«Financial Intermediaries and the Cross-Section of Asset Returns TOBIAS ADRIAN, ERKKO ETULA, and TYLER MUIR∗ ABSTRACT Financial intermediaries trade ...»
THE JOURNAL OF FINANCE • VOL. LXIX, NO. 6 • DECEMBER 2014
Financial Intermediaries and the Cross-Section
of Asset Returns
TOBIAS ADRIAN, ERKKO ETULA, and TYLER MUIR∗
Financial intermediaries trade frequently in many markets using sophisticated models. Their marginal value of wealth should therefore provide a more informative
stochastic discount factor (SDF) than that of a representative consumer. Guided by theory, we use shocks to the leverage of securities broker-dealers to construct an intermediary SDF. Intuitively, deteriorating funding conditions are associated with deleveraging and high marginal value of wealth. Our single-factor model prices size, book-to-market, momentum, and bond portfolios with an R2 of 77% and an average annual pricing error of 1%—performing as well as standard multifactor benchmarks designed to price these assets.
MODERN FINANCE THEORY asserts that asset prices are determined by their covariances with the stochastic discount factor (SDF), which is usually linked to the marginal value of aggregate wealth. Assets that are expected to pay off in future states with high marginal value of wealth are worth more today, as dictated by investors’ ﬁrst-order conditions. Following this theory, much of the empirical asset pricing literature centers on measuring the marginal value of wealth of a representative investor, typically the average household. Speciﬁcally, the SDF is represented by the marginal value of wealth aggregated over all households. However, the logic that leads to this SDF relies on strong assumptions: all households must participate in all markets, there cannot be transactions costs, households have to be able to execute complicated trading ∗ Tobias Adrian is with Capital Markets Function, Research and Statistics Group, Federal Reserve Bank of New York; Erkko Etula is currently with Goldman, Sachs, and Co. (at the time of writing he was with Federal Reserve Bank of New York); and Tyler Muir is with Yale School of Management. We would like to thank Ariel Zucker and Daniel Green for outstanding research assistance. We thank Richard Crump, Kent Daniel, Hans Dewachter, Andrea Eisfeldt, Wayne Ferson, Francesco Franzoni, Campbell Harvey, Ravi Jagannathan, Taejin Kim, Arvind Krishnamurthy, Bryan Kelly, Wolfgang Lemke, Stefan Nagel, Dimitris Papanikolaou, Jonathan Parker, Annette Vissing-Jorgensen, two anonymous referees, and seminar participants at Kellogg School of Management, the Bank of England, the European Central Bank, the Federal Reserve Banks of Boston, Chicago, and New York, the Bank of Finland, HEC Paris, UCLA, ECARES at the Free University of Brussels, SAIF, Moody’s KMV, the SED, EFA, AFA, SoFie, NBER Asset Pricing, Utah Winter Finance Conference, FIRS, and the Fed “Day Ahead” conference for useful comments and suggestions. The views expressed in this paper are those of the authors and do not necessarily reﬂect the position of the Federal Reserve Bank of New York or the Federal Reserve System.
strategies, the moments of asset returns have to be known, and investment strategies have to be continuously optimized based on forward-looking expectations. If these assumptions are violated for some agents, it can no longer be assumed that the marginal value of wealth of the representative household prices all assets.1 For example, if some investors trade only in (say) value stocks, their marginal value of wealth can only be expected to correctly price those stocks. In contrast, should there exist a single class of investors that ﬁts the assumptions of modern ﬁnance theory, their marginal value of wealth can be expected to price all assets.
This paper shifts attention from measuring the SDF of the average household to measuring a “ﬁnancial intermediary SDF.” This approach takes us to a new place in the ﬁeld of empirical asset pricing—rather than emphasize average household behavior, the assumptions of frictionless markets and intertemporally optimizing behavior suggest that ﬁnancial intermediaries be elevated to the center stage of asset pricing. Indeed, ﬁnancial intermediaries ﬁt the assumptions of modern ﬁnance theory nicely: they trade in many asset classes following often complex investment strategies; they face low transaction costs, which allows trading at high frequencies; and they use sophisticated, continuously updated models and extensive data to form forward-looking expectations of asset returns. Therefore, if we can measure the marginal value of wealth for these active investors, we can expect to price a broad class of assets.2 In other words, the marginal value of wealth of intermediaries can be expected to provide a more informative SDF.
Backed by recent theories that give ﬁnancial intermediaries a central role in asset pricing, we argue that the leverage of security broker-dealers is a good empirical proxy for the marginal value of wealth of ﬁnancial intermediaries and that it can thus be used as a representation of the intermediary SDF.
Intuitively, when funding conditions tighten and intermediaries are forced to deleverage, their marginal value of wealth should be high. We ﬁnd remarkably strong empirical support for this hypothesis: exposures to the broker-dealer leverage factor alone can explain the average excess returns on a wide variety of test assets, including equity portfolios sorted by size, book-to-market, and momentum, as well as the cross-section of Treasury bond portfolios sorted by maturity. The broker-dealer leverage factor is successful across all crosssections in terms of high adjusted R2 s, low cross-sectional pricing errors, and prices of risk that are signiﬁcant and remarkably consistent across portfolios.3 When taking all these criteria into account, our single factor outperforms standard multifactor models tailored to price these cross-sections, including the 1 See Jagannathan and Wang (2007) for evidence that households may optimize infrequently and Malloy, Moskowitz, and Vissing-Jorgensen (2009) for evidence that limited participation in the stock market can help explain the cross-section of stock returns and the equity premium puzzle.
2 An insight due to He and Krishnamurthy (2013).
3 The returns on momentum portfolios have thus far been particularly difﬁcult to connect to
Figure 1. Realized versus predicted mean returns: leverage factor.
We plot the realized mean excess returns of 35 equity portfolios (25 size- and book-to-market-sorted portfolios and 10 momentum-sorted portfolios) and six Treasury bond portfolios (sorted by maturity) against the mean excess returns predicted by our single-factor ﬁnancial intermediary leverage model, estimated without an intercept (E[R e ] = βlev λlev ). The sample period is 1968Q1 to 2009Q4. Data are quarterly, but returns are expressed in percent per year.
Fama-French three-factor model and a ﬁve-factor Carhart (1997) model that includes the momentum factor and a bond pricing factor. Figure 1 provides an example of the leverage factor’s pricing performance in a cross-section that spans 35 common equity portfolios sorted on size, book-to-market, and momentum, and six Treasury bond portfolios sorted by maturity. The single-factor model we present explains 77% of the variation in average returns in these cross-sections, with an average absolute pricing error around 1% per annum.
We provide a number of robustness checks that conﬁrm the strong pricing ability of the leverage factor across a variety of equity and bond portfolios.
Most importantly, the fact that we have a one-factor model and use many test assets avoids the typical criticisms that plague asset pricing tests (see Lewellen, Nagel, and Shanken (2010)). We provide simulation evidence supporting Lewellen, Nagel, and Shanken (2010): the probability that a random “noise” factor could spuriously replicate our cross-sectional results, in terms of high R2 and low cross-sectional intercept, is zero. We also construct a tradeable leverage factor mimicking portfolio (LMP), which allows us to conduct pricing exercises at a higher frequency and over a longer time period. In cross-sectional and time-series tests using monthly data, we show that the single-factor mimicking portfolio performs well going back to the 1930s. We also conduct mean-variance analysis and ﬁnd the LMP to have the highest Sharpe ratio 2560 The Journal of Finance R among benchmark portfolio returns. In fact, the mean variance characteristics of the LMP are close to the tangency portfolio on the efﬁcient frontier generated by combinations of the three Fama-French factors and the momentum factor.
As a further robustness check, we use the entire cross-section of stock returns to construct portfolios based on our leverage factor betas and ﬁnd substantial dispersion in average returns that line up well with the postformation leverage betas.
Our empirical results are consistent with a growing theoretical literature on the links between ﬁnancial institutions and asset prices. Most directly, our results support models in which leverage captures the time-varying balance sheet capacity of ﬁnancial intermediaries. As funding constraints tighten, balance sheet capacity falls and intermediaries are forced to deleverage by selling assets at ﬁre sale prices, as in the recent ﬁnancial crisis. These are times when intermediaries’ marginal value of wealth is high. Assets that pay off poorly when constraints tighten and leverage falls are therefore risky and must offer high returns. Equivalently, the cross-sectional price of leverage risk should be positive. These theories imply that leverage captures aspects of the intermediary SDF that other measures (such as aggregate consumption growth or the return on the market portfolio) do not capture. A common thread in these theories is the procyclical evolution of broker-dealer leverage as leverage increases in good times when funding constraints are relaxed.
We provide empirical support for the view that leverage represents funding constraints by showing that our leverage factor correlates with funding constraint proxies such as volatility, the Baa-Aaa spread, asset growth, and a betting-against-beta factor that goes long leveraged low-beta securities and short high-beta securities. Frazzini and Pedersen (2013) show that investors who face funding constraints prefer to hold naturally high-beta securities rather than levering up low-beta ones, resulting in a positive average return spread between a levered low-beta asset and a naturally high-beta asset. This betting-against-beta factor should comove with funding constraints. Consistent with this view, we ﬁnd that our leverage factor correlates well with the betting-against-beta portfolio and explains the cross-section of returns sorted on betas as well.
To the best of our knowledge, we are the ﬁrst to conduct cross-sectional asset pricing tests with ﬁnancial intermediary balance sheet components in the pricing kernel, which provides an explicit link between intermediary balance sheets and asset prices. To quote John H. Cochrane’s (2011, p. 1091) Presidential Address on intermediary-based theories of asset pricing, “A crucial question is, as always, what data will this class of theories use to measure discount rates? Arguing over puzzling patterns of prices is weak. The rational-behavioral debate has been doing that for 40 years, rather unproductively. Ideally, one should tie price or discount-rate variation to central items in the models, such as the balance sheets of leveraged intermediaries.” The remainder of the paper is organized as follows. Section I provides a discussion of related literature, reviewing the theoretical rationalizations for the link between ﬁnancial intermediary leverage and aggregate asset prices.
Financial Intermediaries and the Cross-Section of Asset Returns 2561 Section II describes the data and empirical strategy, and Section III conducts a number of asset pricing tests in the cross-section of stock and bond returns.
Section IV analyzes the properties of the LMP and forms portfolios sorted on leverage betas, providing a variety of robustness checks. Section V discusses challenges for existing theories and directions for future work. Section VI concludes.