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This is an econometric study of noise in the financial markets, based on the Indian stock market. Historically, the role & impact of noise traders in the financial markets has been assumed to be minimal or negligible since noise traders should lose money when trading against rational arbitrageurs. However, Shiller et al. [1] argue that there is little reason to believe that noise traders are unimportant and some reason to suspect that rational arbitrageurs dominate the financial markets. Moreover, De Long et al. [2] have developed formal models that allow for the survival of noise traders. Like any other systematic risk, the risk brought in by the noise traders, due to their random sentiments, should be priced. In this paper, we propose an “opening noise trading model” in which the opening price of the stock contains a component of noise that is assumed to be orthogonal to the true price change caused by the arrival of new information. We also provide evidence of the opening stock price containing noise on an everyday basis among all the Nifty stocks. Furthermore, we have shown how to estimate the share of noise in the opening price.

This paper is an econometric study of opening noise in the financial markets, based on the Indian stock market. An “opening noise trading model” (which is an unobserved-components model) is proposed in this paper in which the opening stock price contains a component of noise that is assumed to be orthogonal to the true price change caused by the arrival of information. Within the framework of [

“Noise traders” are those market participants who trade in the security market without considering the use of finance fundamentals, follow trends, exhibit poor market timing, and tend to underreact or overreact to bad and good news. Noise traders play a very significant role in the literature of finance. The AFA presidential address of [

Two strands of the literature emerged in the 1980s which partially tried to explain this confusion and thereby the term “noise traders” has been given very different interpretation by both. The terms “noise traders” and “liquidity traders” are used interchangeably in the market microstructure literature by researchers to describe traders who do not possess any fundamental information (see e.g., [

It is reasonable to conjecture that traders who simply have a taste for trading or who trade due to psychological biases might behave differently from those who are motivated by liquidity shocks or hedging. In his presidential address, Fisher Black was careful to differentiate between these two types of traders, stating that “People who usually trade on noise are indulged in trading even though from an objective point of view they would be better off not trading. Perhaps the most obvious reason could be that they think the noise they are trading on is information. Or perhaps they just like to trade”.

In this paper, we seek to clarify the market impact and role of noise traders especially in India’s emerging stock market at the individual stock level. More specifically, we aim to quantify the proportion of noise in the opening stock price on daily basis. To provide a sketch of our main empirical results, the new Noise Trading Model reports the maximum of 57% noise share in the opening price and the minimum of 27%. In other words, noise that is accumulated during the non-trading hours plays a significant role in the opening of the day. This implies that the informed traders in the Indian stock market can be more vulnerable to the noise at the beginning of the trading day. The current paper makes two important contributions to the existing literature on noise trading. The first is that this is the first empirical model to quantify the share of noise in the opening price. Second, the paper has significant implications for investors, portfolio managers, and traders as the stock-market participants are the first to benefit. Therefore, the traders can carefully plan their trading strategies by taking into account the opening noise in their respective econometric models.

The remainder of the paper is organized as follows. Section 2 briefs out the literature. Section 3 introduces the model. In Section 4, we describe the data used and discuss the empirical findings. Finally, Section 5 offers the concluding remarks and directions for future research.

Trading takes place when a particular asset is being assigned different values by different market agents/participants. Following [

Kyle [

Previous empirical studies exploring the behavior of the stock price at the opening of the day, includes [

Let P t o be the opening price and P t c the closing price of a stock on day t. Now, let’s define the total return into two components, overnight return (ONR) and the daytime return (DTR). In other words, the close to close return is the sum of day time return and the overnight return.

C C R t = ln ( P t c / P t − 1 c ) (1)

D T R t = ln ( P t c / P t o ) (2)

O N R t = ln ( P t o / P t − 1 c ) (3)

where C C R t , D T R t and O N R t are the close to close return, daytime return and overnight return, respectively. We assume that the news released during the trading day related to both the individual firm and the market is incorporated in the closing price, in keeping with [

Let’s denote the overnight true price change on day t by T O N R t , the true price change during the trading day t by T D T R t and the opening noise on day t by ON. We assume henceforth that T O N R t , T D T R t and ON are uncorrelated with one another for a given day t and also that they are uncorrelated across days. In other words, we assume that there is no noise in the closing stock price and, therefore as implication the close-to-close return is uncorrelated over time.

Moreover, our goal is to better understand the behavior of noise in stock prices in the Indian market, we propose the following unobserved components model defined as follows:

C C R t = T D T R t + T O N R t (4)

O N R t = T O N R t + O N (5)

D T R t = T D T R t − O N (6)

From Equation (4), we have

V a r ( C C R t ) = V a r ( T D T R t ) + V a r ( T O N R t ) (7)

From Equation (5), we have

V a r ( O N R t ) = V a r ( T O N R t ) + V a r ( O N t ) (8)

Similarly, from Equation (6), we have

V a r ( D T R t ) = V a r ( T D T R t ) + V a r ( O N t ) (9)

Solving for these three equations, we get

V a r ( T O N R t ) = [ V a r ( C C R t ) + V a r ( O N R t ) − V a r ( D T R t ) ] 2 (10)

V a r ( T D T R t ) = [ V a r ( C C R t ) + V a r ( D T R t ) − V a r ( O N R t ) ] 2 (11)

V a r ( O N t ) = [ V a r ( O N R t ) + V a r ( D T R t ) − V a r ( C C R t ) ] 2 (12)

Let’s have look at the β from a regression of the close-to-close return (CCR) on the overnight return (ONR):

C C R t = α + β ∗ O N R t + error term ,

where

β = C o v ( C C R t , O N R t ) σ O N R t 2

Now, since C C R t = D T R t + O N R t , we have that:

β = C o v ( O N R t , D T R t ) + C o v ( O N R t , O N R t ) σ O N R t 2

β = C o v ( O N R t , D T R t ) σ O N R t 2 + 1

Also,

C o v ( O N R t , D T R t ) = C o v ( T O N R t + O N , T D T R t − O N ) = − σ O N 2

Combining these two, we have

β = 1 − σ O N 2 σ O N R t 2

1 − β = σ O N 2 σ O N R t 2 (13)

The ratio in the RHS of the equation gives us the ratio of the variance of the noise in the opening price to that of the overnight return. If we can estimate the earlier regression and find the values of ( 1 − β ) it will give us the proportion of variance in the opening price due to noise, what we briefly call the noise share in the opening price.

Our data consists of the constituents of the S&P CNX Nifty index from January 2000 to May 2016.

Daily opening, high, low, and closing (OHLC) prices are used for the empirical analysis. The total data points are 2988. The missing data is replaced by the average of the previous five days. The Nifty 50 Index is a well-diversified index, consisting of fifty liquid stocks from 22 sectors. NSE500 index data for the same time frame is also used for comparison. The Bloomberg was used to extract the open, high, low and close stock prices.

In

This pattern of the mean of ONR being positive while the mean of DTR being negative is true at the level of the individual companies as well, with a few exceptions, such as Bharat Heavy Electricals Ltd, Bajaj Auto and HDFC whose DTR has a positive mean, as reported in

Now we turn to the estimation of the noise share in the opening price, with the summary of our estimates reported in

μ | Σ | |||||
---|---|---|---|---|---|---|

ONR_{t} | DTR_{t} | CCR_{t} | ONR_{t} | DTR_{t} | CCR_{t} | |

Min | −0.13% | −0.42% | −0.06% | 1.00% | 1.89% | 1.73% |

Max | 0.53% | 0.21% | 0.13% | 2.38% | 3.22% | 3.24% |

Mean | 0.20% | −0.14% | 0.06% | 1.53% | 2.57% | 2.51% |

S.D. | 0.10% | 0.11% | 0.04% | 0.29% | 0.37% | 0.40% |

N | 2988 | 2988 | 2988 | 2988 | 2988 | 2988 |

Noise Share | |
---|---|

Min | 26.99% |

Max | 95.03% |

Mean | 56.74% |

S.D. | 12.95% |

Var (TDTR)/Var (TONR) | Var (ON)/Var (TDTR) | Var (ON)/Var (TONR) | |
---|---|---|---|

NIFTY | 18.982 | 0.001 | 0.0319 |

NSE500 | 3.442 | 0.021 | 0.074 |

as compared to the contribution of the variance of opening noise to TDTR (0.001), which implies that the opening noise diminishes as it reaches the closing of the trading day.

In this paper, we have proposed a new model for capturing the opening noise. We also have provided the evidence that opening stock price contains noise on an everyday basis among all the Nifty companies. The two broad implications of noise are:

• Noise allows for speculative trading to occur.

• Noise is an indicator of the market inefficiency.

Because people disagree about the future, they trade speculatively thereby making different predictions about the commodity prices and the fate of companies, including other economic variables. These disagreements among investors stem from the fact that every investor interprets data or information subjectively and differently. But since all the world’s markets are complex, not all of the market data is “information”. The problem of discerning the real information from the noise stems from the fact that many of the daily fluctuations we see in the market are random rather than any meaningful trends. This is the reason why trading happens in the market; because it is a zero-sum game, if every person knew everything then no speculative trade would occur. In the real life we observe that trades occur as a kind of bet on what is noise and what is information, and generally, the technologically advanced and the more skillful gambler wins.

Noise is everywhere in the market and people make it all the time. Black argues that the econometrics is filled with noise in the form of mismeasurements and unobservables. It doesn’t matter that how many variables you put in a model; there are always many more variables to add and the variables you have will always have an error. This is how noise manifests in econometrics. The researchers can build upon this and demonstrate how to profit from the market inefficiency the noise creates.

For the purpose of practicing quant, our study finds contribution in suggesting a trading strategy based on the overnight return (ONR). Based on our study, we suggest that the traders in the Indian stock market shorten the stock at the beginning of the day and lengthen the same stock at the end of the day when the overnight return (ONR) is positive, and when the ONR is negative, buy at the beginning and sell at the end. Despite its simplicity, this trading strategy is highly profitable, because the market is inefficient, due to the significant presence of noise at the opening.

The authors declare no conflicts of interest regarding the publication of this paper.

Zargar, F.N. and Kumar, D. (2019) Opening Noise in the Indian Stock Market: Analysis at Individual Stock Level. Theoretical Economics Letters, 9, 21-32. https://doi.org/10.4236/tel.2019.91003

Μ | σ | |||||
---|---|---|---|---|---|---|

ONR | DTR | CCR | ONR | DTR | CCR | |

ACC IS Equity | 0.167% | −0.124% | 0.044% | 1.260% | 2.460% | 2.328% |

ACEM IS Equity | 0.186% | −0.145% | 0.041% | 1.348% | 2.399% | 2.305% |

ADSEZ IS Equity | 0.187% | −0.187% | 0.000% | 1.521% | 2.979% | 2.904% |

APNT IS Equity | 0.109% | −0.009% | 0.101% | 1.536% | 2.099% | 1.732% |

ARBP IS Equity | 0.319% | −0.243% | 0.076% | 1.671% | 3.010% | 2.928% |

AXSB IS Equity | 0.529% | −0.417% | 0.112% | 2.206% | 3.210% | 2.948% |

BHARTI IS Equity | 0.321% | −0.241% | 0.079% | 1.452% | 2.533% | 2.468% |

BHEL IS Equity | 0.211% | −0.169% | 0.042% | 1.278% | 2.630% | 2.716% |

BHIN IS Equity | −0.132% | 0.208% | 0.081% | 1.594% | 2.590% | 2.289% |

BJAUT IS Equity | 0.078% | 0.031% | 0.111% | 1.316% | 2.186% | 2.088% |

BOB IS Equity | 0.241% | −0.184% | 0.057% | 1.855% | 2.976% | 2.858% |

BOS IS Equity | 0.202% | −0.108% | 0.093% | 1.662% | 2.088% | 1.876% |

BPCL IS Equity | 0.215% | −0.158% | 0.058% | 1.560% | 2.785% | 2.718% |

CIPLA IS Equity | 0.222% | −0.189% | 0.034% | 1.389% | 2.214% | 2.093% |

COAL IS Equity | 0.059% | −0.071% | −0.012% | 1.005% | 1.891% | 1.887% |

DRRD IS Equity | 0.186% | −0.192% | −0.006% | 2.084% | 2.280% | 2.682% |

EIM IS Equity | 0.309% | −0.180% | 0.129% | 2.375% | 3.178% | 2.877% |

GAIL IS Equity | 0.417% | −0.328% | 0.088% | 1.618% | 2.625% | 2.450% |

GRASIM IS Equity | 0.057% | 0.007% | 0.064% | 1.211% | 2.291% | 2.216% |

HCLT IS Equity | 0.310% | −0.367% | −0.058% | 1.752% | 3.220% | 3.241% |

HDFC IS Equity | 0.072% | 0.053% | 0.125% | 1.283% | 2.344% | 2.346% |

HDFCB IS Equity | 0.121% | −0.034% | 0.086% | 1.349% | 2.176% | 2.123% |

HMCL IS Equity | 0.106% | −0.044% | 0.062% | 1.369% | 2.358% | 2.244% |

HNDL IS Equity | 0.155% | −0.147% | 0.008% | 1.700% | 2.856% | 2.721% |

HUVR IS Equity | 0.135% | −0.103% | 0.032% | 1.053% | 2.033% | 1.994% |

ICICIBC IS Equity | 0.237% | −0.168% | 0.069% | 1.772% | 2.816% | 2.903% |

IDEA IS Equity | 0.165% | −0.152% | 0.013% | 1.379% | 2.747% | 2.651% |

IIB IS Equity | 0.355% | −0.267% | 0.088% | 1.919% | 3.196% | 3.101% |

INFO IS Equity | 0.099% | −0.061% | 0.038% | 1.492% | 2.404% | 2.556% |

ITC IS Equity | 0.139% | −0.073% | 0.066% | 1.105% | 2.088% | 2.016% |

KMB IS Equity | 0.261% | −0.158% | 0.103% | 2.055% | 3.175% | 3.160% |

LPC IS Equity | 0.355% | −0.271% | 0.084% | 1.912% | 2.839% | 2.670% |

LT IS Equity | 0.243% | −0.189% | 0.054% | 1.263% | 2.435% | 2.529% |

MM IS Equity | 0.205% | −0.146% | 0.058% | 1.424% | 2.614% | 2.627% |

MSIL IS Equity | 0.131% | −0.031% | 0.100% | 1.345% | 2.389% | 2.242% |
---|---|---|---|---|---|---|

NTPC IS Equity | 0.163% | −0.140% | 0.022% | 1.091% | 2.008% | 1.976% |

ONGC IS Equity | 0.199% | −0.156% | 0.043% | 1.440% | 2.402% | 2.341% |

PWGR IS Equity | 0.111% | −0.092% | 0.019% | 1.372% | 2.125% | 2.017% |

RIL IS Equity | 0.195% | −0.130% | 0.065% | 1.455% | 2.281% | 2.300% |

SBIN IS Equity | 0.204% | −0.152% | 0.052% | 1.289% | 2.374% | 2.387% |

SUNP IS Equity | 0.155% | −0.058% | 0.098% | 1.637% | 2.465% | 2.288% |

TATA IS Equity | 0.257% | −0.226% | 0.032% | 1.930% | 2.843% | 3.038% |

TCS IS Equity | 0.183% | −0.102% | 0.080% | 1.212% | 2.040% | 2.048% |

TECHM IS Equity | 0.228% | −0.171% | 0.056% | 1.539% | 2.835% | 2.722% |

TPWR IS Equity | 0.229% | −0.173% | 0.056% | 1.390% | 2.627% | 2.606% |

TTMT IS Equity | 0.227% | −0.167% | 0.060% | 1.535% | 2.770% | 2.833% |

UTCEM IS Equity | 0.178% | −0.091% | 0.087% | 1.520% | 2.380% | 2.177% |

WIPRO IS Equity | 0.168% | −0.150% | 0.018% | 1.661% | 2.840% | 2.918% |

YES IS Equity | 0.249% | −0.144% | 0.105% | 1.639% | 3.025% | 3.039% |

Noise Share | |
---|---|

ACC IS Equity | 0.69889151 |

ACEM IS Equity | 0.95034648 |

ADSEZ IS Equity | 0.69550231 |

APNT IS Equity | 0.79773095 |

ARBP IS Equity | 0.58776031 |

AXSB IS Equity | 0.66546243 |

BHARTI IS Equity | 0.57675429 |

BHEL IS Equity | 0.36001389 |

BHIN IS Equity | 0.78860927 |

BJAUT IS Equity | 0.62091395 |

BOB IS Equity | 0.59975337 |

BOS IS Equity | 0.65257791 |

BPCL IS Equity | 0.57614297 |

CIPLA IS Equity | 0.63557508 |

COAL IS Equity | 0.50818609 |

DRRD IS Equity | 0.26988735 |

EIM IS Equity | 0.66145242 |

GAIL IS Equity | 0.66936981 |

GRASIM IS Equity | 0.61454726 |

HCLT IS Equity | 0.47783780 |
---|---|

HDFC IS Equity | 0.49683572 |

HDFCB IS Equity | 0.56328682 |

HMCL IS Equity | 0.64023000 |

HNDL IS Equity | 0.63075601 |

HUVR IS Equity | 0.57008818 |

ICICIBC IS Equity | 0.42109029 |

IDEA IS Equity | 0.63542615 |

IIB IS Equity | 0.58160237 |

INFO IS Equity | 0.33002558 |

ITC IS Equity | 0.62169547 |

KMB IS Equity | 0.51098980 |

LPC IS Equity | 0.62697504 |

LT IS Equity | 0.35343761 |

MM IS Equity | 0.48322757 |

MSIL IS Equity | 0.68803893 |

NTPC IS Equity | 0.55368482 |

ONGC IS Equity | 0.57020473 |

PWGR IS Equity | 0.61852222 |

RIL IS Equity | 0.47935338 |

SBIN IS Equity | 0.48148091 |

SUNP IS Equity | 0.65682504 |

TATA IS Equity | 0.34650794 |

TCS IS Equity | 0.48862340 |

TECHM IS Equity | 0.63269124 |

TPWR IS Equity | 0.52766931 |

TTMT IS Equity | 0.42501196 |

UTCEM IS Equity | 0.70066368 |

WIPRO IS Equity | 0.41790085 |

YES IS Equity | 0.48386644 |