DOCSLIB.ORG

The Equity Premium Puzzle and Myopic Loss Aversion

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Equity Premium Puzzle and Myopic Loss Aversion Copenhagen Business School M.Sc. Finance & Strategic Management August 2011 The equity premium puzzle and myopic loss aversion An empirical study of a non-standard preference structure in Sweden By Signe Læssøe and Martin Diernisse Advisor: Lisbeth Funding la Cour Department of Economics 120 standard pages / 272,964 characters ”vi er mennesker – hvorfor bebrejde hinanden, at vi ikke er andet” ”we are human - why blame each other that this is all we are” - Gustav Munch-Petersen (Danish poet, 1912-1938) Executive summary In 1985, Mehra & Prescott introduced the so-called equity premium puzzle, which captured that the historic equity premium in the US for the period 1889-1978, could by no means be explained with a traditional asset pricing model, based on expected utility theory. The authors concluded that the discrepancy had to be explained, by investors being much more risk averse than had previously been assumed, or by concluding that the traditional model did not capture actual investor behavior. This thesis investigates an alternative to the standard investor preferences assumed in the model tested by Mehra & Prescott (1985), namely myopic loss aversion as proposed by Benartzi & Thaler (1995). The model is based on prospect theory of Tversky & Kahneman (1979; 1992), as well as established concepts from the field of behavioral finance. It is descriptive in nature, as it is based on experimental studies of human decision making under risk, rather than relying on assumptions of a purely rational individual. First we expand the study of the equity premium puzzle to the small open economy of Sweden, using the original method of Mehra & Prescott (1985), and the statistical reformulation of the puzzle by Kocherlakota (1996). We start by investigating the period 1919-2010, and reach the surprising conclusion that the equity premium puzzle is not present in Sweden for that period. Based on the previous findings of the puzzle, we re-evaluate our period of analysis, and find that the years before 1925 are highly atypical. We thus eliminate the years from our dataset, and for the revised period from 1925-2010 we find an equity premium puzzle similar to the one found in the US. The result is found to be robust against variations in data input, as well as further changes of the sample period. Next, we investigate whether myopic loss aversion is able to serve as a potential solution to the equity premium puzzle in Sweden. We find that the puzzle can be explained by assuming that investors are loss averse, meaning that a loss hurts them twice as much as a gain pleases them, and that they are myopic in their investment strategy, meaning that they on average evaluate their portfolios too often. Our conclusion is supported by observations of optimal asset allocation, and we find that the implied equity premium would fall, if investors were to evaluate the return on their equity investments, in a more aggregated manner. Finally, we test the sensitivity of our method, against different changes in input variables, and over different sample periods, and again we find that our conclusion is robust. Table of Contents 1. Introduction ................................................................................................................................... 5 1.1 Problem statement.............................................................................................................................. 6 1.2 Methodology ....................................................................................................................................... 7 1.2.1 Structure ....................................................................................................................................... 7 1.2.2 Theoretical foundation ................................................................................................................. 8 1.2.3 Delimitations ................................................................................................................................ 8 Part I: The equity premium puzzle 2. The model of Mehra & Prescott .................................................................................................... 10 2.1 Deduction of the model .................................................................................................................... 12 2.2 Empirical findings of Mehra & Prescott ............................................................................................ 15 2.3 Chapter summary .............................................................................................................................. 17 3. Further empirical validation of the puzzle ...................................................................................... 18 3.1 A statistical approach ........................................................................................................................ 18 3.2 The risk-free rate puzzle .................................................................................................................... 20 3.3 The Equity premium puzzle internationally ...................................................................................... 22 3.4 Chapter summary .............................................................................................................................. 25 4. Potential solutions to the puzzle ................................................................................................... 26 4.1 Biases in data ..................................................................................................................................... 26 4.2 Questioning the assumptions behind model .................................................................................... 28 4.2.1 Assumption 1: Markets are complete ........................................................................................ 28 4.2.2 Assumption 2: No trading barriers ............................................................................................. 30 4.2.3 Assumption 3: Standard preference structure ........................................................................... 31 4.3 Chapter summary .............................................................................................................................. 36 1 Part II: Myopic loss aversion 5. The failure of the standard preference structure ........................................................................... 38 5.1 The axioms of expected utility theory ............................................................................................... 38 5.2 Violations of the axioms .................................................................................................................... 39 5.2.1 Certainty effect and probability sizes ......................................................................................... 39 5.2.2 Intransitive preferences ............................................................................................................. 41 5.2.3 Combining risky prospects ......................................................................................................... 42 5.2.4 Gains versus losses ..................................................................................................................... 44 5.3 Chapter summary .............................................................................................................................. 45 6. Prospect Theory ........................................................................................................................... 46 6.1 The Framing Phase ............................................................................................................................ 46 6.2 The Evaluation Phase ........................................................................................................................ 47 6.3 The Value Function ............................................................................................................................ 47 6.4 The Weighting Function, π ................................................................................................................ 52 6.5 The technical functions of prospect theory ...................................................................................... 53 6.6 Chapter summary .............................................................................................................................. 58 7. Myopic Loss Aversion ................................................................................................................... 60 7.1 Loss aversion ..................................................................................................................................... 60 7.2 Mental accounting............................................................................................................................. 62 7.2.1 Choice bracketing ....................................................................................................................... 62 7.3 Combining loss aversion and myopia ................................................................................................ 64 7.4 Chapter summary .............................................................................................................................. 66 8. Myopic loss aversion empirically ................................................................................................... 67 8.1 Myopic
Load more

Recommended publications
  • Term Premium Puzzle: ∗ an Alternative Explanation ∗ Udc 336.71 336.76 336.67
    FACTA UNIVERSITATIS Series: Economics and Organization Vol. 1, No 9, 2001, pp. 73 - 84 TERM PREMIUM PUZZLE: ∗ AN ALTERNATIVE EXPLANATION ∗ UDC 336.71 336.76 336.67 Srdjan Marinković Faculty of Economics, University of Niš, 18000 Niš, Yugoslavia Abstract. For a long time the significant yield differential between extremely short- term and other short-term default-free government securities, i.e. short-end of yield curve slope has remained unexplained in the economic science. This phenomenon is known as 'term premium puzzle'. Prevailing theory based on consumption failed to explain many other empirically prooved market developments. We offer an explanation to solve the puzzle. The significance of those findings is far reaching than reviling the puzzle. Basic concept is already successfully used to explain many institutional developments, financial intermediary, for example, and can be also used to restate asset-pricing models and the theory of financial crises and disturbances. Key words: yield curve, term premium, liquidity premium, uncertainty, the theory of bank. SHORTCOMINGS OF THE PREVAILING THEORY Consumption based theory of asset pricing seems to say little about various stylised facts concerning the yield curve, such as its predominantly upward slope. This feature of yield curve is especially obvious in its short-end. It implies that short and long-term de- fault risk-free debts are not perfectly substitutable. Time-persistent spread between treas- ury bills maturing for tree and six months, known as 'term premium puzzle', can be ex- plained by means of merely neglected influence of time-horizon on predictability and, as a consequence, on market information efficiency as well.
    [Show full text]
  • The Total Risk Premium Puzzle
    FEDERAL RESERVE BANK OF SAN FRANCISCO WORKING PAPER SERIES The Total Risk Premium Puzzle Òscar Jordà Federal Reserve Bank of San Francisco University of California, Davis Moritz Schularick University of Bonn CEPR Alan M. Taylor University of California, Davis NBER CEPR March 2019 Working Paper 2019-10 https://www.frbsf.org/economic-research/publications/working-papers/2019/10/ Suggested citation: Jordà, Òscar, Moritz Schularick, Alan M. Taylor. 2019. “The Total Risk Premium Puzzle,” Federal Reserve Bank of San Francisco Working Paper 2019-10. https://doi.org/10.24148/wp2019-10 The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the Board of Governors of the Federal Reserve System. The Total Risk Premium Puzzle ? Oscar` Jorda` † Moritz Schularick ‡ Alan M. Taylor § March 2019 Abstract The risk premium puzzle is worse than you think. Using a new database for the U.S. and 15 other advanced economies from 1870 to the present that includes housing as well as equity returns (to capture the full risky capital portfolio of the representative agent), standard calculations using returns to total wealth and consumption show that: housing returns in the long run are comparable to those of equities, and yet housing returns have lower volatility and lower covariance with consumption growth than equities. The same applies to a weighted total-wealth portfolio, and over a range of horizons. As a result, the implied risk aversion parameters for housing wealth and total wealth are even larger than those for equities, often by a factor of 2 or more.
    [Show full text]
  • How Speculation Can Explain the Equity Premium
    How speculation can explain the equity premium Glenn Shafer and Vladimir Vovk The Game-Theoretic Probability and Finance Project Working Paper #47 First posted October 16, 2016. Last revised January 1, 2018. Project web site: http://www.probabilityandfinance.com Abstract When measured over decades in countries that have been relatively stable, re- turns from stocks have been substantially better than returns from bonds. This is often attributed to investors' risk aversion: stocks are thought to be riskier than bonds, and so investors will pay less for an expected return from stocks than for the same expected return from bonds. The game-theoretic probability-free theory of finance advanced in our 2001 book Probability and Finance: It's Only a Game suggests an alternative ex- planation, which attributes the equity premium to speculation. This game- theoretic explanation does better than the explanation from risk aversion in accounting for the magnitude of the premium. Contents 1 Introduction 1 2 What causes volatility? 1 3 What is an efficient market? 2 3.1 The efficient index hypothesis (EIH) . 3 3.2 Mathematical implications of the EIH . 4 4 The equity premium 5 4.1 Why the premium is a puzzle . 5 4.2 The premium implied by the EIH . 6 4.3 The trading strategy that implies the premium . 6 4.4 Implications of the premium . 7 5 The game-theoretic CAPM 8 6 Need for empirical work 9 6.1 Attaining efficiency . 9 6.2 Measuring the equity premium . 9 6.3 Testing the game-theoretic CAPM . 10 7 Acknowledgements 11 8 Relevant GTP papers 11 Other references 12 1 Introduction The game-theoretic probability-free theory of finance advanced in our 2001 book Probability and Finance: It's Only a Game and in subsequent working papers (see Section 8) suggests that the equity premium can be explained by specula- tion.
    [Show full text]
  • NBER WORKING PAPER SERIES FLIGHT to QUALITY, FLIGHT to LIQUIDITY, and the PRICING of RISK Dimitri Vayanos Working Paper 10327 Ht
    NBER WORKING PAPER SERIES FLIGHT TO QUALITY, FLIGHT TO LIQUIDITY, AND THE PRICING OF RISK Dimitri Vayanos Working Paper 10327 http://www.nber.org/papers/w10327 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 February 2004 I thank Viral Acharya, John Cox, Xavier Gabaix, Denis Gromb, Tim Johnson, Leonid Kogan, Pete Kyle, Jonathan Lewellen, Hong Liu, Stew Myers, Jun Pan, Anna Pavlova, Steve Ross, Jiang Wang, Wei Xiong, Jeff Zwiebel, seminar participants at Amsterdam, Athens, Caltech, LSE, LBS, Michigan, MIT, NYU, Princeton, Stockholm, Toulouse, UBC, UCLA, UT Austin, Washington University, and participants at the Econometric Society 2003 Summer Meetings, for helpful comments. I am especially grateful to Jeremy Stein for discussions that helped define this project, and for insightful comments in later stages. Jiro Kondo provided excellent research assistance. Financial support for this research came from the MIT/Merrill Lynch partnership. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. ©2004 by Dimitri Vayanos. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Flight to Quality, Flight to Liquidity, and the Pricing of Risk Dimitri Vayanos NBER Working Paper No. 10327 February 2004 JEL No. G1, G2 ABSTRACT We propose a dynamic equilibrium model of a multi-asset market with stochastic volatility and transaction costs. Our key assumption is that investors are fund managers, subject to withdrawals when fund performance falls below a threshold. This generates a preference for liquidity that is time- varying and increasing with volatility.
    [Show full text]
  • The Equity Premium: Why Is It a Puzzle?
    The Equity Premium: Why Is It a Puzzle? (as corrected February 2003) Rajnish Mehra This article takes a critical look at the equity premium puzzle—the inability of standard intertemporal economic models to rationalize the statistics that have characterized U.S. financial markets over the past century. A summary of historical returns for the United States and other industrialized countries and an overview of the economic construct itself are provided. The intuition behind the discrepancy between model prediction and empirical data is explained. After detailing the research efforts to enhance the model’s ability to replicate the empirical data, I argue that the proposed resolutions fail along crucial dimensions. lmost two decades ago, Edward Prescott Furthermore, this pattern of excess returns to and I (see Mehra and Prescott 1985) chal- equity holdings is not unique to U.S. capital mar- lenged the profession with a poser: The kets. Table 2 confirms that equity returns in other A historical U.S. equity premium (the return developed countries also exhibit this historical reg- earned by a risky security in excess of that earned ularity when compared with the return to debt by a relatively risk free U.S. T-bill) is an order of holdings. The annual return on the U.K. stock mar- magnitude greater than can be rationalized in the ket, for example, was 5.7 percent in the post-WWII context of the standard neoclassical paradigm of period, an impressive 4.6 pp premium over the financial economics. This regularity, dubbed “the average bond return of 1.1 percent.
    [Show full text]
  • The Equity Premium Puzzle: a Review Full Text Available At
    Full text available at: http://dx.doi.org/10.1561/0500000006 The Equity Premium Puzzle: A Review Full text available at: http://dx.doi.org/10.1561/0500000006 The Equity Premium Puzzle: A Review Rajnish Mehra Department of Economics University of California Santa Barbara and NBER [email protected] Boston – Delft Full text available at: http://dx.doi.org/10.1561/0500000006 Foundations and Trends R in Finance Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 USA Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is R. Mehra, The Equity Premium Puzzle: A Review, Foundations and Trends R in Finance, vol 2, no 1, pp 1–81, 2006 ISBN: 978-1-60198-064-9 c 2008 R. Mehra All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Cen- ter, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged.
    [Show full text]
  • The Equity Premium in Retrospect
    Chapter 14 THE EQUITY PREMIUM IN RETROSPECT RAJNISH MEHRA ° University of California, Santa Barbara, and NBER EDWARD C. PRESCOTT∗ University of Minnesota, and Federal Reserve Bank of Minneapolis Contents Abstract 888 Keywords 888 1. Introduction 889 2. The equity premium: history 889 2.1. Facts 889 2.2. Data sources 890 2.2.1. Subperiod 1802–1871 890 2.2.1.1. Equity return data 890 2.2.1.2. Return on a risk-free security 891 2.2.2. Sub-period 1871–1926 891 2.2.2.1. Equity return data 891 2.2.2.2. Return on a risk-free security 891 2.2.3. Sub-period 1926–present 891 2.2.3.1. Equity return data 891 2.2.3.2. Return on a risk-free security 892 2.3. Estimates of the equity premium 892 2.4. Variation in the equity premium over time 895 3. Is the equity premium due to a premium for bearing non-diversifiable risk? 897 3.1. Standard preferences 900 3.2. Estimating the equity risk premium versus estimating the risk aversion parameter 910 3.3. Alternative preference structures 911 3.3.1. Modifying the conventional time – and state – separable utility function 911 3.3.2. Habit formation 912 3.3.3. Resolution 915 ° We thank George Constantinides, John Donaldson, Ellen R. McGrattan and Mark Rubinstein for helpful discussions. Mehra acknowledges financial support from the Academic Senate of the University of California. Prescott acknowledges financial support from the National Science Foundation. Handbook of the Economics of Finance, Edited by G.M.
    [Show full text]
  • Equity Risk Premium Puzzle and Investors' Behavioral Analysis
    Equity Risk Premium Puzzle And Investors’ Behavioral Analysis —A Theoretical and Empirical Explanation From the Stock Markets in U.S. and China Chong Xu QMSS G5999 Master Thesis Columbia University January 5th, 2009 Equity Risk Premium Puzzle and Investors’ Behavioral Analysis Quantitative Methods in the Social Sciences Institute for Social and Economic Research and Policy Columbia University in the City of New York International Affairs Building 420 West 118th Street 8th Floor, mail code 3355 New York, New York 10027 1 Equity Risk Premium Puzzle and Investors’ Behavioral Analysis Abstract: From traditional finance theories, large equity risk premium means high coefficient of relative risk aversion. However, historical data of stock returns in US and China’s stock markets showed that, the corresponding risk aversion level was too high to be reasonable. This phenomenon is called Equity Risk Premium Puzzle. The article attempts to summarize and compare all the possible explanations for this puzzle, and the concept of “Loss Aversion” in behavioral finance theories has been successful in explaining the observed equity risk premium. Using simulations, I confirm the existence of equity risk premium in US and China’s stock markets, and find that US’s stock market generally has a Lower degree of equity risk premium than that of China’s by comparing evaluation periods. Further calculations and predictions provide optimal mix of stocks and bonds in the portfolio to maximum prospective utilities and help raise policy suggestions for minimizing equity risk premium level and stabilizing financial markets in US and China. Keywords: Equity Risk Premium; Behavioral Finance; Loss Aversion JEL Classification: C33, D8, G15 2 Equity Risk Premium Puzzle and Investors’ Behavioral Analysis I.
    [Show full text]
  • The Returns to Entrepreneurial Investment: a Private Equity Premium Puzzle?
    TheReturns to EntrepreneurialInvestment: APrivateEquity Premium Puzzle? By TOBIAS J. MOSKOWITZAND ANNETTE VISSING-JØRGENSEN* Wedocument the return to investing in U.S. nonpublicly traded equity. Entrepre- neurialinvestment is extremely concentrated, yet despite its poor diversi cation, we ndthatthe returns to private equity are no higherthan the returns to public equity. Giventhe large public equity premium, it is puzzling why households willingly investsubstantial amounts in asingleprivately held rm witha seeminglyfar worse risk-returntrade-off. We brie y discusshow large nonpecuniary bene ts, a prefer- encefor skewness, or overestimates of theprobability of survivalcould potentially explaininvestment in private equity despite these ndings. (JEL G11,G12, M13) Assetpricing and investment theory rely crit- tionof equityreturns across nonpublicly traded icallyon our understanding of investors’ port- rms. We analyzeinvestment in and document foliochoices. Yet, entrepreneurial investment, thereturn to allnonpublicly traded equity in the whichrepresents a substantialfraction of many UnitedStates. The total value of privateequity investors’portfolios, is relatively understudied issimilar in magnitude to the public equity andnot well understood. Speci cally, little is marketover our sample period. Despite this, the knownabout the aggregat ereturnto entre- privateequity market has received relatively preneurs’equity investments and the distribu- littleacademic attention. 1 We providethe rst setof estimatesof the returns and risks for the entiremarket
    [Show full text]
  • Solution to the Equity Premium Puzzle
    1 SOLUTION TO THE EQUITY PREMIUM PUZZLE Solution to the Equity Premium Puzzle Atilla Aras November 10, 2020 Funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. 2 SOLUTION TO THE EQUITY PREMIUM PUZZLE Solution to the Equity Premium Puzzle Abstract This study provides a solution of the equity premium puzzle. Questioning the validity of the Arrow-Pratt measure of relative risk aversion for detecting the risk behavior of investors under all conditions, a new tool, that is, the sufficiency factor of the model was developed to analyze the risk behavior of investors. The calculations of this newly tested model show that the value of the coefficient of relative risk aversion is 1.033526 by assuming the value of the subjective time discount factor as 0.99. Since these values are compatible with the existing empirical studies, they confirm the validity of the newly derived model that provides a solution to the equity premium puzzle. Keywords: Finance, risk, the sufficiency factor of the model, coefficient of relative risk aversion, equity premium puzzle 3 SOLUTION TO THE EQUITY PREMIUM PUZZLE 1. Introduction The equity premium puzzle is a quantitative puzzle that implies the inability of intertemporal economic models to explain the large historical equity premium under reasonable parameter values in the US financial markets over the past century. The equity premium puzzle, coined by Mehar and Prescott (1985), arises because high historical equity premium leads to an unreasonably high level of risk aversion among investors according to standard intertemporal economic models.
    [Show full text]
  • Risk and Expected Returns of Private Equity Investments: Evidence Based on Market Prices
    Risk and Expected Returns of Private Equity Investments: Evidence Based on Market Prices Narasimhan Jegadeesha,c, Roman Kräusslb and Joshua Polleta a) Goizueta Business School, Emory University, Atlanta, USA b) VU University Amsterdam, The Netherlands c) National Bureau of Economic Research (NBER) March 2009 Abstract We estimate the risk and expected returns of private equity investments based on the market prices of exchange traded funds of funds that invest in unlisted private equity funds. Our results indicate that the market expects unlisted private equity funds to earn abnormal returns of about one to two percent. We also find that the market expects listed private equity funds to earn zero to marginally negative abnormal returns net of fees. Both listed and unlisted private equity funds have market betas close to one and positive factor loadings on the Fama-French SMB factor. Private equity fund returns are positively correlated with GDP growth and negatively correlated with the credit spread. Finally, we find that market returns of exchange traded funds of funds and listed private equity funds predict changes in self-reported book values of unlisted private equity funds. Keywords: Private equity; listed private equity; risk-return characteristics; funds of funds JEL Classification Code: G12 1 I. Introduction Private equity (PE) refers to equity securities in private companies that are not publicly traded. Private Equity funds that specialize in PE investments opened up this asset class to institutional investors and other capital market participants. The early successes of some large PE funds led to a rapid growth of this asset class. Capital commitment to private equity in the U.S.
    [Show full text]
  • Equity Risk Premium Predictability from Cross-Sectoral Downturns*
    Equity Risk Premium Predictability from Cross-Sectoral Downturns* José Afonso Faias and Juan Arismendi Zambrano This version: July 2017 Abstract We illustrate the role of left tail mean (LTM) in equity risk premium (ERP) predictability. LTM measures the average of pairwise left tail dependency among major equity sectors incorporating endogenous shocks that are imperceptible at the aggregate level. LTM, as the variance risk premium, significantly predicts the ERP in- and out-of- sample, which is not the case with the other commonly used predictors. Ceteris paribus, an increase of two standard deviations in the LTM in a time-varying disaster-risk consumption-based asset pricing model causes an increase of 0.70% in the ERP. This paper contributes to the debate on ERP predictability. Keywords: Predictability, left tail dependence, asset pricing model. JEL classification: G10, G12, G14. *Corresponding author: José Afonso Faias, UCP - Católica Lisbon School of Business & Economics, Palma de Cima, 1649-023 Lisboa, Portugal. Phone +351-217270250. E-mail: [email protected]. Juan Arismendi Zambrano, Department of Economics, Finance and Accounting, Maynooth University -National University of Ireland, Maynooth, Ireland. Phone +353-(0)1- 7083728. E-mail: [email protected]; ICMA Centre – Henley Business School, University of Reading, Whiteknights, RG6 6BA, Reading, UK. Phone +44-1183788239. E-mail: [email protected]. We thank Rui Albuquerque, Gregory Connor, Adam Farago, Campbell Harvey, Joni Kokkonen, Stefan Nagel, Pedro Santa-Clara, Kenneth J. Singleton, Grigory Vilkov, Andrew Vivian, Jessica A. Wachter, and the participants at the 2016 FMA Annual Meeting, 2016 Research in Options, 2017 FMA European Conference, 2017 Multinational Finance Society Annual Meeting, 2017 European Finance Association Annual Meeting, and the 2017 Foro Finanzas for helpful comments and discussions.
    [Show full text]