[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-637873-105":59,"doc-detail-637873-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","variable-rare-disasters-an-exactly-solved-framework-for-ten-puzzles-in-macro-finance-quantitative-macro-finance-risk-premia-model","VARIABLE RARE DISASTERS - AN EXACTLY SOLVED FRAMEWORK FOR TEN PUZZLES IN MACRO-FINANCE - Quantitative macro-finance risk premia model","","Variable Rare Disasters develops a time-varying-severity version of the rare-disaster hypothesis in macro-finance. It incorporates disaster-driven drops in asset fundamentals that generate time-varying risk premia, yielding volatile prices and return predictability. Using linearity-generating processes, the model delivers tractable, closed-form solutions and quantitatively interprets major asset-pricing puzzles, including equity and risk-free rate premia, volatility, return predictability, yield-curve behavior, bond excess-return dynamics, corporate spreads, and deep out-of-the-money put prices.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/variable-rare-disasters-an-exactly-solved-framework-for-ten-puzzles-in-macro-finance-quantitative-macro-finance-risk-premia-model/637873/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/variable-rare-disasters-an-exactly-solved-framework-for-ten-puzzles-in-macro-finance-quantitative-macro-finance-risk-premia-model/637873.png","ImageObject",300,407,{"name":92,"@type":93},"vwvw","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How does variable disaster severity change asset pricing in the model?","Question",{"text":112,"@type":113},"Disasters reduce an asset’s fundamental value by a time-varying amount, which induces time-varying risk premia. This leads to volatile asset prices and return predictability.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why are the prices solvable in closed form?",{"text":117,"@type":113},"The framework uses linearity-generating processes, making the model tractable. As a result, all prices can be solved exactly in closed form.",{"name":119,"@type":110,"acceptedAnswer":120},"Which asset-market puzzles does the framework aim to explain?",{"text":121,"@type":113},"It provides quantitative understanding of ten listed empirical regularities, including the equity premium puzzle, risk-free rate puzzle, excess volatility, aggregate return predictability, and several yield-curve and bond-spread related puzzles.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},637873,1792810969,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},3985747874149,"https://ap-avatar.wpscdn.com/avatar/3a001161165b4dc3d9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1790129441039064114","VARIABLE RARE DISASTERS: AN EXACTLY SOLVED FRAMEWORK FOR TEN PUZZLES IN MACRO-FINANCE∗  \nXAVIER GABAIX  \nThis article incorporates a time-varying severity of disasters into the hypothesis proposed by Rietz (1988) and Barro (2006) that risk premia result from the possibility of rare large disasters. During a disaster an asset’s fundamental value falls by a time-varying amount. This in turn generates time-varying risk premia and, thus, volatile asset prices and return predictability. Using the recent technique of linearity-generating processes, the model is tractable and all prices are exactly solved in closed form. In this article’s framework, the following empirical regularities can be understood quantitatively: (i) equity premium puzzle; (ii) risk-free rate puzzle; (iii) excess volatility puzzle; (iv) predictability of aggregate stock market returns with price-dividend ratios; (v) often greater explanatory power of characteristics than covariances for asset returns; (vi) upward-sloping nominal yield curve; (vii) predictability of future bond excess returns and long-term rates via the slope of the yield curve; (viii) corporate bond spread puzzle; (ix) high price of deep out-of-the-money puts; and (x) high put prices being followed by high stock returns. The calibration passes a variance bound test, as normal-times market volatility is consistent with the wide dispersion of disaster outcomes in the historical record. The model extends to a setting with many factors and to Epstein-Zin preferences. JEL Codes: E43, E44, G12.  \nI. INTRODUCTION  \nThere has been a revival of a hypothesis proposed by Rietz (1988) that the possibility of rare disasters, such as economic depressions or wars, is a major determinant of asset risk premia. Indeed, Barro (2006) has shown that internationally, disasters have been sufficiently frequent and large to make Rietz’s proposal viable and account for the high risk premium on equities. Additionally, the recent economic crisis has given disaster risk a renewed salience.  \nThe rare disaster hypothesis is almost always formulated with constant severity of disasters. This is useful for thinking  \n∗ I thank Alex Chinco, Esben Hedegaard, Farzad Saidi, and Rob Tumarkin for excellent research assistance. For helpful comments, I thank five referees and Robert Barro (the editor), David Chapman, Alex Edmans, Emmanuel Farhi, Francois Gourio, Christian Julliard, Sydney Ludvigson, Anthony Lynch, Thomas Philippon, Jos´eScheinkman, Jos´eUrsua, Stijn van Nieuwerburgh, Adrien Verdelhan, Stan Zin, and seminar participants atAFA, Chicago GSB, Duke, Harvard, Minnesota Workshop in Macro Theory, MIT, NBER, NYU, Paris School of Economics, Princeton, Texas Finance Festival, UCLA, and Washington University at Saint Louis. I thank Robert Barro, Stephen Figlewski, Arvind Krishnamurthy, Jos´eUrsua, Annette Vissing-Jorgensen, and Hao Zhou for their data, and theNSF (grant SES-0820517) for support.  \n The Author(s) 2012. Published by Oxford University Press, on the behalf of President and Fellows of Harvard College. All rights reserved. For Permissions, please email: journals. [permissions@oup.com](permissions@oup.com).  \nThe Quarterly Journal of Economics (2012) 127, 645–700. doi:10. 1093/qje/qjs001 . Advance Access publication on March 14, 2012.  \nDownloaded from [http://qje.oxfordjournals.org/](http://qje.oxfordjournals.org/ at New York University School of Law on May 1)[ at New York University School of Law on May 1](http://qje.oxfordjournals.org/ at New York University School of Law on May 1), 2012  \n646 QUARTERLY JOURNAL OF ECONOMICS  \nabout averages but cannot account for some key features of asset markets, such as volatile price-dividend ratios for stocks, volatile bond risk premia, and return predictability. In this article, I formulatea variable-severity version of the rare disasters hypothesis andinvestigate the impact of time-varying disaster severity on the prices of stocks and bonds as well as on the predictability of ","cbCairI6NszmycZb","https://ap.wps.com/l/cbCairI6NszmycZb","pdf",425737,56,"English","# Introduction\n## Stock Market: Puzzles about the Aggregates\n## Stock Market: Puzzles about the Cross-Section of Stocks","[{\"question\":\"How does variable disaster severity change asset pricing in the model?\",\"answer\":\"Disasters reduce an asset’s fundamental value by a time-varying amount, which induces time-varying risk premia. This leads to volatile asset prices and return predictability.\"},{\"question\":\"Why are the prices solvable in closed form?\",\"answer\":\"The framework uses linearity-generating processes, making the model tractable. As a result, all prices can be solved exactly in closed form.\"},{\"question\":\"Which asset-market puzzles does the framework aim to explain?\",\"answer\":\"It provides quantitative understanding of ten listed empirical regularities, including the equity premium puzzle, risk-free rate puzzle, excess volatility, aggregate return predictability, and several yield-curve and bond-spread related puzzles.\"}]","VARIABLE RARE DISASTERS - AN EXACTLY SOLVED FRAMEWORK FOR TEN PUZZLES IN MACRO-FINANCE - Quantitative macro-finance risk premia model | PDF",1792681597,141]