estimation methods in portfolio selection and the effectiveness of short sales restrictions uk evidence forecasting the mean returns vector and the covariance matrix is a key feature in implementing portfolio theory the performance of the bayes stein method for forecasting these parameters for use in the markowitz model with and without short sales was compared with that of seven other estimation methods and three alternative portfolio selection techniques this paper represents the first large scale empirical investigation of the usefulness of the bayes stein approach using historical data this data was drawn from the london stock exchange in contrast to earlier studies the relative performance of bayes stein was mixed while it produced reasonable estimates of the mean returns vector there were superior methods e g overall mean for estimating the covariance matrix when short sales were permitted when short sales were prohibited actual portfolio performance was clearly improved although there was little to choose between the various estimation methods

more on estimation risk and simple rules for optimal portfolio selection for the risk averse investor consideration of estimation risk is important in selecting an expected utility maximizing portfolio it has previously been shown that the composition of the tangency portfolio is unaffected by the recognition of estimation risk if the full covariance model is used alternatively if the market model is used the composition of the tangency portfolio has been shown to be affected by the recognition of estimation risk however as is demonstrated in this paper the effect will generally not be as substantive as previously believed and in many situations can be safely ignored in order to determine the composition and location of an efficient frontier from which an optimal portfolio will be selected the investor must employ estimates of expected returns variances and covariances for the set of securities under consideration if the investor simply treats the estimated parameter values for the securities as true parameter values then estimation risk will have been ignored and as shown by barry 1 and klein and bawa 14 15 a suboptimal portfolio will most likely have been selected bawa brown and klein 6 and klein and bawa 14 discuss the effects of estimation risk on the selection of an optimal portfolio from a set of risky assets and note that the location but not the composition of the efficient frontier changes when estimation risk is recognized if security returns are generated by a stationary multivariate normal distribution for which the investor has a diffuse prior furthermore brown 8 has shown these results to be robust for severe misspecification of the underlying multivariate distribution of returns e g assuming it to be normal when in actuality it is student t with small degrees of freedom this paper is concerned with the effects of estimation risk on the composition of the tangency portfolio derived from a set of risky assets and a risk free asset under the assumption that the investor has a diffuse prior 1 barry 2 bawa and brown 4 and brown 7 have shown analytically that the composition of the tangency portfolio is unaffected by estimation risk if the full covariance model is used chen and brown 10 have expanded upon the work of brown 9 and have argued that if security returns are generated by the market model then the composition of the tangency portfolio will be substantively different when estimation risk is recognized

estimation risk when theory meets reality estimation risk occurs in the almost universal situation where parameters of importance for decision making are not known with certainty bayes criterion is the procedure consistent with expected utility maximization in the presence of estimation risk three interrelated problems in the presence of estimation risk are analyzed i the choice of the utility maximizing decision rule in a mean variance framework ii the calculation of certainty equivalent returns and iii the valuation of additional sample information

trend growth expectations and u s house prices before and after the crisis abstract we provide an analysis that might help distinguish rationally justified movements in house prices from potentially non rational movements using a two sector business cycle model in which investment in housing is subject to collateral constraints a large portion of the evolution of u s house prices during the past 20 years can be reproduced when expectations of future income growth as published in surveys are used as an input into the model changes in growth expectations translate into corresponding changes in house prices since the value of housing must be linked to expected aggregate income only since about 2005 do actual and model implied house prices clearly diverge calling for explanations not based on economic fundamentals

a model of housing and credit cycles with imperfect market knowledge abstract the paper presents a model of housing and credit cycles featuring distorted beliefs and comovement and mutual reinforcement between house price expectations and price developments via credit expansion contraction positive negative development in house prices fuels optimism pessimism and credit expansion contraction which in turn boost dampen housing demand and house prices and reinforce agents optimism pessimism bayesian learning about house prices can endogenously generate self reinforcing booms and busts in house prices and significantly strengthen the role of collateral constraints in aggregate fluctuations the model can quantitatively account for the 2001 2008 u s boom bust cycle in house prices and associated household debt and consumption dynamics it also demonstrates that allowing for imperfect knowledge of agents a higher leveraged economy is more prone to self reinforcing fluctuations

how not to sell nuclear weapons we consider situations where a sale affects the ensuing interaction between potential buyers these situations are modeled by assuming that an agent who does not acquire the object for sale incurs an identity dependent externality we construct a revenue maximizing auction for the seller we observe that 1 outside options and participation constraints are endogenous 2 the seller extracts surplus also from agents who do not obtain the auctioned object 3 the seller is better off by not selling at all while obtaining some payments if externalities are much larger than valuations

wall street and the housing bubble we analyze whether mid level managers in securitized finance were aware of the housing bubble and a looming crisis in 2004 2006 using their personal home transaction data we find little evidence of them timing the bubble or exercising cautious behavior in purchasing homes relative to two uninformed control groups one composed of non housing equity analysts and the other of non real estate lawyers to the extent that the practice of securitization may have led to lax screening of subprime borrowers the average person in our sample did not expect it to lead to problems in the wider housing market our findings suggest the need to expand the incentives based view of the crisis to incorporate a role for distorted beliefs

information and diversity of analyst opinion this paper examines problems in the use of divergence of analyst opinion as a proxy for estimation risk in empirical studies of security returns and asset pricing models we demonstrate that diversity of opinion can increase even though the amount of private information increases and we show that diversity of opinion may overstate estimation risk if the capital market aggregates the information held by investors we produce empirical results consistent with our conclusions specifically we find that divergence of opinion can produce measures of estimation risk that are inconsistent with a received proxy for estimation risk and with observed common stock returns

financial innovation the discovery of risk and the u s credit crisis abstract financial innovation and overconfidence about the risk of new financial products were key factors behind the 2008 u s credit crisis we show that a model with a collateral constraint in which learning about the risk of a new financial environment interacts with fisherian amplification produces a boom bust cycle in debt asset prices and consumption early realizations of a high borrowing ability regime turn agents optimistic about the persistence probability of this regime conversely the first realization of a low borrowing ability regime turns agents unduly pessimistic the model predicts large increases in household debt land prices and excess returns during 1998 2006 followed by a collapse

expectation shocks and learning as drivers of the business cycle psychological factors market sentiments and less than fully rational shifts in beliefs are widely believed to play a role in the economy yet they are rarely considered in macroeconomic models this paper evaluates the empirical role of expectational shocks on business cycle fluctuations the paper relaxes the rational expectations assumption to exploit survey data on expectations in the estimation of a new keynesian model which allows for learning by economic agents expectation shocks affect the formation of expectations and capture waves of optimism and pessimism that lead agents to form forecasts that deviate from those implied by their learning model the empirical results uncover a crucial role for these novel expectations shocks as a major driving force of the u s business cycle expectation shocks regarding future real activity are the main source of economic fluctuations accounting for roughly half of business cycle fluctuations

labor market dynamics with search frictions and fair wage considerations fairness considerations in wage setting can improve the ability of the diamond mortensen pissarides search and matching model to account for u s labor market dynamics firms production is influenced by workers effort input which depends on whether workers consider the employment relation as fair a typical worker s effort is determined in a comparison of individual current wage with wage norms including the outside option the individual past wage and the wage level in the steady state the fairness considerations in the search framework give rise to endogenous real wage rigidity and realistic volatilities of unemployment vacancies and labor market tightness jel e24 e32 j64

expectations learning and business cycle fluctuations this paper explores an alternative theory based on learning dynamics in the con text of an otherwise standard stochastic growth model we consider an environment in which households and firms have an incomplete model of the macroeconomy knowing only their own objectives constraints and beliefs agents are optimizing have a completely specified belief system but do not know the equilibrium map ping between primitive disturbances the aggregate state of the economy and mar ket clearing prices by extrapolating from historical patterns in observed data they approximate this mapping to forecast variables that are exogenous to their decision problems such as the rental rate of capital and the real wage this belief structure has the property that beliefs affect the true data generating process of the economy which in turn affects belief formation the economy is therefore self referential shifts in beliefs about future returns to labor and capital affect current market clear ing prices which in turn can reinforce beliefs in this environment current prices can become less informative about future economic conditions generating fluctuations in real activity this kind of mechanism driving business cycle fluctuations is found in early writ ings on macroeconomic dynamics for example alfred c pigou 1927 on page 122 writes

optimal portfolio selection under institutional procedures for short selling abstract this study presents and formally justifies a simple ranking approach for optimal portfolio selection under institutional procedures for short selling it also provides economic insights of the explicit solution of the portfolio problem the analysis is applicable to different treatments of the short sale proceeds and any margin deposits in contrast to previous approaches it does not require assumptions that overstate short sale benefits for maintaining analytical tractability and it can easily identify and filter out securities that are undesirable for investing or for short selling thus this study can enhance the usefulness of portfolio modeling for assisting practical investment decisions

stationary equilibria in bargaining with externalities this paper studies infinite horizon bargaining between a seller and multiple buyers when externalities are present we extend the analysis in jehiel and moldovanu by allowing for both pure and mixed equilibria jehiel p moldovanu b 1995a cyclical delay in bargaining with externalities rev econ stud 62 619 637 a characterization of the stationary subgame perfect equilibria in generic games is presented equilibria with delay exist only for strong positive externalities since each buyer receives a positive payoff when the seller makes an agreement with some other buyer positive externalities induce a war of attrition between buyers

estimation risk in farm planning under uncertainty this paper examines the impact of estimation risk on a decision maker s ability to distinguish between the mean variance characteristics of different farm plans the importance of making such distinctions should be clear risk averse decision makers will want to bear risk only if they can be reasonably confident of commensurate increases in expected return when parameters are unknown statistically testing for differences in their estimated values is appropriate an illustration of such tests using data from hazell suggests considerable resources must be devoted toward data generation if normative statements under uncertainty are to be reliable

house prices borrowing constraints and monetary policy in the business cycle i develop a general equilibrium model with sticky prices credit constraints nominal loans and asset prices changes in asset prices modify agents borrowing capacity through collateral value changes in nominal prices affect real repayments through debt deflation monetary policy shocks move asset and nominal prices in the same direction and are amplified and propagated over time the financial accelerator is not constant across shocks nominal debt stabilises supply shocks making the economy less volatile when the central bank controls the interest rate i discuss the role of equity debt indexation and household and firm leverage in the propagation mechanism finally i find that monetary policy should not target asset prices as a means of reducing output and inflation volatility

internal rationality imperfect market knowledge and asset prices we present a decision theoretic framework in which agents are learning about market behavior and that provides microfoundations for models of adaptive learning agents are internally rational i e maximize discounted expected utility under uncertainty given dynamically consistent subjective beliefs about the future but agents may not be externally rational i e may not know the true stochastic process for payoff relevant variables beyond their control this includes future market outcomes and fundamentals we apply this approach to a simple asset pricing model and show that the equilibrium stock price is then determined by investors expectations of the price and dividend in the next period rather than by expectations of the discounted sum of dividends as a result learning about price behavior affects market outcomes while learning about the discounted sum of dividends is irrelevant for equilibrium prices stock prices equal the discounted sum of dividends only after making very strong assumptions about agents market knowledge

short selling and efficient sets the effect of short selling on the composition and location of the efficient set has been analyzed in a variety of ways however the situation typically facing investors where the initial margin requirement is less than 100 percent and the riskfree interest rate that is paid on the short proceeds is less than the rate paid on initial margin has not previously been considered the elton gruber padberg algorithm 1976 1978 subject to certain modifications is shown here to be capable of identifying the efflcient set under such conditions when harry markowitz 1952 developed the notion of efficient sets as a method of identifying an investor s optimal portfolio he did so in a setting where short selling was prohibited since then the effect of short selling on the composition and location of the efficient set has been considered in a variety of ways for example lintner 1965 suggested that short sales be treated from the perspective of a broker dealer where an amount of money equal to the short proceeds must be put up as initial margin with the short seller receiving riskfree interest on both the short proceeds and the margin alternatively black 1972 and merton 1972 assumed that the short seller did not have to put up any initial margin and that the short seller actually got the use of the short proceeds more recently dyl 1975 has assumed that the short seller must put up initial margin that is less than the short proceeds but receives no interest on either the margin or short proceeds this paper is concerned with the generation of efficient sets where short selling is allowed but with certain restrictions attached to it referred to hereafter as restricted short selling in particular initial margin is required but can be met by depositing interest bearing securities with the brokerage firm where the short seller s account is kept furthermore the model allows the short seller to earn interest on the short proceeds accordingly the model

parameter based decision making under estimation risk an application to futures trading this study shows how the standard portfolio model of futures trading should be modified when there is less than perfect information about the relevant parameters estimation risk the standard and the optimal decision rules for futures trading in the presence of estimation risk are compared and discussed an operational model of futures trading for use under estimation risk is advanced in the presence of relevant prior and sample information the model can be used to optimally blend both types of information many of the contributions of economic theory to the study of financial markets involve the use of parameters that are assumed known or estimable by the economic agents examples include the risk premium coefficient 18 and the security market lines that underlie the capital asset pricing model the volatility measures required for option pricing and the minimum variance hedge ratio and expected basis used to construct portfolios of futures contracts and cash positions generally it is left to practitioners to provide estimates of these parameters which are then directly substituted for the actual parameter values of the theoretical model whenever textbooks demonstrate how these parameters can be estimated there is usually a cookbook formula provided that requires some relatively straightforward analysis of the relevant data e g marshall 1989 chapters 6 and 7 cox and rubinstein 1985 chapter 6 the problems with the procedure described above are twofold first the theory has been slow to acknowledge that the practical application of the model almost always involves parameter estimates generally the additional risk of not knowing the true parameters is completely neglected second practitioners or the market participants will often have some type of nonsample information such as insider information or subjective priors that seems relevant for decision making however this potentially important information is ignored altogether when only sample data are used to obtain the parameter estimates

estimation risk and simple rules for optimal portfolio selection elton gruber and padberg egp 6 7 have recently simplified the process of constructing optimal portfolios by developing simple criteria for optimal portfolio selection which do not involve use of mathematical programming their simple decision rules permit one to determine easily which securities to include in an optimal portfolio and how much to invest in each however in practical applications of theoretical models sample estimators are usually treated as if they were true values of unknown parameters as a result the effect of the standard errors of sample estimators on decision rules are completely ignored bawa brown and klein 1 have shown that what is optimal in the absence of estimation risk is not necessarily optimal or even approximately optimal in the presence of estimation risk moreover brown 4 examined optimal portfolio choice under uncertainty for various portfolio selection procedures the diffuse bayes rule the markowitz certainty equivalent ce rule the aggregation ce rule and the equal weight rule 1 and found that the diffuse bayes rule uniformly dominates the markowitz ce rule in repeated samples for the quadratic utility case as the sample size increases the bayes rule becomes superior to the aggregation ce and the equal weight rules in addition the result holds even where the probability distribution of returns is seriously misspecified thus brown s 4 study has clearly indicated that without taking estimation risk into account portfolio selection rules other than the bayes rule can lead investors to select suboptimal portfolios this paper shows by using the single index model for the return generating process that the simple decision rules for optimal portfolio selection derived by elton gruber and padberg 7 are not identical under the bayesian and the traditional methods of analysis 2 moreover in the case where short sales are not

are rational explosive solutions learnable abstract it is commonly believed that rational explosive solutions are unstable or fragile under adaptive learning contrary to this belief the paper shows that under realistic parameterizations rational explosive solutions are both e stable and strongly e stable in a class of models with lagged endogenous variables it also establishes the convergence of least squares learning process to explosive solutions taking a simple cagan model of inflation as an application the paper shows that money supply feedback rule gives rise to a rational explosive solution for prices which is learnable in real time this provides a new potential explanation for historical high inflation finally e stability results for non msv explosive solutions are provided

learning adaptive expectations and technology shocks this study explores the macroeconomic implications of adaptive expectations in a standard growth model we show that the self confirming equilibrium under adaptive expectations is the same as the steady state rational expectations equilibrium for all admissible parameter values but that dynamics around the steady state are substantially different between the two equilibria the differences are driven mainly by the dampened wealth effect and the strengthened intertemporal substitution effect not by escapes emphasised by williams 2003 consequently adaptive expectations can be an important source of frictions that amplify and propagate technology shocks and seem promising for generating plausible labour market dynamics

us stock prices and recency biased learning in the run up to the global financial crisis and its aftermath abstract this paper presents a consumption based asset pricing model in which fluctuations in stock prices are driven by investors time varying subjective expectations about the dividend process in line with the empirical literature investors display recency bias when revising their beliefs about the actual dividend process and recursively discount the precision of past observations recency biased learning significantly improves the ability of the standard model to replicate the boom and bust episode on the us s p 500 stock market in the run up to the global financial crisis and its aftermath along with features of subjective expectations of stock returns documented in survey data

credit cycles redux theoretical studies have shown that under unorthodox assumptions on preferences and production technologies collateral constraints can act as a powerful amplification and propagation mechanism of exogenous shocks we investigate whether or not this result holds under more standard assumptions we find that collateral constraints typically generate small output amplification large amplification is obtained as a knife edge type of result

differential information and security market equilibrium we propose a simple model of equilibrium asset pricing in which there are differences in the amounts of information available for developing inferences about the returns parame ters of alternative securities in contrast with earlier work we show that parameter uncer tainty or estimation risk can have an effect upon market equilibrium under reasonable conditions securities for which there is relatively little information are shown to have relatively higher systematic risk when that risk is properly measured ceteris paribus the initially very limited model is shown to be robust with respect to relaxation of a number of its principal assumptions we provide theoretical support for the empirical examination of at least three proxies for relative information period of listing number of security returns observations available and divergence of analyst opinion

a note on simple criteria for optimal portfolio selection using sharpe s 7 single index model elton gruber and padberg egp 4 5 have established some simple ranking criteria for optimal portfolio selection a further extension has been made by chen and brown 2 and alexander and resnick 1 to incorporate the risk associated with the estimation of input parameters this note explores the economic rationale underlying the portfolio formation process based on the single index model in so doing we seek to enhance the intuitive appeal of the simplified portfolio criteria developed in the above studies to practitioners to this end we restate the egp solution with short sales allowed as

performance of currency portfolios chosen by a bayesian technique 1967 1985 abstract this paper is about normative currency portfolio rules it assumes logarithmic investors who maximize the expected utility from lognormal currency returns with and without short sales restrictions a number of implementable portfolio diversification policies are tried out on a large body of data covering nine major currencies and eighteen years of weekly observations in doing so we present ways of dealing with the estimation risk in an international context the necessary mean and covariance inputs are provided by a bayesian prior on the means and by sample means and covariance matrices which are estimated from weekly sample data while some policies do produce abnormal returns over and beyond proper reward for risk none does so in a statistically significant way this means that the evidence does not allow one to conclude that market participants are improperly diversified as a byproduct of this investigation techniques are found which would allow portfolio managers to earn a proper reward for risk by following a purely mechanical procedure such techniques may be valuable in a multi country world where the aggregate portfolio of currencies and securities is unknown and is not supposed to be efficient

the empirical minimum variance hedge decision making under unknown true parameters estimation risk is discussed along with bayes and parameter certainty equivalent pce criteria bayes criterion incorporates estimation risk in a manner consistent with expected utility maximization the pce method which is the most commonly used is not consistent with expected utility maximization bayes criterion is employed to solve for the minimum variance hedge ratio empirical application of bayes minimum variance hedge ratio is addressed and illustrated simulations shoe that discrepancies between prior and sample parameters may lead to substantial differences between bayesian and pce minimum variance hedges