Информационный центр "Центральный Дом Знаний"
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Cochrane J.H. Asset PricingCochrane J.H. Contents Acknowledgments 2 Preface 8 Part I. Asset pricing theory 12 1 Consumption-based model and overview 13 1.1 Basic pricing equation 14 1.2 Marginal rate of substitution/stochastic discount factor 16 1.3 Prices, payoffs and notation 17 1.4 Classic issues in finance 20 1.5 Discount factors in continuous time 33 1.6 Problems 38 2 Applying the basic model 41 2.1 Assumptions and applicability 41 2.2 General Equilibrium 43 2.3 Consumption-based model in practice 47 2.4 Alternative asset pricing models: Overview 49 2.5 Problems 51 3 Contingent Claims Markets 54 3.1 Contingent claims 54 3.2 Risk neutral probabilities 55 3.3 Investors again 57 3.4 Risk sharing 59 3.5 State diagram and price function 60 4 The discount factor 64 4.1 Law of one price and existence of a discount factor 64 4.2 No-Arbitrage and positive discount factors 69 4.3 An alternative formula, and x* in continuous time 74 4.4 Problems 76 5 Mean-variance frontier and beta representations 77 5. 1 Expected return - Beta representations 77 5.2 Mean-variance frontier: Intuition and Lagrangian characterization 80 5.3 An orthogonal characterization ofthe mean-variance frontier 83 5.4 Spanning the mean-variance frontier 88 5.5 A compilation of properties of R* ,Re* and x* 89 5.6 Mean-variance frontiers for m: the Hansen-Jagannathanbounds 92 5.7 Problems 97 6 Relation between discount factors, betas, and mean-variance frontiers 98 6.1 From discount factors to beta representations 98 6.2 From mean-variance frontier to a discount factor and beta representation 101 6.3 Factor models and discount factors 104 6.4 Discount factors and beta models to mean - variance frontier 108 6.5 Three riskfree rate analogues 109 6.6 Mean-variance special cases with no riskfree rate 115 6.7 Problems 118 7 Implications of existence and equivalence theorems 120 8 Conditioning information 128 8.1 Scaled payoffs 129 8.2 Sufficiency of adding scaled returns 131 8.3 Conditional and unconditional models 133 8.4 Scaled factors: a partial solution 140 8.5 Summary 141 8.6 Problems 142 9 Factor pricing models 143 9.1 Capital Asset Pricing Model (CAPM) 145 9.2 Intertemporal Capital Asset Pricing Model (ICAPM) 156 9.3 Comments on the CAPM and ICAPM 158 9.4 Arbitrage Pricing Theory (APT) 162 9.5 APT vs. ICAPM 171 9.6 Problems 172 Part II. Estimating and evaluating asset pricing models 174 10 GMM in explicit discount factor models 177 10.1 The Recipe 177 10.2 Interpreting the GMM procedure 180 10.3 Applying GMM 184 11 GMM: general formulas and applications 188 11.1 General GMM formulas 188 11.2 Testing moments 192 11.3 Standard errors of anything by delta method 193 11.4 Using GMM for regressions 194 11.5 Prespecified weighting matrices and moment conditions 196 11.6 Estimating on one group of moments, testing on another. 205 11.7 Estimating the spectral density matrix 205 11.8 Problems 212 12 Regression-based tests of linear factor models 214 12.1 Time-series regressions 214 12.2 Cross-sectional regressions 219 12.3 Fama-MacBeth Procedure 228 12.4 Problems 234 13 GMM for linear factor models in discount factor form 235 13.1 GMM on the pricing errors gives a cross-sectional regression 235 13.2 The case ofexcess returns 237 13.3 Horse Races 239 13.4 Testing for characteristics 240 13.5 Testing for priced factors: lambdas orb's? 241 13.6 Problems 245 14 Maximum likelihood 247 14.1 Maximum likelihood 247 14.2 ML is GMM on the scores 249 14.3 When factors are returns, ML prescribes a time-series regression 251 14.4 When factors are not excess returns, ML prescribes a cross-sectional regression 255 14.5 Problems 256 15 Time series, cross-section, and GMM/DF tests of linear factor models 258 15.1 Three approaches to the CAPM in size portfolios 259 15.2 Monte Carlo and Bootstrap 265 16 Which method? 271 Part III. Bonds and options 284 17 Option pricing 286 17.1 Background 286 17.2 Black-Scholes formula 293 17.3 Problems 299 18 Option pricing without perfect replication 300 18.1 On the edges of arbitrage 300 18.2 One-period good deal bounds 301 18.3 Multiple periods and continuous time 309 18.4 Extensions, other approaches, and bibliography 317 18.5 Problems 319 19 Term structure of interest rates 320 19.1 Definitions and notation 320 19.2 Yield curve and expectations hypothesis 325 19.3 Term structure models - a discrete-time introduction 327 19.4 Continuous time term structure models 332 19.5 Three linear term structure models 337 19.6 Bibliography and comments 348 19.7 Problems 351 Part IV. Empirical survey 352 20 Expected returns in the time-series and cross-section 354 20.1 Time-series predictability 356 20.2 The Cross-section: CAPM and Multifactor Models 396 20.3 Summary and interpretation 409 20.4 Problems 413 21 Equity premium puzzle and consumption-based models 414 21.1 Equity premium puzzles 414 21.2 New models 423 21.3 Bibliography 437 21.4 Problems 440 22 References 442 Part V. Appendix 455 23 Continuous time 456 23.1 Brownian Motion 456 23.2 Diffusion model 457 23.3 Ito's lemma 460 23.4 Problems 462 Preface Asset pricing theory tries to understand the prices orvalues ofclaims to uncertain payments. A low price implies a high rate of return, so one can also think of the theory as explaining why some assets pay higher average returns than others. To value an asset, we have to account for the delay and for the risk of its payments. The effects of time are not too difficult to work out. However, corrections for risk are much more important determinants of an many assets' values. For example, over the last 50 years U.S. stocks have given a real return of about 9% on average. Of this, only about 1% is due to interest rates; the remaining 8% is a premium earned for holding risk. Uncertainty, or corrections for risk make asset pricing interesting and challenging. Asset pricing theory shares the positive vs. normative tension present in the rest of economics. Does it describe the way the world does work or the way the world should work? We observe the prices or returns of many assets. We can use the theory positively, to try to understand why prices or returns are what they are. If the world does not obey a model's predictions, we can decide that the model needs improvement. However, we can also decide that the world is wrong, that some assets are "mis-priced" and present trading opportunities for the shrewd investor. This latter use of asset pricing theory accounts for much of its popularity and practical application. Also, and perhaps most importantly, the prices of many assets or claims to uncertain cash flows are not observed, such as potential public or private investment projects, new financial securities, buyout prospects, and complex derivatives. We can apply the theory to establish what the prices of these claims should be as well; the answers are important guides to public and private decisions. Asset pricing theory all stems from one simple concept, derived in the first page of the first Chapter of this book: price equals expected discounted payoff. The rest is elaboration, special cases, and a closet full of tricks that make the central equation useful for one or another application. There are two polar approaches to this elaboration. I will call them absolute pricing and relative pricing.In absolute pricing, we price each asset by reference to its exposure to fundamental sources of macroeconomic risk. The consumption-based and general equilibrium models described below are the purest examples of this approach. The absolute approach is most common in academic settings, in which we use asset pricing theory positively to give an economic explanation for why prices are what they are, or in order to predict how prices might change if policy or economic structure changed. In relative pricing, we ask a less ambitious question. We ask what we can learn about an asset's value given the prices of some other assets. We do not ask where the price of the other set of assets came from, and we use as little information about fundamental risk factors as possible. Black-Scholes option pricing is the classic example of this approach. While limited in scope, this approach offers precision in many applications. Asset pricing problems are solved by judiciously choosing how much absolute and how much relative pricing one will do, depending on the assets in question and the purpose of the calculation. Almost no problems are solved by the pure extremes. For example, the CAPM and its successor factor models are paradigms of the absolute approach. Yet in applications, they price assets "relative" to the market or other risk factors, without answering what determines the market or factor risk premia and betas. The latter are treated as free parameters. On the other end of the spectrum, most practical financial engineering questions involve assumptions beyond pure lack of arbitrage, assumptions about equilibrium "market prices of risk." The central and unfinished task of absolute asset pricing is to understand and measure the sources of aggregate or macroeconomic risk that drive asset prices. Of course, this is also the central question of macroeconomics, and this is a particularly exciting time for researchers who want to answer these fundamental questions in macroeconomics and finance. A lot of empirical work has documented tantalizing stylized facts and links between macroeconomics and finance. For example, expected returns vary across time and across assets in ways that are linked to macroeconomic variables, or variables that also forecast macroeconomic events; a wide class of models suggests that a "recession" or "financial distress" factor lies behind many asset prices. Yet theory lags behind; we do not yet have a well-described model that explains these interesting correlations. In turn, I think that what we are learning about finance must feed back on macroeconomics. To take a simple example, we have learned that the risk premium on stocks - the expected stock return less interest rates - is much larger than the interest rate, and varies a good deal more than interest rates. This means that attempts to line investment up with interest rates are pretty hopeless - most variation in the cost of capital comes from the varying risk premium. Similarly, we have learned that some measure of risk aversion must be quite high, or people would all borrow like crazy to buy stocks. Most macroeconomics pursues small deviations about perfect foresight equilibria, but the large equity premium means that volatility is a first-order effect, not a second-order effect. Standard macroeconomic models predict that people really don't care much about business cycles (Lucas 1987). Asset prices are be-ginningtorevealthattheydo-thattheyforegosubstantialreturnpremiatoavoidassetsthat fall in recessions. This fact ought to tell us something about recessions! |
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Asset Pricing