Asset prices are derived in closed-form in a framework where agents evaluate risk with gain-loss asymmetry: losses relative to a reference point incur discontinuously more disutility than comparable gains. This asymmetry has a dual impact. First, a level effect: risk prices are made higher by the kink in the preferences. Second, a cross-sectional effect: the pricing of risk is higher (lower) for safer (riskier) assets, so expected returns increase non-linearly with the risk-exposures. This second effect, a crucial departure from standard smooth utility models, is weakened by lower specifications of the reference point and by higher volatilities in aggregate risk.
{"title":"Risk Pricing Under Gain-Loss Asymmetry","authors":"Marianne Andries","doi":"10.2139/ssrn.3433953","DOIUrl":"https://doi.org/10.2139/ssrn.3433953","url":null,"abstract":"Asset prices are derived in closed-form in a framework where agents evaluate risk with gain-loss asymmetry: losses relative to a reference point incur discontinuously more disutility than comparable gains. This asymmetry has a dual impact. First, a level effect: risk prices are made higher by the kink in the preferences. Second, a cross-sectional effect: the pricing of risk is higher (lower) for safer (riskier) assets, so expected returns increase non-linearly with the risk-exposures. This second effect, a crucial departure from standard smooth utility models, is weakened by lower specifications of the reference point and by higher volatilities in aggregate risk.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"259 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133464091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Several studies have found that the cross-section of stock returns reflects a risk premium for bearing downside risk; however, existing measures of downside risk have poor power for predicting returns. Therefore, this paper proposes a novel measure of downside risk, the ES-implied beta, to improve the prediction of the cross-section of asset returns. The ES-implied beta explains stock returns over the same period as well as the widely used downside beta, but also has strong predictive power over future returns. In the empirical analysis, although the widely used downside beta shows a weak relation with future expected returns, the ES-implied beta implies a statistically and economically significant risk premium of 0.5 percent per month. The predictive power of the ES-implied beta is not explained by the cross-sectional effects from the CAPM beta, size, book-to-market ratio, momentum, coskewness, cokurtosis or liquidity beta, nor does it depend on the design of the empirical analysis.
{"title":"A Novel Downside Risk Measure and Expected Returns","authors":"Jinjing Liu","doi":"10.2139/ssrn.3406944","DOIUrl":"https://doi.org/10.2139/ssrn.3406944","url":null,"abstract":"Several studies have found that the cross-section of stock returns reflects a risk premium for bearing downside risk; however, existing measures of downside risk have poor power for predicting returns. Therefore, this paper proposes a novel measure of downside risk, the ES-implied beta, to improve the prediction of the cross-section of asset returns. The ES-implied beta explains stock returns over the same period as well as the widely used downside beta, but also has strong predictive power over future returns. In the empirical analysis, although the widely used downside beta shows a weak relation with future expected returns, the ES-implied beta implies a statistically and economically significant risk premium of 0.5 percent per month. The predictive power of the ES-implied beta is not explained by the cross-sectional effects from the CAPM beta, size, book-to-market ratio, momentum, coskewness, cokurtosis or liquidity beta, nor does it depend on the design of the empirical analysis.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127669195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Risk capital allocations are of central importance in performance measurement. A popular solution concept in the academic literature is the Euler rule. This paper studies the volatility of the Euler rule for capital allocation in static and dynamic empirical applications with a simulated history. The Euler rule is not continuous with respect to small changes in the underlying risk capital allocation problem. We show that, when combined with value-at-risk, the Euler rule is very sensitive to empirical measurement error. The use of a known distribution with estimated parameters helps to reduce this error. The Euler rule with an expected shortfall risk measure is less volatile, but it is still more volatile than the proportional rule.
{"title":"Static and Dynamic Risk Capital Allocations With the Euler Rule","authors":"T. Boonen","doi":"10.2139/ssrn.3288592","DOIUrl":"https://doi.org/10.2139/ssrn.3288592","url":null,"abstract":"Risk capital allocations are of central importance in performance measurement. A popular solution concept in the academic literature is the Euler rule. This paper studies the volatility of the Euler rule for capital allocation in static and dynamic empirical applications with a simulated history. The Euler rule is not continuous with respect to small changes in the underlying risk capital allocation problem. We show that, when combined with value-at-risk, the Euler rule is very sensitive to empirical measurement error. The use of a known distribution with estimated parameters helps to reduce this error. The Euler rule with an expected shortfall risk measure is less volatile, but it is still more volatile than the proportional rule.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121053662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dependence of interest rate’s volatility on the level of rates has both general macroeconomic significance and direct consequences on computing market risk metrics such as VAR, SVAR or ES, and counterparty credit risk modelling. Such dependence is investigated and viewed in terms of local elasticity. A new regime at low and negative rates with volatility independent of the level of the rates is found, and three other regimes reported by Deguillaume, Rebonato and Pogudin (2013) are confirmed with more recent data and a larger pool of currencies. A preliminary study into the existence of regimes for break-even inflation is also conducted and indications of regimes are found. One of these regimes has no equivalence in interest rates; it exhibits negative elasticity slope which may imply similar regime if rate levels also reach sufficiently negative values. The overall shape of inflation elasticity resembles a strangle payoff, and we hypothesise that this directly reflects markets’ response to macroeconomic policy of inflation targeting and also indirectly links such policy to the nominal rate regimes. We demonstrate that the incorporation of such regimes in market risk modelling improves its predictive capacity, and for counterparty risk modelling has significant impact on risk and regulatory calculations.
{"title":"Universal Regimes for Rates and Inflation. The Effect of Local Elasticity on Market and Counterparty Risk","authors":"V. Chorniy, V. Kotecha","doi":"10.2139/ssrn.3207209","DOIUrl":"https://doi.org/10.2139/ssrn.3207209","url":null,"abstract":"The dependence of interest rate’s volatility on the level of rates has both general macroeconomic significance and direct consequences on computing market risk metrics such as VAR, SVAR or ES, and counterparty credit risk modelling. Such dependence is investigated and viewed in terms of local elasticity. A new regime at low and negative rates with volatility independent of the level of the rates is found, and three other regimes reported by Deguillaume, Rebonato and Pogudin (2013) are confirmed with more recent data and a larger pool of currencies. A preliminary study into the existence of regimes for break-even inflation is also conducted and indications of regimes are found. One of these regimes has no equivalence in interest rates; it exhibits negative elasticity slope which may imply similar regime if rate levels also reach sufficiently negative values. The overall shape of inflation elasticity resembles a strangle payoff, and we hypothesise that this directly reflects markets’ response to macroeconomic policy of inflation targeting and also indirectly links such policy to the nominal rate regimes. We demonstrate that the incorporation of such regimes in market risk modelling improves its predictive capacity, and for counterparty risk modelling has significant impact on risk and regulatory calculations.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128942420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bochuan Dai, Ben R. Marshall, N. Nguyen, Nuttawat Visaltanachoti
We consider the effectiveness of trailing stop-loss rules which, unlike traditional stop-loss rules, involve the sell trigger price being moved higher to protect profits as prices rise. Our results indicate that while these rules have inferior mean returns to a simple buy-and-hold strategy, they do a good job of stopping losses. They generate superior risk-adjusted returns for investors with normal levels of risk aversion and perform particularly well at reducing downside risk. These results hold in all U.S. stocks and are particular strong for stocks that end up being delisted.
{"title":"Risk Reduction Using Trailing Stop-Loss Rules","authors":"Bochuan Dai, Ben R. Marshall, N. Nguyen, Nuttawat Visaltanachoti","doi":"10.2139/ssrn.3338243","DOIUrl":"https://doi.org/10.2139/ssrn.3338243","url":null,"abstract":"We consider the effectiveness of trailing stop-loss rules which, unlike traditional stop-loss rules, involve the sell trigger price being moved higher to protect profits as prices rise. Our results indicate that while these rules have inferior mean returns to a simple buy-and-hold strategy, they do a good job of stopping losses. They generate superior risk-adjusted returns for investors with normal levels of risk aversion and perform particularly well at reducing downside risk. These results hold in all U.S. stocks and are particular strong for stocks that end up being delisted.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123937554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present new evidence on the predictability of aggregate market returns by developing two new prediction models, one risk-based, and the other purely statistical. The pricing kernel model expresses the expected return as the covariance of the market return with a pricing kernel that is a linear function of portfolio returns. The discount rate model predicts the expected return directly as a function of weighted past portfolio returns. These models provide independent evidence of predictability, with R2 of 16-19% for 1-year returns. We show that innovations in the pricing kernel are associated with the cash flow component of the market return.
{"title":"Expected Returns and Risk in the Stock Market","authors":"M. Brennan, Alex P. Taylor","doi":"10.2139/ssrn.3331573","DOIUrl":"https://doi.org/10.2139/ssrn.3331573","url":null,"abstract":"We present new evidence on the predictability of aggregate market returns by developing two new prediction models, one risk-based, and the other purely statistical. The pricing kernel model expresses the expected return as the covariance of the market return with a pricing kernel that is a linear function of portfolio returns. The discount rate model predicts the expected return directly as a function of weighted past portfolio returns. These models provide independent evidence of predictability, with R2 of 16-19% for 1-year returns. We show that innovations in the pricing kernel are associated with the cash flow component of the market return.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121246684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Borowska, Lennart F. Hoogerheide, S. J. Koopman
We present an accurate and efficient method for Bayesian forecasting of two financial risk measures, Value-at-Risk and Expected Shortfall, for a given volatility model. We obtain precise forecasts of the tail of the distribution of returns not only for the 10-days-ahead horizon required by the Basel Committee but even for long horizons, like one-month or one-year-ahead. The latter has recently attracted considerable attention due to the different properties of short term risk and long run risk. The key insight behind our importance sampling based approach is the sequential construction of marginal and conditional importance densities for consecutive periods. We report substantial accuracy gains for all the considered horizons in empirical studies on two datasets of daily financial returns, including a highly volatile period of the recent financial crisis. To illustrate the flexibility of the proposed construction method, we present how it can be adjusted to the frequentist case, for which we provide counterparts of both Bayesian applications.
{"title":"Bayesian Risk Forecasting for Long Horizons","authors":"A. Borowska, Lennart F. Hoogerheide, S. J. Koopman","doi":"10.2139/ssrn.3339819","DOIUrl":"https://doi.org/10.2139/ssrn.3339819","url":null,"abstract":"We present an accurate and efficient method for Bayesian forecasting of two financial risk measures, Value-at-Risk and Expected Shortfall, for a given volatility model. We obtain precise forecasts of the tail of the distribution of returns not only for the 10-days-ahead horizon required by the Basel Committee but even for long horizons, like one-month or one-year-ahead. The latter has recently attracted considerable attention due to the different properties of short term risk and long run risk. The key insight behind our importance sampling based approach is the sequential construction of marginal and conditional importance densities for consecutive periods. We report substantial accuracy gains for all the considered horizons in empirical studies on two datasets of daily financial returns, including a highly volatile period of the recent financial crisis. To illustrate the flexibility of the proposed construction method, we present how it can be adjusted to the frequentist case, for which we provide counterparts of both Bayesian applications.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129943536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a parsimonious arbitrage-free yield net model for consistent bond pricing across maturities and issuers. Containing a core curve and multiple periphery curves, the yield net is spanned by three layers of factors: base factors spanning all curves, common spread factors spanning all periphery yield spreads, and specific factors each spanning yield spreads of a periphery issuer. Under the arbitrage-free assumption, we prove a parsimonious solution to the risk-neutral process that guarantees strong identification on the latent risk factors and parameters. We apply the model to Treasury yields of Germany and GIIPS countries from 2009 to 2016. The model fits data remarkably well and disentangles the common credit risk, market liquidity risk, and country-specific risks. The results demonstrate that relative risk pricing determines signs and magnitudes of the "flight to liquidity" effect and spillover effects among bonds of different issuers.
{"title":"An Arbitrage-Free Yield Net Model with Application to the Euro Debt Crisis","authors":"Zhiwu Hong, Linlin Niu","doi":"10.2139/ssrn.3325686","DOIUrl":"https://doi.org/10.2139/ssrn.3325686","url":null,"abstract":"We develop a parsimonious arbitrage-free yield net model for consistent bond pricing across maturities and issuers. Containing a core curve and multiple periphery curves, the yield net is spanned by three layers of factors: base factors spanning all curves, common spread factors spanning all periphery yield spreads, and specific factors each spanning yield spreads of a periphery issuer. Under the arbitrage-free assumption, we prove a parsimonious solution to the risk-neutral process that guarantees strong identification on the latent risk factors and parameters. We apply the model to Treasury yields of Germany and GIIPS countries from 2009 to 2016. The model fits data remarkably well and disentangles the common credit risk, market liquidity risk, and country-specific risks. The results demonstrate that relative risk pricing determines signs and magnitudes of the \"flight to liquidity\" effect and spillover effects among bonds of different issuers.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114840327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We apply wavelet analysis to observe financial returns. We demonstrate how useful wavelets can be to separate normal market conditions from stressed market conditions. After noise removal, a process appears to manifest itself during period of financial distress and show a remarkable alignment across asset classes. We finally propose an adaptation of a hidden Markov model used in speech recognition for the simulation of financial returns in the wavelet domain. This model natively acknowledges that daily returns contain different frequency information, simulates realistically over a given risk horizon and captures the tail risk: wild movements unanticipated by usual normality assumptions.
{"title":"A Wavelet Approach to Tail Risk","authors":"Hassan Ennadifi","doi":"10.2139/ssrn.3249928","DOIUrl":"https://doi.org/10.2139/ssrn.3249928","url":null,"abstract":"We apply wavelet analysis to observe financial returns. We demonstrate how useful wavelets can be to separate normal market conditions from stressed market conditions. After noise removal, a process appears to manifest itself during period of financial distress and show a remarkable alignment across asset classes. We finally propose an adaptation of a hidden Markov model used in speech recognition for the simulation of financial returns in the wavelet domain. This model natively acknowledges that daily returns contain different frequency information, simulates realistically over a given risk horizon and captures the tail risk: wild movements unanticipated by usual normality assumptions.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123620747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We compute monthly correlation matrices of 25 global futures markets in four asset classes: fixed income, commodities, equities, fx. Comparing and grouping those correlation matrices leads to distinct «regimes» in time. We can characterize these regimes by futures market returns, finding patterns between risk-on and risk-off assets. One of those regimes is especially «risk-off». We can also characterize these regimes by CS hedge fund index returns. In the «risk-off» regime, they also underperform. The Eurekahedge EHF funds show a similar performance behaviour according to strategies across regimes as the CS hedge fund indices. The dispersion across the Eurekahedge EHF funds for each month is largest in the «risk-off» regime.
{"title":"Hedge Fund Returns Characterized by Correlation Regimes (Presentation Slides)","authors":"Peter Schwendner","doi":"10.2139/ssrn.3451211","DOIUrl":"https://doi.org/10.2139/ssrn.3451211","url":null,"abstract":"We compute monthly correlation matrices of 25 global futures markets in four asset classes: fixed income, commodities, equities, fx. Comparing and grouping those correlation matrices leads to distinct «regimes» in time. We can characterize these regimes by futures market returns, finding patterns between risk-on and risk-off assets. One of those regimes is especially «risk-off». We can also characterize these regimes by CS hedge fund index returns. In the «risk-off» regime, they also underperform. The Eurekahedge EHF funds show a similar performance behaviour according to strategies across regimes as the CS hedge fund indices. The dispersion across the Eurekahedge EHF funds for each month is largest in the «risk-off» regime.","PeriodicalId":187811,"journal":{"name":"ERN: Other Econometric Modeling: Capital Markets - Risk (Topic)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121798393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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