###### Options

Type

applied research project

Start Date

01 June 2010

End Date

31 May 2013

Status

completed

Keywords

Behavioral finance

Regression trees

Investor sentiment

Computational statistics

Portfolio selection

Pricing kernel

Asset pricing

Boosting

Machine learning

Description
In the classical finance literature, the pricing kernel (or stochastic discount factor) represents the unified framework for asset pricing (see Cochrane 2001). Two results from finance theory imply the centrality of the pricing kernel. First, in the absence of risk-free arbitrage, prices can always be written as expected payoffs weighted by the pricing kernel (see Duffie 1988). Second, in many representative agent models the pricing kernel can be easily linked to investor's preferences when these satisfy the expected utility theory of von Neumann and Morgenstern (1944). Behavioural finance identifies several pricing anomalies or puzzles, i.e., empirical observations that cannot be understood using classical models for asset pricing. However, pricing anomalies generally do not imply risk-free arbitrage investment opportunities, thus the pricing kernel remains the unified framework for asset pricing also in the context of behavioral asset pricing. The question of how the investor sentiment, i.e., the way people form beliefs in practice (thus also their biases), impacts the pricing kernel has recently attracted the attention of researchers; see, for example, De Bondt and Thaler (1985), Lee, Shleifer, and Thaler (1991), Swaminathan (1996), Neal and Wheatley (1998), Shefrin (1999), Han (2004) and Baker and Wurgler (2006). Shefrin (2001) and De Giorgi and Post (2008) propose behavioral asset pricing models where the link between the pricing kernel and the investor sentiment is formalized. In De Giorgi and Post (2008) the pricing kernel corresponds to a distortion of markets' returns which implies a pessimistic view on the market, i.e., investors attach higher probabilities to negative returns compared to the true distribution. The aim of this project is to contribute to this growing literature on behavioral asset pricing. More specifically, we want to (1) Extend the asset pricing model of De Giorgi and Post (2008) along several directions, in order to derive a formal link between the pricing kernel and the investor sentiment under more general assumptions on the market and on investors' preferences, compared to De Giorgi and Post (2008). (2) Use advanced techniques from computational statistics to calibrate the model from point (1) on market data, in particular the dynamics of the pricing kernel and the link to a set of behavioral risk factors. (3) Derive directly from market data a model-independent estimation of the pricing kernel and link it to a set of behavioral risk factors. (4) Develop a time-series model for the pricing kernel. (5) Apply the results from the previous points to price options and to derive behavioral investment strategies.

Leader contributor(s)

Funder(s)

Topic(s)

Behavioral finance

Regression trees

Investor sentiment

Computational statistics

Portfolio selection

Pricing kernel

Asset pricing

Boosting

Machine learning

Method(s)

Theoretical and empirical study

Range

HSG Internal

Range (De)

HSG Intern

Eprints ID

63181

Reference Number

130078

9 results

Now showing
1 - 9 of 9

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Publication

#### CAPM Equilibria with Prospect Theory Preferences

2011
,
Levy, Haim
,
Hens, Thorsten

Under the assumption of normally distributed returns, we analyze whether the Cumulative Prospect Theory of Tversky and Kahneman (1992) is consistent with the Capital Asset Pricing Model. We find that in every financial market equilibrium, the Security Market Line Theorem holds. However, under the functional form for the utility index suggested by Tversky and Kahneman (1992), the conditions for existence of financial market equilibria exclude economically meaningful equilibria. We suggest an alternative functional form that is consistent with both, the experimental results of Tversky and Kahneman (1992), and also with the existence of economically meaningful equilibria.

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Publication

#### A Behavioral Foundation of Reward-Risk Portfolio Selection and the Asset Allocation Puzzle

2008
,
Hens, Thorsten
,
Mayer, Janos

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Publication

#### Loss Aversion with Multiple Investment Goals

2011-10-01
,
De Giorgi, Enrico

This paper presents a time-continuous portfolio selection model with loss averse investors, who possess multiple investment goals at different time horizons. The model assumes partial narrow framing. Investors follow a two-step approach. First, they optimally allocate wealth among investment goals. Second, they determine an optimal investment strategy for each investment goal separately. We show that when loss aversion is according to the experimental findings, investors mainly invest their wealth to reach long-term goals and adopt investment strategies with high leverage to reach short-term goals. The overall strategy also display high leverage. The same patterns is observed when loss aversion is extreme and goals are very ambitious. By contrast, when loss aversion is extreme but goals are not too ambitious, investors mainly invest to reach short-term goals and adopt safe investment strategies for this purpose.

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Publication

#### Prospect Theory and Mean-Variance Analysis: Does it Make a Difference in Wealth Management?

2009-07-01
,
De Giorgi, Enrico
,
Hens, Thorsten

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Publication

#### A Concave Security Market Line

2012
,
De Giorgi, Enrico
,
Post, Thierry
,
Yalcin, Atakan

We provide theoretical and empirical arguments in favor of a concave shape for the security market line, or a diminishing marginal premium for market risk. In capital market equilibrium with binding portfolio restrictions, different investors generally hold different sets of risky securities. Despite the differences in composition, the optimal portfolios generally share a joint exposure to systematic risk. Equilibrium in this case can be approximated by a concave relation between expected return and market beta rather than the traditional linear relation. An empirical analysis of U.S. stock market data confirms the existence of a significant and robust, concave cross-sectional relation between average return and estimated past market beta. We estimate that the market-risk premium is at least five to six percent per annum for the average stock, substantially higher than conventional estimates.

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Publication

#### Two Paradigms and Nobel Prizes in Economics: A Contradiction or Coexistence?

2012-03
,
De Giorgi, Enrico
,
Hens, Thorsten
,
Levy, Haim

Markowitz and Sharpe won the Nobel Prize in Economics for the development of Mean-Variance (M-V) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected utility (EU) maximisation in the face of risk aversion. Kahneman and Tversky suggest Prospect Theory (PT) as an alternative paradigm to EU theory. They show that investors distort probabilities, make decisions based on change of wealth, exhibit loss aversion and maximise the expectation of an S-shaped value function, which contains a risk-seeking segment. Can these two apparently contradictory paradigms coexist? We show in this paper that although CPT (and PT) is in conflict to EUT, and violates some of the CAPM's underlying assumptions, the Security Market Line Theorem (SMLT) of the CAPM is intact in the CPT framework. Therefore, the CAPM is intact also in CPT framework.

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Publication

#### A Behavioral Explanation of the Asset Allocation Puzzle

2011-12-01
,
De Giorgi, Enrico

This paper combines a behavioral reward-risk model based on prospect theory with multiple investment accounts to explain the asset allocation puzzle, that is, the observation that investors violate the two-fund separation property of
optimal mean-variance allocations. In a empirical analysis with U.S. data, the authors show that investors with preference according to the behavioral reward-risk model and multiple investment accounts, invest a higher proportion into bonds and large cap stocks as their risk tolerance diminishes, consistently with the empirical findings.

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Publication

#### Dynamic Portfolio Choice and Asset Pricing with Narrow Framing and Probability Weighting

2012-07
,
De Giorgi, Enrico
,
Legg, Shane

This paper shows that the framework proposed by Barberis and Huang (2009) to incorporate narrow framing and loss aversion in dynamic models of portfolio choice and asset pricing can be extended to also account for probability weighting and a value function which is convex on losses and concave on gains. We show that the addition of probability weighting and a convex-concave value function reinforces previous applications of narrow framing and cumulative prospect theory to explain the stock market non-participation puzzle and the equity premium puzzle. Moreover, we show that a convex-concave value function generates new wealth effects that are consistent with empirical observations on stock market participation.

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Publication

#### Loss Aversion with a State-dependent Reference Point

2011-04-29
,
De Giorgi, Enrico
,
Post, Thierry

This study investigates reference-dependent choice with a stochastic, state-dependent reference point. The optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) if the reference point is selected fully endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. We develop a choice model in which adjustment costs can cause stickiness relative to an initial, exogenous reference point. Using historical U.S. investment benchmark data, we show that this model is consistent with diversification across bonds and stocks for a wide range of evaluation horizons, despite the historically high-risk premium of stocks compared to bonds.