Download or read book TAIL RISK HEDGING Creating Robust Portfolios for Volatile Markets written by Vineer Bhansali and published by McGraw Hill Professional. This book was released on 2013-12-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: "TAIL RISKS" originate from the failure of mean reversion and the idealized bell curve of asset returns, which assumes that highly probable outcomes occur near the center of the curve and that unlikely occurrences, good and bad, happen rarely, if at all, at either "tail" of the curve. Ever since the global financial crisis, protecting investments against these severe tail events has become a priority for investors and money managers, but it is something Vineer Bhansali and his team at PIMCO have been doing for over a decade. In one of the first comprehensive and rigorous books ever written on tail risk hedging, he lays out a systematic approach to protecting portfolios from, and potentially benefiting from, rare yet severe market outcomes. Tail Risk Hedging is built on the author's practical experience applying macroeconomic forecasting and quantitative modeling techniques across asset markets. Using empirical data and charts, he explains the consequences of diversification failure in tail events and how to manage portfolios when this happens. He provides an easy-to-use, yet rigorous framework for protecting investment portfolios against tail risk and using tail hedging to play offense. Tail Risk Hedging explores how to: Generate profits from volatility and illiquidity during tail-risk events in equity and credit markets Buy attractively priced tail hedges that add value to a portfolio and quantify basis risk Interpret the psychology of investors in option pricing and portfolio construction Customize explicit hedges for retirement investments Hedge risk factors such as duration risk and inflation risk Managing tail risk is today's most significant development in risk management, and this thorough guide helps you access every aspect of it. With the time-tested and mathematically rigorous strategies described here, including pieces of computer code, you get access to insights to help mitigate portfolio losses in significant downturns, create explosive liquidity while unhedged participants are forced to sell, and create more aggressive yet tail-risk-focused portfolios. The book also gives you a unique, higher level view of how tail risk is related to investing in alternatives, and of derivatives such as zerocost collars and variance swaps. Volatility and tail risks are here to stay, and so should your clients' wealth when you use Tail Risk Hedging for managing portfolios. PRAISE FOR TAIL RISK HEDGING: "Managing, mitigating, and even exploiting the risk of bad times are the most important concerns in investments. Bhansali puts tail risk hedging and tail risk management under a microscope--pricing, implementation, and showing how we can fine-tune our risk exposures, which are all crucial ways in how we can better weather our bad times." -- ANDREW ANG, Ann F. Kaplan Professor of Business at Columbia University "This book is critical and accessible reading for fiduciaries, financial consultants and investors interested in both theoretical foundations and practical considerations for how to frame hedging downside risk in portfolios. It is a tremendous resource for anyone involved in asset allocation today." -- CHRISTOPHER C. GECZY, Ph.D., Academic Director, Wharton Wealth Management Initiative and Adj. Associate Professor of Finance, The Wharton School "Bhansali's book demonstrates how tail risk hedging can work, be concretely implemented, and lead to higher returns so that it is possible to have your cake and eat it too! A must read for the savvy investor." -- DIDIER SORNETTE, Professor on the Chair of Entrepreneurial Risks, ETH Zurich

Download or read book Bond Portfolio Investing and Risk Management written by Vineer Bhansali and published by McGraw Hill Professional. This book was released on 2010-09-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the fine art of risk measurement and control—from a senior member of PIMCO! Bond Portfolio Investing and Risk Management is designed for one purpose—to help you do the most important part of your job. A top player in the upper echelon of PIMCO, Vineer Bhansali understands the nuances and complexities of managing risk in fixed-income investing better than anyone. In this highly practical guide, he puts his years of experience and the latest research to work in order to help you contend with such issues as: Liquidity and stress risks Asset allocation Market anomalies Cross-market relationships Tail-risk measurement Cyclical returns Macroeconomic data Bond Portfolio Investing and Risk Management details the tools used to offset risk, including their advantages and drawbacks, and explains when to use each one. Bhansali provides practical investment techniques to give you a firm handle on the value and risk of a fixed-income instrument.

Download or read book The Second Leg Down written by Hari P. Krishnan and published by John Wiley & Sons. This book was released on 2017-02-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cut risk and generate profit even after the market drops The Second Leg Down offers practical approaches to profiting after a market event. Written by a specialist in global macro, volatility and hedging overlay strategies, this book provides in-depth insight into surviving in a volatile environment. Historical back tests and scenario diagrams illustrate a variety of strategies for offsetting portfolio risks with after-the-fact options hedging, and the discussion explores how a mixture of trend following and contrarian futures strategies can be beneficial. Without a rational analysis-based approach, investors often find themselves having to cut risk and buy protection just as options are at their most over-priced. This book provides practical strategies, expert analysis and the knowledge base to assist you in recovering your portfolio. Hedging strategies are often presented as expensive and unnecessary, especially during a bull market. When equity indices and other unstable assets drop, they find themselves stuck – hedging is now at its most expensive, but it is imperative to hedge or face liquidation. This book shows you how to salvage the situation, with strategies backed by expert analysis. Identify the right hedges during high volatility Generate attractive risk-adjusted returns Learn new strategies for offsetting risk Know your options for when losses have already occurred Imagine this scenario: you've incurred significant losses, you're approaching risk limits, you must cut risk immediately, yet slashing positions would damage the portfolio – what do you do? The Second Leg Down is your emergency hotline, with practical strategies for dire conditions.

Download or read book Market Tremors written by Hari P. Krishnan and published by Springer Nature. This book was released on 2021-09-14 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the Global Financial Crisis, the structure of financial markets has undergone a dramatic shift. Modern markets have been “zombified” by a combination of Central Bank policy, disintermediation of commercial banks through regulation, and the growth of passive products such as ETFs. Increasingly, risk builds up beneath the surface, through a combination of excessive leverage and crowded exposure to specific asset classes and strategies. In many cases, historical volatility understates prospective risk. This book provides a practical and wide ranging framework for dealing with the credit, positioning and liquidity risk that investors face in the modern age. The authors introduce concrete techniques for adjusting traditional risk measures such as volatility during this era of unprecedented balance sheet expansion. When certain agents in the financial network behave differently or in larger scale than they have in the past, traditional portfolio theory breaks down. It can no longer account for toxic feedback effects within the network. Our feedback-based risk adjustments allow investors to size their positions sensibly in dangerous set ups, where volatility is not providing an accurate barometer of true risk. The authors have drawn from the fields of statistical physics and game theory to simplify and quantify the impact of very large agents on the distribution of forward returns, and to offer techniques for dealing with situations where markets are structurally risky yet realized volatility is low. The concepts discussed here should be of practical interest to portfolio managers, asset allocators, and risk professionals, as well as of academic interest to scholars and theorists.

Download or read book Strategic Asset Allocation written by John Y. Campbell and published by OUP Oxford. This book was released on 2002-01-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.

Download or read book A New Heuristic Measure of Fragility and Tail Risks written by Mr.Nassim N. Taleb and published by International Monetary Fund. This book was released on 2012-08-01 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a simple heuristic measure of tail risk, which is applied to individual bank stress tests and to public debt. Stress testing can be seen as a first order test of the level of potential negative outcomes in response to tail shocks. However, the results of stress testing can be misleading in the presence of model error and the uncertainty attending parameters and their estimation. The heuristic can be seen as a second order stress test to detect nonlinearities in the tails that can lead to fragility, i.e., provide additional information on the robustness of stress tests. It also shows how the measure can be used to assess the robustness of public debt forecasts, an important issue in many countries. The heuristic measure outlined here can be used in a variety of situations to ascertain an ordinal ranking of fragility to tail risks.

Download or read book Tail Risk Hedging written by Andrew Rozanov and published by . This book was released on 2014 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Factor Investing and Asset Allocation A Business Cycle Perspective written by Vasant Naik and published by CFA Institute Research Foundation. This book was released on 2016-12-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rule Based Investing written by Chiente Hsu and published by Pearson Education. This book was released on 2014 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Use rule-based investment strategies to maintain trading and investment discipline, and protect yourself from fear, greed, pride, and other costly emotions! Since the mid-1990s, assets under management in rule-based or non-discretionary hedge funds have outgrown those in discretionary or qualitative funds. Recent research shows that rule-based funds have outperformed discretionary funds on a risk-adjusted basis over the past 30 years, and have especially outperformed during recent financial crises. This is the first comprehensive guide to designing and applying these sophisticated strategies. Combining academic rigor and practical applications, it explains what rule-based investment strategies are, how to construct them, and how to distinguish bad ones from good ones. Unlike any other guide, it systematically covers every facet of the topic, including Forex, rates, emerging markets, equity, volatility, and other key topics. Credit Suisse head of global strategy and modeling, Chiente Hsu, covers carry, momentum, seasonality, and value-based strategies; as well as the construction of portfolios of rule-based strategies that support diversification. Replete with realistic examples, this book will be a valuable resource for everyone concerned with effective investing, from traders to specialists in applied corporate finance.

Download or read book Dynamic Hedging written by Nassim Nicholas Taleb and published by John Wiley & Sons. This book was released on 1997-01-14 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Destined to become a market classic, Dynamic Hedging is the only practical reference in exotic options hedgingand arbitrage for professional traders and money managers Watch the professionals. From central banks to brokerages to multinationals, institutional investors are flocking to a new generation of exotic and complex options contracts and derivatives. But the promise of ever larger profits also creates the potential for catastrophic trading losses. Now more than ever, the key to trading derivatives lies in implementing preventive risk management techniques that plan for and avoid these appalling downturns. Unlike other books that offer risk management for corporate treasurers, Dynamic Hedging targets the real-world needs of professional traders and money managers. Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management. Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.

Download or read book Investment Strategies of Hedge Funds written by Filippo Stefanini and published by John Wiley & Sons. This book was released on 2010-03-11 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the fastest growing investment sectors ever seen, hedge funds are considered by many to be exotic and inaccessible. This book provides an intensive learning experience, defining hedge funds, explaining hedge fund strategies while offering both qualitative and quantitative tools that investors need to access these types of funds. Topics not usually covered in discussions of hedge funds are included, such as a theoretical discussion of each hedge fund strategy followed by trading examples provided by successful hedge fund managers.

Download or read book The Dao of Capital written by Mark Spitznagel and published by John Wiley & Sons. This book was released on 2013-08-16 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: As today's preeminent doomsday investor Mark Spitznagel describes his Daoist and roundabout investment approach, “one gains by losing and loses by gaining.” This is Austrian Investing, an archetypal, counterintuitive, and proven approach, gleaned from the 150-year-old Austrian School of economics, that is both timeless and exceedingly timely. In The Dao of Capital, hedge fund manager and tail-hedging pioneer Mark Spitznagel—with one of the top returns on capital of the financial crisis, as well as over a career—takes us on a gripping, circuitous journey from the Chicago trading pits, over the coniferous boreal forests and canonical strategists from Warring States China to Napoleonic Europe to burgeoning industrial America, to the great economic thinkers of late 19th century Austria. We arrive at his central investment methodology of Austrian Investing, where victory comes not from waging the immediate decisive battle, but rather from the roundabout approach of seeking the intermediate positional advantage (what he calls shi), of aiming at the indirect means rather than directly at the ends. The monumental challenge is in seeing time differently, in a whole new intertemporal dimension, one that is so contrary to our wiring. Spitznagel is the first to condense the theories of Ludwig von Mises and his Austrian School of economics into a cohesive and—as Spitznagel has shown—highly effective investment methodology. From identifying the monetary distortions and non-randomness of stock market routs (Spitznagel's bread and butter) to scorned highly-productive assets, in Ron Paul's words from the foreword, Spitznagel “brings Austrian economics from the ivory tower to the investment portfolio.” The Dao of Capital provides a rare and accessible look through the lens of one of today's great investors to discover a profound harmony with the market process—a harmony that is so essential today.

Download or read book A Primer on Managing Sovereign Debt Portfolio Risks written by Thordur Jonasson and published by International Monetary Fund. This book was released on 2018-04-06 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides an overview of sovereign debt portfolio risks and discusses various liability management operations (LMOs) and instruments used by public debt managers to mitigate these risks. Debt management strategies analyzed in the context of helping reach debt portfolio targets and attain desired portfolio structures. Also, the paper outlines how LMOs could be integrated into a debt management strategy and serve as policy tools to reduce potential debt portfolio vulnerabilities. Further, the paper presents operational issues faced by debt managers, including the need to develop a risk management framework, interactions of debt management with fiscal policy, monetary policy, and financial stability, as well as efficient government bond markets.

Download or read book Risk Analysis and Portfolio Modelling written by Elisa Luciano and published by MDPI. This book was released on 2019-10-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Risk Measurement is a challenging task, because both the types of risk and the techniques evolve very quickly. This book collects a number of novel contributions to the measurement of financial risk, which address either non-fully explored risks or risk takers, and does so in a wide variety of empirical contexts.

Download or read book Smart er Investing written by Elisabetta Basilico and published by Palgrave Macmillan. This book was released on 2020-12-26 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book identifies and discusses the most successful investing practices with an emphasis on the academic articles that produced them and why this research led to popular adoption and growth in $AUM. Investors are bombarded with ideas and prescriptions for successful investing every day. Given the steady stream of information on stock tips, sector timing, asset allocation, etc., how do investors decide? How do they judge the quality and reliability of the investment advice they are given on a day-to-day basis? This book identifies which academic articles turned investment ideas were the most innovative and influential in the practice of investment management. Each article is discussed in terms of the asset management process: strategy, portfolio construction, portfolio implementation, and risk management. Some examples of topics covered are factor investing, the extreme growth of trading instruments like Exchange Traded Funds, multi-asset investing, socially responsible investing, big data, and artificial intelligence. This book analyzes a curated selection of peer-reviewed academic articles identified among those published by the scientific investment community. The book briefly describes each of the articles, how and why each one changed the way we think about investing in that specific asset class, and provides insights as to the nuts and bolts of how to take full advantage of this successful investment idea. It is as timely as it is informative and will help each investor to focus on the most successful strategies, ideas, and implementation that provide the basis for the efficient accumulation and management of wealth.

Download or read book Revisiting Risk Weighted Assets written by Vanessa Le Leslé and published by International Monetary Fund. This book was released on 2012-03-01 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we provide an overview of the concerns surrounding the variations in the calculation of risk-weighted assets (RWAs) across banks and jurisdictions and how this might undermine the Basel III capital adequacy framework. We discuss the key drivers behind the differences in these calculations, drawing upon a sample of systemically important banks from Europe, North America, and Asia Pacific. We then discuss a range of policy options that could be explored to fix the actual and perceived problems with RWAs, and improve the use of risk-sensitive capital ratios.

Download or read book Optimization Based Models for Measuring and Hedging Risk in Fixed Income Markets written by Johan Hagenbjörk and published by Linköping University Electronic Press. This book was released on 2019-12-09 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The global fixed income market is an enormous financial market whose value by far exceeds that of the public stock markets. The interbank market consists of interest rate derivatives, whose primary purpose is to manage interest rate risk. The credit market primarily consists of the bond market, which links investors to companies, institutions, and governments with borrowing needs. This dissertation takes an optimization perspective upon modeling both these areas of the fixed-income market. Legislators on the national markets require financial actors to value their financial assets in accordance with market prices. Thus, prices of many assets, which are not publicly traded, must be determined mathematically. The financial quantities needed for pricing are not directly observable but must be measured through solving inverse optimization problems. These measurements are based on the available market prices, which are observed with various degrees of measurement noise. For the interbank market, the relevant financial quantities consist of term structures of interest rates, which are curves displaying the market rates for different maturities. For the bond market, credit risk is an additional factor that can be modeled through default intensity curves and term structures of recovery rates in case of default. By formulating suitable optimization models, the different underlying financial quantities can be measured in accordance with observable market prices, while conditions for economic realism are imposed. Measuring and managing risk is closely connected to the measurement of the underlying financial quantities. Through a data-driven method, we can show that six systematic risk factors can be used to explain almost all variance in the interest rate curves. By modeling the dynamics of these six risk factors, possible outcomes can be simulated in the form of term structure scenarios. For short-term simulation horizons, this results in a representation of the portfolio value distribution that is consistent with the realized outcomes from historically observed term structures. This enables more accurate measurements of interest rate risk, where our proposed method exhibits both lower risk and lower pricing errors compared to traditional models. We propose a method for decomposing changes in portfolio values for an arbitrary portfolio into the risk factors that affect the value of each instrument. By demonstrating the method for the six systematic risk factors identified for the interbank market, we show that almost all changes in portfolio value and portfolio variance can be attributed to these risk factors. Additional risk factors and approximation errors are gathered into two terms, which can be studied to ensure the quality of the performance attribution, and possibly improve it. To eliminate undesired risk within trading books, banks use hedging. Traditional methods do not take transaction costs into account. We, therefore, propose a method for managing the risks in the interbank market through a stochastic optimization model that considers transaction costs. This method is based on a scenario approximation of the optimization problem where the six systematic risk factors are simulated, and the portfolio variance is weighted against the transaction costs. This results in a method that is preferred over the traditional methods for all risk-averse investors. For the credit market, we use data from the bond market in combination with the interbank market to make accurate measurements of the financial quantities. We address the notoriously difficult problem of separating default risk from recovery risk. In addition to the previous identified six systematic risk factors for risk-free interests, we identify four risk factors that explain almost all variance in default intensities, while a single risk factor seems sufficient to model the recovery risk. Overall, this is a higher number of risk factors than is usually found in the literature. Through a simple model, we can measure the variance in bond prices in terms of these systematic risk factors, and through performance attribution, we relate these values to the empirically realized variances from the quoted bond prices. De globala ränte- och kreditmarknaderna är enorma finansiella marknader vars sammanlagda värden vida överstiger de publika aktiemarknadernas. Räntemarknaden består av räntederivat vars främsta användningsområde är hantering av ränterisker. Kreditmarknaden utgörs i första hand av obligationsmarknaden som syftar till att förmedla pengar från investerare till företag, institutioner och stater med upplåningsbehov. Denna avhandling fokuserar på att utifrån ett optimeringsperspektiv modellera både ränte- och obligationsmarknaden. Lagstiftarna på de nationella marknaderna kräver att de finansiella aktörerna värderar sina finansiella tillgångar i enlighet med marknadspriser. Därmed måste priserna på många instrument, som inte handlas publikt, beräknas matematiskt. De finansiella storheter som krävs för denna prissättning är inte direkt observerbara, utan måste mätas genom att lösa inversa optimeringsproblem. Dessa mätningar görs utifrån tillgängliga marknadspriser, som observeras med varierande grad av mätbrus. För räntemarknaden utgörs de relevanta finansiella storheterna av räntekurvor som åskådliggör marknadsräntorna för olika löptider. För obligationsmarknaden utgör kreditrisken en ytterligare faktor som modelleras via fallissemangsintensitetskurvor och kurvor kopplade till förväntat återvunnet kapital vid eventuellt fallissemang. Genom att formulera lämpliga optimeringsmodeller kan de olika underliggande finansiella storheterna mätas i enlighet med observerbara marknadspriser samtidigt som ekonomisk realism eftersträvas. Mätning och hantering av risker är nära kopplat till mätningen av de underliggande finansiella storheterna. Genom en datadriven metod kan vi visa att sex systematiska riskfaktorer kan användas för att förklara nästan all varians i räntekurvorna. Genom att modellera dynamiken i dessa sex riskfaktorer kan tänkbara utfall för räntekurvor simuleras. För kortsiktiga simuleringshorisonter resulterar detta i en representation av fördelningen av portföljvärden som väl överensstämmer med de realiserade utfallen från historiskt observerade räntekurvor. Detta möjliggör noggrannare mätningar av ränterisk där vår föreslagna metod uppvisar såväl lägre risk som mindre prissättningsfel jämfört med traditionella modeller. Vi föreslår en metod för att dekomponera portföljutvecklingen för en godtycklig portfölj till de riskfaktorer som påverkar värdet för respektive instrument. Genom att demonstrera metoden för de sex systematiska riskfaktorerna som identifierats för räntemarknaden visar vi att nästan all portföljutveckling och portföljvarians kan härledas till dessa riskfaktorer. Övriga riskfaktorer och approximationsfel samlas i två termer, vilka kan användas för att säkerställa och eventuellt förbättra kvaliteten i prestationshärledningen. För att eliminera oönskad risk i sina tradingböcker använder banker sig av hedging. Traditionella metoder tar ingen hänsyn till transaktionskostnader. Vi föreslår därför en metod för att hantera riskerna på räntemarknaden genom en stokastisk optimeringsmodell som också tar hänsyn till transaktionskostnader. Denna metod bygger på en scenarioapproximation av optimeringsproblemet där de sex systematiska riskfaktorerna simuleras och portföljvariansen vägs mot transaktionskostnaderna. Detta resulterar i en metod som, för alla riskaverta investerare, är att föredra framför de traditionella metoderna. På kreditmarknaden använder vi data från obligationsmarknaden i kombination räntemarknaden för att göra noggranna mätningar av de finansiella storheterna. Vi angriper det erkänt svåra problemet att separera fallissemangsrisk från återvinningsrisk. Förutom de tidigare sex systematiska riskfaktorerna för riskfri ränta, identifierar vi fyra riskfaktorer som förklarar nästan all varians i fallissemangsintensiteter, medan en enda riskfaktor tycks räcka för att modellera återvinningsrisken. Sammanlagt är detta ett större antal riskfaktorer än vad som brukar användas i litteraturen. Via en enkel modell kan vi mäta variansen i obligationspriser i termer av dessa systematiska riskfaktorer och genom prestationshärledningen relatera dessa värden till de empiriskt realiserade varianserna från kvoterade obligationspriser.