SSRN Author: Anish ShahAnish Shah SSRN Content
https://privwww.ssrn.com/author=2303590
https://privwww.ssrn.com/rss/en-usTue, 13 Jul 2021 01:31:19 GMTeditor@ssrn.com (Editor)Tue, 13 Jul 2021 01:31:19 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Portfolio Risks under Estimation Uncertainty and Price MovementRisk decomposition is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose contributions to net risk are estimated and reported. Convention regards the inputs—portfolio weights and covariance—as fixed and known, but portfolio composition changes with price movement and estimates have errors. Since behavior only in the direction of net risk is counted, hedged effects are invisible regardless of size. What if numbers aren’t exact? Hedge instability manifests in proportion to underlying gross (not net) exposure, akin to leverage. For example, in a market-neutral portfolio, market is the largest risk in each side, conventionally uncounted since hedged, and extremely consequential under small deviations. To solve the problem, this paper models weights and parameters as uncertain. Evaluating a portfolio across the range of possibility measures risks better and ...
https://privwww.ssrn.com/abstract=3774239
https://privwww.ssrn.com/2041604.htmlMon, 12 Jul 2021 11:03:29 GMTREVISION: Portfolio Risks under Estimation Uncertainty and Price MovementRisk decomposition is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose contributions to net risk are estimated and reported. Convention regards the inputs—portfolio weights and covariance—as fixed and known, but portfolio composition changes with price movement and estimates have errors. Since behavior only in the direction of net risk is counted, hedged effects are invisible regardless of size. What if numbers aren’t exact? Hedge instability manifests in proportion to underlying gross (not net) exposure, akin to leverage. For example, in a market-neutral portfolio, market is the largest risk in each side, conventionally uncounted since hedged, and extremely consequential under small deviations. To solve the problem, this paper models weights and parameters as uncertain. Evaluating a portfolio across the range of possibility measures risks better and ...
https://privwww.ssrn.com/abstract=3774239
https://privwww.ssrn.com/2039993.htmlTue, 06 Jul 2021 11:25:11 GMTREVISION: Portfolio Risks under Estimation Uncertainty and Price MovementRisk decomposition is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose contributions to net risk are estimated and reported. Convention regards the inputs—portfolio weights and covariance—as fixed and known, but portfolio composition changes with price movement and estimates have errors. Since behavior only in the direction of net risk is counted, hedged effects are invisible regardless of size. What if numbers aren’t exact? Hedge instability manifests in proportion to underlying gross (not net) exposure, akin to leverage. For example, in a market-neutral portfolio, market is the largest risk in each side, conventionally uncounted since hedged, and extremely consequential under small deviations. To solve the problem, this paper models weights and parameters as uncertain. Evaluating a portfolio across the range of possibility measures risks better and ...
https://privwww.ssrn.com/abstract=3774239
https://privwww.ssrn.com/2039616.htmlFri, 02 Jul 2021 12:50:49 GMTREVISION: Risk under Parameter Uncertainty and Price MovementRisk decomposition is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose contributions to net risk are estimated and reported. Convention regards the inputs—portfolio weights and covariance—as fixed and known, but real weights change with price movement and estimates are imperfect. A problem arises because only the direction of net risk is counted and hedged effects go unseen regardless of size. What if numbers aren’t exact? The latent risk and instability of offsetting effects manifest in proportion to magnitude, akin to leverage. For example, in a market-neutral portfolio, market is the largest risk in each side, conventionally uncounted since hedged, and extremely consequential under small deviations. As a solution, this paper treats weights and parameters as uncertain for a realistic appraisal that surfaces hidden fragility. No longer ...
https://privwww.ssrn.com/abstract=3774239
https://privwww.ssrn.com/2039447.htmlFri, 02 Jul 2021 10:29:43 GMTNew: Uncertain Risk ParityRisk parity is a portfolio construction technique that scales sections of a portfolio (eg, stocks, bonds, currencies, commodities) so that forecasted contributions to net portfolio risk match the budget. Because risks are measured from a point estimate of covariance, the method is subject to problems of estimation error. This paper treats covariance as uncertain in order to find a risk parity weighting that does not count on perfectly optimized hedges and is robust to changes in regime. Separately, of general interest are the uncertain risk contributions calculated en route. Reporting a portfolio’s uncertain risk decomposition puts a band around numbers and reveals fragility. For example, a market could seem hedged in a long–short portfolio but surface as the biggest risk when parameters are considered across their error range.
https://privwww.ssrn.com/abstract=3875322
https://privwww.ssrn.com/2038910.htmlWed, 30 Jun 2021 16:11:25 GMTREVISION: Uncertain Risk ParityRisk parity is a portfolio construction technique that scales sections of a portfolio-e.g., stocks, bonds, currencies, commodities-so that forecasted contributions to net portfolio risk match the budget. Because risks are measured from a point-estimate of covariance, the method is subject to problems of estimation error. This paper treats covariance as uncertain in order to find a risk parity weighting that doesn't count on perfectly optimized hedges and is robust to changes in regime.<br><br>Separately, of general interest are the uncertain risk contributions calculated en route. Reporting a portfolio's uncertain risk decomposition puts a band around numbers and reveals fragility. For example, market could seem hedged in a long-short portfolio but surface as the biggest risk when parameters are considered across their error range.
https://privwww.ssrn.com/abstract=3406321
https://privwww.ssrn.com/2037815.htmlMon, 28 Jun 2021 14:27:42 GMTREVISION: Risk under Uncertainty and Price Movement'Risk decomposition' is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose separate contributions to net risk are estimated and reported. Though the numbers appear elsewhere, e.g., in risk parity portfolio construction, the most common application is risk assessment.<br>With portfolio weights fixed and point-estimated covariance taken as true, conventional calculations regard the system as static and known. In reality, composition shifts with price movement and estimates have error. A problem arises from the simplification because only behavior perceived as in the direction of net risk is counted; hedged effects vanish regardless of size. For example, in a market-neutral portfolio, market is the largest risk in each side, uncounted since apparently hedged, and extremely consequential under small deviations from perception. As a solution, this paper ...
https://privwww.ssrn.com/abstract=3774239
https://privwww.ssrn.com/2037812.htmlMon, 28 Jun 2021 14:26:18 GMTREVISION: Risk under Uncertainty and Price MovementRisk contributions apportion portfolio risk, the risk that remains after internal hedging, to the portfolio's separate parts. Parts can be concrete—e.g., individual securities, holdings grouped by sector—or abstract, e.g., exposures to risk factors. The numbers are typically used for risk assessment though appear elsewhere, for example, in risk parity portfolio construction.<br><br>Conventional calculations come from a point-estimate of covariance and fixed portfolio weights. However, estimates have error, and composition continuously shifts with price movement.<br><br>Because what's measured is the net after offsetting effects irrespective of their absolute size, apparently-hedged risks can be consequential if misestimated or slightly perturbed. As a solution, this paper treats parameters and weights as uncertain for a truer assessment that measures latent fragility.
https://privwww.ssrn.com/abstract=3774239
https://privwww.ssrn.com/2030565.htmlFri, 04 Jun 2021 10:04:14 GMTREVISION: Uncertain Covariance Models and Uncertainty-Penalized Portfolio OptimizationCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, and hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values remain inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. Applications include more informative portfolio risk assessment, uncertainty-penalized optimization to counter estimation error and improve realized utility, and uncertainty ...
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/2027545.htmlMon, 24 May 2021 17:54:14 GMTREVISION: Uncertain Risk ParityRisk parity is a portfolio construction technique that scales sections of a portfolio-e.g., stocks, bonds, currencies, commodities-so that forecasted contributions to net portfolio risk match the budget. Because risks are measured from a point-estimate of covariance, the method is subject to problems of estimation error. This paper treats covariance as uncertain in order to find a risk parity weighting that doesn't count on perfectly optimized hedges and is robust to changes in regime.<br><br>Separately, of general interest are the uncertain risk contributions calculated en route. Reporting a portfolio's uncertain risk decomposition puts a band around numbers and reveals fragility. For example, market could seem hedged in a long-short portfolio but surface as the biggest risk when parameters are considered across their error range.
https://privwww.ssrn.com/abstract=3406321
https://privwww.ssrn.com/2025511.htmlMon, 17 May 2021 14:46:10 GMTREVISION: Uncertain Risk ParityRisk parity is a portfolio construction technique that scales sections of a portfolio-e.g., stocks, bonds, currencies, commodities-so that forecasted contributions to net portfolio risk match the budget. Because risks are measured from a point-estimate of covariance, the method is subject to problems of estimation error. This paper treats covariance as uncertain in order to find a risk parity weighting that doesn't count on perfectly optimized hedges and is robust to changes in regime.<br><br>Separately, of general interest are the uncertain risk contributions calculated en route. Reporting a portfolio's uncertain risk decomposition puts a band around numbers and reveals fragility. For example, market could seem hedged in a long-short portfolio but surface as the biggest risk when parameters are considered across their error range.
https://privwww.ssrn.com/abstract=3406321
https://privwww.ssrn.com/2016815.htmlThu, 22 Apr 2021 11:08:39 GMTREVISION: Uncertain Covariance Models and Uncertainty-Penalized Portfolio OptimizationCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, and hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values remain inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. Applications include more informative portfolio risk assessment, uncertainty-penalized optimization to counter estimation error and improve realized utility, and uncertainty ...
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/2014983.htmlSat, 17 Apr 2021 09:51:22 GMTREVISION: Short-Term Risk and Adapting Covariance Models to Current Market ConditionsCovariance models of stock returns appear throughout the investment process, e.g., forecasting portfolio risk, hedging, constructing mean-variance optimal portfolios, and algorithmic trading. Typically built from historic time-series, they estimate the past but–because markets and regimes continually change–not the present and future.<br><br>There are non-time-series, instantaneous ways to infer or predict volatility, e.g., option implied volatility, intra-period trading range, machine learning on alternative data. This paper describes a conceptual framework and algorithm for incorporating these inferences into any linear factor covariance model so that it represents one's beliefs about future behavior instead of echoing the past.
https://privwww.ssrn.com/abstract=2501071
https://privwww.ssrn.com/2012507.htmlThu, 08 Apr 2021 13:53:18 GMTREVISION: Uncertain Risk ParityRisk parity is a portfolio construction technique that scales sections of a portfolio-e.g., stocks, bonds, currencies, commodities-so that forecasted contributions to net portfolio risk match the budget. Because risks are measured from a point-estimate of covariance, the method is subject to problems of estimation error. This paper treats covariance as uncertain in order to find a risk parity weighting that doesn't count on perfectly optimized hedges and is robust to changes in regime.<br><br>Separately, of general interest are the uncertain risk contributions calculated en route. Reporting a portfolio's uncertain risk decomposition puts a band around numbers and reveals fragility. For example, market could seem hedged in a long-short portfolio but surface as the biggest risk when parameters are considered across their error range.
https://privwww.ssrn.com/abstract=3406321
https://privwww.ssrn.com/1982339.htmlWed, 20 Jan 2021 09:19:46 GMTREVISION: Uncertain Covariance ModelsCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, and hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values remain inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. Applications include more informative portfolio risk assessment, uncertainty-penalized optimization to counter estimation error and improve realized utility, and uncertainty ...
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/1979013.htmlSat, 09 Jan 2021 16:18:08 GMTREVISION: Uncertain Covariance ModelsCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, and hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values remain inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. Applications include more informative portfolio risk assessment, uncertainty-penalized optimization to counter estimation error and improve realized utility, and uncertainty ...
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/1971366.htmlSun, 13 Dec 2020 10:03:24 GMTREVISION: Uncertain Covariance ModelsCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values are still inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. The additional information can be used to improve investment decisions, for example, by penalizing uncertainty during portfolio optimization to mitigate estimation error problems.
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/1966883.htmlTue, 01 Dec 2020 12:34:25 GMTREVISION: Uncertain Covariance ModelsCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values are still inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. The additional information can be used to improve investment decisions, for example, by penalizing uncertainty during portfolio optimization to mitigate estimation error problems.
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/1965984.htmlSat, 28 Nov 2020 11:39:19 GMTREVISION: Uncertain Covariance ModelsCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values are still inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. The additional information can be used to improve investment decisions, for example, by penalizing uncertainty during portfolio optimization to mitigate estimation error problems.
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/1965649.htmlFri, 27 Nov 2020 09:57:46 GMTREVISION: Uncertain Covariance ModelsCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values are still inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. The additional information can be used to improve investment decisions, for example, by penalizing uncertainty during portfolio optimization to mitigate estimation error problems.
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/1954917.htmlSat, 24 Oct 2020 09:37:36 GMTREVISION: Uncertain Covariance ModelsCovariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values are still inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. The additional information can be used to improve investment decisions, for example, by penalizing uncertainty during portfolio optimization to mitigate estimation error problems.
https://privwww.ssrn.com/abstract=2616109
https://privwww.ssrn.com/1953705.htmlWed, 21 Oct 2020 08:15:27 GMTREVISION: Uncertain Risk ParityRisk parity is a portfolio construction technique that scales sections of a portfolio—e.g., stocks, bonds, currencies, commodities—so that forecasted contributions to net portfolio risk match the budget. Because risks are measured from a point-estimate of covariance, the method is subject to problems of estimation error. This paper treats covariance as uncertain in order to find a risk parity weighting that doesn't count on perfectly optimized hedges and is robust to changes in regime.<br><br>Separately, of general interest are the uncertain risk contributions calculated en route. Reporting a portfolio's uncertain risk decomposition puts a band around numbers and reveals fragility. For example, market could seem hedged in a long-short portfolio but, examined with uncertainty, surface as the biggest risk when values fall across estimates' range of error instead of at a point.<br>
https://privwww.ssrn.com/abstract=3406321
https://privwww.ssrn.com/1948559.htmlWed, 07 Oct 2020 08:10:49 GMTREVISION: Uncertain Risk ParityRisk parity is portfolio construction technique that, using risk alone, scales each part of a portfolio—e.g., stocks, bonds, currencies, commodities—so that its forecasted contribution to net portfolio risk matches its budgeted risk. Because risks are measured using a point-estimate of covariance, the method is subject to problems of estimation error. This paper performs risk parity with covariance modeled as uncertain in order to achieve a weighting robust to changes in regime and hidden risks from misperceived hedging.<br><br>The uncertain risk contributions, calculated en route, have value well beyond risk parity. Reporting a portfolio's “uncertain risk decomposition” reveals the range around numbers and, more important, the risks that arise from inexact knowledge, e.g., market's going from invisible to the biggest latent risk in a seemingly beta-hedged long-short portfolio.<br>
https://privwww.ssrn.com/abstract=3406321
https://privwww.ssrn.com/1947345.htmlFri, 02 Oct 2020 11:30:26 GMTREVISION: Uncertain Risk ParityRisk parity is portfolio construction technique that, using risk alone, scales each part of a portfolio — e.g., stocks, bonds, currencies, commodities — so that its contribution to net portfolio risk matches its budgeted risk. Because risks are measured using a point-estimate of covariance, the method is subject to problems of estimation error. This paper performs risk parity with covariance modeled as uncertain in order to achieve a weighting robust to changes in regime and hidden risks from misperceived hedging.<br><br>The uncertain risk contributions, calculated en route, have value well beyond risk parity. Reporting a portfolio’s “uncertain risk decomposition” reveals the range around numbers and, more important, the risks that arise from inexact knowledge, e.g., market’s going from invisible to the biggest latent risk.
https://privwww.ssrn.com/abstract=3406321
https://privwww.ssrn.com/1944721.htmlFri, 25 Sep 2020 08:35:13 GMT