The impact of the Ameritrade Online Investor Index on the autocorrelations and cross-correlations of market returns.

Willey, Thomas

ABSTRACT

This paper investigates the value of the information contained in the Ameritrade Online Investors Index (AOII) for the returns of two exchange traded funds. The AOII measures the buying and selling decisions for a group of online investors. The returns of the funds for the Nasdaq 100 and the S&P Mid-Cap 400 are examined using the quartiles of the Index. Overall, results show no influence on the returns from a broad market index and a negative impact from the lagged value of the return of the given fund. An investment strategy is suggested that incorporates short-selling when low values of the AOII are found in conjunction with negative returns of a given asset.

INTRODUCTION

The predictability of market returns is a topic of great interest to practitioners and financial researchers. If financial markets are truly efficient and follow a random-walk process, the cost of developing a forecast of future returns is an unrecoverable investment of time, energy and resources. At the other end of the efficiency spectrum, perhaps the future return on a market portfolio of securities is somehow linked to readily available public information and some degree of predictability is attainable. In this paper, the daily returns for two exchange traded funds, the first for the Nasdaq 100 (Ticker: QQQ) and the second for the Standard & Poor's Mid-Cap 400 (Ticker: MDY), are examined to measure the role an index of online investors play in determining future market returns.

The explosive growth of the Internet and online trading, in conjunction with vast amounts of financial information, are some of the major forces that shape individual investor decision making today. Recent papers by Miller (1988), Lakonishok and Maberly (1990) and Abraham and Ikenberry (1994) investigated the way investors use information in making investment choices. Their central conclusions are that there are certain time periods where it is more costly to process and use information in buying and selling choices for investors. More specifically, Abraham and Ikenberry state that increased costs to process information exist during the work week and this result leads to increased selling and lower returns of securities on Mondays. The benefits and costs of information processing by online traders are one of the primary research questions for this study.

Chordia and Swaminathan (2000) employed autocorrelations and cross-correlations and found that returns on stocks with high trading volume can be used to predict returns of low trading volume stocks, regardless of the size of the firm. This paper uses a methodology implemented by Perfect and Peterson (1997) and Higgins, Howton and Perfect (2000) by investigating the autocorrelations and cross-correlations in the returns of two exchange traded funds (ETFs) for two major market indices. While the two previous articles investigated the returns of an asset on a given day of the week, this research looks at the role a given level of buying and selling by online investors play in determining market returns. The daily autocorrelations of the QQQ will be examined first, followed by the daily cross-correlations between the QQQ and the ETF for the broader market index of the S&P 500. For comparison purposes, similar results are provided for the MDY. Finally, the relative strengths of the two statistical measures will be estimated jointly to determine if the lagged returns of a given security or the cross-correlations dominate the most recent return of the examined stock.

DATA

One of the major online brokerage firms, Ameritrade, has began to publish the Ameritrade Online Investor Index (AOII), a daily measure of the amount of buyer participation based on a decisions made by the firm's online investors (Ameritrade Press Release, 12/1/1999). On every trading day, after the U.S. markets have closed, Ameritrade posts the Ameritrade Index page on the Internet. One of the stated goals of the index is to measure the individual investment decisions of online investment individuals. The AOII is presented as the percent of online traders that were buyers, and is found by dividing the number of buyers of equities by the sum of buyers and sellers of equities. For the initial day of the study, the AOII was reported as 37.68%, which indicated approximately 38% of all buyers and sellers would have been buying stocks and the remaining 62% would have been selling equities. The study period for the AOII data begins on February 1, 2000 and ends on September 22, 2000, a total of one hundred and sixty-four daily returns. The maximum value for the AOII of 89.03% and therefore, the strongest bull sentiment for the study period was April 12. The strongest bearish value for the index of 12.27% was on May 30, which indicates that approximately 86% of online investors were selling securities on that day.

On the whole, online investors were net purchasers of securities with a median value of 51.94% for the AOII. The total observations for the sample period were further divided into quartiles to facilitate the use of indicator variables to represent the online buyer's purchasing sentiments. The first quartile, from the minimum of 12.27% to 39.51%, represented the selling sentiment of the study, while the fourth quartile, which ranged from 67.48% to the maximum of 89.03%, can be thought of as the buying segment of the sample period.

The data for the market returns was derived from three exchange-traded funds (ETFs) or index tracking stocks. These securities are a relatively new innovation for the financial markets, first introduced in 1995, but have gained a great amount of popularity in recent years. According to the Wall Street Journal (January 29, 2001), the astronomical compound growth rate in ETFs was about 118%, from $6.8 billion in 1997 an estimated $70 billion at year-end 2000. These assets are traded on the American Stock Exchange and have become some of the most active issues traded there. The most widely held and most active issues for the 2000 trading year were the Nasdaq 100 tracking index, known as the Cube and the mirror of the S&P 500, referred to as Spiders (ticker symbol SPY). The Cube's trading volume for 2000 was $6,973.8 million, trailed by $1,932.7 for the SPY. A related ETF that tracks the S&P Mid-Cap 400 Index was chosen as a comparison index to the QQQ. For the entire year of 2000, the return on the MDY was 16.3% (with a volume of $212.4 million) versus annual returns of --36.2% and --10.7% for the Cube and the Spider, respectively. The primary focus of the analysis will be for the returns of the QQQ. For comparison purposes, the MDY returns will be examined separately, while the percentage change in the SPY will be used as the market return for both examined securities.

METHODOLOGY

The data analysis begins by examining the daily returns for ETFs for the Nasdaq 100, the S&P Mid-Cap 400 and the S&P 500 Stock Index. Results for the hypothesis test for the mean return differing from zero are also reported. After the initial analysis of daily returns, the examination of daily autocorrelations follows by estimating regression equations for each security (Higgins and Peterson (1999)). The autocorrelations are analyzed for patterns in the four trading quartiles for the QQQ returns and the MDY comparison returns.

Daily dummy variables are used to segment the values of the AOII into four quartiles based on the proportion of the online investor's buying percentage. Daily returns for each index tracking security are regressed on the daily dummy variables and the lagged daily returns using the following equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Where: [R.sub.t] = Daily returns for the sample at time t; [R.sub.t-1] = Daily returns for the sample at time t-1; [Q.sub.1t], [Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] = Dummy variables for the quartiles of the AOII; and [e.sub.t] = a random error term.

Equation 1 was estimated separately for the QQQ and the MDY securities. The model does not include an intercept and uses a dummy variable for each quartile of the AOII index to control for differences in daily average returns that may lead to spurious autocorrelations (Higgins, Howton and Perfect (2000)). In the first equation, the beta coefficients estimate daily autocorrelation terms. The Newey and West (1987) correction for autocorrelation and heteroskedasticity in the residual terms was used to estimate the first-order autocorrelations.

The existence of cross-correlations between a broad market index, the SPY, and the QQQ index are also examined. To test this relationship, Equation 2 will be estimated by regressing daily QQQ returns on the AOII dummy variables and the lagged market returns:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Where: [R.sub.qqq,t] = Daily returns for QQQ security at time t; [R.sub.spy,t-1] = Daily returns for SPY security at time t-1; [Q.sub.1t], [Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] = Dummy variables for the quartiles of the AOII; and [e.sub.t] = a random error term.

The Newey and West (1987) correction was applied to the second equation and the gamma coefficients measure the daily cross-correlations. For comparison purposes, the daily cross-correlations were also estimated for the MDY security.

A final set of regression equations are estimated to measure which of the two hypothesized daily effects, autocorrelations or cross-correlations, exhibit a stronger influence on the returns of the examined securities. If the autocorrelations dominate the cross-correlations, the current returns are shaped to a greater degree by the most recent return of the security. On the other hand, conditions in the broader market would be more valuable to investors, if the cross-correlations showed a higher amount of influence relative to the autocorrelations. Equation 3 is used to measure the relative influences of the daily autocorrelations and cross-correlations on the QQQ returns:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Where: [R.sub.qqq,t] = Daily returns for QQQ security at time t; [R.sub.qqq,t-1] = Daily returns for QQQ security at time t-1; [R.sub.spy,t-1] = Daily returns for SPY security at time t-1; [Q.sub.1t], [Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] = Dummy variables for the quartiles of the AOII; and et = a random error term.

The returns on the MDY security are also examined using Equation 3 by regressing the current return on the first lags of the security's return and the broad market return of the SPY index shares. As in the previous two equations, the Newey and West (1987) correction is used to guard against potential biases in the estimates. The beta coefficients estimate the daily autocorrelations and the gamma values are measuring the cross-correlations with the SPY security. Three separate hypothesis tests will be performed to determine if the intercepts, autocorrelations and crosscorrelations are jointly equal to zero.

RESULTS

Table 1 contains the statistical characteristics for the average daily percent returns for the QQQ series, the matching MDY returns and the SPY index. All of the returns are positive and statistically different from zero on days when the AOII fell in the first quartile. This is somewhat unexpected, since the values for the online investors buying decisions in this quartile represent trading days where only a 12 % to a maximum of 40% were buying and the remaining 88% to 60% were selling. Also, during the most active buying period of the fourth quartile, when the online traders were purchasing stocks 67% to 89% of the time, the returns for each of the three assets were negative and statistically significant. Based on this initial analysis, online investors do not appear to be able to generate returns that differ from zero, instead the buying signals are associated with drops in the market and decisions to sell correspond to positive returns.

The daily autocorrelation values are presented in Table 2. Section A contains the autocorrelation values for the QQQ security, the autocorrelations for the MDY matching sample are in Section B and the results for the SPY are shown in Section C. None of the autocorrelation terms are statistically significant for the broad market index of the SPY exchange traded fund. For the QQQ and the MDY returns, both of the first quartile autocorrelations are negative and statistically significant. In comparing the QQQ to the MDY, the returns for the QQQ indicate a stronger negative relationship than the returns for the MDY. Also, the autocorrelations for the second and fourth quartiles for the QQQ are negative and statistically different from zero. The joint null hypothesis that all of the coefficients are zero is rejected with a p-values of less than 5% for both the QQQ and the MDY.

In order to investigate the possibility that online investors are incorporating other market information into their investing decisions, the daily cross-correlations between the QQQ and SPY securities are presented in Section A of Table 3. Section B contains a similar analysis for the MDY and the broader market index security. For the QQQ, evidence exists that online investors are reacting negatively to other market conditions. The cross-correlations for the first and second quartiles are both statistically different from zero. This result follows the findings for the autocorrelations, with once again the strongest negative coefficient found for the first quartile. Based on the hypothesis test results, the daily cross-correlations are not equal to each other. No statistically significant cross-correlations were found for the MDY.

The final examination of the quartiles of the online investor's decisions is presented in Table 4. The results for the autocorrelations and cross-correlations for QQQ are shown in Section A, while Section B has the results for the MDY. For the eight possible cross-correlation terms, only the fourth quartile for QQQ exhibited statistical significance with the SPY. For the first and fourth quartiles for both the QQQ and the MDY securities, the most recent returns are negatively related to the lagged value of each the respective securities. Also, the second quartile for the QQQ is negative and significantly different from zero. None of the three remaining autocorrelations were statistically significant. The joint hypothesis tests indicate all of the autocorrelation coefficients for both securities are not equal to zero. The practical conclusion to this result is that investors should evaluate the AOII, if the index increases (decreases), implement the contrarion decision is to sell (buy). In other words, online investors are not very accurate in predicting future returns in the examined ETFs of the QQQ and the MDY.

CONCLUSION

The specific purpose of this research was to investigate the influence the readily available Ameritrade Online Investor Index exerted on the returns of two actively traded exchange traded funds. For the returns of the Cube, the autocorrelations (three of the four quartiles) dominated the influence of the cross-correlations (one of the four quartiles) with the market index. These results show that current returns react inversely to the lag of the most recent value of the same return, rather than other market information. For the Mid-Cap SPDR, only the first and fourth quartile's autocorrelations were statistically significant and negative. No evidence of the influence of the returns of the broad market index was found.

In a broader sense, this paper presents an extension of the tests for financial market efficiency. Unlike previously documented exceptions to this core concept, such as the January effect and the day-of-the week anomalies, the information contained in the buying and selling decisions of this group of online were not associated with positive returns in the examined assets. Instead, an active investment strategy could be devised using short-selling of the QQQ. The decision rule incorporates the interaction between a negative return on the Cube and the AOII ending between 12% to 40%, if these conditions are met, the investor should short-sell the Nasdaq 100 fund. Otherwise, holding the current position would be the correct choice. Future research is planned to test the return generating capabilities of the proposed strategy.

REFERENCES

Abraham, A. & D. Ikenberry (1994). The individual investor and the weekend effect. Journal of Financial and Quantitative Analysis, (June), 263-277.

Ameritrade Press Release (1999). Ameritrade launches online investor index: First daily measurement of behavior of online investors. (December 1).

Chordia, T. & B. Swaminathan (2000). Trading volume and cross-autocorrelations in stock returns. Journal of Finance, (April), 913-935.

Higgins, E. & D. Peterson (1999). Day-of-the-week autocorrelations, cross-autocorrelations, and the weekend effect. The Financial Review, (November), 159-170.

Higgins, E., S. Howton & S. Perfect (2000). The impact of the day of the week on IPO return autocorrelation and cross-correlation. Quarterly Journal of Business and Economics, (Winter), 57-67.

Lakonishok, J. & E. Maberly (1990). The weekend effect: Trading patterns of individual and institutional investors. Journal of Finance, (March), 231-243.

Miller, E. (1988). Why a weekend effect? Journal of Portfolio Management, (Summer), 43-49.

Newey, W. & K. West (1987). A simple, positive, semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, (May), 703-708.

Perfect, S. & D. Peterson (1997). Day-of-the-week effects in the long-run performance of initial public offerings, Financial Review, (February), 49-70.

Thomas Willey, Grand Valley State University

Table 1--Average Daily Percent Returns

This table presents the sample means for the daily returns of the
index tracking securities for the Nasdaq 100 (QQQ), S&P Mid-Cap

400 (MDY) and the S&P 500 (SPY). The quartiles for the Ameritrade
Online Investors Index (AOII) were used to partition the returns.
The AOII represents the percentage of the firm's online investors
who were buyers of securities on day t. The sample size is 164
observations. The p-value represents the results for the hypothesis
test that the mean return equals zero.

 First Second Third Fourth
Index All Days Quartile Quartile Quartile Quartile

QQQ 0.0217 2.9618 0.8252 -0.6605 -3.0396
(p-value) (0.9336) (0.0001) (0.0181) (0.0943) (0.0001)
MDY 0.1273 1.3945 0.3953 -0.0431 -1.2373
(p-value) (0.3411) (0.0001) (0.0732) (0.8393) (0.0001)
SPY 0.0289 0.9422 0.2148 -0.0741 -0.9671
(p-value) (0.7871) (0.0001) (0.2049) (0.6646) (0.0001)

Table 2--Autocorrelation Patterns in QQQ, MDY and SPY Daily Returns

This table presents the results for the daily autocorrelation
terms. Sections A, B and C contain the QQQ returns, the MDY returns
and the SPY returns. In the regression model, [R.sub.t] and
[R.sub.t-1] are the daily percent returns for the respective index
tracking securities on day t and day t - 1. The [Q.sub.1t],
[Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] are dummy variables that
equal one when the AOII falls in a given quartile and zero
otherwise. Standard errors for the regression coefficients are
adjusted using the Newey and West (1987) correction. The sample
sizes for all regression models are 163. The Chi-Square value for
the joint hypothesis test for the equality of the coefficients is
also presented.

 Coefficient with p-value in
 parentheses

 Intercepts Autocorrelation
AOII Dummy Variable ([a.sub.i]) Terms ([b.sub.i])

Section A: Daily Autocorrelation Terms for QQQ

First Quartile 3.2826 -0.4501
 (0.0001) (0.0005)
Second Quartile 1.0252 -0.2729
 (0.0004) (0.0151)
Third Quartile -0.6748 -0.1607
 (0.0663) (0.3101)
Fourth Quartile -3.4535 -0.3009
 (0.0001) (0.0459)
Joint Test of Equality 183.8118 23.0421
 (0.0001) (0.0001)

Section B: Daily Autocorrelation Terms for MDY

First Quartile 1.5242 -0.2088
 (0.0001) (0.0067)
Second Quartile 0.4336 -0.1273
 (0.0292) (0.4359)
Third Quartile -0.0514 -0.1183
 (0.8028) (0.3455)
Fourth Quartile -1.2911 -0.1744
 (0.0001) (0.1228)
Joint Test of Equality 76.0879 11.2198
 (0.0001) (0.0242)

Section C: Daily Autocorrelation Terms for SPY

First Quartile 1.0068 -0.1785
 (0.0001) (0.1761)
Second Quartile 0.2387 -0.1821
 (0.1231) (0.2518)
Third Quartile -0.0886 -0.1464
 (0.5892) (0.2172)
Fourth Quartile -0.9219 0.1416
 (0.0001) (0.4658)
Joint Test of Equality 52.9839 5.1978
 (0.0001) (0.2676)

Table 3--Daily Cross-Correlations Between QQQ and MDY Daily Returns

This table examines the predictive ability of the lagged index
tracking security for the S&P 500 for the daily returns of the
Nasdaq 100 and the S&P 400 Mid-Cap Index. Section A contains the
cross-correlations between the QQQ returns and the S&P 500 Index.
Section B presents the cross-correlations between the MDY returns
and the S&P 500 Index. In the regression models below,
[R.sub.QQQ,t] and [R.sub.MDY,t] are the daily percent returns on
day t for QQQ sample and the MDY matching sample, respectively, and
[R.sub.SPY,t-1] is the return on day t - 1 for the S&P 500 index
security. The [Q.sub.1t], [Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] are
dummy variables that equal one when the AOII falls in a given
quartile and zero otherwise. Standard errors for the regression
coefficients are adjusted using the Newey and West (1987)
correction. The sample sizes for all regression models are 163. The
Chi-Square value for the joint hypothesis test for the equality of
the coefficients is also presented.

 Coefficient with p-value
 in parentheses

 Cross-
 Correlation
 Intercepts Terms

AOII Dummy Variable ([a.sub.i]) ([c.sub.i])

Section A: Daily Cross-Correlations Between the QQQ
and the SPY

First Quartile 3.2476 -0.7567
 (0.0001) (0.0022)
Second Quartile 0.8854 -0.4591
 (0.0062) (0.0967)
Third Quartile -0.6962 -0.3599
 (0.0594) (0.1641)
Fourth Quartile -3.1163 -0.2406
 (0.0001) (0.5542)
Joint Test of Equality 153.2097 14.4015
 (0.0001) (0.0061)

Section B: Daily Cross-Correlations Between the MDY
and the SPY

First Quartile 1.4358 -0.0871
 (0.0001) (0.5821)
Second Quartile 0.4101 -0.1117
 (0.0501) (0.6018)
Third Quartile -0.0565 -0.1365
 (0.7817) (0.4212)
Fourth Quartile -1.2485 -0.0348
 (0.0001) (0.8791)
Joint Test of Equality 74.3691 1.2453
 (0.0001) (0.8706)

Table 4--Daily Autocorrelation and Cross-Correlations Between QQQ and
MDY Daily Returns

This table compares the predictive ability of daily
autocorrelations and cross-correlations for the QQQ and MDY
indices. Section A contains the autocorrelations in the QQQ sample
and the cross-correlations between the QQQ returns and the S&P 500
Index. Section B presents the autocorrelations in the MDY sample
and the cross-correlations between the MDY returns and the S&P 500
Index. In the regression models below, [R.sub.QQQ,t]
[R.sub.QQQ,t-1] [R.sub.MDY,t] and [R.sub.MDY,t-1] are the daily
percent returns on day t and day t-1 for QQQ sample and the MDY
matching sample, respectively, and [R.sub.SPY,t-1] is the return on
day t - 1 for the S&P 500 index security. The [Q.sub.1t],
[Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] are dummy variables that
equal one when the AOII falls in a given quartile and zero
otherwise. Standard errors for the regression coefficients are
adjusted using the Newey and West (1987) correction. The sample
sizes for all regression models are 163. The Chi-Square value for
the joint hypothesis test for the equality of the coefficients is
also presented.

 Coefficient with p-value in parentheses

 Cross-
 Autocorrelation Correlation
 Intercepts Terms Terms

AOII Dummy Variable ([a.sub.i]) ([b.sub.i]) ([c.sub.i])

Section A: Daily Autocorrelations and Cross-Correlations for the QQQ
Returns

First Quartile 3.3099 -0.3433 -0.2767
 (0.0001) (0.0114) (0.2657)
Second Quartile 1.0622 -0.3955 0.4031
 (0.0002) (0.0119) (0.3607)
Third Quartile -0.6891 -0.0795 -0.2171
 (0.0723) (0.7851) (0.6502)
Fourth Quartile -3.4481 -0.4783 0.7839
 (0.0001) (0.0058) (0.0542)
Joint Test of Equality 189.9817 20.4103 5.9856
 (0.0001) (0.0004) (0.2002)

Section B: Daily Autocorrelations and Cross-Correlations for the MDY
Returns

First Quartile 1.5382 -0.5191 0.4487
 (0.0001) (0.0363) (0.1593)
Second Quartile 0.4333 -0.1238 -0.0052
 (0.0262) (0.5396) (0.9852)
Third Quartile -0.0553 -0.0485 -0.0896
 (0.7851) (0.8569) (0.8024)
Fourth Quartile -1.2398 -0.2759 0.2592
 (0.0001) (0.0496) (0.3478)
Joint Test of Equality 82.8184 8.6432 2.9251
 (0.0001) (0.0707) (0.5705)