Intermediary asset pricing: New evidence from many asset classes

TL;DR: The authors found that the price of risk for intermediary capital shocks is consistently positive and of similar magnitude when estimated separately for individual asset classes, suggesting that financial intermediaries are marginal investors in many markets and hence key to understanding asset prices.

About: This article is published in Journal of Financial Economics.The article was published on 2017-10-01 and is currently open access. It has received 290 citations till now. The article focuses on the topics: Consumption-based capital asset pricing model & Capital asset pricing model.

Summary

1 Introduction

• Intermediary asset pricing theories offer a new perspective for understanding risk premia.
• It is likely that intermediaries are marginal investors in many asset markets, and that their marginal value of wealth is a plausible pricing kernel for a broad cross-section of securities.
• The authors main empirical result is that assets’ exposure to intermediary capital ratio shocks (in- novations in ηt) possess a strong and consistent ability to explain cross-sectional differences in average returns for assets in seven different markets, including equities, US government and corpo- rate bonds, foreign sovereign bonds, options, credit default swaps (CDS), commodities, and foreign exchange (FX).
• In Section 4, the authors explore potential explanations for conflicting results in their analysis versus AEM.
• AEM focus on the definition of the security broker-dealer sector and associated book leverage ratios provided in the Federal Reserve’s Flow of Funds.

2 Intermediary capital risk in a two-factor asset pricing model

• The authors propose a two-factor model in which the intermediary’s equity capital ratio enters the pricing kernel alongside aggregate wealth.
• Section 2.1 provides an argument for why this specification captures the intermediary’s marginal value of wealth and thus why it prices all asset classes in which the intermediary participates as a marginal investor.
• There are various economic mechanisms for why and how the intermediary’s capital ratio affects its marginal value of wealth, and Section 2.2 lays out one such theory based on He and Krishnamurthy (2012).

2.1 Intermediary capital ratio and pricing kernel

• Traditional consumption-based asset pricing models (Campbell and Cochrane, 1999; Bansal and Yaron, 2004) are cast in a complete market where the marginal investor is a consumer household.
• For these same markets, intermediaries take over the role of marginal trader, raising the possibility that their marginal value of wealth is better suited as an empirical pricing kernel.
• The exact functional form in (2), which arises from existing theories under appropriate assumptions, is intuitive.
• The second and more novel aspect of intermediary asset pricing models is the role of ηt.
• It captures the intuition that an intermediary’s risk bearing capacity is in- 8 hibited when its equity capital is low.

2.2 An intermediary asset pricing model

• The authors now provide a theoretical framework where the exact intermediary pricing kernel in (2) arises in general equilibrium.
• For the pricing kernel specification (2) to price assets, the authors require that the 12We need not to specify the utility function of households as the intermediary’s optimality condition yields the pricing relations that they take to data.the authors.
• 13Although the assumption in He and Krishnamurthy (2012, 2013) appears rather stark, it is consistent with He et al. (2010) who document that mortgage-related toxic assets are always on the balance sheet of financial intermediaries (mainly commercial banks) at the height of the crisis, 2008Q4 to 2009Q1.
• 14In He and Krishnamurthy (2012, 2013), households can also access risky assets indirectly through the intermediary sector with certain agency frictions, which could bind (the “constrained” region) or not (the “unconstrained” region).
• 11 intermediary’s capital ratio is positively correlated with its wealth share ηt.

3 Cross-Sectional Analysis

• The authors present their main empirical results in this section.
• After explaining the data construction, the authors perform formal cross-sectional asset pricing tests for a variety of asset classes.

3.1.1 Primary dealers’ market equity capital ratio

• The authors definition of the intermediary sector is the set of primary dealers.
• 17For comparison, the authors focus on US-only firms in Table 2, and define the total broker-dealer sector as the set of US primary dealers plus any firms with a broker-dealer SIC code (6211 or 6221).
• Book value of debt is equal to total assets less common equity, using the most recent data available for each firm at the end of a calendar quarter.
• Intermediary capital falls during recessions and reaches its nadir in the 2008 financial crisis.
• All correlations reflect pro-cyclicality of the capital ratio (or counter-cyclicality of leverage) in that 18In this time-series regression with quarterly frequency, the estimated AR(1) coeffcient is 0.94.

3.1.2 Asset portfolios

• A key feature distinguishing their paper from existing literature is their use of test portfolios that span a wide range of asset classes.
• For corporate bonds, the authors use ten portfolios sorted on yield spreads from Nozawa (2014).
• Because some asset classes (such as CDS and commodities) are only available toward the end of their sample, the tests of all portfolios use an unbalanced panel of portfolio returns.

3.2 Cross-sectional asset pricing tests

• The authors turn next to formal cross-sectional asset pricing tests.
• These assess whether differential exposure to intermediary capital shocks across assets can explain the variation in their expected returns.
• The authors investigate each asset class separately, and also conduct joint tests using the full universe of asset classes together.

3.2.1 Estimated price of intermediary capital risk across asset classes

• The authors investigation of these seven asset classes begins with cross-sectional asset pricing tests in each class separately.
• The risk-free term structure is constructed using swap rates for maturities 3 and 6 months and US Treasury yields for maturities from 1 year to 10 years (data from Gürkaynak et al., 2007).
• The last column of Table 5 reports results when all 125 portfolios from seven asset classes are included simultaneously in the cross-sectional test.
• Section 5.7 reports estimation results that impose the model restriction γk = 0, which produces nearly identical results.
• The significance of intermediary capital risk after controlling for the market return indicates that their pricing kernel statistically improves on the CAPM for all sets of test assets.

3.2.2 Are prices of risk similar across asset classes?

• The sign of the estimated price of risk for intermediary capital factor is consistently positive across all asset classes in Table 5.
• 18 the equilibrium consistency of risk prices across all assets.
• The test in the last column of Table 5, i.e., the “all portfolios” column, indeed imposes that risk prices are equal across asset classes.
• Second, financial intermediaries are actively making trading decisions in all asset markets.

3.2.3 Are primary dealers special?

• The authors next explore the role of their specific intermediary sector definition for the preceding results.
• The authors conduct placebo tests that replicate their cross section analysis, but replace the capital ratio of primary dealers with that of other “intermediary” definitions.
• First, the authors consider defining intermediaries according to SIC codes of US broker-dealers—codes 6211 (“security brokers, dealers, and flotation companies”) and 6221 (commodity contracts brokers and dealers)—but exclude firms that are designated NY Fed primary dealers.
• Only equities and CDS show a significantly positive price of capital ratio risk based 19 on this intermediary definition; the estimated price of capital risk in other asset classes is either insignificant or has a negative sign.
• Overall, Table 6 provides additional indirect evidence supporting their assumption that primary dealers are pricing-relevant financial intermediaries.

3.2.4 Which is more important for pricing, equity or debt?

• The authors investigate which of these is the more important driver of their asset pricing result.
• The decomposition in (10) also implies that the equity growth rate shock carries a positive price of risk, while price of the debt growth rate shock should be negative.
• For the “all portfolios” test, the price of intermediary equity risk is 9% per quarter.
• The magnitudes are often small and insignificant.
• In sum, these results suggest that while book debt innovations play some role in their main pricing results, it is the market equity component of the capital ratio that is most important for the effects that the authors document.

4.1 Brief review of AEM

• AEM is an important precursor to their paper and is the first paper to bring the intermediary-based pricing paradigm into the conversation of “mainstream” empirical pricing models.
• This has the interpretation that intermediary marginal value of wealth is higher when its leverage is lower, or equivalently implies that a high equity capital ratio indicates intermediary financial distress.
• Due to the reciprocal relationship between capital ratio and leverage, AEM’s finding is in direct contradiction with their finding of a robust positive price of risk price on the intermediary capital ratio.
• It stands to reason, therefore, that their empirical measures do not behave inversely to one another as predicted.

4.2 Empirical performance of AEM in many asset classes

• First, the authors extend their multiple asset class tests to better understand the empirical performance of AEM’s intermediary pricing kernel.
• For equities and US bonds, the AEM leverage factor carries a significantly positive price, which essentially replicates the key findings reported by AEM (with the exception that their “US bonds” definition also includes corporates).
• The options market is an interesting case; in the horse-race specification, the lack of statistical significance for their measure appears due to the large and significant negative price of risk on the AEM factor.
• The authors emphasis on a variety of asset classes is the key empirical feature that distinguishes their paper from AEM.
• 23 Presumably, derivatives contracts or OTC markets are too sophisticated to be directly accessed by most household investors.

4.3 Data source and measurement

• The authors measure of financial distress differs from AEM in both the definition of a financial intermediary and the data sources employed.
• The authors define intermediaries as the set of primary dealers and rely on market equity and book debt data for their publicly traded holding companies.
• AEM define intermediaries as the set of broker-dealer firms (often bank holding company subsidiaries) that feed into the Flow of Funds broker-dealer accounts, and use the book equity and debt data reported in those accounts.
• The two key differences are (i) their use of market values for constructing capital ratios, versus AEM’s reliance on accounting book values, and (ii) their use of data at the holding company level, versus the broker-dealer subsidiary level information in the Flow of Funds.
• The authors explore the role of these differences in this section.

4.3.1 Market leverage vs. book leverage

• The authors aim in constructing the capital ratio is to provide a current measure of financial distress that reflects the information available in prevailing market prices.
• Virtually all intermediary asset pricing theories would suggest using market values, which reflect forward looking information available in traded securities prices.
• It includes most broker-dealer firms that file the Financial and Operational Combined Uniform Single report or the Finances and Operations of Government Securities Brokers and Dealers (FOGS) report with their regulator (e.g. FINRA).
• A negative correlation between book and market leverage in their sample could help explain the conflicting risk prices estimated in their study and that of AEM.

4.3.2 Holding company vs. broker-dealer subsidiary

• The more likely discrepancy between AEM and their paper is that the authors measure financial distress at the holding company level for primary dealers, while the Flow of Funds data used by AEM only aggregates balance sheet information at the broker-dealer subsidiary level.
• Flow of Funds data come from quarterly FOCUS and FOGS reports filed with the Securities and Exchange Commission (SEC) by these broker-dealer arms in isolation from other parts of their larger institutions.
• The holding companies of primary dealers also often hold significant commercial banking businesses,34 making the distinction between holding company and broker-dealer arm potentially im- portant.
• If internal capital markets are important sources of funds for broker-dealer subsidiaries, then the capital ratio of the intermediary’s holding company is the economically relevant measure of financial distress.
• In the three weeks before it filed for bankruptcy, approximately $220 million was trans- ferred to the holding company from its broker-dealer arm in the form of short-term loans.

4.4 Differences in theoretical motivation

• The interpretation of differences in their empirical results is complicated by the fact that different intermediary models predict different signs for the price of risk on intermediary capital shocks.
• More importantly, the authors believe that given the spectrum of complexities in real world financial intermedi- ation that these models may be attempting to describe, it should not be surprising that different intermediary models give opposing predictions.
• During a downturn when marginal value of wealth is likely to be high for all investors, hedge funds (who are perhaps closer to the type of intermediary described by debt constraint models) sell their assets to commercial banks (who may be better described by equity constraint models), and so leverage of these two sectors moves in opposite directions.

5.1 Pre-crisis and post-1990 subsamples

• Table 11 presents the performance of their intermediary capital risk factor and the AEM leverage factor during the 1970Q1–2006Q4 sample, which excludes the dramatic fluctuations associated with the financial crisis.
• The authors find that pre-crisis prices of capital ratio risk are substantially smaller in three asset classes, US bonds, sovereign bonds, and commodities.
• In the other four asset classes, the price of intermediary capital risk remains economically large.
• In the “all portfolios” case, the risk price estimate is 9% per quarter, identical to that in the full sample and highly significant.
• The authors separately investigate the recent sample beginning in 1990 in Table 12.

5.2 Monthly frequency

• The authors main analysis focuses on the quarterly frequency, corresponding to the frequency of balance sheet data going into their capital ratio measure.
• As a result, one can construct the monthly capital ratio for primary dealers by using the monthly market equity information from CRSP, together with the most recent quarterly book debt of their holding companies in Compustat.
• The authors repeat their cross section analysis 30 at the monthly frequency.
• The estimated price of intermediary capital risk remains positive for all asset classes.
• From Table 7 in Section 3.2.4 the authors observe that book debt growth does possess some pricing power, which suggests a potential explanation for the weaker monthly performance of their intermediary capital risk factor.

5.3 Time-series return predictability

• A common prediction of dynamic intermediary asset pricing models is that the risk premium is time-varying, implying predictability in asset returns based on lagged state variables that captures financial distress.
• The authors framework requires additional structure to derive the time-varying risk premium, which is typically a nonlinear function of the state variable.
• The model’s prediction is generally supported by Table 14, which reports a significantly positive b̂k for five of the seven asset classes at the 10% significance level, and in four classes is significant at the 5% significance level.
• The dependent variable in the last column of Table 14 is the weighted average of individual asset class portfolio returns, with weights inversely proportional to the unconditional standard deviation of a portfolio’s return.
• The authors find a positive one-year-ahead predictive coefficient in the “all portfolios” test with a t-statistic of 2.89.38.

5.4 Single factor models

• The authors main analysis focuses on a two-factor structure for the pricing kernel.
• The empirical price of risk associated with the market return is generally insignificant in Table 5.
• 32 take opposite signs in CDS, Options, and FX markets.
• The take-away is basically the same as from the baseline two-factor model.

5.5 Intermediary equity return

• As explained in equation (4) in Section 2.2, the representative intermediary’s pricing kernel only depends on its own net worth W.
• The authors find a significantly positive price for all asset classes other than the Fama-French 25 portfolios at the 10% level.
• This is because the pricing kernel is the marginal investor’s marginal utility of consumption, and the consumption of log investors is always a constant fraction of their wealth.
• Indeed, when the authors include the market return as another factor in panel (b) of Table 15, they recover estimates that are closely in line with their baseline results from Table 5.
• Overall, the results in this table suggest that primary dealers’ equity return plays a similar role as the capital risk factor, offering further evidence in support of intermediary asset pricing models.

5.6 Comparison with other factors

• A large literature investigates factors that explain the cross section of asset returns.
• These analyses focus on the pricing of US equities and have not been tested as pricing factors in many of the 39This value-weighted equity return is slightly different from the intermediary equity growth rate constructed in Section 3.2.4.
• The latter “intermediary equity growth rate” includes new equity issuance, while the equity return does not.
• In Table 17, the authors compare the pricing power of their intermediary capital ratio factor relative to the CAPM, the Fama and French (1993, 2015) three- and five-factor models, the momentum factor, and the Pástor and Stambaugh (2003) liquidity factor.
• The table reports the cross section R2 and MAPE with and without the intermediary capital factor.

5.7 Cross-sectional tests without an intercept

• The empirical specification (8) allows the intercept γk, to vary across asset classes.
• This additional theoretical restriction might not be valid given potential model misspecification; however, it may matter for the empirical cross-asset pattern of estimated prices of intermediary capital risk λkη.
• The authors find that constraining the intercept to zero has a minor impact on the prices of intermediary capital risk that they estimate and, if anything, their statistical significance improves.

6 Conclusion

• The authors find that differences in assets’ exposure to innovations in the capital ratio of primary dealers explain variation in expected excess returns on equities, US bonds, foreign sovereign bonds, options, CDS, commodities, and currencies.
• The authors intermediary capital risk factor carries a positive price of risk and is strongly pro-cyclical, implying counter-cyclical intermediary leverage.
• 40Because their capital ratio factor is non-traded and theoretically motivated, statistically oriented models such as the Fama-French three and five-factor models are not natural benchmarks for comparison.
• And both models will always lose in sample against ad hoc factor models that find nearly ex post efficient portfolios.”.
• Nonetheless, some readers may find the comparison is informative.

Figures

Table 9: Expected Returns and Risk Exposure by Asset Class: AEM Leverage Factor Average excess returns µi−rf , and risk exposures (betas) to the Adrian et al. (2014a) leverage factor (AEM) and to the excess return on the market (βi,W ), across portfolios in each asset class. The quarterly sample is 1970Q1–2012Q4. The intermediary capital ratio is the ratio of total market equity to total market assets (book debt plus market equity) of primary dealer holding companies. Shocks to capital ratio are defined as AR(1) innovations in the capital ratio, scaled by the lagged capital ratio. The AEM leverage factor, defined as the seasonally adjusted growth rate in broker-dealer book leverage level from Flow of Funds, is from its authors. Betas are estimated in a first-stage time-series regression.

Table 5: Cross-sectional Asset Pricing Tests by Asset Class

Figure 4: Intermediary Capital Measures Comparison

Table 10: Horse-races with the AEM Leverage Factor

Table 14: Predictive Regressions by Asset Class

Table 13: Cross-sectional Tests at the Monthly Frequency

Table 18: Cross-sectional Tests without an Intercept

Table 6: Primary Dealers are Special: a Placebo Test

Figure 3: Pricing Errors: All Portfolios

Table 17: Comparison with Commonly-used Pricing Factors

Figure 2: Intermediary Capital Risk Price λη Estimates by Asset Class

Table 12: Cross-sectional Asset Pricing Tests by Asset Class: Recent Sample Risk price estimates for shocks to the intermediary capital ratio (HKM) or the Adrian et al. (2014a) leverage factor (AEM), and the excess return on the market. Here we focus on the more recent quarterly sample 1990Q1–2012Q4. Risk prices are the mean slopes of period-by-period cross-sectional regressions of portfolio excess returns on risk exposures (betas). Betas are estimated in a first-stage time-series regression. The intermediary capital ratio is the ratio of total market equity to total market assets (book debt plus market equity) of primary dealer holding companies. Shocks to capital ratio are defined as AR(1) innovations in the capital ratio, scaled by the lagged capital ratio. The AEM leverage factor, defined as the seasonally adjusted growth rate in broker-dealer book leverage level from Flow of Funds, is from its authors. Mean absolute pricing error (MAPE) is in percentage terms. Relative risk aversion (RRA) is the price of intermediary capital risk factor, scaled by its variance. Fama-MacBeth t-statistics (t-FM) adjust for cross-asset correlation in the residuals. The more robust GMM t-statistics (t-GMM) additionally correct for estimation error of the time-series betas.

Table 7: Market Equity is More Important for Pricing than Book Debt

Table 2: Primary Dealers as Representative Financial Intermediaries

Figure A.1: Pricing Errors

Table 1: Primary Dealers as of February 11, 2014

Table 16: Intermediary Equity Return

Table 3: Pair-wise Correlations

Table A.1: Primary Dealers, 1960–2014

Figure 1: Intermediary Capital Ratio and Risk Factor

Table 8: Cross-sectional Asset Pricing Tests by Asset Class: AEM Leverage Factor Risk price estimates for the Adrian et al. (2014a) leverage factor (AEM) and the excess return on the market. Risk prices are the mean slopes of period-by-period cross-sectional regressions of portfolio excess returns on risk exposures (betas). Betas are estimated in a first-stage time-series regression. The quarterly sample is 1970Q1–2012Q4. The AEM leverage factor, defined as the seasonally adjusted growth rate in broker-dealer book leverage level from Flow of Funds, is from its authors. Mean absolute pricing error (MAPE) is in percentage terms. Relative risk aversion (RRA) is the price of intermediary capital risk factor, scaled by its variance. Fama-MacBeth t-statistics (t-FM) adjust for cross-asset correlation in the residuals. The more robust GMM t-statistics (t-GMM) additionally correct for estimation error of the time-series betas.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Nber working paper series intermediary asset pricing: new evidence from many asset classes" ?

This is true not only for commonly studied equity and government bond market portfolios, but also for other more sophisticated asset classes such as corporate and sovereign bonds, derivatives, commodities, and currencies. The price of risk for intermediary capital shocks is consistently positive and of similar magnitude when estimated separately for individual asset classes, suggesting that financial intermediaries are marginal investors in many markets and hence key to understanding asset prices.