Speculative Betas

• Published date: 01 October 2016
• Author: DAVID A. SRAER,HARRISON HONG
• Date: 01 October 2016
• DOI: http://doi.org/10.1111/jofi.12431

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 5 •OCTOBER 2016

Speculative Betas

HARRISON HONG and DAVID A. SRAER∗

ABSTRACT

The risk and return trade-off, the cornerstone of modern asset pricing theory,is often

of the wrong sign. Our explanation is that high-beta assets are prone to speculative

overpricing. When investors disagree about the stock market’s prospects, high-beta

assets are more sensitive to this aggregate disagreement, experience greater diver-

gence of opinion about their payoffs, and are overpriced due to short-sales constraints.

When aggregate disagreement is low,the Security Market Line is upward-sloping due

to risk-sharing. When it is high, expected returns can actually decrease with beta. We

confirm our theory using a measure of disagreement about stock market earnings.

THERE IS COMPELLING EVIDENCE that high-risk assets often deliver lower ex-

pected returns than low-risk assets. This is contrary to the risk-return trade-off

at the heart of neoclassical asset pricing theory. The high-risk, low-return puz-

zle literature, which dates back to Black (1972) and Black, Jensen, and Scholes

(1972), shows that low-risk stocks, as measured by a stock’s comovement with

the stock market or Sharpe’s (1964) capital asset pricing model (CAPM) beta,

have significantly outperformed high-risk stocks over the last 30 years.1Baker,

Bradley,and Wurgler (2011) further show that since January 1968 the cumula-

tive performance of stocks has actually been declining with beta. For instance,

∗Harrison Hong is in the Department of Economics, Princeton University. David A. Sraer is

in the Department of Economics and Haas School of Business, UC Berkeley. Hong acknowledges

support from the National Science Foundation through grant SES-0850404. Sraer gratefully ac-

knowledges support from the European Research Council (Grant No. FP7/2007-2013 - 249429) as

well as the hospitality of the Toulouse School of Economics. Weare especially grateful to Ken Sin-

gleton (the Editor) and two anonymous referees for helping us improve the paper significantly.For

insightful comments, we also thank Harjoat Bhamra, Andrea Frazzini, Augustin Landier, Lasse

Pedersen, Ailsa Roell, Jianfeng Yu, and seminar participants at MIT Sloan, Toulouse School of

Economics, Norges Bank-Stavanger Microstructure Conference, Norges Bank, Brazilian Finance

Society Meetings, Indiana University, Arizona State University, 2nd Miami Behavioral Finance

Conference, CNMV Securities Market Conference, University of Bocconi, University of Lugano,

University of Colorado, Brandeis University, Temple University,Hong Kong University of Science

and Technology, Duisenberg School Behavioral Finance Conference, Western Finance Associa-

tion, China International Finance Conference, Harvard Business School, USC, Q-Group, Helsinki

Behavioral Finance Conference, BI Bergen, IMF, Singapore Management University, Boston Col-

lege, McGill University, NYU Five Star Conference, Oxford-Man, Essec, NOVA-Catholica Lisbon,

ISCTE, Ohio State University, Rice University, University of Texas at Austin, University of Wis-

consin, and EDHEC-Princeton Conference. The authors have no material financial or nonfinancial

interests related to this research, as identified in the Journal of Finance’s disclosure policy.

1A nonexhaustive list of studies includes Blitz and Vliet (2007), Cohen, Polk, and Vuolteenaho

(2005), and Frazzini and Pedersen (2014).

DOI: 10.1111/jofi.12431

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2096 The Journal of Finance R

a dollar invested in a value-weighted portfolio of the lowest quintile of beta

stocks would have yielded $96.21 ($15.35 in real terms) at the end of December

2010, while a dollar invested in the highest quintile of beta stocks would have

yielded around $26.39 ($4.21 in real terms). Relatedly, Baker, Bradley, and

Wurgler (2011) and Frazzini and Pedersen (2014) both point out that a strat-

egy of shorting high-beta stocks and buying low-beta stocks generates excess

profits as large as famous excess stock return predictability patterns such as

the value growth or price momentum effects.2

In early work, Black (1972) originally tries to reconcile a flat Security Mar-

ket Line by relaxing one of the central CAPM assumptions of borrowing at

the risk-free rate. He shows that, in the presence of borrowing constraints,

risk-tolerant investors desiring more portfolio volatility will demand high-beta

stocks since they cannot simply lever up the tangency portfolio. However, bor-

rowing constraints can only deliver a flatter Security Market Line relative to

the CAPM, not a downward-sloping one; investors would not bid up high-beta

stock prices to the point of having lower returns than low-beta stocks. Indeed,

it is difficult to get a downward-sloping line even if one introduces noise traders

as in Delong et al. (1990) or liquidity shocks as in Campbell, Grossman, and

Wan g (1993), since noise traders or fundamental risk in these models lead to

higher expected returns.3

In contrast to Black (1972), we provide a theory for the high-risk and low-

return puzzle even when investors can borrow at the risk-free rate. We show

that relaxing the other CAPM assumptions of homogeneous expectations and

costless short-selling can deliver rich patterns in the Security Market Line, in-

cluding an inverted-U shape or even a downward-sloping line. Our model starts

from a CAPM framework, in which firms’ cash flows follow a one-factor model

and there are a finite number of securities so that markets are incomplete. We

allow investors to disagree about the market or common factor of firms’ cash

flows and prohibit some investors from short-selling. Investors only disagree

about the mean of the common factor of cash flows. There are two groups of

investors, buyers such as retail mutual funds (MFs) that cannot short and

arbitrageurs such as hedge funds (HFs) that can short.

Substantial evidence supports both of these assumptions. First, there is

time-varying disagreement among professional forecasters’ and households’

expectations about many macroeconomic state variables such as market earn-

ings, industrial production (IP) growth, and inflation (Cukierman and Wachtel

2The value-growth effect (Fama and French (1992), Lakonishok, Shleifer, and Vishny (1994)),

buying stocks with low price-to-fundamental ratios and shorting those with high ratios, generates

a reward-to-risk or Sharpe (1964) ratio that is two-thirds of a zero-beta-adjusted strategy of buying

low-beta stocks and shorting high-beta stocks. The corresponding figure for the momentum effect

(Jegadeesh and Titman (1993)), buying the past year’s winning stocks and shorting the past year’s

losing stocks, is roughly three-fourths of the long low-beta, short high-beta strategy.

3Indeed, most behavioral models would not deliver such a pattern. In Barberis and Huang

(2001), mental accounting by investors still leads to a positive relationship between risk and

return. The exception is the model of overconfident investors and the cross section of stock returns

in Daniel, Hirshleifer, and Subrahmanyam (2001), which might yield a negative relationship as

well but not the new patterns for beta that we document below.

Speculative Betas 2097

(1979), Kandel and Pearson (1995), Mankiw, Reis, and Wolfers (2004), Lamont

(2002)). Such aggregate disagreement might emanate from many sources in-

cluding heterogeneous priors or cognitive biases like overconfidence.4Second,

short-sales constraints bind for some investors for institutional reasons rather

than due to the physical cost of shorting.5For instance, many investors in the

stock market such as retail MFs, which in 2010 had 20 trillion dollars of assets

under management, are prohibited by charter from shorting either directly

(Almazan et al. (2004)) or indirectly through the use of derivatives (Koski and

Pontiff (1999)). Indeed, only a smaller subset of investors, such as HFs with

1.8 trillion dollars in assets under management in 2010, can and do short.

Our main result is that high-beta assets are overpriced compared to low-

beta assets when disagreement about the common factor of firms’ cash flows

is high. If investors disagree about the mean of the common factor, then their

forecasts for the payoffs of high-beta stocks will naturally diverge more than

their forecasts for low-beta ones. In other words, beta amplifies disagreement

about the macroeconomy. Because of short-sales constraints, high-beta stocks,

which are more sensitive to aggregate disagreement than low-beta stocks, are

only held in equilibrium by optimists, as pessimists are sidelined. This greater

divergence of opinion creates overpricing of high-beta stocks compared to low-

beta stocks (Miller (1977) and Chen, Hong, and Stein (2002)).6Arbitrageurs

attempt to correct this mispricing but their limited risk-bearing capacity results

in limited shorting, leading to equilibrium overpricing.7

That more disagreement on high-beta stocks leads to overpricing of these

stocks is far from obvious in an equilibrium model like ours. Optimistic in-

vestors can achieve large exposure to the common factor by buying high-beta

stocks or levering up low-beta ones. If high-beta stocks are overpriced, opti-

mistic investors should favor the levering up of low-beta assets, which could

potentially undo the initial mispricing. The key reason why this does not occur

in our model is that, when markets are incomplete (which is implicit in all

theories of limits of arbitrage, as in Delong et al. (1990) or Shleifer and Vishny

(1997), and most modern asset pricing models (Merton (1987)), idiosyncratic

risk matters for investors’ portfolios. In our context, while levering up low-

beta stocks increases the exposure to the common factor, it also magnifies the

4See Hong and Stein (2007) for a discussion of the various rationales. A large literature starting

with Odean (1999) and Barber and Odean (2001) argues that retail investors engage in excessive

trading due to overconfidence.

5See Lamont (2004) for a discussion of the many rationales for the bias against shorting in

financial markets, including historical events such as the Great Depression in which short-sellers

were blamed for the crash of 1929.

6A general disagreement structure about both means and covariances of asset returns with

short-sales restrictions in a CAPM setting is developed in Jarrow (1980). He shows that short-

sales restrictions in one asset might increase the prices of others. It turns out that a focus on a

simpler one-factor disagreement structure about common cash flows yields closed-form solutions

and a host of testable implications for the cross section of asset prices that would otherwise not be

possible.

7High-beta stocks might also be more difficult to arbitrage because of incentives for benchmark-

ing and other agency issues (Brennan (1993), Baker, Bradley, and Wurgler (2011)).