在一個有效率的股票市場中，投資人唯有承擔高於平均水準的風險才能獲得高於平均水準的報酬，隱含風險與報酬之間呈現正向關係。然而，Ang, Hodrick, Xing, and Zhang (2006, 2009)的實證研究發現，風險與報酬之間呈現負向關係，亦即高風險的股票會有較低的報酬。由於此現象違反了高風險高報酬的預期心理，被定義為「低波動度異常現象(low volatility anomaly)」。本研究以1965年1月至2010年12月間標準普爾500指數中的成分股為研究樣本，驗證在不同風險因子模型下的風險調整後報酬(risk-adjusted return)，是否仍然存在低波動度異常現象。此外，本研究將投資人情緒(investor sentiment)納入Fama-French-Carhart四因子迴歸模型中，進一步探討投資人情緒對於低波動度異常現象的影響。
本研究做多低波動度投資組合，並且放空高波動度投資組合，形成零交易成本的多空操作策略。實證結果顯示(1)經過三因子與四因子的風險調整後報酬，仍然存在低波動度效應(low volatility effect)。(2)加入投資人情緒作為風險因子後，投資人情緒對於低波動度效應具有正向的預測力。(3)只有在景氣擴張時期下，投資人情緒能正向預測低波動度效應；而在景氣衰退時期下，並未發現投資人情緒能預測低波動度效應的證據。此外，本研究考量到分組後樣本數太少和波動度叢聚(volatility clustering)的問題，透過改變投資組合的建構方式以測試上述的結果是否具有穩健性，實證結果發現改變投資組合的建構方式後結果仍然相同。

In an efficient market, investors earn above-average returns when they take above-average risks. This indicates that there is a positive relationship between risk and return. However, Ang, Hodrick, Xing, and Zhang (2006, 2009) suggested that stocks with higher risk tend to have lower returns. This phenomenon fights against the psychological expectations of high risk and high return. Hence, the phenomenon is defined as “low volatility anomaly”. We use constituent stocks of the S&P 500 index from January 1965 to December 2010 to examine whether the low volatility anomaly exists under different risk-factor models. Moreover, we add investor sentiment variable into the Fama-French-Carhart four-factor model, to further explore the impact of investor sentiment on the low volatility anomaly.
We form a long-short strategy through longing low volatility portfolio and shorting high volatility portfolio. The results show the following findings. First, the low volatility effect exists under the three-factor and four-factor models. Second, after we add investor sentiment as a risk factor into regression, results imply that investor sentiment positively predicts the low volatility effect. Third, only in periods of economic expansion, investor sentiment could positively and significantly predict the low volatility effect. Finally, there are some problems to overcome. One problem is, if sample stocks are divided into five groups according to volatilities, each group’s size will be too small. The other problem is that the possible existence of volatility clustering phenomenon might affect our empirical findings. Therefore, we conducted robustness testing through changing portfolios’ compositions, the results are the same as our main findings.

學位論文審定書........................................................................................................i
摘要........................................................................................................................ii
Abstract..................................................................................................................iii
目錄........................................................................................................................iv
圖次........................................................................................................................v
表次........................................................................................................................vi
第一章 緒論.............................................................................................................1
第一節 研究背景與動機.........................................................................................1
第二節 研究目的與問題.........................................................................................3
第三節 研究架構...................................................................................................4
第二章 文獻探討.......................................................................................................6
第一節 低波動度效應............................................................................................6
第二節 低獨特風險效應.........................................................................................9
第三節 投資人情緒..............................................................................................12
第三章 研究方法.....................................................................................................14
第一節 研究樣本.................................................................................................14
第二節 波動度計算..............................................................................................16
第三節 投資組合的建構.......................................................................................16
第四節 研究假說.................................................................................................18
第五節 建立迴歸模型...........................................................................................19
第四章 實證結果與討論...........................................................................................24
第一節 風險因子調整之迴歸分析結果....................................................................24
第二節 投資人情緒因子與時變性系統風險之迴歸分析結果.......................................26
第三節 不同景氣狀態下投資人情緒因子之迴歸分析結果..........................................28
第四節 穩健性測試..............................................................................................30
第五章 結論............................................................................................................34
參考文獻................................................................................................................36

Ang, A., Hodrick, R.J., Xing, Y., and Zhang, X. (2006). The cross‐section of volatility and
expected returns. The Journal of Finance, 61(1), 259-299.
Ang, A., Hodrick, R.J., Xing, Y., and Zhang, X. (2009). High idiosyncratic volatility and
low returns: International and further us evidence. Journal of Financial Economics,
91(1), 1-23.
Asness, C., Frazzini, A., and Pedersen, L.H. (2012). Leverage aversion and risk parity.
Financial Analysts Journal, 68(1), 47-59.
Baker, M., Bradley, B., and Wurgler, J. (2011). Benchmarks as limits to arbitrage:
Understanding the low-volatility anomaly. Financial Analysts Journal, 67(1), 40-54.
Baker, M., and Wurgler, J. (2006). Investor sentiment and the cross‐section of stock
returns. The Journal of Finance, 61(4), 1645-1680.
Baker, N.L., and Haugen, R.A. (2012). Low risk stocks outperform within all observable
markets of the world.
Bali, T.G., and Cakici, N. (2008). Idiosyncratic volatility and the cross section of
expected returns. Journal of Financial and Quantitative Analysis, 43(01), 29-58.
Bali, T.G., Cakici, N., and Whitelaw, R.F. (2011). Maxing out: Stocks as lotteries and the
cross-section of expected returns. Journal of Financial Economics, 99(2), 427-446.
Bali, T.G., Cakici, N., Yan, X.S., and Zhang, Z. (2005). Does idiosyncratic risk really
matter? The Journal of Finance, 60(2), 905-929.
Benos, A.V. (1998). Aggressiveness and survival of overconfident traders. Journal of
Financial Markets, 1(3), 353-383.
Blitz, D., and van Vliet, P. (2007). The volatility effect. Journal of Portfolio Management,
34(1), 102-113.
Bris, A., Goetzmann, W.N., and Zhu, N. (2007). Efficiency and the bear: Short sales and
markets around the world. The Journal of Finance, 62(3), 1029-1079.
Brockman, P., and Yan, X. (2008). The time-series behavior and pricing of idiosyncratic
volatility: Evidence from 1926 to 1962.
Brown, G.W., and Cliff, M.T. (2004). Investor sentiment and the near-term stock market.
Journal of Empirical Finance, 11(1), 1-27.
Brown, G.W., and Cliff, M.T. (2005). Investor sentiment and asset valuation*. The Journal
of Business, 78(2), 405-440.
Carhart, M.M. (1997). On persistence in mutual fund performance. The Journal of
Finance, 52(1), 57-82.
Chang, E.C., Cheng, J.W., and Yu, Y. (2007). Short‐sales constraints and price
discovery: Evidence from the hong kong market. The Journal of Finance, 62(5),
2097-2121.
Chung, S.-L., Hung, C.-H., and Yeh, C.-Y. (2012). When does investor sentiment predict
stock returns? Journal of Empirical Finance, 19(2), 217-240.
Cornell, B. (2009). The pricing of volatility and skewness: A new interpretation. The
Journal of Investing, 18(3), 27-30.
Daniel, K., Hirshleifer, D., and Subrahmanyam, A. (1998). Investor psychology and
security market under‐and overreactions. The Journal of Finance, 53(6), 1839-1885.
De Bondt, W.F.M., and Thaler, R.H. (1985). Does the stock market overreact? The
Journal of Finance, 40(3), 793-805.
Dutt, T., and Humphery-Jenner, M. (2013). Stock return volatility, operating performance
and stock returns: International evidence on drivers of the ‘low volatility’anomaly.
Journal of Banking and Finance, 37(3), 999-1017.
Fama, E.F., and French, K.R. (1993). Common risk factors in the returns on stocks and
bonds. Journal of Financial Economics, 33(1), 3-56.
Fama, E.F., and French, K.R. (1996). Multifactor explanations of asset pricing
anomalies. The Journal of Finance, 51(1), 55-84.
Frazzini, A., and Pedersen, L.H. (2014). Betting against beta. Journal of Financial
Economics, 111(1), 1-25.
Fu, F. (2009). Idiosyncratic risk and the cross-section of expected stock returns. Journal
of Financial Economics, 91(1), 24-37.
Goetzmann, W.N., and Kumar, A. (2008). Equity portfolio diversification*. Review of
Finance, 12(3), 433-463.
Goyal, A., and Santa‐Clara, P. (2003). Idiosyncratic risk matters! The Journal of Finance,
58(3), 975-1008.
Guo, H., and Savickas, R. (2010). Relation between time-series and cross-sectional
effects of idiosyncratic variance on stock returns. Journal of Banking and Finance,
34(7), 1637-1649.
Ho, C., and Hung, C.-H. (2009). Investor sentiment as conditioning information in asset
pricing. Journal of Banking and Finance, 33(5), 892-903.
Hou, K., and Loh, R. (2012). Have we solved the idiosyncratic volatility puzzle.
Huang, W., Liu, Q., Rhee, S.G., and Zhang, L. (2010). Return reversals, idiosyncratic
risk, and expected returns. Review of Financial Studies, 23(1), 147-168.
Jiang, G.J., Xu, D., and Yao, T. (2009). The information content of idiosyncratic volatility.
Journal of Financial and Quantitative Analysis, 44(01), 1-28.
Kahneman, D., and Tversky, A. (1979). Prospect theory: An analysis of decision under
risk. Econometrica: Journal of the Econometric Society, 263-291.
Lamont, O. (2004). Short sale constraints and overpricing.
Levy, H. (1978). Equilibrium in an imperfect market: A constraint on the number of
securities in the portfolio. The American Economic Review, 643-658.
Lewellen, J., and Nagel, S. (2006). The conditional capm does not explain asset-pricing
anomalies. Journal of Financial Economics, 82(2), 289-314.
Lichtenstein, S., Fischhoff, B., and Phillips, L.D. (1977). Calibration of probabilities: The
state of the art: Springer.
Malkiel, B.G., and Fama, E.F. (1970). Efficient capital markets: A review of theory and
empirical work*. The Journal of Finance, 25(2), 383-417.
Malkiel, B.G., and Xu, Y. (2002). Idiosyncratic risk and security returns.
Markowitz, H. (1952). Portfolio selection*. The Journal of Finance, 7(1), 77-91.
Merton, R.C. (1973). An intertemporal capital asset pricing model. Econometrica: Journal
of the Econometric Society, 867-887.
Miller, E.M. (1977). Risk, uncertainty, and divergence of opinion. The Journal of Finance,
32(4), 1151-1168.
Ofek, E., Richardson, M., and Whitelaw, R.F. (2004). Limited arbitrage and short sales
restrictions: Evidence from the options markets. Journal of Financial Economics,
74(2), 305-342.
Riley, T.B. (2014). Two essays on the low volatility anomaly.
Shefrin, H., and Statman, M. (1994). Behavioral capital asset pricing theory. Journal of
Financial and Quantitative Analysis, 29(03), 323-349.
Shefrin, H., and Statman, M. (2000). Behavioral portfolio theory. Journal of Financial and
Quantitative Analysis, 35(02), 127-151.
Stambaugh, R.F., Yu, J., and Yuan, Y. (2012). The short of it: Investor sentiment and
anomalies. Journal of Financial Economics, 104(2), 288-302.
Tversky, A., and Kahneman, D. (1974). Judgment under uncertainty: Heuristics and
biases. Science, 185(4157), 1124-1131.
Yamada, T. (2013). Long-term verification of low volatility stock investment. Public Policy
Review, 9(3), 553-574.
Yamada, T., and Nagawatari, M. (2011). Investor expectations and the volatility puzzle in
the japanese stock market. The Securities Analysts Association of Japan, 1-15.
Yamada, T., and Uesaki, I. (2009). Low volatility strategy in global equity markets.
Securities Analysts Journal, 47(6), 97-110.
Yu, J., and Yuan, Y. (2011). Investor sentiment and the mean–variance relation. Journal
of Financial Economics, 100(2), 367-381.