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John Cochrane: Ast Pricing
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Preface
Ast pricing theory tries to understand the prices or values of claims to uncertain payments.A low price implies a high rate of return,so one can also think of the theory as explaining why some asts pay higher average returns than others.
To value an ast,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 many asts’values.For example,over the last50years U.S.stocks have given a real return of about9%on average.Of this,only about1%is due to interest rates;the remaining8%is a premium earned for holding risk.Uncertainty,or corrections for risk make ast pricing interesting and challenging.
Ast pricing theory shares the positive versus normative tension prent in the rest of economics.Does it describe the way the world does work,or the way the world should work?We obrve the prices or returns of many asts.We can u 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 asts are“mis-priced”and prent trading opportunities for the shrewd investor.This latter u of ast pricing theory accounts for much of its popularity and practical application.Also,and perhaps most importantly,the prices of many asts or claims to uncertain cashflows are not obrved,such as potential public or private investment projects,newfinancial curities, buyout prospects,and complex derivatives.We can apply the theory to establish what the prices of the claims should be as well;the answers are important guides to public and private decisions.
Ast pricing theory all stems from one simple concept,prented in thefirst page of thefirst chapter of this book:price equals expected discounted payoff.The rest is elaboration,special cas,and a clot
xiii
xiv Preface full of tricks that make the central equation uful for one or another application.
There are two polar approaches to this elaboration.I call them abso-lute pricing and relative pricing.In absolute pricing,we price each ast by reference to its exposure to fundamental sources of macroeconomic risk. The consumption-bad and general equilibrium models are the purest examples of this approach.The absolute approach is most common in academic ttings,in which we u ast 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 ast’s value given the prices of some other asts.We do not ask where the prices of the other asts came from,and we u as lit-tle information about fundamental risk factors as possible.Black–Scholes option pricing is the classic example of this approach.While limited in scope,this approach of
fers precision in many applications.
Ast pricing problems are solved by judiciously choosing how much absolute and how much relative pricing one will do,depending on the asts in question and the purpo of the calculation.Almost no prob-lems 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 asts“relative”to the market or other risk fac-tors,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,even the most practicalfinancial engineering questions usually involve assumptions beyond pure lack of arbitrage,assumptions about equilibrium“market prices of risk.”
The central and unfinished task of absolute ast pricing is to under-stand and measure the sources of aggregate or macroeconomic risk that drive ast prices.Of cour,this is also the central question of macroeco-nomics,and this is a particularly exciting time for rearchers who want to answer the fundamental questions in macroeconomics andfinance.
A lot of empirical work has documented tantalizing stylized facts and links between macroeconomics andfinance.For example,expected returns vary across time and across asts in ways that are linked
to macroeco-nomic variables,or variables that also forecast macroeconomic events;a wide class of models suggests that a“recession”or“financial distress”fac-tor lies behind many ast prices.Yet theory lags behind;we do not yet have a well-described model that explains the interesting correlations.
In turn,I think that what we are learning aboutfinance must feed back on macroeconomics.To take a simple example,we have learned that the risk premium on stocks—the expected stock return less inter-est rates—is much larger than the interest rate,and varies a good deal
Preface xv more than interest rates.This means that attempts to line investment up with interest rates are pretty hopeless—most variation in the cost of capi-tal 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 devi-ations about perfect-foresight equilibria,but the large equity premium means that volatility is afirst-order effect,not a cond-order effect.Stan-dard macroeconomic models predict that people really do not care much about business cycles(Lucas[1987]).Ast prices reveal that they do—that they forego substantial return premia to avoid asts that fall in reces-sions.This fact ought to tell us something about recessions!
This book advocates a discount factor/generalized method of moments view of ast pricing theory and associated empirical procedures.
I summarize ast pricing by two equations:
p t=E(m t+1x t+1)
m t+1=f(data,parameters)
where p t=ast price,x t+1=ast payoff,m t+1=stochastic discount factor.
The major advantages of the discount factor/moment condition approach are its simplicity and universality.Where once there were three apparently different theories for stocks,bonds,and options,now we e each as special cas of the same theory.The common language also allows us to u insights from eachfield of application in otherfields.
This approach allows us to conveniently parate the step of specify-ing economic assumptions of the model(cond equation)from the step of deciding which kind of empirical reprentation to pursue or under-stand.For a given model—choice of f(·)—we will e how thefirst equa-tion can lead to predictions stated in terms of returns,price-dividend ratios,expected return-beta reprentations,m
oment conditions,continu-ous versus discrete-time implications,and so forth.The ability to translate between such reprentations is also very helpful in digesting the results of empirical work,which us a number of apparently distinct but funda-mentally connected reprentations.
Thinking in terms of discount factors often turns out to be much simpler than thinking in terms of portfolios.For example,it is easier to insist that there is a positive discount factor than to check that every possible portfolio that dominates every other portfolio has a larger price, and the long arguments over the APT stated in terms of portfolios are easy to digest when stated in terms of discount factors.
The discount factor approach is also associated with a state-space geometry in place of the usual mean-variance geometry,and this book emphasizes the state-space intuition behind many classic results.
xvi Preface For the reasons,the discount factor language and the associated state-space geometry are common in academic rearch and high-tech practice.They are not yet common in textbooks,and that is the niche that this book tries tofill.
I also diverge from the usual order of prentation.Most books are structured following the history of
thought:portfolio theory,mean-variance frontiers,spanning theorems,CAPM,ICAPM,APT,option pricing,andfinally consumption-bad model.Contingent claims are an esoteric extension of option pricing theory.I go the other way around: contingent claims and the consumption-bad model are the basic and simplest models around;the others are specializations.Just becau they were discovered in the opposite order is no reason to prent them that way.
I also try to unify the treatment of empirical methods.A wide variety of methods are popular,including time-ries and cross-ctional regres-sions,and methods bad on generalized method of moments(GMM)and maximum likelihood.However,in the end all of the apparently differ-ent approaches do the same thing:they pick free parameters of the model to make itfit best,which usually means to minimize pricing errors;and they evaluate the model by examining how big tho pricing errors are.
As with the theory,I do not attempt an encyclopedic compilation of empirical procedures.The literature on econometric methods contains lots of methods and special cas(likelihood ratio analogues of common Wald tests;cas with and without risk-free asts and when factors do and do not span the mean-variance frontier,etc.)that are ldom ud in practice.I try to focus on the basic ideas and on methods that are actually ud in practice.
The accent in this book is on understanding statements of theory,and working with that theory to applications,rather than rigorous or general proofs.Also,I skip very lightly over many parts of ast pricing theory that have faded from current applications,although they occupied large amounts of the attention in the past.Some examples are portfolio p-aration theorems,properties of various distributions,or asymptotic APT. While portfolio theory is still interesting and uful,it is no longer a cor-nerstone of pricing.Rather than u portfolio theory tofind a demand curve for asts,which intercted with a supply curve gives prices,we now go to prices directly.One can thenfind optimal portfolios,but it is a side issue for the ast pricing question.
My prentation is consciously informal.I like to e an idea in its simplest form and learn to u it before going back and understanding all the foundations of the ideas.I have organized the book for similarly minded readers.If you are hungry for more formal definitions and back-ground,keep going,they usually show up later on.
