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Working Papers

 

Archives: WP version of published papers

 

  • "Arbitrage Pricing Theory, the Stochastic Discount Factor and Estimation of Risk Premia from Portfolios", by M. Hashem Pesaran and Ron P. Smith, CESifo Working Paper No. 9001, July 2021.

    Abstract: The arbitrage pricing theory (APT) attributes differences in expected returns to exposure to systematic risk factors, which are typically assumed to be strong. In this paper we consider two aspects of the APT. Firstly we relate the factors in the statistical factor model to a theoretically consistent set of factors defined by their conditional covariation with the stochastic discount factor (mt) used to price securities within inter-temporal asset pricing models. We show that risk premia arise from non-zero correlation of observed factors with mt; and the pricing errors arise from the correlation of the errors in the statistical factor model with mt: Secondly we compare estimates of factor risk premia using portfolios with the ones obtained using individual securities, and show that the identification conditions in terms of the strength of the factor are the same and that, in general, no clear cut ranking of the small sample bias of the two estimators is possible.
    JEL Classifications: C38, G12
    Key Words: Arbitrage Pricing Theory, Stochastic Discount Factor, portfolios, factor strength, identification of risk premia, two-pass regressions, Fama-MacBeth.
    Full Text: https://www.cesifo.org/en/publikationen/2021/working-paper/arbitrage-pricing-theory-stochastic-discount-factor-and-estimation

     

  • "Factor Strengths, Pricing Errors, and Estimation of Risk Premia", by M. Hashem Pesaran and Ron P. Smith, March 2021, CESifo Working Paper No. 8947.

    Abstract: This paper examines the implications of pricing errors and factors that are not strong for the Fama-MacBeth two-pass estimator of risk premia and its asymptotic distribution when T is fixed with n → ∞, and when both n and T → ∞, jointly. While the literature just distinguishes strong and weak factors we allow for degrees of strength using a recently developed measure. Our theoretical results have important practical implications for empirical asset pricing. Pricing errors and factor strength matter for consistent estimation of risk premia and subsequent inference, thus an estimate of factor strength is required before attempting to estimate risk. Finally, using a recently developed procedure we provide rolling estimates of factor strengths for the five Fama-French factors, and show that only the market factor can be viewed as strong.
    JEL Classifications: C380, G120
    Key Words: factor strength, pricing errors, risk premia, Fama and MacBeth two-pass estimators, Fama-French factors, panel R2.
    Full Text: https://www.cesifo.org/en/publikationen/2021/working-paper/factor-strengths-pricing-errors-and-estimation-risk-premia

     

  • "COVID-19 Time-varying Reproduction Numbers Worldwide: An Empirical Analysis of Mandatory and Voluntary Social Distancing", by Alexander Chudik, M. Hashem Pesaran and Alessandro Rebucci, March 2021.

    Abstract: This paper estimates time-varying COVID-19 reproduction numbers worldwide solely based on the number of reported infected cases, allowing for under-reporting. Estimation is based on a moment condition that can be derived from an agent-based stochastic network model of COVID-19 transmission. The outcomes in terms of the reproduction number and the trajectory of per-capita cases through the end of 2020 are very diverse. The reproduction number depends on the transmission rate and the proportion of susceptible population, or the herd immunity effect. Changes in the transmission rate depend on changes in the behavior of the virus, reflecting mutations and vaccinations, and changes in people's behavior, reflecting voluntary or government mandated isolation. Over our sample period, neither mutation nor vaccination are major factors, so one can attribute variation in the transmission rate to variations in behavior. Evidence based on panel data models explaining transmission rates for nine European countries indicates that the diversity of outcomes resulted from the non-linear interaction of mandatory containment measures, voluntary precautionary isolation, and the economic incentives that governments provided to support isolation. These effects are precisely estimated and robust to various assumptions. As a result, countries with seemingly different social distancing policies achieved quite similar outcomes in terms of the reproduction number. These results imply that ignoring the voluntary component of social distancing could introduce an upward bias in the estimates of the effects of lock-downs and support policies on the transmission rates.
    JEL Classifications: D0, F6, C4, I120, E7
    Key Words: COVID-19, SIR model, epidemics, multiplication factor, under-reporting, social distancing, self-isolation.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp21/CPR_covid_2021_Mar_15_WP.pdf
    Public Codes: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp21/codes.zip

     

  • "Matching Theory and Evidence on Covid-19 using a Stochastic Network SIR Model", by M. Hashem Pesaran and Cynthia Fan Yang, November 2020.

    Abstract: This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic models. These moment conditions are used to investigate identification and estimation of recovery and transmission rates. The paper then proposes simple moment-based rolling estimates and shows them to be fairly robust to the well-known under-reporting of infected cases. Empirical evidence on six European countries match the simulated outcomes, once the under-reporting of infected cases is addressed. It is estimated that the number of reported cases could be between 3 to 9 times lower than the actual numbers. Counterfactual analysis using calibrated models for Germany and UK show that early intervention in managing the infection is critical in bringing down the reproduction numbers below unity in a timely manner.
    JEL Classifications: C13, C15, C31, D85, I18, J18
    Key Words: Covid-19, multigroup SIR model, basic and effective reproduction numbers, rolling window estimates of the transmission rate, method of moments, calibration and counterfactual analysis.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp20/PY_epidemic_network_Nov_10_2020.pdf

     

  • "Regional Heterogeneity and U.S. Presidential Elections: Real-Time 2020 Forecasts and Evaluation", by Rashad Ahmed and M. Hashem Pesaran, October 2020, revised April 2021.

    Abstract: This paper exploits cross-sectional variation at the level of U.S. counties to generate real-time forecasts for the 2020 U.S. presidential election. The forecasting models are trained on data covering the period 2000-2016, using high-dimensional variable selection techniques. Our county-based approach contrasts the literature that focuses on national and state level data but uses longer time periods to train their models. The paper reports forecasts of popular and electoral college vote outcomes and provides a detailed ex post evaluation of the forecasts released in real time prior to the election. It is shown that all of these forecasts outperform autoregressive benchmarks, with a pooled national model using One-Covariate-at-a-time-Multiple-Testing (OCMT) variable selection significantly outperforming all models in forecasting both the U.S. mainland national vote share and electoral college outcomes (forecasting 236 electoral votes for the Republican party compared to 232 realized). This paper also shows that key determinants of voting outcomes at the county level include incumbency effects, unemployment, poverty, educational attainment, house price changes, and international competitiveness. The results are also supportive of myopic voting: economic uctuations realized a few months before the election tend to be more powerful predictors of voting outcomes than their long-horizon analogues.
    JEL Classifications: C53, C55, D72
    Key Words: Real-time Forecasts, Popular and Electoral College Votes, Simultaneity, High Dimensional Forecasting Models, Lasso, One Covariate at a time Multiple Testing, OCMT.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp21/AhmedPesaran_Elections-Apr-28-2021.pdf
    Reference: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp20/AhmedPesaran_Elections-Oct-18-2020.pdf

     

  • "A Counterfactual Economic Analysis of Covid-19 Using a Threshold Augmented Multi-Country Model", by Alexander Chudik, Kamiar Mohaddes, M. Hashem Pesaran, Mehdi Raissi, and Alessandro Rebucci, September 2020.

    Abstract: This paper develops a threshold-augmented dynamic multi-country model (TG-VAR) to quantify the macroeconomic effects of Covid-19. We show that there exist threshold effects in the relationship between output growth and excess global volatility at individual country levels in a significant majority of advanced economies and in the case of several emerging markets. We then estimate a more general multi-country model augmented with these threshold effects as well as long term interest rates, oil prices, exchange rates and equity returns to perform counterfactual analyses. We distinguish common global factors from trade-related spillovers, and identify the Covid-19 shock using GDP growth forecast revisions of the IMF in 2020Q1. We account for sample uncertainty by bootstrapping the multi-country model estimated over four decades of quarterly observations. Our results show that the Covid-19 pandemic will lead to a significant fall in world output that is most likely long-lasting, with outcomes that are quite heterogenous across countries and regions. While the impact on China and other emerging Asian economies are estimated to be less severe, the United States, the United Kingdom, and several other advanced economies may experience deeper and longer-lasting effects. Non-Asian emerging markets stand out for their vulnerability. We show that no country is immune to the economic fallout of the pandemic because of global interconnections as evidenced by the case of Sweden. We also find that long-term interest rates could fall significantly below their recent lows in core advanced economies, but this does not seem to be the case in emerging markets.
    JEL Classifications: C32, E44, F44
    Key Words: Threshold-augmented Global VAR (TGVAR), international business cycle, Covid-19, global volatility, threshold effects
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp20/TGVAR_COVID-19_200917_WP.pdf
    VOXeu Article: https:/voxeu.org/article/economic-consequences-covid-19-multi-country-analysis

     

  • "Variable Selection and Forecasting in High Dimensional Linear Regressions with Parameter Instability", by Alexander Chudik, M. Hashem Pesaran and Mahrad Sharifvaghe, July 2020, revised April 2021.

    Abstract: This paper is concerned with the problem of variable selection and forecasting in the presence of parameter instability. There are a number of approaches proposed for forecasting in the presence of time-varying parameters, including the use of rolling windows and exponential down-weighting. However, these studies start with a given model specification and do not consider the problem of variable selection, which is complicated by time variations in the effects of signals on target variables. In this study we investigate whether or not we should use weighted observations at the variable selection stage in the presence of parameter instability, particularly when the number of potential covariates is large. Amongst the extant variable selection approaches we focus on the recently developed One Covariate at a time Multiple Testing (OCMT) method. This procedure allows a natural distinction between the selection and forecasting stages. We establish three main theorems on selection, estimation post selection, and in-sample fit. These theorems provide justification for using the full (not down-weighted) sample at the selection stage of OCMT and down-weighting of observations only at the forecasting stage (if needed). The benefits of the proposed method are illustrated by empirical applications to forecasting monthly stock market returns and quarterly output growths.
    JEL Classifications: C22, C52, C53, C55
    Key Words: Time-varying parameters, high-dimensional, multiple testing, variable selection, Lasso, one covariate at a time multiple testing (OCMT), forecasting, monthly returns, Dow Jones
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp21/CPS_OCMT_Break_Forecatsing_04_23_2021f.pdf

     

  • "Voluntary and Mandatory Social Distancing: Evidence on COVID-19 Exposure Rates from Chinese Provinces and Selected Countries", by Alexander Chudik, M. Hashem Pesaran and Alessandro Rebucci, CESifo Working Paper No. tbc, April 2020.

    Abstract: This paper estimates time-varying COVID-19 reproduction numbers worldwide solely based on the number of reported infected cases, allowing for under-reporting. Estimation is based on a moment condition that can be derived from an agent-based stochastic network model of COVID-19 transmission. The outcomes in terms of the reproduction number and the trajectory of per-capita cases through the end of 2020 are very diverse. The reproduction number depends on the transmission rate and the proportion of susceptible population, or the herd immunity effect. Changes in the transmission rate depend on changes in the behavior of the virus, reflecting mutations and vaccinations, and changes in people's behavior, reflecting voluntary or government mandated isolation. Over our sample period, neither mutation nor vaccination are major factors, so one can attribute variation in the transmission rate to variations in behavior. Evidence based on panel data models explaining transmission rates for nine European countries indicates that the diversity of outcomes results from the non-linear interaction of mandatory containment measures, voluntary precautionary isolation, and the economic incentives that governments provided to support isolation. These effects are precisely estimated and robust to various assumptions. As a result, countries with seemingly different social distancing policies achieved quite similar outcomes in terms of the reproduction number. These results imply that ignoring the voluntary component of social distancing could introduce an upward bias in the estimates of the effects of lock-downs and support policies on the transmission rates. The full set of estimation results and the replication package are available on the authors' websites.
    JEL Classifications: D0, F6, C4, I120, E7
    Key Words: COVID-19, SIR model, epidemics, exposed population, measurement error, social distancing, self-isolation, employment loss.
    Full Text: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3576703

     

  • "The Role of Factor Strength and Pricing Errors for Estimation and Inference in Asset Pricing Models", by M. Hashem Pesaran and Ron P. Smith, CESifo Working Paper No. tbc, October 2019.

    Abstract: In this paper we are concerned with the role of factor strength and pricing errors in asset pricing models, and their implications for identification and estimation of risk premia. We establish an explicit relationship between the pricing errors and the presence of weak factors that are correlated with stochastic discount factor. We introduce a measure of factor strength, and distinguish between observed factors and unobserved factors. We show that unobserved factors matter for pricing if they are correlated with the discount factor, and relate the strength of the weak factors to the strength (pervasiveness) of non-zero pricing errors. We then show, that even when the factor loadings are known, the risk premia of a factor can be consistently estimated only if it is strong and if the pricing errors are weak. Similar results hold when factor loadings are estimated, irrespective of whether individual returns or portfolio returns are used. We derive distributional results for two pass estimators of risk premia, allowing for non-zero pricing errors. We show that for inference on risk premia the pricing errors must be sufficiently weak. We consider both when n (the number of securities) is large and T (the number of time periods) is short, and the case of large n and T. Large n is required for consistent estimation of risk premia, whereas the choice of short T is intended to reduce the possibility of time variations in the factor loadings. We provide monthly rolling estimates of the factor strengths for the three Fama-French factors over the period 1989-2018.
    JEL Classifications: C38, G12
    Key Words: Arbitrage Pricing Theory, APT, factor strength, identification of risk premia, two-pass regressions, Fama-French factors.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp19/Factor-Strength-and-APT-October-16-2019.pdf

     

  • "Long-Term Macroeconomic Effects of Climate Change: A Cross-Country Analysis", by Matthew E. Kahn, Kamiar Mohaddes, Ryan N. C. Ng, M. Hashem Pesaran, Mehdi Raissi and Jui-Chung Yang, CESifo Working Paper No. 7738, July 2019.

    Abstract: We study the long-term impact of climate change on economic activity across countries, using a stochastic growth model where labour productivity is affected by country-specific climate variables-defined as deviations of temperature and precipitation from their historical norms. Using a panel data set of 174 countries over the years 1960 to 2014, we find that per-capita real output growth is adversely affected by persistent changes in the temperature above or below its historical norm, but we do not obtain any statistically significant effects for changes in precipitation. Our counterfactual analysis suggests that a persistent increase in average global temperature by 0.04℃ per year, in the absence of mitigation policies, reduces world real GDP per capita by 7.22 percent by 2100. On the other hand, abiding by the Paris Agreement, thereby limiting the temperature increase to 0.01℃ per annum, reduces the loss substantially to 1.07 percent. These effects vary significantly across countries. We also provide supplementary evidence using data on a sample of 48 U.S. states between 1963 and 2016, and show that climate change has a long-lasting adverse impact on real output in various states and economic sectors, and on labour productivity and employment.
    JEL Classifications: C33, O40, O44, O51, Q51, Q54
    Key Words: Climate change, economic growth, adaptation, counterfactual analysis.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp19/Climate Growth_190701.pdf

     

  • "Short T Dynamic Panel Data Models with Individual, Time and Interactive Effects", by Kazuhiko Hayakawa, M. Hashem Pesaran and L. Vanessa Smith, September 2018, revised February 2020

    Abstract: This paper proposes a quasi maximum likelihood (QML) estimator for short T dynamic fixed effects panel data models allowing for interactive effects through a multi-factor error structure. The proposed estimator is robust to the heterogeneity of the initial values and common unobserved effects, whilst at the same time allowing for standard fixed and time effects. It is applicable to both stationary and unit root cases. Order conditions for identification of the number of interactive effects are established, and conditions are derived under which the parameters are almost surely locally identified. It is shown that global identification is possible only when the model does not contain lagged dependent variables. The QML estimator is proven to be consistent and asymptotically normally distributed. A sequential multiple testing likelihood ratio procedure is also proposed for estimation of the number of factors which is shown to be consistent. Finite sample results obtained from Monte Carlo simulations show that the proposed procedure for determining the number of factors performs very well and the QML estimator has small bias and RMSE, and correct empirical size in most settings. The practical use of the QML approach is illustrated by means of two empirical applications from the literature on cross county crime rates and cross country growth regressions.
    JEL Classifications: C12, C13, C23.
    Key Words: short T dynamic panels, unobserved common factors, quasi maximum likelihood, interactive effects, multiple testing, sequential likelihood ratio tests, crime rate, growth regressions.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp20/HPS_11Feb20.pdf
    SSRN Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3268434

     

  • "Land Use Regulations, Migration and Rising House Price Dispersion in the U.S.", by Wukuang Cun and M. Hashem Pesaran. April 2018, revised October 2018

    Abstract: This paper develops and solves a dynamic spatial equilibrium model of regional housing markets in which house prices are jointly determined with location-to-location migration flows. Agents optimize period-by-period and decide whether to remain where they are or migrate to a new location at the start of each period. The agent's optimal location choice and the resultant migration process is shown to be Markovian with the transition probabilities across all location pairs given as non-linear functions of wage and housing cost differentials, which are time varying and endogenously determined. On the supply side, in each location the construction …firms build new houses by combining land and residential structures; with housing supplies endogenously responding to migration flows. The model can be viewed as an example of a dynamic network where regional housing markets interact with each other via migration flows that function as a source of spatial spill-overs. It is shown that the deterministic version of the model has a unique equilibrium and a unique balanced growth path. We estimate the state-level supplies of new residential land from the model using housing market and urban land acreage data. These estimates are shown to be significantly negatively correlated with the Wharton Residential Land Use Regulatory Index. The model can simultaneously account for the rise in house price dispersion and the interstate migration in the U.S.. Counterfactual simulations suggest that reducing either land supply differentials or migration costs could significantly lower house price dispersion.
    JEL Classifications: E0, R23, R31
    Key Words: House price dispersion, endogenous location choice, interstate migration, land-use restriction, spatial equilibrium.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp18/PC_Housing_Paper_2018_10_09.pdf
    SSRN Working Paper Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3162399

  • "An Augmented Anderson-Hsiao Estimator for Dynamic Short-T Panels", by Alexander Chudik and M. Hashem Pesaran, CESifo WP no. 6688. October 2017, revised March 2021

    Abstract: This paper introduces the idea of self-instrumenting endogenous regressors in settings when the correlation between these regressors and the errors can be derived and used to bias-correct the moment conditions. The resulting bias-corrected moment conditions are less likely to be subject to the weak instrument problem and can be used on their own or in conjunction with other available moment conditions to obtain more efficient estimators. This approach can be applied to estimation of a variety of models such as spatial and dynamic panel data models. This paper focuses on the latter, and proposes a new estimator for short T dynamic panels by augmenting Anderson and Hsiao (AAH) estimator with bias-corrected quadratic moment conditions in first differences which substantially improve the small sample performance of the AH estimator without sacrificing on the generality of its underlying assumptions regarding the fixed effects, initial values, and heteroskedasticity of error terms. Using Monte Carlo experiments it is shown that AAH estimator represents a substantial improvement over the AH estimator and more importantly it performs well even when compared to Arellano and Bond and Blundell and Bond (BB) estimators that are based on more restrictive assumptions, and continues to have satisfactory performance in cases where the standard GMM estimators are inconsistent. Finally, to decide between AAH and BB estimators we also propose a Hausman type test which is shown to work well when T is small and n sufficiently large.
    JEL Classifications: C12, C13, C23.
    Key Words: Short-T Dynamic Panels, GMM, Bias-Corrected Moment Conditions, BMM, Self-Instrumenting, Nonlinear Moment Conditions, Panel VARs, Hausman Test, Monte Carlo Evidence.
    Full Text: http://www.econ.cam.ac.uk/emeritus/mhp1/wp21/CP_BMM_2021_Mar_23.pdf
    Code and Data: http://www.econ.cam.ac.uk/emeritus/mhp1/wp21/codes_and_data.zip
     

  • "Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities", by M. Hashem Pesaran and Takashi Yamagata, March 2017, revised January 2018

    Abstract: This paper considers tests of zero pricing errors for the linear factor pricing model when the number of securities, N, can be large relative to the time dimension, T, of the return series. We focus on class of tests that are based on Student t tests of individual securities which have a number of advantages over the existing standardised Wald type tests, and propose a test procedure that allows for non-Gaussianity and general forms of weakly cross correlated errors. It does not require estimation of an invertible error covariance matrix, it is much faster to implement, and is valid even if N is much larger than T. Monte Carlo evidence shows that the proposed test performs remarkably well even when T = 60 and N = 5; 000. The test is applied to monthly returns on securities in the S&P 500 at the end of each month in real time, using rolling windows of size 60. Statistically signifi…cant evidence against Sharpe-Lintner CAPM and Fama-French three factor models are found mainly during the recent fi…nancial crisis. Also we fi…nd a signifi…cant negative correlation between a twelve-months moving average p-values of the test and excess returns of long/short equity strategies (relative to the return on S&P 500) over the period November 1994 to June 2015, suggesting that abnormal pro…ts are earned during episodes of market ineffiencies.
    JEL Classifications: C12, C15, C23, G11, G12
    Key Words: CAPM, Testing for alpha, Weak and spatial error cross-sectional dependence, S&P 500 securities, Long/short equity strategy.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp18/PY_LFPM_30_Jan_2018.pdf
    Supplement: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp17/PY_LFPM_11_March_2017_Supplement.pdf
     

  • "Business Cycle Effects of Credit Shocks in a DSGE Model with Firm Defaults", by M. Hashem Pesaran and TengTeng Xu, CWPE Working paper. No. 1159, CESifo Working Paper No. 3609, IZA Discussion Paper No. 6027, October 2011, revised April 2016

    Abstract: This paper proposes a new theoretical framework for the analysis of the relationship between credit shocks, firm defaults and volatility. The key feature of the modelling approach is to allow for the possibility of default in equilibrium. The model is then used to study the impact of credit shocks on business cycle dynamics. It is assumed that firms are identical ex ante but differ ex post due to different realizations of firm-specific technology shocks, possibly leading to default by some firms. The implications of firm defaults for the balance sheets of households and banks and their subsequent impacts on business uctuations are investigated within a dynamic stochastic general equilibrium framework. Results from a calibrated version of the model suggest that, in the steady state, a firm's default probability rises with its leverage ratio and the level of uncertainty in the economy. A positive credit shock, defined as a rise in the loan-to-deposit ratio, increases output, consumption, hours and productivity, and reduces the spread between loan and deposit rates. Interestingly, the effects of the credit shock tend to be highly persistent, even without price rigidities and habit persistence in consumption behavior.
    JEL Classifications: E32, E44, E50, G21.
    Key Words: Firm Defaults; Credit Shocks; Financial Intermediation; Interest Rate Spread; Uncertainty.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp16/MacroCredit_PesaranXu_April-2016.pdf
    Supplement: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp11/MacroCredit_ 5Oct2011_Supplement.pdf

     

  • "Optimality and Diversifiability of Mean Variance and Arbitrage Pricing Portfolios", by M. Hashem Pesaran, and Paolo Zaffaroni, CESifo Working Papers No. 2857, October, 2009

    Abstract: This paper investigates the limit properties of mean-variance (mv) and arbitrage pricing (ap) trading strategies using a general dynamic factor model, as the number of assets diverge to infinity. It extends the results obtained in the literature for the exact pricing case to two other cases of asymptotic no-arbitrage and the unconstrained pricing scenarios. The paper characterizes the asymptotic behaviour of the portfolio weights and establishes that in the non-exact pricing cases the ap and mv portfolio weights are asymptotically equivalent and, moreover, functionally independent of the factors conditional moments. By implication, the paper sheds light on a number of issues of interest such as the prevalence of short-selling, the number of dominant factors and the granularity property of the portfolio weight.
    JEL Classifications: Large Portfolios, Factor Models, Mean-Variance Portfolio, Arbitrage Pricing, Market (Beta) Neutrality, Well Diversification.
    Key Words: C32, C52, C53, G11.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/wp09/pz_port_17_October_09.pdf