The Importance of Risk Preference Parameters in Prospect Theory: Evidence from Mutual Fund Flows

Abstract

In this paper, we use the well-documented mutual fund flow-performance relationship to infer information about investors’ preferences. We show that applying preference parameter values from experimental settings to market data can significantly understate the role of prospect theory in explaining investor behavior. We find evidence that mutual fund investors exhibit loss aversion and differential attitudes toward risk over losses (risk-seeking) and gains (risk-averse) but no significant probability weighting when evaluating fund performance. Our results apply more strongly to retail funds compared to institutional funds, consistent with the view that prospect theory is more relevant for retail investors. Finally, we show that, for parameter values that best explain fund flows, prospect theory outperforms the global risk aversion framework and widely-used asset pricing models in explaining investors’ responses to fund performance.

Keywords:

• G11
• G23
• G40
• loss aversion
• mutual fund flows
• prospect theory
• reference-dependent preferences

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 See Shefrin and Statman (1985), Odean (1998), Grinblatt and Han (2005), Frazzini (2006), and Barberis and Xiong (2009) on how prospect theory can account for the disposition effect, Benartzi and Thaler (1995), Barberis, Huang, and Santos (2001) for the equity premium puzzle, and Ingersoll and Jin (2013), Wang, Yan, and Yu (2017), An et al. (2020) for the lack of a positive risk-return relation for stocks as well as the negative risk premium for idiosyncratic risk and lottery preferences.

2 See Ang et al. (2006, Ang et al. 2009), Blitz and van Vliet (2007), Baker, Bradley, and Wurgler (2011), and Frazzini and Pedersen (2014).

3 See Gu and Yoo (2021), Guo and Schönleber (2021), Han, Sui, and Yang (2021), and Gupta, Mishra, and Jacob (2022) as examples of studies that adopt the Kahneman and Tversky (1992) parameter values to explain mutual fund flows.

4 Apart from experiments, studies that structurally estimate agents’ preferences use data from betting (Golec and Tamarkin (1998; Jullien and Salanié (2000; Snowberg and Wolfers (2010; Andrikogiannopoulou and Papakonstantinou (2019) and insurance markets (Cohen and Einav (2007; Syndor (2010; Barseghyan et al. (2013).

5 The power utility function reduces to log utility for $\theta =1,$ while $\theta =0$ implies risk neutrality.

6 Specifically, experiment participants prefer a sure gain of $50 over a 50% chance of gaining $100 (risk-averse behavior over gains), while they prefer a 50% chance of losing $100 over a sure loss of $50 (risk-seeking behavior over losses). 100, suggesting risk − averse behavior overgains, yet they turn to risk − seeking behavior over losses, as they prefera 50% chance of losing.

7 CRSP objective codes are constructed using objective codes from three different sources (Wiesenberger, Strategic Insight, and Lipper) in order to provide continuity in style classifications. Detailed information can be found at http://www.crsp.com/products/documentation/crsp-style-code.

8 Index funds and ETFs reflect purely factor returns without margin for discretionary managerial performance. As a result, the well-known performance-flow relationship, which we use to infer information about investors’ preferences, exists prominently among actively managed funds (see, e.g. Sirri and Tufano (1998), Chevalier and Ellison (1997), Barber, Huang, and Odean (2016). We exclude these funds based on an index fund or ETF flag or on a fund name containing a string associated with index funds or ETFs.

9 We sum the TNA of each share class to obtain a fund’s TNA. Fund age is defined as the age of the oldest share class. We calculate the value-weighted averages of monthly return, expense ratio, and turnover ratio across share classes. The fund objective is defined based on the largest share class of the fund.

10 We consider an alternative definition of fund flows following Spiegel and Zhang (2013) in robustness tests (section 5.6). Also, we obtain qualitatively similar results when we apply the Berk and Tonks (2007) fund flow correction: $$F_{\mathit{\text{it}}}=\frac{{\mathit{\text{TNA}}}_{\mathit{\text{it}}}-(1+R_{\mathit{\text{it}}}){\mathit{\text{TNA}}}_{\mathit{\text{it}}-1}}{(1+R_{\mathit{\text{it}}}){\mathit{\text{TNA}}}_{\mathit{\text{it}}-1}}$$

11 Initially, we assume no probability weighting ($\gamma =\delta =1$), but we relax this assumption in Section 4.4.

12 The control variables include logarithms of fund size and age, turnover and expense ratios, a load dummy indicating whether any of the fund’s share classes charge front-end or back-end loads, and the logarithm of fund family size.

13 The time-variation of the flow-performance relationship has been extensively documented in the literature, and it has been associated with market conditions (Franzoni and Schmalz (2017), uncertainty (Starks and Sun (2016) and alpha dispersion (Harvey and Liu 2019).

14 The Morningstar risk-adjustment methodology imposes $\theta =3$ (see https://www.morningstar.com/content/dam/marketing/shared/research/methodology/771945_Mornin gstar_Rating_for_Funds_Methodology.pdf).

15 For now, we assume no probability weighting, but we relax this assumption in the next subsection.

16 Overall, the utility function that corresponds to the parameter value vector with $\alpha =0.85,$ $\beta =0.90,$ and $\lambda =1.45$ exhibits the characteristic S-shape (see Figure A1), suggesting that mutual fund investors are risk-seeking over losses (convex part) and risk-averse over gains (concave part).

17 To circumvent the computational challenges arising from the number of parameters to consider, we use wider grids for RDP parameters and set the PW parameters to be equal ($\gamma =\delta$). Specifically, we let $\lambda$ take values from 0.5 to 2.5 in increments of 0.25, and $\alpha ,$ $\beta ,$ and $\gamma =\delta$ range from 0.4 to 1.2 in increments of 0.1.

18 Note that our sample includes both small and large funds (Table 1), and only excludes very small mutual funds (less than $15 million in TNA) as detailed in Section 3.

19 These results remain consistent across all our robustness tests in Section 5.6.

20 Since our results indicate that investors exhibit RDP but no significant probability weighting, we use the term “RDP” in Tables and Figures, thereafter, when we refer to the prospect theory framework with $\gamma =\delta =1.$

21 It is not clear over which horizon investors evaluate the performance of their investments. In our study, we use a one-year horizon following the literature on the mutual fund flow-performance relationship (Sirri and Tufano (1998; Chevalier and Ellison (1997), and Benartzi and Thaler (1995) who suggest that one year is a plausible period for investors to evaluate their returns and determine whether they have made losses or gains.

22 Note that preferences under GRA with $\theta =0$ or under prospect theory with $\lambda =\alpha =\beta =1$ also correspond to risk neutrality. Since our analysis focuses on cross-sectional tests, excess returns can be regarded as equivalent to raw or market-adjusted returns.

23 A one standard deviation increase in RDP-GRA ($\sigma =0.28\%$) corresponds to a 0.7% increase in monthly flows.

24 CRSP institutional (retail) fund flags are based on the Lipper categorization method, according to which a fund share class is classified as Institutional if it has a minimum investment requirement of at least $100,000 and if its shares are distributed to or through an institution (see Salganik-Shoshan (2016). Also, CRSP institutional (retail) fund flags are available from 1999 onward. For years prior to 1999, we backfill this information whenever it is available. Additionally, we categorize funds with names containing ”Class I,” ”Class Y,” ”Class X,” ”Class K,” ”Institutional,” ”Inst,” ”Trust Class,” ”Premier Class,” and ”Fiduciary Class” as institutional, and funds with names containing ”Retail” and ”Ret” as retail.

25 We obtain qualitatively similar results when we restrict our sample to purely institutional or retail funds (i.e., with 100% of assets held in respective share classes).

26 In an average month, 59% of the funds in our sample outperform the monthly risk-free rate, while 61% and 46% have returns over zero and market return, respectively.

27 Early studies that focus on the return-chasing behavior of investors use a one-year horizon (e.g., Sirri and Tufano (1998), Chevalier and Ellison (1997), whereas more recent studies that examine risk-adjusted returns use a longer time period (e.g., Barber, Huang, and Odean (2016; Berk and van Binsbergen (2016). Morningstar evaluates the performance of a fund using 3, 5, or 10 years of data depending on data availability.

28 Spiegel and Zhang (2013) argue that the convexity in the flow-performance relationship is caused by heterogeneous responses of investors, and it disappears when fund flows are defined as changes in market shares: $$F_{\mathit{\text{it}}}^{\mathit{\text{SZ}}}=\frac{{\mathit{\text{TNA}}}_{\mathit{\text{it}}}}{\overline{\mathit{\text{TotalTN}}{A}_t}}-\frac{{\mathit{\text{TNA}}}_{\mathit{\text{it}}-1}}{\mathit{\text{TotalTN}}{A}_{t-1}}$$ where $\mathit{\text{TotalTN}}{A}_{t-1}$ is the sum of the TNA of all funds in the sample as of month $t-1$ and $\overline{\mathit{\text{TotalTN}}{A}_t}$ is the sum of the TNA of the same funds that existed in $t-1$ as of t.

29 In untabulated results, our baseline findings also remain strongly robust in the presence of controls for Morningstar ratings (Evans and Sun 2021; Ben-David et al. 2022).