

In order to check this contention, we estimate the proportion of small trades in total trades of the Dow Jones Industrial Average (DIJA) stocks using trade data from NYSE TAQ (Trade and Quote) databank. We follow the approach of Barclay and Warner (1993) and Chan and Fong (2000) in defining orders with less than 500 shares as small trades. We then calculate the ratio of the number of small trades to total trades for each day. The daily result is aggregated into a quarterly measure for each stock, and then the cross-sectional average of all 30 Dow stocks is estimated.Footnote 16 For the period 1993–2005,Footnote 17 the quarterly average small trade ratio is 0.608 with a standard deviation of 0.034. Its correlation with ACR is 71.8 %, and 50.3 % with the logarithmic ACR. Both correlations are significant at the 1 % level. This strong correlation lends support to our notion of ACR as a proxy of trading noisiness.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J. When noise trading fades, volatility rises. Rev Quant Finan Acc 47, 475–512 (2016). https://doi.org/10.1007/s11156-015-0508-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11156-015-0508-2

Keywords

JEL Classification

Search

Navigation