# Stock Price Reactions to Merger and Acquisition in India

Mergers and Acquisitions are seen as an important exercise in corporate restructuring. India is emerging as one of the top countries in M&A deals. In an efficient market M&A announcements will have an immediate effect on the stock price of that firm. Investors can earn significant returns during an M&A deal.

Event Study Methodology is used to find the effect of an event on a specific dependent variable. Here the merger or acquisition announcement is an event and the underlying stock price is the dependent variable. The event study will study the change in stock price beyond expectation which we call the abnormal return over a period of time called an event window.

In this project using an event study methodology we measure the abnormal returns (actual – predicted returns) during an event window, on stock prices of selected firms which have undergone an M&A deal. An econometric model is also developed for calculating predicted returns during the event window.

## INTRODUCTION:

Mergers and Acquisitions and Corporate Restructuring are among the key areas of Corporate Finance. Every day investment bankers work on M&A transactions to bring separate companies together and form a larger one. M&A deals often make news. Deals are worth hundreds of thousands or millions or even billions of dollars. They have become popular due to enhanced competition, breaking of trade barriers, free flow of capital across countries and globalization of businesses.

Mergers and acquisitions (M&As) in India surged by 270% in terms of deal value from jan 2011 to march 2011. The deal value came to around $18.31 billion. According to Hong Kong based research agency mergermarket, this is nearly four times of the previous year’s first quarter of $4.94 billion1. Experts believe that this trend is set to continue as healthy firms in India are seeking for more of M&A deals.

“Inbound M&A drove deals in Q1 2011 with India proving itself an attractive investment destination as it lured buyers in the energy, insurance and IT space. Despite the ongoing wave of corporate scandal and political corruption, India will continue to entice suitors on the back of strong fundamentals such as its growing population. Buyers from typical markets such as the US, Europe and Japan could be joined by those from Korea and Russia and deals across borders – consumer, financial services, energy, industrial, engineering and chemicals – will continue. Overseas activity in energy, consumer and IT is also expected to grow.”

– Spokesperson, Mergermarket Asia Pacific

So how does an investor benefit from this? A popular belief is that mergers and acquisitions strengthen businesses by making their operations more synergetic. Announcements of mergers and acquisitions immediately impact a target company’s stock price, as induced reaction in the stock market cause investors to revise expectations about the company’s future profitability2.

1 http://www.indiaincorporated.com/index/item/158-india-on-big-ticket-ma-spree-in-2011.html

2.Panayides and Gong, 2002, The Stock Market Reaction to Merger and Acquisition Announcements in Liner

### Shipping

An event study is a statistical method used to study the impact of a corporate event. In a corporate context, the usefulness of event studies arises from the fact that the magnitude of abnormal performance at the time of an event provides a measure of the unanticipated impact of this type of event on the wealth of the firms’ claimholders3.

Here the corporate event of interest is mergers and acquisitions and its impact on the stock price of the underlying firm is studied. Event studies are frequently used to test market efficiency4. Measurement of Abnormal Returns in an event window is the central focus in an event study. Abnormal Returns is the difference between the Actual returns and Expected returns.

Expected returns during the event window are calculated using the Box Jenkins Methodology, popularly known as the ARIMA Model. Box-Jenkins forecasting models are based on statistical concepts and principles and are able to model a wide spectrum of time series behavior. It has a large class of models to choose from and a systematic approach for identifying the correct model form. There are both statistical tests for verifying model validity and statistical measures of forecast uncertainty.

3. S.P. Kothari and Jerold B. Warner, 2006, Econometrics of Event Studies.

4. Brown and Warner, 1980, Using daily stock returns – The case of event studies

## Objective of the Project:

To Measure the Abnormal Returns on Stock Prices around the Event.

To Develop an Econometric Model in Predicting Abnormal Returns.

To test the hypothesis that investors do not earn any abnormal returns during an event

## Limitations of the Study:

Larger samples are difficult to use because abnormal returns has to be calculated individually. Using all the samples would have made the research more robust.

Various forecasting models are available. We will be sticking to ARIMA model.

Valuation of the firm after a merger or acquisition and its financial performance is out of scope.

## Report Organization:

Section 2 presents the Literature Review on M&A effect. Section 3 starts with a small introduction to mergers, types of mergers, acquisitions and motives of a merger or acquisition. Section 4 explains what an event study analysis is and the steps involved in conducting such a study. A Null and Alternate Hypothesis which needs to be tested is defined. Section 5 briefly outlines the time series analysis. Concept of stationarity, methods to test stationarity, transforming non-stationary time series data to stationary time series data and the Box-Jenkins ARIMA methodology of forecasting the stock returns is presented. Section 6 presents the procedure followed in the statistical tool – E-Views for forecasting the expected returns. Section 7 provides the sample data collected for the analysis. . Section 8 presents the Findings and Analysis. Section 9 presents the conclusion. Section 10 provides the scope for further studies.

## LITERATURE REVIEW:

Isfandiyar Shaheen (2006) in his paper Stock Market Reaction to Acquisition Announcements using an Event Study Approach has determined target firms experience significant positive abnormal returns during an acquisition announcement. The abnormal returns are maximum the day after an event. He has developed a linear regression model in predicting abnormal returns. The event window chosen is 11 days i.e. [-5, +5] and 120 days prior to event is used for estimating the normal returns. The Normal Returns is computed using the market model.

Nikolas Papasyriopoulos’s team have used the event study methodology introduced by Brown and Warner (1985) for six Greek industrial and construction firms. They have measured the abnormal returns on stock prices on the day of the acquisition announcement. Estimation period and event period in their market model is -211 -11 -10, +10 respectively. In order to allow for asymmetric effect of news on the abnormal returns they use an E-GARCH model for period -211,-1. Empirical results show that on day t=0, AAR go slightly positive, while CAAR remain positive (0.4% and 1.3% respectively).

Roland and Henryk in their paper ARIMA modeling of Event Induced Stock Price Reactions in Austria have used an event study to observe impact of corporate announcements on the stock prices. They have used ARIMA time series models in forecasting the normal returns. But they have taken dividend announcement as an event.

Carl B. McGowan, Jr and Zunaidah Sulong in “A Note On The Effect Of M&A Announcements On Stock Price Behavior And Financial Performance Changes: The Case Of Arab Malaysian Bank Berhad And Hong Leong Bank Berhad” examined the effect of M&A announcements on the stock price behavior for two anchor banks in Malaysia. Their analysis uses the event study technique, the Naïve Model, a model that is based on Market Model with constrained α = 0 and β = 1 to compute the abnormal returns surrounding the M&A announcement date and to evaluate the effect of M&A announcement on the banks’ return. The results from event study showed that the M&A completion announcements are treated as positive information by the market.

Panayides and Gong (2002) in The Stock Market Reaction to Merger and Acquisition

Announcements in Liner Shipping studied the stock reaction to M&A announcements in liner shipping. Their event study analysis led to the conclusion that all firms saw their stock price increase rapidly on the announcement of the proposed events, which is long anticipated by the industry.

S.P. Kothari and Jerold B. Warner, 2006 in Econometrics of Event Studies provide an overview of event study methods. They present new evidence illustrating that properties of event study methods can vary by calendar time period and can depend on event sample firm characteristics such as volatility. This reinforces the importance of using stratified samples to examine event study statistical properties.

PengCheng Zhu and Shavin Malhotra , 2008 in Announcement Effect and Price Pressure: An Emperical Study of Cross Border acquisitions by Indian firms examines the short term stock performance of a sample on Indian Firms acquiring US firms in the period 1999-2005. Event Study shows that Indian Stock Market react positively to the acquisition announcement. They find that the positive abnormal returns last only for three days after which the returns become negative.

Arun Kumar Gopalaswamy, Debashis Acharya, Jaideep Malik, 2008 in Stock price reaction to merger announcements: an empirical note on Indian markets investigates the differences in stock price reaction of target and acquiring companies due to merger announcements. The role of insider information before merger announcements is also empirically tested and explained to be the cause for observed pre-announcement price run-ups. The investigation has been carried out using traditional event study methodology. Various event windows have been considered and compared to find out the period where the price run-up initiates. They see an upward trend in cumulative abnormal returns for companies in the pre-announcement period which in turn is indicative of insider information or anticipation. In addition, the evidence also suggests that around the announcement period the returns for the acquiring companies are higher than those for the target companies. In the post amalgamation period there is a downward trend in the cumulative returns implying a negative result of the merger.

## MERGERS AND ACQUISITIONS:

A firm can grow its business either through internal expansion or external expansion. Internal expansion can include adopting new technology, business reengineering, new products, new marketing strategies, etc. External expansion includes mergers and acquisitions. It is the fastest growing option available for the firms5.

M&As in India has grown rapidly after the economic reforms of 1991.In the past few years we have seen major M&A deals like the Tata steel-Corus, Vodafone-Hutch Essar, Hindalco-Novellis, Ranbaxy-Daiichi Sankyo, Tata motors-Jaguar Land Rover6and the very latest which is still running in news is the Cairn-Vedanta deal7.

## Merger:

A merger or amalgamation is a combination of two or more businesses into one business. In a merger all assets and liabilities of the amalgamating companies become assets and liabilities of the amalgamated company. It can be through:

Absorption: Absorption is a combination of two or more companies into an ‘existing company’. All companies except one lose their identity in such a merger.

Consolidation: A consolidation is a combination of two or more companies into a ‘new company’. In this form of merger, all companies are legally dissolved and a new entity is created. Here, the acquired company transfers its assets, liabilities and shares to the acquiring company for cash or exchange of shares.

A fundamental characteristic of merger (either through absorption or consolidation) is that the acquiring company (existing or new) takes over the ownership of other companies and combines their operations with its own operations.

5. http://business.gov.in/growing_business/mergers_acq.php

6. http://business.mapsofindia.com/finance/mergers-acquisitions/mergers-and-acquisitions.html

7. http://www.indiaincorporated.com/maas/item/161-vedanta-grabs-%C2%A3920mn-stake-in-cairn-india.html

There are three major types of mergers:

Horizontal merger: is a combination of two or more firms in the same area of business.

Vertical merger: is a combination of two or more firms involved in different stages of production or distribution of the same product. Vertical merger may take the form of forward or backward merger. When a company combines with the supplier of material, it is called backward merger and when it combines with the customer, it is known as forward merger.

Conglomerate merger: is a combination of firms engaged in unrelated lines of business activity.

## Acquisition:

An acquisition may be defined as an act of acquiring effective control by one company over assets or management of another company without any combination of companies. Thus, in an acquisition two or more companies may remain independent, separate legal entities, but there may be a change in control of the companies. When an acquisition is ‘forced’ or ‘unwilling’, it is called a takeover. When managements of acquiring and target companies mutually and willingly agree for the takeover, it is called acquisition or friendly takeover.

## Why merge or acquire?

Enhancing profitability because a combination of two or more companies may result in more than average profitability due to cost reduction and efficient utilization of resources. It accelerates company’s growth

Economies of scale arise when increase in the volume of production leads to a reduction in the cost of production per unit. This is because, with merger, fixed costs are distributed over a large volume of production causing the unit cost of production to decline.

Operating economies: a combined firm may avoid or reduce over-lapping functions and consolidate its management functions such as manufacturing, marketing, R&D and thus reduce operating costs.

## EVENT STUDY ANALYSIS:

An event study measures the impact of a particular from a firm’s stock price. Events can be anything like:

Dividend announcement

Earnings announcement

New Product Launch

Product Recall

Merger or Acquisition announcement

Change in Management. Etc.,

The event study determines whether there is an abnormal stock price effect associated with an event. From this, we can infer the significance of the event. The key assumption of the event study is that the market must be efficient. So that the effects of the event will be reflected immediately in the stock prices of the company.

Basic Idea: To calculate the Abnormal Return. This gives the impact of an event on Stock Price.

Abnormal Return = Actual return when the event took place –

Normal Return If the Event had not taken place.

## TimeLine:

T0

T1

Event

Estimation Window: To estimate the normal return

Event Window

## Event Study Procedure:

Event Identified: Mergers and Acquisitions.

Event Window: This is the period over which the stock price Abnormal Returns is calculated. The event window is 11 days so as to incorporate the markets ongoing adjustments to the news. Thus the event window is [-5, +5].

Estimation Window: This is the period over which the stock price Normal Returns is calculated. A period of 120 days is adequate since daily returns daily returns data for the 120 days prior to the event date is sufficient in formulating a benchmark for normal returns. Thus the estimation window is [-120, -5].

Model to Estimate Normal Return: Auto Regressive Integrated Moving Average (ARIMA) model to be used in estimating the normal return during the event window.

Abnormal return (AR): Calculate abnormal return using data in the event window. ARi,t = Ri,t – E(Ri,t)

Ri,t = Actual Returns

E (Ri,t) = Expected return on security ‘i’ during time period‘t’.

Cumulative Abnormal returns (CAR): Calculate cumulative abnormal return using the abnormal returns. This measures the impact over a number of days. The cumulative abnormal return for security i is the sum of abnormal returns in an event window time period.

Average Abnormal returns (AAR): The sample average abnormal return at time t,

ARt is the arithmetic mean of n stocks.

Cumulative Average Abnormal returns (CAAR): The cumulative average abnormal average return of CAR from event time t0 to t1 is the sum of ARt from t0 to t1.

## Hypothesis Testing:

Since this study empirically examines stock market reaction to mergers and acquisitions announcement the hypotheses being tested are:

H01: The investors cannot earn abnormal returns by trading in the stocks after the M&A Announcements.

H02: The Average Abnormal Returns and the Cumulative Average Abnormal Returns are close to zero.

The test statistic is simply the ratio of day t average abnormal returns to its estimated standard deviation, where

N-1

Where AR (bar) is the average of the ARs over the period

(N = number of days from t = m until t = n).

where N is the number of days in the CAR statistics.

The null hypotheses that the M&A completion announcement does not have any significant influence of the stocks return (i.e., H0: AR = 0 and CAR = 0) are to be tested at 5 percent significant level. If the AR or CAR is statistically significant, then, the M&A announcement is seen to have an effect on the stock returns8.

8. Carl B. McGowan, Jr and Zunaidah Sulong in “A Note On The Effect Of M&A Announcements On Stock Price Behavior And Financial Performance Changes: The Case Of Arab Malaysian Bank Berhad And Hong Leong Bank Berhad

## TIME SERIES ANALYSIS:

## Concept of Stationarity:

A Random or Stochastic Process is a collection of random variables ordered in time. We call a stochastic process purely random if it has zero mean, constant variance and is serially uncorrelated.

A stochastic process is said to be stationary if its mean and variance are constant over time and the value of the covariance between the two time periods depends only on the distance or gap or lag between the two time periods and not the actual time at which the covariance is computed. If a time series is stationary, its mean, variance, and autocovariance (at various lags) remain the same at any point. They are time invariant.

A non-stationary time series will have a time varying mean and/or variance. If a time series is non-stationary, we can study its behavior only for the time period under consideration. So it is not possible to generalize it to other time periods. Therefore, for the purpose of forecasting, non-stationary time series will be of no value.

Stock prices follow a Random Walk Model (RMW) i.e. they are non stationary.

To estimate the normal returns in the event window, the following should be taken care:

Test for the stationarity of data.

Transform the non- stationary data into stationary.

Use ARIMA model to estimate the stock prices and thereby calculate the returns during the event window.

## Tests for Stationarity:

Autocorrelation Function (ACF) and Correlogram.

Unit Root Test – Dickey-Fuller Test & Augmented Dickey-Fuller Test

## The above tests can be carried out using the statistical package E-Views.

## Transforming Non Stationary Time Series:

Difference-Stationary Processes: If a time series has a unit root, the first differences of such time series are stationary. So take the first differences of the time series.

## Forecasting Model:

## An Autoregressive (AR) Process:

If we model Yt as (Yt − δ) = α (Yt −1 − δ) + ut

Where δ is the mean of Y and where ut is an uncorrelated random error term with zero mean and constant variance σ2 (i.e. white noise), then we say that Yt follows a first-order autoregressive or AR (1) stochastic process. This model says that the forecast value of Y at time t is simply some proportion α of its value at time (t − 1) plus a random shock.

In general, we can have

(Yt − δ) = α1 (Yt −1 − δ) + α2(Yt −2 − δ) + ·· ·+αp(Yt −p − δ) + ut

In which case Yt is a pth-order autoregressive or AR (p) process

A Moving Average (MA) Process

Suppose we model Y as follows:

Yt = μ + β0ut + β1ut−1

Where μ is a constant white noise stochastic error term. Here Y at time t is equal to a constant plus a moving average of the current and past error terms. We say that Y follows a first-order moving average, or an MA (1), process.

More generally,

Yt = μ + β0ut + β1ut −1 + β2ut−2 + ·· ·+βqut−q is an MA (q) process.

In short, a moving average process is simply a linear combination of white noise error terms.

### An Autoregressive and Moving Average (ARMA) Process:

If Y has characteristics of both AR and MA then it is ARMA. Thus Yt follows an ARMA(1, 1) process if it can be written as:

Yt = θ + α1 Yt −1 + β0ut + β1ut−1

There is one autoregressive and one moving average term. θ represents a constant term.

In general, in an ARMA ( p, q) process, there will be p autoregressive and q moving average terms.

### An Autoregressive Integrated Moving Average (ARIMA) Process:

The mean and variance for a weakly stationary time series are constant and its covariance is time-invariant. If the time series are non-stationary then they are integrated.

If a time series is integrated of order 1 I(1), its first differences are I(0) is stationary. Similarly, if a time series is I(2), its second difference is I(0). In general, if a time series is I(d), after differencing it d times we obtain an I(0) series. Therefore, if we have to difference a time series d times to make it stationary and then apply the ARMA (p, q) model to it. We say that the original time series is ARIMA(p, d, q), that is, it is an Auto Regressive Integrated Moving Average time series, where p denotes the number of autoregressive terms, d the number of times the series has to be differenced before it becomes stationary, and q the number of moving average terms.

### The Box–Jenkins (BJ) ARIMA Methodology:

The Box-Jenkins approach consists of extracting the predictable movements (pattern) from the observed data through a series of iterations. One first tries to identify a possible model from a general class of linear models. The chosen model is then checked against the historical data to see if it accurately describes the underlying process that generates the series. The model fits well if the differences between the original data and the forecasts are small, independent, and random. If the specified model is not satisfactory, the process is repeated by using another model designed to improve the original one. The process is repeated until a satisfactory model is found.

The BJ methodology helps in identifying the type of process the time series follows i.e. whether it is an AR or MA or ARMA or ARIMA process. The objective of BJ methodology is to identify and estimate a statistical model which can be used for forecasting.

It consists of the following steps:

## Identification of the model:

There are two phases to the identification of an appropriate Box-Jenkins model:

Changing the data, if necessary, into a stationary time series and

Determining the tentative model by analyzing the autocorrelation and partial autocorrelation functions.

The autocorrelation coefficient measures the relationship, or correlation, between a set of observation’s and a lagged set of observations in a time series. Given the time series (Z1, Z2, Z3, …., Zn), the autocorrelation between Zt, and Zt+k (denoted by k) measures the correlation between the pairs (Z1, Z1+k), (Z2, Z2+k), (Z3, Z3+k), .… ,(Zn, Zn+k).

The sample autocorrelation coefficient (rk) is an estimate of k. When the sample autocorrelation coefficients are computed for lag 1, lag 2, lag 3, and so on and are graphed (rk versus k), the result is usually called the sample autocorrelation function (ACF) or a correlogram. This graph is useful both in determining whether or not a series is stationary and in identifying a tentative ARIMA model.

A partial correlation coefficient is the measure of the relationship between two variables when the effect of other variables has been removed or held constant. The partial autocorrelation coefficient (kk) is the measure of the relationship between the stationary time-series variables Zt and Zt+k when the effect of the intervening variables Zt+1, Zt+2,…., Zt+k has been removed. This adjustment is made to see if the correlation between Zt and Zt+k is due to the intervening variables or if there is something else causing the relationship.

## Type of Model

### Typical pattern of ACF

### Typical pattern of PACF

### AR(p)

Decays exponentially or with damped sine wave pattern or both

Significant spikes through lags p

### MA(q)

Significant spikes through lags q

Declines exponentially

### ARMA(p, q)

Exponential decay

Exponential decay

Since we are considering the stock returns which are already stationary we need not again take the first difference. So the models developed in our case can be ARMA but not ARIMA.

Parameter estimation of the chosen model:

In the estimation step, we first compute initial estimates for the parameters of the tentative model and then allow the computer program to generate the final estimates by an iterative process.

Diagnostic Checking :

Here we check if the estimated residuals are white noise. After the equation of the tentative model has been derived, diagnostic checks are performed to test the adequacy and closeness of fit of the model to the data. We do this by running tests on the residuals () and by testing the significance and relationships of the parameters.

If the residuals are truly random, the autocorrelations and partial autocorrelations calculated using the residuals should be statistically equal to zero. If they are not, this is an indication that we have not fitted the correct model to the data. When this is the case, the residual ACF and PACF will contain information about which alternate models to consider.

Forecasting:

Once the appropriate model has been found, it can be integrated (trend introduced into the

model) and future forecasts can be found.

### The above tests can be carried out using the statistical package E-Views as explained in the following section.

## FORECASTING USING EVIEWS:

Let me consider an example ACC Limited for forecasting stock returns.

### Step 1: File -> Open -> Foreign data as workfile

file open.bmp

### Step 2: Open the returns file from the workfile window. From the returns screen select view for graph, descriptive statistics and tests, Correlogram and Unit Root Test.

retruns.bmp

### Step 3:

unit root test.bmp

In the test type select Augmented Dickey Fuller and click on OK. If the data is not stationary we select the 1st difference or second difference to convert to stationary time series data.

### Step 4:

The NULL Hypothesis states that Returns has a unit root, meaning the data the non stationary. From the ADF test statistic, since the t-value is statistically significant at 1%, 5% and 10% levels we reject the null hypothesis and say the data is stationary.

2. ADF.bmp

### Step 5:

The coefficient values in the correlogram are zero or near zero within 95% confidence limits. This shows that the return series is stationary.

3. corrof ret.bmp

### Step 6: Select Quick -> Estimate Equation for estimating the equation.

estimate eqn.bmp

eqn specification.bmp

In the specification window write the equation in the form:

dependent_variable c ar(p) ma(q) : for an ARMA process.

dependent_variable c ar(p) : for an AR process.

dependent_variable c ma(q) : for an MA process.

Provide the sample data for estimation. We have 131 data points’ i.e. 120 data points of estimation window. 5 days of pre-estimation window. 1 day of deal date and 5 days of post-estimation window. We will choose 110 data points for estimating the equation and to forecast for the remaining 11 data points.

4. arma22eqn.bmp

At 5% level the Prob value shows that AR(2) and MA(2) are significant.

The criterions to judge for the best model are as follows:

Relatively small of Schwarz criterion

Relatively small of Standard Error of Regression

Relatively high adjust R2

Q- statistics and correlogram show that there is no significant pattern left in the ACFs and PACFs of the residuals, it means the residuals of the selected model are white noise.

Step 7:

From the equation window select View->Residual Tests-> Correlogram-Q-statistics

corr of resid.bmp

5. corr of resid.bmp

The correlogram of residuals show that there is no significant pattern in the ACFs and PACFs of the residuals, it means the residuals of the selected model are white noise. We can stop at here and don’t need to further consider another AR (p) and MA (q).

## Model Selection Process in Box Jenkins Methodology:

ARMA (1, 0)..??

ARMA (2, 0)..??

ARMA (1, 1)..??

ARMA (2, 1)..??

ARMA (0, 1)..??

ARMA (3, 0)

ARMA (2, 2)

ARMA (3, 2)

ARMA (1, 2)

ARMA (0, 2)

In General:

ARMA (n, n – 1)

ARMA (n-1, n-1)

ARMA (n, 0)

ARMA (n-2, n-1)

ARMA (0, n-1)

### Step 8: From the correlogram of residuals click on forecast to get the forecast window.

forecat.bmp

Change the forecast sample to those data points which you want to forecast. Since I have 131 data points and I have used 110 data points for estimation, I need to forecast for the remaining samples from 111 to 131.

If you select dynamic forecasting, EViews will perform a multi-step forecast of Y, beginning at the start of the forecast sample. The initial observation in the forecast sample will use the actual value of lagged Y. Forecasts for subsequent observations will use the previously forecasted values of Y

Static forecasting performs a series of one-step ahead forecasts of the dependent variable. For each observation in the forecast sample, EViews computes always using the actual value of the lagged variable.

EViews provides us with statistics, with which the quality of different forecasts can be compared. The Theil Inequality Coefficient is an indicator of the quality of forecasts.

The Bias Proportion indicates to what extent the forecasts deviate systematically from the level of observation. A low value shows that this unsatisfactory feature of the model is not very important.

The Variance Proportion indicates whether the variability of forecasts deviates from the variability of the data. In the case of dynamic forecasts this proportion is usually high, because forecasts tend to be constant.

The Covariance Proportion is a measu

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