The Perception of Dependence, Investment Decisions, and Stock Prices

• Author: MARTIN WEBER,MICHAEL UNGEHEUER
• Published date: 01 April 2021
• DOI: http://doi.org/10.1111/jofi.12993
• Date: 01 April 2021

THE JOURNAL OF FINANCE •VOL. LXXVI, NO. 2 •APRIL 2021

The Perception of Dependence, Investment

Decisions, and Stock Prices

MICHAEL UNGEHEUER and MARTIN WEBER*

ABSTRACT

How do investors perceive dependence between stock returns; and how does their per-

ception of dependence affect investments and stock prices? We show experimentally

that investors understand differences in dependence, but not in terms of correlation.

Participants invest as if applying a simple counting heuristic for the frequency of

comovement. They diversify more when the frequency of comovement is lower even

if correlation is higher due to dependence in the tails. Building on our experimen-

tal f‌indings, we empirically analyze U.S. stock returns. We identify a robust return

premium for stocks with high frequencies of comovement with the market return.

IN THIS PAPER,WE STUDY how dependence between stock returns affects in-

vestment decisions and stock prices. Based on four laboratory experiments,

we show that participants are able to understand dependence between fre-

quent moderate returns. However, despite spending more time viewing ex-

treme returns, most participants are not able to correctly answer questions

about dependence in tail states. This result is in line with evidence from neu-

roscience that humans f‌ind it diff‌icult to detect and adapt to extreme realiza-

tions (D’Acremont and Bossaerts (2016)). Consequently, participants’ beliefs

about overall dependence tend to increase with the frequency of comovement

between stock returns, as if participants were using a counting heuristic. Con-

sistent with their beliefs about overall dependence, participants diversify more

*Michael Ungeheuer is at Aalto University. Martin Weber is at the University of Mannheim

and the Centre for Economic Policy Research. We are grateful to Stefan Nagel (the Editor), an

anonymous Associate Editor, two anonymous referees, as well as Peter Bossaerts, Dan Egan,

Markus Glaser, Alexander Hillert, Zwetelina Iliewa, Heiko Jacobs, Matti Keloharju, Christopher

Koch, Anja Kunzmann, Christine Laudenbach, Christoph Merkle, Hannes Mohrschladt, Alexan-

dra Niessen-Ruenzi, Stefan Ruenzi, André Schmelzer, and Ellapulli Vasudevan for valuable com-

ments. We also thank seminar participants at the University of Mannheim and the Ludwig Max-

imilian University of Munich, as well as conference participants at the Experimental Finance

Conference 2015, the ESA Conference 2015, the Research in Behavioral Finance Conference Am-

sterdam 2016, the SGF Conference 2017, the Boulder Summer Conference 2017, the DGF Confer-

ence 2017, and the AEA Conference 2018. Weber thanks the German Research Foundation(DFG),

Research Grant WE993/15-1, and the University of Mannheim’s Area of Banking, Finance & In-

surance for f‌inancial support. The authors do not have any potential conf‌licts of interest to disclose

as identif‌ied in The Journal of Finance’s disclosure policy.

Correspondence: Michael Ungeheuer, Aalto University; e-mail: michael.ungeheuer@aalto.f‌i.

DOI: 10.1111/jof‌i.12993

© 2020 the American Finance Association

797

798 The Journal of Finance®

when the frequency of comovement between stock returns decreases, even if

the correlation increases due to strong positive dependence in extreme returns.

We apply our insights on the perception of dependence from the laboratory

to U.S. stock returns over the 1963 to 2015 period in a test of the capital asset

pricing model (CAPM; Sharpe (1964), Lintner (1965), Mossin (1966)). We f‌ind

that stocks with higher frequencies of comovement with the market return ex-

hibit a robust return premium. This result is consistent with investors requir-

ing a reward for holding stocks with high perceived dependence, in line with

the CAPM. In contrast, beta as measured by historical return correlations—

the most commonly used proxy for expected systematic risk in tests of the

CAPM—is not priced in the cross section of stock returns (Fama and French

(2004)).

In many economic decisions, dependence between different sources of risk

plays an important role. In f‌inance, the impact of dependence on portfolio se-

lection has been a focal topic since Markowitz (1952). Consider the investment

decision of how much to allocate to asset classes such as stocks, bonds, and

real estate. Empirically, the returns of these asset classes are mutually de-

pendent. Investing in asset classes that increase in value when other asset

classes decline in value (negative dependence) reduces overall portfolio risk. As

in Markowitz (1952), economists have mainly used the expected Pearson cor-

relation to capture dependence in these diversif‌ication decisions. Asset classes

that have low correlation with a portfolio provide “insurance” for unexpectedly

low- or high-portfolio returns and as a result decrease portfolio return vari-

ance. They should therefore have a high weight in optimal portfolios. Building

on Markowitz (1952), Sharpe (1964) shows that in equilibrium, the high di-

versif‌ication benef‌its of assets with low dependence on market returns (or low

beta) should lead to higher prices and lower expected returns.

However, historical stock returns provide little evidence of realized beta be-

ing priced (Fama and French (2004)). One reason may be that investors per-

ceive dependence differently than as observed correlation or beta. For instance,

they might use a simple counting heuristic and thus understand the frequency

of comovement between stock returns (i.e., the frequency of equally signed

stock returns), underweighting extreme returns relative to correlation. In sup-

port of this hypothesis, evidence from neuroscience suggests that humans

have diff‌iculty detecting and adapting to extreme realizations (D’Acremont and

Bossaerts (2016)). Extreme realizations are intrinsic to f‌inancial markets and

modern society with large-scale human interaction, but relatively new from an

evolutionary perspective, which might explain this diff‌iculty. Extreme realiza-

tions also heavily inf‌luence correlation, so that signif‌icant differences between

a perception of dependence driven by observed correlation versus observed fre-

quency of comovement can be expected. In contrast to econometricians (e.g.,

Bollerslev, Todorov, and Li (2013)), experimental researchers have neglected

the importance of dependence between the tails of distributions or, more gener-

ally, measures of dependence beyond correlation. In particular, the experimen-

tal literature on portfolio selection does not address the following questions:

How do investors perceive dependence in the presence of extreme returns, and

The Perception of Dependence, Investment Decisions, and Stock Prices 799

how does such perception inf‌luence their investment decisions? We provide an-

swers to these questions and then link our experimental insights to historical

stock returns by testing the CAPM using a measure of dependence motivated

by how experimental participants perceive dependence in the laboratory.

We run four individual investment experiments to analyze how varying de-

pendence between stock returns affects investment decisions. We vary the de-

pendence between the returns of two stocks across treatments in a counter-

balanced design, keeping marginal distributions (return means, volatilities,

extrema, etc.) constant. We then ask participants to invest their endowment in

the two stocks and elicit their beliefs about dependence between stock returns.

In our f‌irst experiment, we vary linear dependence1(i.e., we vary dependence

in moderate and extreme returns synchronously) in three treatments to pro-

vide a baseline for tests on dependence in the tails versus moderate returns.

We f‌ind that participants’ beliefs are consistent with changes in dependence.

Consequently, participants diversify less when dependence increases, in line

with Markowitz (1952). In our next three experiments, we test the hypothesis

that people have diff‌iculty adapting to dependence in extreme returns by vary-

ing nonlinear dependence. In particular, we decrease dependence in moderate

returns and increase dependence in extreme returns from one treatment to

the other. We f‌ind that participants’ overall beliefs are driven by dependence

in frequent moderate returns, consistent with a counting heuristic. Partici-

pants mostly do not understand dependence in extreme returns and diversify

less when dependence increases in moderate returns, even if correlation de-

creases due to decreasing dependence in extreme returns. Thus, their behavior

is exactly the opposite of what one would expect according to Markowitz (1952)

in combination with observed return correlations. In summary, while partici-

pants do account for differences in dependence, their beliefs and choices are not

explained by observed correlation but rather by perceived dependence under a

simple counting heuristic.

Based on this insight, we turn to historical stock returns and test whether

perceived dependence is priced. If investors’ beliefs about dependence and in-

vestment decisions are driven by dependence in frequent returns instead of

correlation, this could lead to a return premium for stocks with higher frequen-

cies of comovement with the market, in line with the CAPM (Sharpe (1964)).

We test this hypothesis using U.S. stock returns for the 1963 to 2015 period

and f‌ind evidence of a return premium for stocks that frequently have the

same sign in stock return as the S&P 500. In particular, we estimate a pre-

mium of 4.28% per year (Carhart alpha =5.54%) for high-minus-low quintile

stock returns when sorting by frequency of comovement. This premium is not

explained by a large number of factor models. In Fama and MacBeth (1973)

regressions, we show that other measures of dependence such as downside

risk and measures of idiosyncratic risk such as idiosyncratic volatility do not

1We use the term “linear dependence” when the expected value of one stock’s return is linear

in the other stock’s return, that is, E(r1|r2)=a+b·r2. If this relation does not hold, we refer to

the dependence between the two stocks as “nonlinear.”