Demand System Asset Pricing Introduction

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Demand System Asset PricingIntroductionRalph S.J. Koijenaa UniversityMotohiro YogobRobert J. Richmondcof Chicago, Booth School of Business, NBER, and CEPRb Princetonc NewUniversity and NBERYork University, Stern School of Business1 / 16

Agenda1. Introduction to demand systems in asset pricing.2. Connecting demand systems to traditional models in finance.3. Estimating asset demand systems.4. Demand systems and the cross-section of US stock returns:Measuring liquidity, decomposing returns, and predictability.5. Decomposing equity valuations using demand systems.6. A global demand system for FX, bond, and stock markets.7. Discussion of research topics.2 / 16

Modern approaches to asset pricingIIMuch of asset pricing evolves around models of the stochasticdiscount factor (SDF, “M”).Broadly speaking, there are four classes of models:1. Empirical models with traded factors.E.g., Fama and French, Hou, Xue, and Zhang, Asness, Moskowitz, andPedersen, as well as much of the recent machine-learning literature.3 / 16

Modern approaches to asset pricingIIMuch of asset pricing evolves around models of the stochasticdiscount factor (SDF, “M”).Broadly speaking, there are four classes of models:1. Empirical models with traded factors.E.g., Fama and French, Hou, Xue, and Zhang, Asness, Moskowitz, andPedersen, as well as much of the recent machine-learning literature.2. Empirical models with non-traded factors.E.g., Chen, Roll, and Ross and much of the work using macroeconomicseries as pricing factors.3 / 16

Modern approaches to asset pricingIIMuch of asset pricing evolves around models of the stochasticdiscount factor (SDF, “M”).Broadly speaking, there are four classes of models:1. Empirical models with traded factors.E.g., Fama and French, Hou, Xue, and Zhang, Asness, Moskowitz, andPedersen, as well as much of the recent machine-learning literature.2. Empirical models with non-traded factors.E.g., Chen, Roll, and Ross and much of the work using macroeconomicseries as pricing factors.3. Euler equation models of a class of investors.E.g., Vissing-Jorgensen, as well as the recent literature on broker-dealers.3 / 16

Modern approaches to asset pricingIIMuch of asset pricing evolves around models of the stochasticdiscount factor (SDF, “M”).Broadly speaking, there are four classes of models:1. Empirical models with traded factors.E.g., Fama and French, Hou, Xue, and Zhang, Asness, Moskowitz, andPedersen, as well as much of the recent machine-learning literature.2. Empirical models with non-traded factors.E.g., Chen, Roll, and Ross and much of the work using macroeconomicseries as pricing factors.3. Euler equation models of a class of investors.E.g., Vissing-Jorgensen, as well as the recent literature on broker-dealers.4. Macro-finance models.E.g., Campbell and Cochrane, Bansal and Yaron, Barro, Gabaix, andWachter.3 / 16

Modern approaches to asset pricingIIMuch of asset pricing evolves around models of the stochasticdiscount factor (SDF, “M”).Broadly speaking, there are four classes of models:1. Empirical models with traded factors.E.g., Fama and French, Hou, Xue, and Zhang, Asness, Moskowitz, andPedersen, as well as much of the recent machine-learning literature.2. Empirical models with non-traded factors.E.g., Chen, Roll, and Ross and much of the work using macroeconomicseries as pricing factors.3. Euler equation models of a class of investors.E.g., Vissing-Jorgensen, as well as the recent literature on broker-dealers.4. Macro-finance models.E.g., Campbell and Cochrane, Bansal and Yaron, Barro, Gabaix, andWachter.IHow do we measure success? E[MR] 1.3 / 16

Current models inadequate to answer some key questionsICentral questions surrounding financial markets are “quantityquestions”1. How much do prices of Treasuries, MBS, credits, . . . movewhen the FED purchases 100bn of corporate bonds?2. How does the growth of ESG, smart beta, and passiveinvesting affect valuations and expected returns?3. How does the global savings glut (or, the savings glut of therich) impact fixed income markets?4. How much do retail investors contribute to the recent rally inthe stock market?4 / 16

Current models inadequate to answer some key questionsICentral questions surrounding financial markets are “quantityquestions”1. How much do prices of Treasuries, MBS, credits, . . . movewhen the FED purchases 100bn of corporate bonds?2. How does the growth of ESG, smart beta, and passiveinvesting affect valuations and expected returns?3. How does the global savings glut (or, the savings glut of therich) impact fixed income markets?4. How much do retail investors contribute to the recent rally inthe stock market?IThe modern asset pricing models are not set up to answerthese questions.IINo market clearing (third class of models).Unrealistic demand elasticities.4 / 16

What is demand system asset pricing?IThe goal of demand system asset pricing is to jointly explainasset prices, asset characteristics, macro fundamentals, andportfolio quantities.IIndeed, like anywhere else in economics, we are interested inunderstanding both prices and quantities, not just prices.5 / 16

What is demand system asset pricing?IThe goal of demand system asset pricing is to jointly explainasset prices, asset characteristics, macro fundamentals, andportfolio quantities.IIndeed, like anywhere else in economics, we are interested inunderstanding both prices and quantities, not just prices.How does this differ from traditional asset pricing research?I1. New data: Use portfolio holdings in equilibrium asset pricing.2. New methods: Estimating asset demand curves.3. New measures of success: Realistic empirical models andtheoretical micro foundations of demand curves explaining howdemand curves depend on beliefs, agency frictions, regulation,risk constraints, . . . .IA successful model of the asset demand system, combinedwith market clearing, implies a successful asset pricing model.5 / 16

Connecting the SDF and demand system approachesIIAny asset pricing model that starts from preferences, beliefs,. . . , implies1. An SDF that can be used to price assets using E [MR] 1.that can be used to price assets by2. A demand system, Qi (P), Pimposing market clearing, i Qi (P) S.Additional reasons to study asset demand systems1. Testing theories Demand curves depend on ex-ante informationand can provide more powerful tests of asset pricing modelsthan Euler equation tests that average ex-post returns.2. New moments By testing the model’s implications for demandcurves (e.g., demand elasticities and cross-elasticities), weexpand the set of testable moments in a meaningful way.IIAs we will see, it makes asset pricing more “tangible” andremoves some of the “dark matter.”Demand-based approach explored in the 60s and 70s byBrainard, Friedman, Tobin, and others.6 / 16

Demand elasticities in standard asset pricing modelsIIn modeling investors’ demand curves, elasticities andcross-elasticities are key.IAsset pricing theories generally imply downward-slopingdemand.IRisk aversion, inter-temporal hedging demand (Merton, 1973),price impact (Wilson, 1979, and Kyle, 1989).IIt is a quantitative question: What is the slope of the demandcurve?ILet us consider a standard CAPM calibration followingPetajisto (2009) to fix ideas.7 / 16

Demand elasticities in standard asset pricing modelsCARA - normal model:I N stocks with supply un each.I Risk-free rate with infinitely-elastic supply, normalized to 0.I Liquidating dividend for stock nX n an bn F e n ,where F is the common factor and en the idiosyncratic risk.8 / 16

Demand elasticities in standard asset pricing modelsCARA - normal model:I N stocks with supply un each.I Risk-free rate with infinitely-elastic supply, normalized to 0.I Liquidating dividend for stock nX n an bn F e n ,Iwhere F is the common factor and en the idiosyncratic risk.Distributional assumptions2F N(0, σm),en N(0, σe2 ).8 / 16

Demand elasticities in standard asset pricing modelsCARA - normal model:I N stocks with supply un each.I Risk-free rate with infinitely-elastic supply, normalized to 0.I Liquidating dividend for stock nX n an bn F e n ,Iwhere F is the common factor and en the idiosyncratic risk.Distributional assumptions2F N(0, σm),Ien N(0, σe2 ).There exists a continuum of investors that aggregate to arepresentative consumer with CARA preferencesmax E [ exp( γW )],θiW W0 NXn 1θn (Xn Pn ).8 / 16

Demand elasticities in standard asset pricing modelsISolving for equilibrium demand and set it equal to supply, un X2 2 2P n an γ σmum bm bn (σmbn σe2 )un .m6 nThe price discount will be dominated by the first term, notsupply (the second term).9 / 16

Demand elasticities in standard asset pricing modelsICalibrationII2N 1000, ai 105, bi 100, σe2 900, σm 0.04, ui 1, 5γ 1.25 10 . Market risk premium equals 5%, all stocks have a price of100, a market beta of 1, and a standard deviation idiosyncraticrisk of 30%.A supply shock of -10% to a stock: un 0.9 for one stock.10 / 16

Demand elasticities in standard asset pricing modelsICalibrationIIIIIII2N 1000, ai 105, bi 100, σe2 900, σm 0.04, ui 1, 5γ 1.25 10 . Market risk premium equals 5%, all stocks have a price of100, a market beta of 1, and a standard deviation idiosyncraticrisk of 30%.A supply shock of -10% to a stock: un 0.9 for one stock.The price of the stock increases by 0.16bp.Part of this increase is due to the reduction in the aggregatemarket risk premium as there is less aggregate risk Allstocks increase by 0.05bp.Hence, the differential impact is only 0.11bp. This is what wemean with virtually flat demand curves.Intuitively, stocks are just very close substitutes. What mattersmost is a stock’s beta and its contribution to aggregate risk.0.10Price elasticity of demand: ΔQ/QΔP/P 0.000016 ' 6, 250.10 / 16

Empirical estimates of the micro elasticityIHarris and Gurel (1986) and Shleifer (1986) look at theimpact of stocks that are included in the S&P500 index.IIf (i) index inclusions are exogenous and (ii) a fraction ofinvestors inelastically allocates capital to stocks included inthe index, then we can measure the slope of demand curves.IImportantly, in this literature, we can measure Δ ln P well, butnot Δ ln Q.11 / 16

Empirical estimates of the micro elasticityIIIndex providers run surveys to estimate the assets trackingtheir benchmarks.See for instance Chang, Hong, and Liskovich (2015):12 / 16

History of demand elasticity estimatesISource: Wurgler and Zhuravskaya (2002).13 / 16

effect of addition on raw returns. The outcome variable is monthly stock returnsand the independent variable is an indicator for addition to the Russell 2000index. Monthly returns are shown for the month immediately before (May) andfour months following index membership determination (June, July, August,and September), and t-statistics are reported in parentheses. Only firms thatwere members of the Russell 1000 index at the end of May are used.I BasedNoticeonthatChang,the coefficientof interestfor June returnsis 0.05theandreturnsis significantHong,and Liskovich(2015),dueat1% level. This means therea 5% additioneffect when comparing hat just crossed the 1000 cutoff and firms that just missed it. Notice that thereEvidence from Russell additions and deletionsTable 4Returns fuzzy RDAddition effectMayD0 003( 0 14)1055JunJulAugSep0 050(2 65)0 003( 0 11)0 035(1 59)0 021( 0 89)105710531052Jul1047Deletion effectDMayJunAugSep0 005(0 32)0 054(3 00)0 019( 0 96)0 002( 0 09)0 011(0 53)15451533152615461519The table reports the results of a fuzzy RD design. The following eq uation is estimated. 0 1() [ 0 1 ()] The outcome variable is monthly stock returns and the independent variableis an indicator for membership14 / 16

Evidence from Russell index changes and Japanese QEIImplied price elasticity of demand:II1.5 if all assets benchmarked are used.0.4 if only passive assets are assumed to respond. Demand is more inelastic in the second case as the pricechange is caused by a smaller demand shock (only passiveassets).IBarbon and Gianinazzi (2019) estimate a short- and long-rundemand elasticity of one using Japan’s equity QE program.IHence, demand is much less elastic than what is implied bythe CAPM (recall: the demand elasticity is 6,250 intraditional models).Unknowns:IIIMicro cross-elasticity (impact on Google of adding Apple to anindex).Macro elasticity.15 / 16

Next stepsIToday, we develop and implement empirical models of assetdemand systems and connect it to traditional finance theory.IHowever, this research agenda is in its infancy and muchexciting work lies ahead of us.Examples of key questions we need answers to:IIIIHow do we reliably estimate asset demand curves?Empirics and theory: How can we micro-found the demandcurves of different investors (e.g., hedge and mutual funds,insurers, . . . )? How important are beliefs, agency frictions,regulations, . . . ?How do households allocate capital to various institutions?IHoldings data are widely available, across countries and assetclasses.IWith a realistic demand system in hand, there are manyapplications as we discuss at the end of today.16 / 16

Demand elasticities in standard asset pricing models IIn modeling investors’ demand curves, elasticities and cross-elasticities are key. IAsset pricing theories generally imply downward-sloping demand. I Risk aversion, inter-temporal hedging demand (Me

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