隨著散戶投資人在金融市場中的影響力日益增強，了解認知偏誤如何影響
資產價格變得至關重要。本研究探討了概率加權函數的曲率參數在股票報
酬預測與經濟價值方面的作用，該參數透過對概率的扭曲來反映投資人的
風險感知。我們運用結合粒子濾波法的經驗定價核方法來構建概率加權指
數（PWI），並評估其預測能力。實證結果顯示，PWI 具有一定程度的報
酬預測能力，能提供超越傳統預測變數的額外資訊，並透過投資策略創造
經濟價值，表現優於簡單的買入持有策略。此外，進一步分析發現，PWI
主要透過貼現率通道影響報酬，與傳統基於投資人情緒的預測因子有所不
同。本研究的發現突顯了認知偏誤在資產定價中的關鍵作用，並提出PWI
作為一種潛在的行為財務型預測因子。

As retail investors increasingly influence financial markets, understanding how cognitive biases affect asset prices is crucial. This study examines the return predictability and economic value of the curvature parameter of probability weighting function, which captures investors’ risk perception through prob ability distortions. Using a empirical pricing kernel approach with particle filtering, we construct a Probability Weighting Index (PWI) and analyze
its predictive power. Empirical results suggest that PWI exhibits a certain degree of predictive power, provides incremental information beyond traditional predictors, and offers economic value through an investment strategy that outperforms the buy-and-hold approach. Further analysis indicates that PWI primarily predicts returns through the discount rate channel, distinguishing it from sentiment-based predictors. Our findings highlight the role of cognitive biases in asset pricing by introducing PWI as a potential behavioral-based predictor.

Azimi, M., Ghazi, S., and Schneider, M. (2024). Probability weighting and equity pre mium prediction: Investing with optimism. Financial Management.
Baele, L., Driessen, J., Ebert, S., Londono, J. M., and Spalt, O. G. (2019). Cumulative prospect theory, option returns, and the variance premium. The Review of Financial Studies, 32(9):3667–3723.
Barber, B. M. and Odean, T. (2000). Trading is hazardous to your wealth: The common stock investment performance of individual investors. The Journal of Finance, 55(2):773–806.
Barberis, N. and Huang, M. (2008). Stocks as lotteries: The implications of probability weighting for security prices. American Economic Review, 98(5):2066–2100.
Boudoukh, J., Michaely, R., Richardson, M., and Roberts, M. R. (2007). On the im portance of measuring payout yield: Implications for empirical asset pricing. The Journal of Finance, 62(2):877–915.
Breeden, D. T. and Litzenberger, R. H. (1978). Prices of state-contingent claims implicit in option prices. Journal of Business, pages 621–651.
Brown, G. W. and Cliff, M. T. (2005). Investor sentiment and asset valuation. The journal of Business, 78(2):405–440.
Campbell, J. Y. (1987). Stock returns and the term structure. Journal of Financial Economics, 18(2):373–399.
Campbell, J. Y. and Shiller, R. J. (1988). The dividend-price ratio and expectations of future dividends and discount factors. The Review of Financial Studies, 1(3):195-228.
Campbell, J. Y. and Thompson, S. B. (2008). Predicting excess stock returns out of sample: Can anything beat the historical average? The Review of Financial Studies, 21(4):1509–1531.
Charupat, N., Deaves, R., Derouin, T., Klotzle, M., and Miu, P. (2013). Emotional balance and probability weighting. Theory and Decision, 75:17–41.
Chateauneuf, A., Eichberger, J., and Grant, S. (2007). Choice under uncertainty with the best and worst in mind: Neo-additive capacities. Journal of Economic Theory, 137(1):538–567.
Chen, T.-Y., Lin, Y.-L., and Tzeng, L. Y. (2024). Estimating probability weighting functions through option pricing bounds. The Review of Asset Pricing Studies, 14(3):513–543.
Chiang, I.-H. E. and Hughen, W. K. (2017). Do oil futures prices predict stock returns? Journal of Banking & Finance, 79:129–141.
Cochrane, J. H. (2008). The dog that did not bark: A defense of return predictability. The Review of Financial Studies, 21(4):1533–1575.
De Giorgi, E. G. and Legg, S. (2012). Dynamic portfolio choice and asset pricing with narrow framing and probability weighting. Journal of Economic Dynamics and Control, 36(7):951–972.
Driessen, J., Ebert, S., and Koëter, J. (2025). π-capm: The classical capm with proba bility weighting and skewed assets. Review of Financial Studies.
Fama, E. F. and French, K. R. (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics, 25(1):23–49.
Fama, E. F. and Schwert, G. W. (1977). Asset returns and inflation. Journal of Financial Economics, 5(2):115–146.
Gonzalez, R. and Wu, G. (1999). On the shape of the probability weighting function. Cognitive Psychology, 38(1):129–166.
Goyal, A. and Welch, I. (2008). A comprehensive look at the empirical performance of equity premium prediction. The Review of Financial Studies, 21(4):1455–1508.
He, X. D. and Sun, Y. (2023). Dynamic portfolio selection and asset pricing under neo-additive probability weighting. Available at SSRN 4455110.
Huang, D., Jiang, F., Tu, J., and Zhou, G. (2015). Investor sentiment aligned: A powerful predictor of stock returns. The Review of Financial Studies, 28(3):791–837.
Kumar, A. (2009). Hard-to-value stocks, behavioral biases, and informed trading. Journal of Financial and Quantitative Analysis, 44(6):1375–1401.
Lewellen, J. (2004). Predicting returns with financial ratios. Journal of Financial Eco nomics, 74(2):209–235.
Li, B. (2020). Option-implied filtering: evidence from the garch option pricing model. Review of Quantitative Finance and Accounting, 54(3):1037–1057.
Lopes, H. F. and Tsay, R. S. (2011). Particle filters and bayesian inference in financial econometrics. Journal of Forecasting, 30(1):168–209.
Ludvigson, S. C. and Ng, S. (2007). The empirical risk–return relation: A factor analysis approach. Journal of Financial Economics, 83(1):171–222.
McLean, R. D. and Pontiff, J. (2016). Does academic research destroy stock return predictability? The Journal of Finance, 71(1):5–32.
Meng, J. and Weng, X. (2018). Can prospect theory explain the disposition effect? A new perspective on reference points. Management Science, 64(7):3331–3351.
Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. The Review of Economics and Statistics, pages 247–257.
Polkovnichenko, V. and Zhao, F. (2013). Probability weighting functions implied in options prices. Journal of Financial Economics, 107(3):580–609.
Prelec, D. (1998). The probability weighting function. Econometrica, pages 497–527. Quiggin, J. (1982). A theory of anticipated utility. Journal of Economic Behavior & Organization, 3(4):323–343.
Rapach, D. E., Strauss, J. K., and Zhou, G. (2010). Out-of-sample equity premium prediction: Combination forecasts and links to the real economy. The Review of Financial Studies, 23(2):821–862.
Rosenberg, J. V. and Engle, R. F. (2002). Empirical pricing kernels. Journal of Financial Economics, 64(3):341–372.
Shefrin, H. and Statman, M. (1985). The disposition to sell winners too early and ride losers too long: Theory and evidence. The Journal of finance, 40(3):777–790.
Shi, Y., Cui, X., and Zhou, X. Y. (2023). Beta and coskewness pricing: Perspective from probability weighting. Operations Research, 71(2):776–790.
Shleifer, A. and Vishny, R. W. (1997). The limits of arbitrage. The Journal of Finance, 52(1):35–55.
Stambaugh, R. F. (1999). Predictive regressions. Journal of Financial Economics, 54(3):375–421.
Stock, J. H. and Watson, M. W. (2004). Combination forecasts of output growth in a seven-country data set. Journal of Forecasting, 23(6):405–430.
Tversky, A. and Kahneman, D. (1992). Advances in prospect theory: Cumulative repre sentation of uncertainty. Journal of Risk and Uncertainty, 5:297–323.
Wang, Y., Pan, Z., Liu, L., and Wu, C. (2019). Oil price increases and the predictability of equity premium. Journal of Banking & Finance, 102:43–58.