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Researchers try to uncover whether investor sentiment measures are able to explain returns volatility and whether the investors price the volatility induced by sentiment. The

latter implies that investor sentiment is a systematic risk because only risks that cannot be eliminated through diversification are priced. Besides, there are attempts to investigate the impact of investor sentiment on investors’ propensity to take risk.

Investor sentiment lends an explanation to excess returns volatility. Shiller (1989) finds that the volatility of closed-end fund discounts is greater than the volatility of its dividends and attributes to the phenomena to investors’ irrationality. Pontiff (1997) extends the study, and compares the returns volatility of a closed-end fund with its’ underlying assets. The closed- end funds’ returns volatility is 64% more volatile than its underlying assets. In addition, the funds’ stock price returns in excess of net asset value returns can be better explained by sentiment risk instead of the Fama and French (1993) measures of risks for market, value and size. These early evidences indirectly attribute to returns volatility to fluctuations in investor sentiment. Following these prior studies and motivated by Delong et.al (1990b), Brown (1999) uses sentiment index constructed from the AAII survey, to directly test the sentiment-volatility hypothesis. The findings support the proposition that returns volatility increases due to noise traders trading on sentiment.

Baker and Wurgler (2006, 2007) suggest that hard-to-value and hard-to-arbitrage stocks are highly volatile and tend to record lower returns following high sentiment period. These studies not only provide empirical evidence on the sentiment-return relationship, but also indirectly explain why the risk-return trade off does not hold at times. Noise traders tend to overprice assets during high sentiment periods. The returns are lower due to a high purchase price and subsequent price reversals due to over-pricing. This explains the reason why there is no compensation for sentiment-induced volatility.

Incorporating the changing market dynamics into the volatility model is expected to produce better estimates for risk. However, the market data and macroeconomic information are not always available in high frequency. Mitra, Mitra and Dibartolomeo (2009) propose an alternative solution. They include two common measures of investor sentiment: options implied volatility and news sentiment, into the model to improve the estimation of the portfolio risk (volatility). Options implied volatility is a forward-looking measure of investors’ expectations for future volatility. It can be calculated up to per minute basis, while news can be converted into sentiment measure on daily basis. These variables improve the volatility estimates.

Based on the above studies, several sentiment measures are identified as explanatory factors to returns volatility. Yang and Wu (2010) construct nine sentiment measures from four categories of trading data, including overall trading, margin trading, TAIEX options and foreign plus institutional investors. They conduct Grey analysis to determine the sequential relationships among these factors, and rank them according to the domination power in determining the relationship with price volatility. The resulted ranking is as follow: short-sales volumes, open interest, put-call ratios, trading volume and finally buy-sell orders.

However, not all studies corroborate the sentiment induce volatility paradigm. Since there are evidences on a bi-directional sentiment-returns relationship (see Brown & Cliff, 2004; Solt & Statman, 1988), it is reasonable to suspect that there is a two-way sentiment-volatility relationship. Wang, Keswani and Taylor (2006) suggest that the prior evidence could be spurious due to the role of returns on predicting volatility being omitted. There is evidence that lags of returns and lags of volatility Granger-cause sentiment, but no countervailing proof is found in their study.

Based on the present evidence, it is reasonable to maintain that at least some portion of the return volatility can be attributed to investor sentiment. This has motivated further tests on whether the volatility arising from sentiment trading is priced. Some research investigates a more general question, for example whether sentiment can predict returns or if sentiment factors enter the returns generating process. The role of investor sentiment as a risk factor is implicitly implied if sentiment is priced, evidenced by investor sentiment significantly predicting returns (Elton et al., 1998; Kumar & Lee, 2006; Sias, Starks, & Tinic, 2001) .

Another line of research explicitly models the investor sentiment into the volatility equation. This enables the examination of the role of investor sentiment on volatility as a measure of risk. However, very few studies have tested this. The theory was first proposed by Lee, Shleifer and Thaler (1991), which states that closed-end funds and small stocks face noise trader risk. There should be compensation for bearing the risk. This motivates Lee, Jiang and Indro (2002) to carry out empirical tests. They explicitly model the sentiment factor in the mean and variance equation in a GARCH model. Fitting the model to U.S. aggregate data, they find that a positive (negative) change in sentiment leads to the following week’s lower (higher) conditional volatility. Moreover, the positive relationship between returns and change in sentiment suggests that investors systematically price the sentiment as if it is a risk measure. Beaumont, Daele, Frijns, Lehnert, & Muller (2008) apply the same model to US market daily data and draw the same conclusion. In spite of this, the impact of sentiment on volatility is not confirmed by Samsell (2007) when the empirical model is tested with monthly data.