R ETURNS , O RDER I MBALANCES , AND I NVESTOR S ENTIMENT

To examine the tripartite associations among ETF returns, order imbalances, and investor sentiment indicators, this paper exerts a signed measure of order imbalances plus sentiment indicators to investigate the empirical evidences. Order imbalances are separated by positivity and negativity. In the first hypothesis, we intend to understand whether the predictive power for ETF returns will increase when adding the chosen investor sentiment indicators into the original liquidity model in the table 4 of Chordia et al. (2002). Due to the quantity of the data, the period covers from 1995 to 2003 for

SPY, and from 2001 to 2003 for QQQQ.³

Panel A of Table 1 reports the descriptive statistics for SPY, and Panel B for QQQQ. The descriptive statistics include mean, median, standard deviation, maximum, and minimum. The average returns in SPY model is 0.03%, and in QQQQ model is -0.08%. The standard deviation of returns in SPY model is smaller than that in QQQQ model, and this is because the characteristics of the component stocks in QQQQ are similar to small stocks. The means of VIX, put-call ratio, and AAII in SPY model are 23.0745, 0.6931, and 1.9797, respectively. The means of VXN, put-call ratio, and AAII in QQQQ model are 43.6440, 0.7740, and 1.8613, respectively.

Panel C presents the correlation coefficients for SPY, and Panel D for QQQQ.

As we can see in these two panels, the correlation coefficients among the investor sentiment indicators are significant in both SPY and QQQQ model. Except for AAII, the dependent variable almost correlated significantly the independent variables. The lagged positive and negative returns significantly correlate investor sentiment indicators. The correlation coefficients between investor sentiment indicators and order imbalances seem to be less significant, especially in QQQQ model.

Table 2 shows the empirical results of the Equation 1 which consists of two targeted ETFs and the models with or without sentiment indicators. All the figures in Table 2 have been standardized, but the raw data are used in Table 1. The contemporaneous order imbalances are significantly and positively related to ETF returns in all ETF models. This relationship implies that excess buy (sell) orders drive up (down) market returns. This result is consistent with the empirical consequence of Chordia et al. (2002). However, according to Chordia et al. (2002), it seems unlikely that order imbalances can be a sign of a profit opportunity because only specialists know order imbalances in real time for individual stocks and no specialists know

3 The period is from 1995/9/27 to 2003/12/31 for SPY, and from 2001/2/1 to 2003/12/31 for QQQQ.

order imbalances for all stocks in aggregate. Furthermore, the one-day lagged order imbalances seem to have no significant influence on ETF returns in our empirical results, and only the lagged excess sell orders are significant in the SPY model with sentiment. The lagged negative returns are significantly and negatively related to the ETF returns. The lagged positive returns are significantly related to the ETF returns in the SPY model with sentiment factor; however, under other conditions, the relationship is insignificant. This implies that only the past negative returns are related to contemporaneous returns, and the predictive power of the past positive returns is unclear.

As can be seen in table 2, the relationship between investor sentiment indicators and ETF returns are negative. This result means when sentiment is high, the ETF returns are relatively low, and vice versa. According to the previous research and theories, both of the influencing directions between sentiment and market returns are supported. The empirical results indicate that the relationship is negative. On one hand, the viewpoint which Brown and Cliff (2004) propose in their paper may be right, namely the ‗bargain shopper‘ effect really exists. On the other hand, the

‗hold-more‘ effect is smaller than the effect of the ‗overreaction of noise traders‘ in the see-saw battle which is mentioned in the papers of De Long et al. (1990) and Lee et al. (2002). As a result, the negative relationship between ETF returns and investor sentiment indicators is consistent with the previous theories.

Moreover, VIX and VXN are the indicators standing for implied volatility of S&P 500 and Nasdaq 100, respectively. The put-call ratio equals total trading volume of put option contracts divided by total trading volume of call option contracts. In this paper, we measure AAII by the ratio of the bearish percentage to the bullish percentage. Although all of these indicators may represent different meanings originally, they can be a symbol of investor sentiment in different aspects to explain

investor sentiments.

The next part of Table 2 demonstrates the adjusted R² for the models with or without investor sentiment indicators. It is obvious that the adjusted R² of the models with or without sentiment indicators increase largely. This result means that the three new-coming investor sentiment indicators certainly have explanatory power on market returns, and this is consistent with previous research.

To sum up, we find that investor sentiment indicators really have the marginal explanatory power on market returns beyond the contemporaneous order imbalances and lagged negative returns. This discovery also reveals that investor sentiment indicators can be used as a sign of predicting investment opportunity, and it proves that our first hypothesis is significantly valid. There is something vague, however, about the influencing directions of investor sentiment indicators on market returns.

Although some scholars believe that the relationship between investor sentiment and market returns is positive from their empirical studies, there are other theories stating that the changing direction is negative. We think this difference may result from the chosen variables. The confusion about the changing directions and the using timing of sentiment indicators still need more detailed studies in the future to resolve.