1. 1 View Bias towards Ambiguity, Expectile CAPM and the Anomalies Wei Hu, ZhenLong Zheng

2. Campbell (2000), Asset Pricing at the Millennium Theorists develop models with testable predictions; empirical researchers document “puzzles” –stylised facts that fail to fit established theories –and this stimulates the development of new theories. Such a process is part of the normal development of any science. 2

3. 3 Motivation Beta coefficient mean reverse Expected utility maximization axiom Risk preference & confidence Risk & uncertainty Equity premium puzzle

4. 4 Main work New concept of risk-reward measurement (Non-perfect information, view tendency) Revised expected utility maximization axiom Redo Merton problem VLS econometrics method (GMM+VLS) Empirical Analysis

5. 5 A general framework of risk-reward measurement -Concept Mean & Variance (OLS) Median & Absolute deviation (LAD) Quantile & Weighted absolute deviation (Quantile regression) Expetile & Variancile (???) E (Reward) D (Risk)

6. 6 A general framework of risk-reward measurement -Definition

7. 7 A general framework of risk-reward measurement -More detail Quantile Expectile

8. 8 A general framework of risk-reward measurement -Remark

9. 9 A general framework of risk-reward measurement -Explanatio n Perfect information vs Non-perfect information / E+D vs maxmin Question: same minimum? Answer: quantile Question: information fully used? Answer: No + inconvenience  Expectile Table 2.2-1 Perfect Information Based Decision Making Table 2.2-2 Non- perfect Information Based Decision Making

10. 10 A general framework of risk-reward measurement -Intuition Figure2.2-1 Probability Adjustment under Non-perfect Information (Pessimistic Investor )

11. 11 A general framework of risk-reward measurement -Comparison

12. 12 A general framework of risk-reward measurement -Property

13. A general framework of risk-reward measurement -Property 13

14. 14 Expectile CAPM Model -Assumption Assumption1: time interval between each decision is infinitesimal Assumption2: prices are diffusion processes Assumption3: only consumption and portfolio process are controllable Assumption4: No exogenous endowment Assumption5: Homogenous investors

15. 15 Expectile CAPM - Modellin g St: boundary condition: budget equations: assumption2:

16. Expectile CAPM Model - Result 16

17. 17 Expectile CAPM Model -Model specification systematic risk is the weighted average of exposed risk and potential risk Figure 3.2-1-adjusted risk-reward projection D

18. 18 New approach to explain equity premium puzzle Equity premium puzzle can be explained in a way that people are pessimistic when there is no perfect information in the postwar US

19. 19 How to estimate VCAPM? Why new econometrics model? Model correct specification requires But

20. 20 VLS Comparison  VLS vs.OLS  VLS vs. WLS  VLS vs.Quantile regression

21. How to estimate VCAPM? We establish the VLS methodology by listing all the assumptions, finding new estimators, and proving the asymptotic consistency and normality in large sample analysis. We develop the hypothesis testing by the case of conditional homoskedadticity and heteroskedasticty. We estimate and test the expectile based unconditional CAPM theory through the conditional GMM being restricted by a view bias based linear condition. 21

22. 22 How to estimate VCAPM?

23. 23 Empirical Results(1) Assume risk aversion is constant 3,then from We get find theta is between o.47 to 0.53 with mean 0.497 using US. post war data. The periodicity is 60 months.

24. 24

25. 25 Empirical Results(2) From spectral analysis. 13 of 20 stocks share a compatible periodicity with view tendency.

26. Contributions We define the expectile and variacile We revise the expectation utility maximization axiom into an expectile utility maximization axiom. We redo Merton Problem under the expectile framework, and extend the CAPM theory. we develope a new econometrics methodology, the view bias adjusted least square (VLS) to test the extended CAPM theory. 26

27. Contributions we demonstrate the advantage of the expectile based asset pricing theory through empirical application. Our approach solves the two categories of anomalies within one integrated and extended asset pricing theoretical framework. The advantage of our approach is that not only does the expectile take the merits of quantile, but also the expectile based asset pricing framework takes the merits of expectation framework. 27

28. 28 Thanks! welcome to visit: http://efinance.org.cn