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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Finance Series
- Sprache: Englisch
A practitioner's guide to ex-post performance measurement techniques
Risk within asset management firms has an undeserved reputation for being an overly complex, mathematical subject. This book simplifies the subject and demonstrates with practical examples that risk is perfectly straightforward and not as complicated as it might seem. Unlike most books written on portfolio risk, which generally focus on ex-ante risk from an academic perspective using complicated language and no worked examples, this book focuses on ex-post risk from a buy side, asset management, risk practitioners perspective, including a number of practical worked examples for risk measures and their interpretation.
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Seitenzahl: 184
Veröffentlichungsjahr: 2012
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Contents
Cover
Series Page
Title Page
Copyright
Dedication
Preface
Acknowledgements
Chapter 1: Introduction
DEFINITION OF RISK
Chapter 2: Descriptive Statistics
Mean (or arithmetic mean)
Annualised return
Continuously compounded returns (or log returns)
Winsorised mean
Mean absolute deviation (or mean deviation)
Variance
Mean difference (absolute mean difference or Gini mean difference)
Relative mean difference
Bessel's correction (population or sample, n or n−1)
Sample variance
Standard deviation (variability or volatility)
Annualised risk (or time aggregation)
The Central Limit Theorem
Janssen annualisation
Frequency and number of data points
Normal (or Gaussian) distribution
Histograms
Skewness (Fisher's or moment skewness)
Sample skewness
Kurtosis (Pearson's kurtosis)
Excess kurtosis (or Fisher's kurtosis)
Sample kurtosis
Bera-Jarque statistic (or Jarque-Bera)
Covariance
Sample covariance
Correlation (ρ)
Sample correlation
Up capture indicator
Down capture indicator
Up number ratio
Down number ratio
Up percentage ratio
Down percentage ratio
Percentage gain ratio
Hurst index (or Hurst exponent)
Bias ratio
Chapter 3: Simple Risk Measures
Performance appraisal
Sharpe ratio (reward to variability, Sharpe index)
Roy ratio
Risk free rate
Alternative Sharpe ratio
Revised Sharpe ratio
Adjusted Sharpe ratio
Skewness-kurtosis ratio
MAD ratio
Gini ratio
Relative risk
Tracking error (or tracking risk, relative risk, active risk)
Relative skewness
Relative kurtosis
Information ratio
Geometric information ratio
Modified information ratio
Adjusted information ratio
Relative Hurst
Chapter 4: Regression Analysis
Regression equation
Regression alpha (αR)
Regression beta (βR)
Regression epsilon (R)
Capital Asset Pricing Model (CAPM)
Beta (β) (systematic risk or volatility)
Jensen's alpha (Jensen's measure or Jensen's differential return or ex-post alpha)
Annualised alpha
Bull beta (β+)
Bear beta (β−)
Beta timing ratio
Market timing
Systematic risk
R2 (or coefficient of determination)
Specific or residual risk
Treynor ratio (reward to volatility)
Modified Treynor ratio
Appraisal ratio (or Treynor-Black ratio)
Modified Jensen
Fama decomposition
Selectivity
Diversification
Net selectivity
Fama-French three factor model
Three factor alpha (or Fama-French alpha)
Carhart four factor model
Four factor alpha (or Carhart's alpha)
K ratio
Chapter 5: Drawdown
Drawdown
Average drawdown
Maximum drawdown (or peak to valley drawdown)
Largest individual drawdown
Recovery time (or drawdown duration)
Drawdown deviation
Ulcer index
Pain index
Calmar ratio (or drawdown ratio)
MAR ratio
Sterling ratio
Sterling-Calmar ratio
Burke ratio
Modified Burke ratio
Martin ratio (or Ulcer performance index)
Pain ratio
Lake ratio
Peak ratio
Chapter 6: Partial Moments
Downside risk (or semi-standard deviation)
Pure downside risk
Half variance (or semi-variance)
Upside risk (or upside uncertainty)
Mean absolute moment
Omega ratio (Ω)
Bernardo and Ledoit (or gain-loss) ratio
d ratio
Omega-Sharpe ratio
Sortino ratio
Reward to half-variance
Downside risk Sharpe ratio
Downside information ratio
Kappa (Kl) (or Sortino-Satchell ratio)
Upside potential ratio
Volatility skewness
Variability skewness
Farinelli-Tibiletti ratio
Prospect ratio
Chapter 7: Extreme Risk
Extreme events
Extreme value theory
Value at risk (VaR)
Relative VaR
Ex-post VaR
Potential upside (gain at risk)
Percentile rank
VaR calculation methodology
Parametric VaR
Modified VaR
Historical simulation (or non-parametric)
Monte Carlo simulation
Which methodology for calculating VaR should be used?
Frequency and time aggregation
Time horizon
Window length
Reward to VaR
Reward to relative VaR
Double VaR ratio
Conditional VaR (expected shortfall, tail loss, tail VaR or average VaR)
Upper CVaR or CVaR+
Lower CVaR or CVaR−
Tail gain (expected gain or expected upside)
Conditional Sharpe ratio (STARR ratio or reward to conditional VaR)
Modified Sharpe ratio (reward to modified VaR)
Tail risk
Tail ratio
Rachev ratio (or R ratio)
Generalised Rachev ratio
Drawdown at risk
Conditional drawdown at risk
Reward to conditional drawdown
Generalised Z ratio
Chapter 8: Fixed Income Risk
Pricing fixed income instruments
Redemption yield (yield to maturity)
Weighted average cash flow
Duration (effective mean term, discounted mean term or volatility)
Macaulay duration
Macaulay-Weil duration
Modified duration
Portfolio duration
Effective duration (or option-adjusted duration)
Duration to worst
Convexity
Modified convexity
Effective convexity
Portfolio convexity
Bond returns
Duration beta
Reward to duration
Chapter 9: Risk-adjusted Return
Risk-adjusted return
M2
M2 excess return
Differential return
GH1 (Graham & Harvey 1)
GH2 (Graham & Harvey 2)
Correlation and risk-adjusted return M3
Return adjusted for downside risk
Adjusted M2
Omega excess return
Chapter 10: Which Risk Measure to Use?
WHY MEASURE EX-POST RISK?
WHICH RISK MEASURES TO USE?
WHICH MEASURES ARE ACTUALLY USED?
WHICH RISK MEASURES SHOULD REALLY BE USED?
Chapter 11: Risk Control
REGULATIONS IN THE INVESTMENT RISK AREA
RISK CONTROL STRUCTURE
RISK MANAGEMENT
Glossary of Key Terms
Appendix A: Composite Internal Risk Measures
Appendix B: Absolute Risk Dashboard
Appendix C: Relative Risk Dashboard
Bibliography
Index
For other titles in the Wiley Finance series please see www.wiley.com/finance
© 2013 John Wiley & Sons, Ltd
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Library of Congress Cataloging-in-Publication Data
Bacon, Carl R. Practical risk-adjusted performance measurement / Carl R. Bacon. p. cm. Includes bibliographical references and index. ISBN 978-1-118-36974-6 (cloth) 1. Financial risk management. 2. Performance standards. 3. Risk management. I. Title. HD61.B33 2013 658.15′5–dc23 2012023317
A catalogue record for this book is available from the British Library.
ISBN 978-1-118-36974-6 (hardback) ISBN 978-1-118-39153-2 (ebk)
ISBN 978-1-118-39152-5 (ebk) ISBN 978-1-118-39137-2 (ebk)
To my parents
Preface
“Beauty is in the eye of the beholder.”
Margaret Wolfe Hungerford (1855–1897), Molly Bawn 1878
The book I wanted to read on risk did not exist and this book attempts to fill that gap. There are many books and articles, perhaps hundreds, written on the subject of portfolio risk but for the most part they focus on ex-ante risk, tend to be highly academic with authors seemingly in a competition to present the material in as complex a language as possible and are typically devoid of worked examples. This book is written for risk and performance measurement practitioners from a buy side, asset management perspective, focusing on quantitative ex-post measures rather than the qualitative aspects of risk.
Risk has an undeserved reputation within asset management firms for being an overly complex, mathematical subject. The purpose of this book is to simplify the subject and demonstrate with many practical examples that risk is perfectly straightforward and not as complicated as it might seem.
In addition I wanted to document, with appropriate referencing, as many discrete ex-post risk measures as possible in a structured format, filling gaps, encouraging consistency, suggesting new measures and highlighting possible areas of confusion or misrepresentation. In truth many of these measures are rarely used in practice, often for good reason.
This book will not recommend any particular risk measure, although it is difficult to disguise my preferences and prejudices. Risk like beauty is very much in the eye of the beholder and different risk measures will suit different investment strategies or investor concerns at different times. This book should provide enough information and insight for the reader to determine their own preferences.
In terms of structure Chapter 1 is naturally an introduction to the subject of risk in the context of asset management firms. In Chapter 2 the foundations are laid introducing the descriptive statistics that will be used in later chapters. The following chapters are structured according to the type of risk measure being considered, simple measures in Chapter 3, regression measures in Chapter 4, drawdown in Chapter 5, partial moments in Chapter 6, extreme risk in Chapter 7, risk measures for fixed income instruments in Chapter 8 and risk-adjusted returns in Chapter 9.
In the penultimate Chapter 10 there is a discussion about which risk measures to use and finally in Chapter 11 their application in terms of risk control.
The objective of this book is to provide a complete list of ex-post risk measures used by asset managers. Although some have little merit I've avoided censoring measures I dislike. If a risk measure is not included, perhaps it's in continuous not discrete form, maybe I don't fully understand it with enough confidence to write about it, or in a few rare cases I've determined that it literally has no merit.
Acknowledgements
My thanks are owed to many that have contributed to this book, both directly and indirectly, working colleagues over many years, attendees at my various training courses and workshops which I hope will continue, attentive readers of my previous books that have spotted a number of errors and indeed made many good suggestions, numerous fellow GIPS® committee members that have been so insightful and of course the many authors that have laid the foundations of this subject.
I'm particularly thankful to the diligent reviewers of this book: Kate Maryniak and Ralph Purtscher-Wydenbruck of StatPro, Jerry Pinto, CFA of CFA Institute, Philip Lawton, CFA, CIPM, PRM of Aite Group, Colin Morrison of Paradigm Investment Consulting Ltd and Dimitri Senik, CFA, FCCA.
Of course all errors and omissions are my own
Carl R. Bacon CIPM Deeping St James April [email protected]
1
Introduction
“Money is like muck, not good except it be spread.”
Francis Bacon (1561–1626)
DEFINITION OF RISK
Risk means very different things to different audiences at different times; risk is truly in the eye of the beholder. In the context of portfolio management the Oxford English Dictionary provides a surprisingly good definition of risk:
The potential impact of an event determined by combining the likelihood of the event occurring with the impact should it occur.
Risk is the combination of exposure and uncertainty. As Holton1 (2004) so eloquently points out it is not risky to jump out of an aircraft without a parachute, death is certain. Holton also points out that we can never operationally define risk; at best, we can operationally define our perception of risk.
Another common and effective, but broader definition of risk is exposure to uncertainty.
Risk types
Within asset management firms there are many types of risk that should concern portfolio managers and senior management. For convenience I've chosen to classify risk into five main categories:
These risks are ranked in my priority order of concern at the point in time I assumed the role of Director of Risk Control at an asset management firm in the late 1990s.2 What I didn't appreciate fully then, but appreciated much later, is that priorities will vary through time; during the credit crisis I'm sure counterparty risk became the number one priority for many firms.
Although a major concern of all asset managers, reputational risk does not warrant a separate category; a risk failure in any category can cause significant damage to a firm's reputation.
Compliance or regulatory risk is the risk of breaching a regulatory, client or internally imposed guideline, restriction or clear limit. I draw no distinction between internal or external limits; the breach of an internal limit indicates a control failure, which could just as easily have been a regulatory, or client mandated limit. Of course the financial impact of breaching limits can be significant; in August 1996 Peter Young of Morgan Grenfell Asset Management allegedly cost Deutsche Bank £300 to £400 million in compensation payments to investors in highly regulated authorised unit trusts. Peter Young used Luxembourg listed shell companies to circumvent limits on unlisted and risky holdings.
Operational risk, often defined as a residual catch all category to include risks not defined elsewhere, actually includes the risk of human error, fraud, system failure, poor controls, management failure and failed trades. Risks of this type are more common but usually less severe. Nevertheless it is important to continuously monitor errors and near misses of all types, even those that do not result in financial loss. An increase in the frequency of errors regardless of size or sign may indicate a more serious problem that requires further investigation and corrective action. Although typically small in size, operational errors can lead to large losses. In December 2005 a trader at the Japanese brokerage firm Mizuho Securities made a typing error and tried to sell 610,000 shares at 1 yen apiece in recruiting company J-Com Co., which was debuting on the exchange, instead of an intended sale of one share at 610,000 yen, an example of fat-finger syndrome. Mizuho lost approximately 41 billion yen.
Liquidity risk is the risk that assets cannot be traded quickly enough in a market to change asset and risk allocations, realise profits or prevent losses. Perhaps liquidity risk has received less attention than it should in the past but it is capable of causing significant damage. Understanding liquidity risk in both normal and turbulent markets is a crucial element of effective risk control; the relatively recently identified phenomenon of crowded exits is a characteristic of those turbulent markets.
Counterparty risk occurs when counterparties are unwilling or unable to fulfil their contractual obligations, at its most basic through corporate failure. Counterparty exposure could include profits on an OTC derivatives contract, unsettled transactions, cash management, administrators, custodians, prime brokers, and even with the comfort of appropriate collateral the failure to return stock that has been used for stock lending. Perhaps the most obvious example of counterparty risk is the failure of Lehman Brothers in September 2008.
In the middle office of asset management firms we are most concerned with portfolio risk, which I define as the uncertainty of meeting client expectations. Is the portfolio managed in line with the client's investment objectives? The consequences of not meeting client expectations can be quite severe. Early in 2001,3 the Unilever Superannuation Fund sued Merrill Lynch for damages of £130 million claiming negligence that Merrill Lynch had not sufficiently taken into account the risk of underperformance. Ultimately the case was settled out of court for an undisclosed sum, believed to be £70 million, the perception to many being that Unilever won.
I'm sure readers can quickly add to this brief list of risks and extend through various subdivisions, but I'm fairly certain any risk I've not mentioned so far can be allocated to one or more of the above categories.
Credit risk (or issuer risk) as opposed to counterparty risk is a type of portfolio risk. Credit risk or default risk is the investor's risk of a borrower failing to meet their financial commitments in full. The higher the risk of default the higher the rate of interest investors will demand to lend their capital. Therefore the reward or returns in terms of higher yields must offset the increased risk of default. Similarly market, currency and interest rate risks taken by portfolio managers in the pursuit of client objectives would constitute portfolio risks in this context.
Risk management v risk control
It is useful to distinguish between the ways portfolio managers and risk professionals see risk. For this purpose, let us refer to portfolio managers as “risk managers” and to risk professionals as “risk controllers”. Then there is a clear distinction between risk management and risk control. As risk managers, portfolio managers are paid to take risk, and they need to take risk in order to achieve higher returns. For the risk manager “Risk is good”.
Risk controllers on the other hand are paid to monitor risk; their role is to measure risk and make transparent to the entire firm how much risk is being taken by the portfolio manager (and often from their perspective to reduce risk). The risk controller's objective is to reduce the probability or eliminate entirely a major loss event on their watch. For the risk controller “Risk is bad”.
Risk managers' and risk controllers' objectives are in conflict leading to a natural tension between them. To resolve this conflict we need measures that assess the quality of return and answer the question, “Are we achieving sufficient return for the risk taken?”
Risk aversion
It is helpful to assume that investors are risk averse, that is to say, that given portfolios with equal rates of return they will prefer the portfolio with the lowest risk.
Investors will only accept additional risk if they are compensated by the prospect of higher returns.
Ex-post and ex-ante
Risk is calculated in two fundamentally different ways, ex-post and ex-ante. Ex-post or historical risk is the analysis of risk after the event; it answers the question how risky has the portfolio been in the past.
On the other hand ex-ante risk or prospective risk is forward looking, based on a snapshot of the current securities and instruments within the portfolio and their historical relationship with each other; it is an estimate or forecast of the future risk of the portfolio. Obviously the use of historical returns and correlations to forecast future risk is problematic, particularly for extreme, low probability events. Increasing the length of the historical track record or increasing the frequency of observations does not always result in an improvement because of the changing nature of markets and underlying securities. Older returns may be less reliable for future predictions, but on the other hand more recent observations may not include the more extreme results.
Ex-post and ex-ante risk calculations are substantially different and therefore can lead to completely different results and conclusions. Differences between ex-post and ex-ante risk calculations provide significant additional information which should be monitored continuously.
Dispersion
For the most part risk managers and risk controllers use dispersion measures of return as a proxy for their perception of risk.
1 Glyn A. Holton (2004) Defining Risk. Financial Analysts Journal 60(6).
2 In truth I did not identify liquidity risk as a separate risk category at the time.
3 A.F. Perold and R. Alloway (2003) The Unilever Superannuation Fund vs. Merrill Lynch. Harvard Business School Publishing.
