VILLANUEVA DE LA SERENA HOSPITAL DE SANTA JUSTA

Robert Bordleya _{and Luisa Tibiletti}b

a_{Department of Industrial Engineering and Operations Management, University of Michigan, USA. Email:} [email protected], b_{Department of Management, University of Torino, Corso Unione Sovietica 218/bis,}

10134 Torino, Italy. Email: [email protected]

Abstract

According to the paradigms of behavioral finance, investors’ loss-gain profile is framed according to the reference point (e.g. the status quo) or multiple reference points (e.g. the minimum requirement, the status quo and the goal). However empirical tests show that investors’ loss aversion and gain appetite is also affected by the market trend mood (see Hwang and Satchell, 2010; Hofschire et al, 2013).

By setting up an asset allocation optimization problem performed in US and UK financial markets, Hwang and Satchell (2010) show that investors are far more loss averse during bull markets than during bear markets. Several empirical tests lend support that tendency. Hofschire et al. (2013) claim that despite the stock bull market started since 2009 investors act as loss adverse agents and continue to shun to invest n equities.

This article proposes to go a step further in investigating the following questions: How do investors identify the bullish and bearish market trend? Does the evidence: “investors display more loss aversion during bull markets than during bear markets” ground on sound normative framework?

To answer the former question we introduce a definition for investor’s perceived market trend. We claim that investors watch through “reference-dependent glasses” the market sentiment indicators and elaborate personal vision of the market mood. The latter question is positively answered. In Theorem 1 we show that investors are normatively loss averse during perceived bullish markets, and the sentiment is reversed during perceived bearish trends. The key insight is the one-to-one relationship between the perceived distribution of the market sentiment indicator and the investor normalized utility function.

A more detailed account of our findings follows.

First, we discuss how to identify the subjective investor mood on bullish and bearish trends. To this purpose we discuss the separate values given by the market sentiment of the selected indicator (e.g. the Forex or the stock sentiment indicator) that expresses institutional investors’ views ground on fundamental and technical analysis and professional investors’ forecasts and the subjective reference point (e.g. the status quo). We claim that the investor perceives a bullish or bearish trend on the basis of the mismatch between the market sentiment indicator figure and the subjective reference point, respectively.

Second, we suggest a user-friendly method for investors to tailor the utility function to their loss-gain profile. Following the seminal intuition of Borch (1968) summarized by the Berhold (1973, p. 825) phrase “there are advantages to having the utility function represented by a distribution”, we illustrate how to get full information about loss-gain attitudes using the cumulative distribution function (c.d.f.) of the performance benchmark (e.g. the S&P 500 index, MSCI index among others) used in investment evaluation. We show the equivalence between the c.d.f. of the benchmark to meet and the normalized investor cardinal utility function.

Third. Although over 30 years have gone by the Kahneman and Tversky (1979) ground-breaking work, there is no uniquely agreed-upon loss aversion and risk appetite definitions (for a review see Abdellaoui et al., 2007; and Ghossoub, 2012). On the path of Bordley et al. (2014) we propose a loss aversion and

Why are investors loss averters during bull markets and gain seekers during bear markets?

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1st International Conference on Business Management  

risk appetite definition. The loss aversion definitions introduced by Kahneman and Tversky (1992, p. 303) and Kahneman and Tversky (1979, p. 279) follow as special cases.

Fourth, we present the main contribution of the paper. In presence of a singular preference point, loss aversion and risk appetite definitions turn out to be formally equivalent to the van Zwet (1979) asymmetry conditions characterizing asymmetrical unimodal distributions. Theorem 1 states the one-to- one relationship between perceived bullish/bearish market trend and loss aversion/gain appetite preference.

Then we address the question whether the most popular utility functions, as the exponential, the Kahneman-power type and kinked linear enjoy the van Zwet (1979) asymmetry conditions. The answer is positive. In fact, the above utility functions properly re-scaled, can be read as c.d.f. belonging to the Pearson family.

In presence of multiple reference points, the asymmetrical sentiment towards loss-gain is related to the location of reference points respect to the market sentiment value.

In conclusion, our findings match a twofold aim. First, we provide theoretical foundations to the numerous empirical studies postulating that investors are far more loss averse during bull markets than during bear markets (see Hwang and Satchell, 2010; Hofschire et al, 2013). Second, we prove that during reference-dependent bullish markets investors are normatively lead to loss aversion, vice versa during reference-dependent bearish markets the sentiment is normatively switched to gain appetite (see Theorem 1). That provides also a descriptive and normative ground to the popular dictum: “Be Fearful When Others Are Greedy and Greedy When Others Are Fearful” inviting investors to be loss averters during bull markets and gain seekers during bear markets.

References

Berhold, M.H. (1973). The use of distribution functions to represent utility functions, Management Science, 19, 825- 829.

Borch, K. (1968). Decision rules depending on the probability of ruin, Oxford Economic Papers, 20, 1-10.

Bordley, R., LiCalzi, M., & Tibiletti, L. (2014). A target-based foundation for the “hard-easy effect” bias, Working

Paper n. 23/2014, October 2014, Università Ca’ Foscari Venezia, Italia, ISSN: 2239-2734.

Ghossoub, M. (2012) Towards a Purely Behavioral definition of loss Aversion, SSRN Electronic Journal 03/2012; DOI: 10.2139/ssrn.2028146

Hofschire, D., Embo-Mattingly, L., Gold, E., & Blackwell, C., (2013). Is Loss aversion causing Investors to Shun Equities?, Market Perspectives, Fidelity Investments.

Hwang, S., & Satchell, S.E. (2010). How Loss Averse Are Investors in Financial Markets?, Journal of Banking &

Finance, 34, 2425-2438

Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decisions Under Risk, Econometrica, 47(2), 263-91.

Kahneman, D., Tversky, A. (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty,

Journal of Risk and Uncertainty, 5, 297-323.

1st International Conference on Business Management Universitat Politècnica de València, 2015 DOI: http://dx.doi.org/10.4995/ICBM.2015.1418