Over the past years, there has been ample research on the noise trader risk and the relationship between stock returns and the noise traders’ sentiment. In this section we provide a review of literature related to our perspective and motivation for further empirical investigation.
Economists have been debating the effect, if any, of uninformed investors—so-called noise traders—have on the price of finance for decades. Early papers (Friedman, 1953; Fama, 1965) argue noise traders are unimportant in the financial asset price formation process because trades of the rational arbitrageurs drive prices close to their fundamental values.
However, some evidences of the market anomalies challenge this efficient markets theory.
Black (1986) considers the noise of a large number of small events is often a causal factor that is much more powerful than a small number of large events can be. Noise not only causes markets to be inefficient, but also prevents us from taking advantage of inefficiencies within the markets.
De Long, Shleifer, Summers, and Waldmann (1990a) suggest, if some investors trade on a
“noisy” signal that is unrelated to fundamental values, then asset prices will deviate from their intrinsic value. Noise traders can introduce a systematic risk that is priced. In their model, changing investor sentiment can create deviations in price from fundamental value that are unpredictable. In the short run, arbitrageurs betting against mispricing run the risk, and investor sentiment becomes more extreme and prices move even further away from fundamental values. The potential loss and the arbitrageurs’ risk aversion reduce the positions which they are willing to take. In the long run, the prices will revert to their fundamental values. This process may not be very smooth, and may take a long time. Finally, arbitrage cannot completely eliminate mispricing and investor sentiment ultimately affects security prices in equilibrium.
Lee, Shleifer, and Thaler (1991) suggest closed-end fund discounts are a measure of the sentiment of individual investors. This sentiment is widespread to affect the small stocks prices in the same way that it influences the closed-end funds. Smaller stocks must also be underpriced relative to their fundamentals, since the same investor sentiment affects small stocks and so makes them riskier. That the small firms appear to earn excess returns is well-known as the small firm effect.
A number of researchers, such as Black (1986), De Long, Shleifer, Summers, and Waldmann (1990a; 1990b), and Barberis, Shleifer, and Vishny (1998) have more formally modeled the role of investor sentiment. But their models are difficult to test directly, because they usually involve sources of noise which are difficult to measure.
Many papers’ findings show sentiment as having a predictive capability for returns. Neal and Wheatley (1998) find the discounts on closed-end funds and the redemptions of mutual funds predict equity returns.
Fisher and Statman (2000) studied three groups of investors, Wall Street strategists, writer of investment newsletters, and individual investors, which denote large, medium, and small investors respectively. They found the sentiment of small and large investors are reliable contrary indicators for future S&P 500 returns.
Simon and Wiggins (2001) find sentiment indicators such as the VIX, the put-call ratio, and the ARMS had significant predictive power for subsequent S&P futures over the sample periods January 1989 through June 1999.
Lee, Jiang, and Indro (2002) estimate a GARCH-in-mean model which includes contemporaneous shifts in investor sentiment in the mean equation and lagged shifts in sentiment in the conditional volatility equation. They use the sentiment survey indicator provided by Investor’s Intelligence to examine the impact of changes in investor sentiment on
the conditional volatilities of the DJIA, S&P 500, and NASDAQ indices, which are estimated from the GJR-GARCH model. They find sentiment can affect returns through volatility.
Many papers also investigated the relationship between sentiment and volatility. Brown (1999) examines whether investors’ sentiments relate to the volatility of closed-end fund returns. He uses both direct investor survey (the American Association of Individual Investors Sentiment Survey) and closed-end fund discounts as measures of sentiment and finds individual investor sentiment is related to increased volatility in closed-end fund discounts.
He also finds that deviations from the average level of sentiment are associated with increases in fund volatility only during trading hours. Lee, Jiang, and Indro (2002) find that bullish (bearish) changes in sentiment result in downward (upward) adjustments in volatility. Wang, Keswani, and Taylor (2006) find ARMS has predictive power for future realized volatility but that this is limited when returns are included.
However, many researchers find that sentiment indicators might be caused by returns or volatility. Fisher and Statman (2000) found high S&P 500 returns during one month can make individual investors and newsletter writers bullish on their sentiments.
Brown and Cliff (2004) use a large number of sentiment indicators to investigate investor sentiment and its relationship to near-term stock market returns. They find that past market returns are also an important determinant of sentiment and sentiment has little predictive power for future stock returns. And Wang, Keswani, and Taylor (2006) also find most sentiment measures are caused by returns and volatility.
In summary, the literature tells us that sentiment may be useful for forecasting return and volatility. It also tells us that this relationship may be influenced by the behavior of returns.
Engle (1982) proposed the Autoregressive Conditional Heteroskedasticity (ARCH) model which has become the most famous model in processing the conditional volatility. The ARCH
model which would be possibly the most important innovation in modeling markets volatility changes adopts the effect of past residuals and helps explain the volatility clustering phenomenon. In traditional econometrics models, the one period forecast variance is assumed to be constant. But the ARCH model assumes that variance of residuals to be time varying and conditional on past sample. And Bollerslev (1986) proposed the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model which brings the previous volatility term into the ARCH model. The GARCH model is widely applied in research of financial and economic time series. Engle’s (1982) ARCH model extended to allow the conditional variance to be a determinant of the mean and is called ARCH-M.
Some latest researches are interested in the asymmetry effect of the volatility. Nelson (1991) gave different weights to different sign of residuals. Glosten, Jagannathan and Runkle (1993) used a dummy variable to catch the additional impact of the negative return.
Engle and Lee (1999) propose the component GARCH model. In their model, the conditional variance of stock returns has been decomposed in a statistical unobserved component model to describe the long-run (trend) and the short-run (transitory) movement of stock market volatility.
The GARCH model can let us consider excess return and conditional volatility of excess return contemporaneously, therefore we use a GJR-GARCH model to model the noise trader risk. In addition, we estimate a component GARCH to find whether effect of sentiment in the transitory component is larger and more significant than in the permanent component.
3 Data
3.1. Direct sentiment measures
There are two indices that directly measure the sentiment of market participants. The first is a survey conducted by the American Association of Individual Investors (AAII). AAII has conducted a sentiment survey by polling a random sample of its members each week, beginning in July 1987. The association asks each participant whether they are bearish, bullish, or neutral about the stock market in 6 months. Only subscribers to AAII can vote. Since this sentiment survey is targeted towards individuals, this can be interpreted as an individual sentiment measure. We use the bullish percentage as a measure of investor sentiment in this paper.
The second survey is conducted by Investors Intelligence (II). Since 1964, Investors Intelligence compiles its sentiment data weekly by categorizing approximately 150 market newsletters. Newsletters are read and marked as bullish, bearish, or neutral starting on Friday each week. The results are reported on the following Wednesday. We interpret the bullish percentage compiled by Investors Intelligence as a proxy for institutional sentiment, because a lot of the writers of those newsletters are past or current market professionals.
Fisher and Statman (2000) use II and AAII index as medium and small investors’
sentiment respectively. They found the relationship between II and AAII sentiment index is strong and the AAII bullish percentage index is reliable contrary indicators for future S&P 500 returns.
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We find AAII and II have some similarities that they have the same long run trend and
their correlation coefficient is 0.513088. AAII and II have strong correlation. But we can see that AAII fluctuates stronger than II, because AAII represent the small investors’ sentiment and small investors are influenced by information of market easier than other investors.
3.2. Indirect sentiment measures
Brown et al. (2004) find that many commonly used indirect measures of sentiment are related to direct surveys of investor sentiment. They examine many financial indicators, which they categorize into a number of main groups. We use the three categories here, and we choose some of these indicators as our indirect sentiment measures. In addition, we also add some market measures in this paper.
3.2.1. Market performance
The ARMS (or TRIN) index is developed by Richard Arms in 1967 and first introduced by Barron’s in the same year. One of the first to adopt this indicator in his market analysis was Richard Russell, the last living Dow Theorist and writer of the Dow Theory Letters. The ARMS Index is a market breadth and strength indicator, which attempts to analyze the relationship between the number of advancing and declining issues and the advancing and declining volume.
The ARMS index is the ratio of the number of advances to declines standardized by their respective volumes. It is calculated as:
# / /#
# / /#
t t t t
t
t t t t
Adv AdvVol DecVol Dec ARMS = Dec DecVol = AdvVol Adv
where #Advt, #Dect,AdvVolt, andDecVolt, respectively, denote the number of advancing issues, the number of declining issues, the trading volume of advancing issues, and the trading volume of declining issues. An ARMS Index reading of one implies that the market is in balance, while a reading above one implies more volume is moving into declining stocks (bearish) and vice versa. When the market is more bearish, the trading volume of declining issues will rise and the ARMS Index will greater. When the market is more bullish, the trading volume of advancing issues will rise and the ARMS Index will go down. The ARMS Index can also be used as an oversold/overbought indicator when smoothed by a simple moving average – such as using a 10-day or a 21-day moving average. Wang et al. (2006) find that ARMS has predictive power for future realized volatility. Our ARMS daily data is obtained form Bloomberg.
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3.2.2. Derivatives variables
The put-call trading volume ratio (PCV) and the put-call open interest ratio (PCO) are also the measures of market participants’ sentiment. The PCV equals the trading volume of put options divided by the trading volume of call options. The market participants buy put to hedge their spot positions, when their sentiment is bearish. The PCV then goes up, because the trading volume of put options increases in relation to the trading volume of call options, and vice versa.
We also can calculate the ratio by using the open interest of options instead of trading volume. The PCO is a good measure of sentiment, because it can reflect the sentiment at the end of the day or the week. Option open interest is used to proxy for heterogeneous beliefs as the put/call open interest ratio is widely used in behavioral finance as a measure of investor
sentiments (e.g. Dennis and Mayhew, 2002). We use the OEX put-call trading volume ratio and the OEX put-call open interest ration here. The daily data is obtained from Bloomberg.
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3.2.3. Other sentiment proxies
Many other variables don’t fall neatly within one of the aforementioned categories. IPO activity is often considered a measure of sentiment because of the information asymmetries between managers and investors. We include monthly data on initial public offering first day returns (IPORET) and the number of offerings (IPON) in this paper. The number of initial public offering and the first day return of initial public offering are both a bullish market indicator. These IPO monthly data are reported by Ritter (http://bear.cba.ufl.edu/ritter).
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3.3. Sample period and stock return proxies
Our daily, weekly, and monthly samples cover the period from August 22, 1996 to December 31, 2007, July 24, 1987 to December 28, 2007, and February 01, 1971 to December 31, 2006, respectively. Three different market indices which are the DJIA, S&P500, and NASDAQ are used to characterize the overall performance of the market. The DJIA is a price-weighted average of 30 large “blue-chip” stocks. Although the limitations in the composition and construction of the index are well known, yet, it is the most widely followed and reported stock index. The S&P500 and NASDAQ are both value-weighted indices that reflect the return of large and small capitalization stocks respectively. The data of DJIA, S&P500, and NASDAQ are obtained from yahoo finance.
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As reported in Panel B of Figure 5, the volatility of excess return of NASDAQ is greater than DJIA and S&P500, because NASDAQ index is composed of many small high tech companies where many of their investors are small investor and they tend to be easily influenced by noise information.
Panel A of Figure 5 shows the daily close prices of DJIA, S&P500, and NASDAQ from August 22, 1996 to December 31, 2007. As reported in Panel A of Figure 5, we find the close prices are unusual from March 29, 2000 to April 27, 2000, especially in NASDAQ. During this period, the close price of NASDAQ drops off substantially from 4958.56 to 3774.03. The excess returns of stock index are an abnormal negative. It appears commonly in all three indices and obviously in NASDAQ index. This phenomenon is commonly known as the bursting of the dot-com bubble.
The average three-month T-Bill yield is used as a proxy for the risk-free rate of interest in computing the excess returns for each stock index. The daily and weekly three-month T-Bill yield is obtained from Bloomberg and the monthly three- month T-Bill yield is obtained from Taiwan Economic Journal (TEJ).
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