Overview. Market Risk. Market Risk. Implications. Market Risk 17/11/2014 CHAPTER 10. Market Risk
|
|
- Lindsey Summers
- 7 years ago
- Views:
Transcription
1 CHAPTER 10 Edited by Bo Sjö Overview This chapter discusses the nature of market risk and measures of market risk: 1) Value at Risk (VaR) or RiskMetrics 2) Historic or Back Simulation 3) Monte Carlo simulation - briefly > Finally, consider the link between market risk (VaR) and capital requirements according to Basel McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved. Recall the basic accounting identity E = A -D If market foces changes the prices of assets and liabilities it will affect equity (and thus reserves): E = A D If E < 0: You are out of buiness! You are also out when E is less than required minum reserves. We need to know (i) how big are normal day-to-day fluctuations, and (ii) how big are possible abnormal fluctuations and (iii) not totally unlikely extremely abnormal fluctuations? The answer is the basis for risk management and the level of reserves needed to survive. Need not necessarily survive (iii) above Implications Emphasizes importance of: Measurement of exposure to risk factors Control mechanisms for direct market risk Hedging mechanisms And, of interest to regulators (i) Need to monitor the exposure (ii) Set limits to excessive exposure Market risk is the uncertainty resulting from unpredicted changes in market prices of assets Consider changes in interest rates, exchange rates, equity and other assets Can be measured over periods as short as one day Usually measured (i) in terms of dollar, exposure amount or (ii) as a relative amount against some benchmark
2 Ask the Following Questions What are normalday-to-day fluctuations on the market? What are abnormal fluctuations? To sort out the normal from the abnormal -look at the historical distribution of changes in asset prices (i) Calculate the sample Mean and variance of r (ii) Calculate a confidence intervall around the mean fluctuations of r! (iii) Outside the confidence intervall consider it Abnormal (adverse movements) Measurement Important in terms of: Management information (control & management) Setting limits to risk exposure Resource allocation (the risk-return tradeoff) Performance evaluation Measurement Regulation: -BIS (Bank of International Settlements) and Fed (Federal Reserve Bank of USA) regulate market risk via capital requirements leading to potential for overpricing of risks -Allowances for the use of internal models to calculate capital requirements (=Set necessary reserves) Calculating Exposure What is the estimated loss under adverse (=extreme) circumstances? Three major approaches: 1) VaRor JPM RiskMetrics (or variance/ covariance approach) 2) Historic or Back Simulation 3) Monte Carlo Simulation JP Morgan VaR JP Morgan developed the Value at Risk VaR concept into a commerical idea. They called it RiskMetrics (Trade Mark) Now RiskMetrics is run by separate company owned by JPM & Reuters The RiskMetrics Model The Idea is to determine DEAR(Daily Earnings At Risk) = dollar value of position (price sensitivity potential adverse move in yield) DEAR = dollar market value of position price volatility price volatility = price sensitivity of position (Duration) potential adverse move in yield
3 VaR Daily Earnings at Risk DEAR can be stated as: DEAR = (MD) (potential adverse daily yield move) where, MD = Modified duration (D(1+r) D = Macaulay duration, instead of r = interest rate we can use y = yield. To Calculate DEAR: Here is the answer to our?:s Confidence Intervals ±(Mean of r) 1.96 Standard deviation of r Here we have assumed that r has a normal frequency distribution, with 5% risk at both sides => 2.5% is abnormal (bad). Other risk levels: ±1.65 σ 90% confidence interval, 5% adverse moves ± 1.96 σ 95 % confidence interval, 2.5 % adverse moves ± 2.33 σ 98 % confidence interval, 1% adverse moves ± 2.66 σ 99% confidence interval, 0.5% adverse moves Confidence Intervals If we assume that changes in r (and thus the yield) are normally distributed => we can construct confidence intervals for DEAR Assuming normality, 90% of the time the disturbance will be within ±1.65 standard deviations of the mean 5% of the extreme values remain in each tail of the distribution, see next slide which shows the distribution (possible values) of r for a sevenyear zero coupon bondwith mean = 0. Adverse 7-Year Rate Move
4 Basis Points Changes in interest rates are measured in Basis Points Decimals of per cent. One basis point is 0.01% or basis points = 1%. Confidence Intervals: Example Suppose that we are long in 7-year zerocoupon bonds and we define bad yield changes such that there is only a 5% chance of the yield change being exceeded in either direction. Assuming normality, 90% of the time yield changes will be within 1.65 standard deviations of the mean. If the standard deviation is 10 basis points ( or 0.1%), this corresponds to = Probability of yield increases greater than 16.5 basis points is 5% N Confidence Intervals: Example D = 7 years. Yield on the bond = 7.243%, so MD = years Price volatility = (MD) (Potential adverse change in yield) = (6.527) ( ) = 1.077% DEAR = Market value of position (Price volatility) = ($1,000,000) (.01077) = $10,770 Confidence Intervals: Example To calculate the potential loss for more than one day (say a trading week): Market value at risk (VaR N ) = DEAR N Example: For a five-day period, VaR 5 = $10,770 5 = $24, Foreign Exchange In the case of foreign exchange, DEAR is computed in the same fashion we employed for interest rate risk, but there is a correlation across exchange rates. DEAR = dollar value of position FX rate volatility, where the FX rate volatility is taken as 1.65 σ FX Statistical Formulas Calculate the (arithmetic) mean Variance (and standard deviation) Correlation coefficient
5 Skewed distribution Example: One-day 90 per cent VaR of portfolio, showing next day positions, (with skewed distributionan 10 % risk at the lower end. Equities For equities, total risk = systematic risk + unsystematic risk If the portfolio is well diversified, then DEAR = dollar value of position stock market return volatility, where market volatility taken as 1.65 σ m If not well diversified, a degree of error will be built into the DEAR calculation Estimation FX VaR Convert today s FX positions into dollar equivalents at today s FX rates Measure sensitivity of each position Calculate its delta Measure risk Actual percentage changes in FX rates for each of past 500 days Rank days by risk from worst to best Aggregating DEAR Estimates Cannot simply sum up individual DEARs, since the individual DEAR are correlated (ρ) with each other. To aggregate two DEARs we require the correlation coefficient (ρ ac ) between the DEARs Two-asset case: DEAR portfolio= [DEAR a2 + DEAR b2 + 2ρ ab DEAR a DEAR b + 2ρ ac ] 1/ Three assets case DEAR: Large US Banks 2005 & 2008 In order to aggregate the DEARs from individual exposures we require the correlation matrix, the correlations among all pairs of DEARs. The three-asset case: DEAR portfolio= [DEAR a2 + DEAR b2 + DEAR c2 + 2ρ ab DEAR a DEAR b + 2ρ ac DEAR a DEAR c + 2ρ bc DEAR b DEAR c ] 1/
6 Problems with VaR 1) Historical data (means and variances), used from 100 days rolling windows might not reflect the future. The worst day is yet to come perhaps. => Remember to predic future volatility. 2) Volatility is persistent, high volatility today will be followed by high volatity tomorrow. Changes in prices, exchange rates,interesr rates etc are not indedendent. => GARCH models to predict future volatility. 3) The Normal distribution will under-estimate the frequency of abnormal changes. Real world data show much fatter tails than the Normal distribution. => Look for other distributios than the normal. The Advantage of VaR It is, or should be, a forward looking measure, using predicted future volatility. Not be based on historical data (backward looking) only. With VaR it is possible to measure risk when risk is taken! The risk manager can interact with traders immediately to measure and control risk. If your predictions are good, VaR works fine. Works well in the short-run, in periods with small changes in prices and interest rates. VaR is a simple question with a simple answer. The weakness, which is difficult calculate when the economy is changing Historic or Back Simulation Basic idea: Revalue the current portfolio with historical prices. Say 500 days back. Then calculate 5% worst-case outcomes (25 th lowest value of 500 days). Only 5% of the outcomes are lower in terms of less value. Historic or Back Simulation Advantages: Simplicity Does not need correlations or standard deviations of individual asset returns Does not require normal distribution of returns (which is a critical assumption for RiskMetrics) Directly provides a worst case value Weaknesses Disadvantage: 500 observations is not very many from a statistical standpoint Increasing number of observations by going back further in time is not desirable Could weight recent observations more heavily and go further back Backward looking only, focus on historical data. Monte Carlo Simulation To overcome problem of limited number of observations, simulate different possible prices. Start by estimating the historical variance-covariance matrix and use a random number generator to synthesize observations Objective is to replicate the distributionof observed outcomes with synthetic data
7 Regulatory Models BIS (including FED) approach: Market risk may be calculated using standard BIS model Specific risk charge depending who is the borrower and time to maturity Different reserve % for different type (above) Subject to regulatory permission, large banks may be allowed to use their internal models as the basis for determining capital requirements (VaR) BIS Model Specific risk charge: Risk weights absolute dollar values of long and short positions General market risk charge: reflect modified durations expected interest rate shocks for each maturity Vertical offsets: Adjust for basis risk Horizontal offsets within/between time zones Web Resources For information on the BIS framework, visit: Bank for International Settlement Federal Reserve Bank Large Banks: Using Internal Models In calculating DEAR, adverse change in rates defined as 99th percentile (rather than 95th under RiskMetrics) Minimum holding period is 10 days (means that RiskMetrics DEAR multiplied by 10 ). Capital charge will be higher of: Previous day s VAR (or DEAR 10) Average Daily VAR over previous 60 days times a multiplication factor American Banker Banker of America Bank for International Settlements Federal Reserve J.P. Morgan Chase RiskMetrics Pertinent Websites
An introduction to Value-at-Risk Learning Curve September 2003
An introduction to Value-at-Risk Learning Curve September 2003 Value-at-Risk The introduction of Value-at-Risk (VaR) as an accepted methodology for quantifying market risk is part of the evolution of risk
More informationDr Christine Brown University of Melbourne
Enhancing Risk Management and Governance in the Region s Banking System to Implement Basel II and to Meet Contemporary Risks and Challenges Arising from the Global Banking System Training Program ~ 8 12
More informationFinancial-Institutions Management. Solutions 2
Solutions Chapter 10: Market Risk Fixed Income Instruments and DEAR 4. Follow Bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,40,55. The bond is trading at a yield
More informationCalculating VaR. Capital Market Risk Advisors CMRA
Calculating VaR Capital Market Risk Advisors How is VAR Calculated? Sensitivity Estimate Models - use sensitivity factors such as duration to estimate the change in value of the portfolio to changes in
More informationEffective Techniques for Stress Testing and Scenario Analysis
Effective Techniques for Stress Testing and Scenario Analysis Om P. Arya Federal Reserve Bank of New York November 4 th, 2008 Mumbai, India The views expressed here are not necessarily of the Federal Reserve
More informationThe Best of Both Worlds:
The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk Jacob Boudoukh 1, Matthew Richardson and Robert F. Whitelaw Stern School of Business, NYU The hybrid approach combines the two most
More informationContents. List of Figures. List of Tables. List of Examples. Preface to Volume IV
Contents List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.1 Value at Risk and Other Risk Metrics 1 IV.1.1 Introduction 1 IV.1.2 An Overview of Market
More informationCredit Risk Stress Testing
1 Credit Risk Stress Testing Stress Testing Features of Risk Evaluator 1. 1. Introduction Risk Evaluator is a financial tool intended for evaluating market and credit risk of single positions or of large
More informationNorthern Trust Corporation
Northern Trust Corporation Market Risk Disclosures June 30, 2014 Market Risk Disclosures Effective January 1, 2013, Northern Trust Corporation (Northern Trust) adopted revised risk based capital guidelines
More informationManaging Risk/Reward in Fixed Income
INSIGHTS Managing Risk/Reward in Fixed Income Using Global Currency-Hedged Indices as Benchmarks In the pursuit of alpha, is it better to use a global hedged or unhedged index as a benchmark for measuring
More informationJornadas Economicas del Banco de Guatemala. Managing Market Risk. Max Silberberg
Managing Market Risk Max Silberberg Defining Market Risk Market risk is exposure to an adverse change in value of financial instrument caused by movements in market variables. Market risk exposures are
More informationStochastic Analysis of Long-Term Multiple-Decrement Contracts
Stochastic Analysis of Long-Term Multiple-Decrement Contracts Matthew Clark, FSA, MAAA, and Chad Runchey, FSA, MAAA Ernst & Young LLP Published in the July 2008 issue of the Actuarial Practice Forum Copyright
More informationCapital Allocation and Bank Management Based on the Quantification of Credit Risk
Capital Allocation and Bank Management Based on the Quantification of Credit Risk Kenji Nishiguchi, Hiroshi Kawai, and Takanori Sazaki 1. THE NEED FOR QUANTIFICATION OF CREDIT RISK Liberalization and deregulation
More informationA comparison of Value at Risk methods for measurement of the financial risk 1
A comparison of Value at Risk methods for measurement of the financial risk 1 Mária Bohdalová, Faculty of Management, Comenius University, Bratislava, Slovakia Abstract One of the key concepts of risk
More informationFinancial-Institutions Management
Solutions 3 Chapter 11: Credit Risk Loan Pricing and Terms 9. County Bank offers one-year loans with a stated rate of 9 percent but requires a compensating balance of 10 percent. What is the true cost
More information1.2 Structured notes
1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used
More informationInsights. Investment strategy design for defined contribution pension plans. An Asset-Liability Risk Management Challenge
Insights Investment strategy design for defined contribution pension plans Philip Mowbray Philip.Mowbray@barrhibb.com The widespread growth of Defined Contribution (DC) plans as the core retirement savings
More informationConcepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance)
Concepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance) Mr. Eric Y.W. Leung, CUHK Business School, The Chinese University of Hong Kong In PBE Paper II, students
More informationAsset Liability Management
e-learning and reference solutions for the global finance professional Asset Liability Management A comprehensive e-learning product covering Global Best Practices, Strategic, Operational and Analytical
More informationCaput Derivatives: October 30, 2003
Caput Derivatives: October 30, 2003 Exam + Answers Total time: 2 hours and 30 minutes. Note 1: You are allowed to use books, course notes, and a calculator. Question 1. [20 points] Consider an investor
More informationHow To Know Market Risk
Chapter 6 Market Risk for Single Trading Positions Market risk is the risk that the market value of trading positions will be adversely influenced by changes in prices and/or interest rates. For banks,
More informationFinancial Evolution and Stability The Case of Hedge Funds
Financial Evolution and Stability The Case of Hedge Funds KENT JANÉR MD of Nektar Asset Management, a market-neutral hedge fund that works with a large element of macroeconomic assessment. Hedge funds
More informationRESP Investment Strategies
RESP Investment Strategies Registered Education Savings Plans (RESP): Must Try Harder Graham Westmacott CFA Portfolio Manager PWL CAPITAL INC. Waterloo, Ontario August 2014 This report was written by Graham
More informationChapter 6 The Tradeoff Between Risk and Return
Chapter 6 The Tradeoff Between Risk and Return MULTIPLE CHOICE 1. Which of the following is an example of systematic risk? a. IBM posts lower than expected earnings. b. Intel announces record earnings.
More informationProbability Models of Credit Risk
Probability Models of Credit Risk In discussing financial risk, it is useful to distinguish between market risk and credit risk. Market risk refers to the possibility of losses due to changes in the prices
More information1. Currency Exposure. VaR for currency positions. Hedged and unhedged positions
RISK MANAGEMENT [635-0]. Currency Exposure. ar for currency positions. Hedged and unhedged positions Currency Exposure Currency exposure represents the relationship between stated financial goals and exchange
More informationCHAPTER 7: OPTIMAL RISKY PORTFOLIOS
CHAPTER 7: OPTIMAL RIKY PORTFOLIO PROLEM ET 1. (a) and (e).. (a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash and real estate.
More informationACI THE FINANCIAL MARKETS ASSOCIATION
ACI THE FINANCIAL MARKETS ASSOCIATION EXAMINATION FORMULAE 2009 VERSION page number INTEREST RATE..2 MONEY MARKET..... 3 FORWARD-FORWARDS & FORWARD RATE AGREEMENTS..4 FIXED INCOME.....5 FOREIGN EXCHANGE
More informationCITIGROUP INC. BASEL II.5 MARKET RISK DISCLOSURES AS OF AND FOR THE PERIOD ENDED MARCH 31, 2013
CITIGROUP INC. BASEL II.5 MARKET RISK DISCLOSURES AS OF AND FOR THE PERIOD ENDED MARCH 31, 2013 DATED AS OF MAY 15, 2013 Table of Contents Qualitative Disclosures Basis of Preparation and Review... 3 Risk
More informationRisk Management for Fixed Income Portfolios
Risk Management for Fixed Income Portfolios Strategic Risk Management for Credit Suisse Private Banking & Wealth Management Products (SRM PB & WM) August 2014 1 SRM PB & WM Products Risk Management CRO
More informationRegulatory and Economic Capital
Regulatory and Economic Capital Measurement and Management Swati Agiwal November 18, 2011 What is Economic Capital? Capital available to the bank to absorb losses to stay solvent Probability Unexpected
More informationFinal Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator
University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights
More informationVALUATION OF FIXED INCOME SECURITIES. Presented By Sade Odunaiya Partner, Risk Management Alliance Consulting
VALUATION OF FIXED INCOME SECURITIES Presented By Sade Odunaiya Partner, Risk Management Alliance Consulting OUTLINE Introduction Valuation Principles Day Count Conventions Duration Covexity Exercises
More informationCONTENTS. List of Figures List of Tables. List of Abbreviations
List of Figures List of Tables Preface List of Abbreviations xiv xvi xviii xx 1 Introduction to Value at Risk (VaR) 1 1.1 Economics underlying VaR measurement 2 1.1.1 What is VaR? 4 1.1.2 Calculating VaR
More information4. ANNEXURE 3 : PART 3 - FOREIGN EXCHANGE POSITION RISK
Annexure 3 (PRR) - Part 3, Clause 18 - Foreign Exchange Position Risk Amount 4 ANNEXURE 3 : PART 3 - FOREIGN EXCHANGE POSITION RISK (a) CLAUSE 18 - FOREIGN EXCHANGE POSITION RISK AMOUNT (i) Rule PART 3
More informationValidating Market Risk Models: A Practical Approach
Validating Market Risk Models: A Practical Approach Doug Gardner Wells Fargo November 2010 The views expressed in this presentation are those of the author and do not necessarily reflect the position of
More informationQuantitative Methods for Finance
Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain
More informationHow Many Days Equal A Year? Non-trivial on the Mean-Variance Model
How Many Days Equal A Year? Non-trivial on the Mean-Variance Model George L. Ye, Dr. Sobey School of Business Saint Mary s University Halifax, Nova Scotia, Canada Christine Panasian, Dr. Sobey School of
More informationVANDERBILT AVENUE ASSET MANAGEMENT
SUMMARY CURRENCY-HEDGED INTERNATIONAL FIXED INCOME INVESTMENT In recent years, the management of risk in internationally diversified bond portfolios held by U.S. investors has been guided by the following
More informationUsing Duration Times Spread to Forecast Credit Risk
Using Duration Times Spread to Forecast Credit Risk European Bond Commission / VBA Patrick Houweling, PhD Head of Quantitative Credits Research Robeco Asset Management Quantitative Strategies Forecasting
More informationConcentrated Stock Diversification Analysis
Concentrated Stock Diversification Analysis Example analysis Three Harbor Drive, Suite 315 Sausalito, CA 94965 (415) 339-4300 www.aperiogroup.com Copyright 2013 Aperio Group LLC Aperio v. [Latin] to make
More informationAn Attractive Income Option for a Strategic Allocation
An Attractive Income Option for a Strategic Allocation Voya Senior Loans Suite A strategic allocation provides potential for high and relatively steady income through most credit and rate cycles Improves
More informationMatching Investment Strategies in General Insurance Is it Worth It? Aim of Presentation. Background 34TH ANNUAL GIRO CONVENTION
Matching Investment Strategies in General Insurance Is it Worth It? 34TH ANNUAL GIRO CONVENTION CELTIC MANOR RESORT, NEWPORT, WALES Aim of Presentation To answer a key question: What are the benefit of
More informationSEI s Approach to Asset Allocation
SEI s Approach to Asset Allocation Presented by: Jim Smigiel Managing Director and Portfolio Manager Portfolio Strategies Group What is diversification? Sharpe ratio? Peak Sharpe Ratio Loss of efficiency:
More informationStatistics for Retail Finance. Chapter 8: Regulation and Capital Requirements
Statistics for Retail Finance 1 Overview > We now consider regulatory requirements for managing risk on a portfolio of consumer loans. Regulators have two key duties: 1. Protect consumers in the financial
More informationMeasurement of Banks Exposure to Interest Rate Risk and Principles for the Management of Interest Rate Risk respectively.
INTEREST RATE RISK IN THE BANKING BOOK Over the past decade the Basel Committee on Banking Supervision (the Basel Committee) has released a number of consultative documents discussing the management and
More information1) What kind of risk on settlements is covered by 'Herstatt Risk' for which BCBS was formed?
1) What kind of risk on settlements is covered by 'Herstatt Risk' for which BCBS was formed? a) Exchange rate risk b) Time difference risk c) Interest rate risk d) None 2) Which of the following is not
More informationKey Concepts and Skills
Chapter 10 Some Lessons from Capital Market History Key Concepts and Skills Know how to calculate the return on an investment Understand the historical returns on various types of investments Understand
More informationModule 5 Index CFDs. Course #: Title. Version 1 August 2013 1
Module 5 Index CFDs Course #: Title Topic 1: S&P/ASX 200 CFDs... 3 Initial margin... 3 Variation margins... 3 Cashflows... 4 Topic 2: S&P/ASX 200 CFD strategies... 6 Trade broad market movements... 6 Protect
More informationSENSITIVITY ANALYSIS AND INFERENCE. Lecture 12
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationRisk Based Capital Guidelines; Market Risk. The Bank of New York Mellon Corporation Market Risk Disclosures. As of June 30, 2014
Risk Based Capital Guidelines; Market Risk The Bank of New York Mellon Corporation Market Risk Disclosures As of June 30, 2014 1 Basel II.5 Market Risk Quarterly Disclosure Introduction Since January 1,
More informationRisk Based Capital Guidelines; Market Risk. The Bank of New York Mellon Corporation Market Risk Disclosures. As of December 31, 2013
Risk Based Capital Guidelines; Market Risk The Bank of New York Mellon Corporation Market Risk Disclosures As of December 31, 2013 1 Basel II.5 Market Risk Annual Disclosure Introduction Since January
More informationINTRODUCTION TO VALUE AT RISK (VaR)
CHAPTER ONE INTRODUCTION TO VALUE AT RISK (VaR) CHAPTER OUTLINE 1.1 Economics underlying VaR Measurement 1.1.1 What is VaR? 1.1.2 Calculating VaR 1.1.3 The assumptions behind VaR calculations 1.1.4 Inputs
More informationDistinction Between Interest Rates and Returns
Distinction Between Interest Rates and Returns Rate of Return RET = C + P t+1 P t =i c + g P t C where: i c = = current yield P t g = P t+1 P t P t = capital gain Key Facts about Relationship Between Interest
More informationReducing Active Return Variance by Increasing Betting Frequency
Reducing Active Return Variance by Increasing Betting Frequency Newfound Research LLC February 2014 For more information about Newfound Research call us at +1-617-531-9773, visit us at www.thinknewfound.com
More informationEffective Stress Testing in Enterprise Risk Management
Effective Stress Testing in Enterprise Risk Management Lijia Guo, Ph.D., ASA, MAAA *^ Copyright 2008 by the Society of Actuaries. All rights reserved by the Society of Actuaries. Permission is granted
More informationThis paper is not to be removed from the Examination Halls
~~FN3023 ZB d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZB BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences,
More informationThe CAPM (Capital Asset Pricing Model) NPV Dependent on Discount Rate Schedule
The CAPM (Capital Asset Pricing Model) Massachusetts Institute of Technology CAPM Slide 1 of NPV Dependent on Discount Rate Schedule Discussed NPV and time value of money Choice of discount rate influences
More informationUnderstanding Currency
Understanding Currency Overlay July 2010 PREPARED BY Gregory J. Leonberger, FSA Director of Research Abstract As portfolios have expanded to include international investments, investors must be aware of
More informationMarket Risk Capital Disclosures Report. For the Quarter Ended March 31, 2013
MARKET RISK CAPITAL DISCLOSURES REPORT For the quarter ended March 31, 2013 Table of Contents Section Page 1 Morgan Stanley... 1 2 Risk-based Capital Guidelines: Market Risk... 1 3 Market Risk... 1 3.1
More informationFIN 683 Financial Institutions Management Foreign-Currency Risk
FIN 683 Financial Institutions Management Foreign-Currency Risk Professor Robert B.H. Hauswald Kogod School of Business, AU Global Banks Globalization of financial markets has increased foreign exposure
More informationRiskMetrics TM Technical Document
.P.Morgan/Reuters RiskMetrics TM Technical Document Fourth Edition, 1996 New York December 17, 1996.P. Morgan and Reuters have teamed up to enhance RiskMetrics. Morgan will continue to be responsible for
More informationChapters 15. Delta Hedging with Black-Scholes Model. Joel R. Barber. Department of Finance. Florida International University.
Chapters 15 Delta Hedging with Black-Scholes Model Joel R. Barber Department of Finance Florida International University Miami, FL 33199 1 Hedging Example A bank has sold for $300,000 a European call option
More informationState of the Art Virtual Portfolio Management: Building Skills that Matter
State of the Art Virtual Portfolio Management: Building Skills that Matter There are many ways for students to play stock market games or more generally, participate in a virtual portfolio simulation:
More informationIndex Options Beginners Tutorial
Index Options Beginners Tutorial 1 BUY A PUT TO TAKE ADVANTAGE OF A RISE A diversified portfolio of EUR 100,000 can be hedged by buying put options on the Eurostoxx50 Index. To avoid paying too high a
More informationThe Investment Implications of Solvency II
The Investment Implications of Solvency II André van Vliet, Ortec Finance, Insurance Risk Management Anthony Brown, FSA Outline Introduction - Solvency II - Strategic Decision Making Impact of investment
More informationCFA Examination PORTFOLIO MANAGEMENT Page 1 of 6
PORTFOLIO MANAGEMENT A. INTRODUCTION RETURN AS A RANDOM VARIABLE E(R) = the return around which the probability distribution is centered: the expected value or mean of the probability distribution of possible
More informationETF Specific Data Point Methodologies
ETF Specific Data Point ethodologies orningstar ethodology Paper December 31 2010 2010 orningstar Inc. All rights reserved. The information in this document is the property of orningstar Inc. eproduction
More informationEDF CEA Inria School Systemic Risk and Quantitative Risk Management
C2 RISK DIVISION EDF CEA Inria School Systemic Risk and Quantitative Risk Management EDF CEA INRIA School Systemic Risk and Quantitative Risk Management Regulatory rules evolutions and internal models
More informationSummary of Interview Questions. 1. Does it matter if a company uses forwards, futures or other derivatives when hedging FX risk?
Summary of Interview Questions 1. Does it matter if a company uses forwards, futures or other derivatives when hedging FX risk? 2. Give me an example of how a company can use derivative instruments to
More informationExperience with external active fixed income managers - NBIM
Page 1 of 5 Experience with external active fixed income managers This article summarises nearly five years experience with external fixed income managers. During this period, net excess return in relation
More informationRisk and Return in the Canadian Bond Market
Risk and Return in the Canadian Bond Market Beyond yield and duration. Ronald N. Kahn and Deepak Gulrajani (Reprinted with permission from The Journal of Portfolio Management ) RONALD N. KAHN is Director
More informationSolution: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*:
Problem 1. Consider a risky asset. Suppose the expected rate of return on the risky asset is 15%, the standard deviation of the asset return is 22%, and the risk-free rate is 6%. What is your optimal position
More informationCALYPSO ENTERPRISE RISK SYSTEM
1 CALYPSO ENTERPRISE RISK SYSTEM Dr Philip Symes Introduction 2 Calypso's Enterprise Risk Service (ERS) is part of their Front-to-Back software system. Calypso ERS provides the Middle Office risk function.
More informationSeeking a More Efficient Fixed Income Portfolio with Asia Bonds
Seeking a More Efficient Fixed Income Portfolio with Asia s Seeking a More Efficient Fixed Income Portfolio with Asia s Drawing upon different drivers for performance, Asia fixed income may improve risk-return
More informationGN47: Stochastic Modelling of Economic Risks in Life Insurance
GN47: Stochastic Modelling of Economic Risks in Life Insurance Classification Recommended Practice MEMBERS ARE REMINDED THAT THEY MUST ALWAYS COMPLY WITH THE PROFESSIONAL CONDUCT STANDARDS (PCS) AND THAT
More informationUnderstanding investment concepts
Version 4.2 This document provides some additional information to help you understand the financial planning concepts discussed in the SOA in relation to. Important information This document has been published
More informationRisk Management for Alternative Investments
Risk Management for Alternative Investments Prepared for the CAIA Supplementary Level II Book Philippe Jorion* June 18, 2012 *Philippe Jorion is a Professor at the Paul Merage School of Business, University
More informationMeasuring Exchange Rate Fluctuations Risk Using the Value-at-Risk
Journal of Applied Finance & Banking, vol.2, no.3, 2012, 65-79 ISSN: 1792-6580 (print version), 1792-6599 (online) International Scientific Press, 2012 Measuring Exchange Rate Fluctuations Risk Using the
More informationChapter 9. The Valuation of Common Stock. 1.The Expected Return (Copied from Unit02, slide 36)
Readings Chapters 9 and 10 Chapter 9. The Valuation of Common Stock 1. The investor s expected return 2. Valuation as the Present Value (PV) of dividends and the growth of dividends 3. The investor s required
More informationJose Rodicio, ASA, CFA, FRM Deputy Chief Insurance Risk Officer ING Latin America Atlanta Actuarial Club March 26, 2009
Enterprise Risk Management and Economic Capital at ING A practical approach Jose Rodicio, ASA, CFA, FRM Deputy Chief Insurance Risk Officer ING Latin America Atlanta Actuarial Club March 26, 2009 Agenda
More informationBRUNEL UNIVERSITY Economics and Finance EC1004 LECTURE 10. Issues in commercial bank risk management. Reading: Madura Chapter 19
BRUNEL UNIVERSITY Economics and Finance EC1004 LECTURE 10 Issues in commercial bank risk management Reading: Madura Chapter 19 We are going to discuss the overall nature of risk control in banks and related
More informationRobert and Mary Sample
Comprehensive Financial Plan Sample Plan Robert and Mary Sample Prepared by : John Poels, ChFC, AAMS Senior Financial Advisor February 11, 2009 Table Of Contents IMPORTANT DISCLOSURE INFORMATION 1-7 Presentation
More informationManual for SOA Exam FM/CAS Exam 2.
Manual for SOA Exam FM/CAS Exam 2. Chapter 6. Variable interest rates and portfolio insurance. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam Instructions: Please read carefully The exam will have 1 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation questions.
More informationDiscussion paper on the impact on the volatility of own funds of the revised IAS 19
POSITION PAPER Our reference: 2014/00028 Your reference: EBA/DP/2014/01 1 (10) 11/04/2014 European Banking Authority Discussion paper on the impact on the volatility of own funds of the revised IAS 19
More informationUsing Currency Futures to Hedge Currency Risk
Using Currency Futures to Hedge Currency Risk By Sayee Srinivasan & Steven Youngren Product Research & Development Chicago Mercantile Exchange Inc. Introduction Investment professionals face a tough climate.
More informationERM Exam Core Readings Fall 2015. Table of Contents
i ERM Exam Core Readings Fall 2015 Table of Contents Section A: Risk Categories and Identification The candidate will understand the types of risks faced by an entity and be able to identify and analyze
More informationMLC MasterKey Unit Trust Product Disclosure Statement (PDS)
MLC MasterKey Unit Trust Product Disclosure Statement (PDS) Preparation date 1 July 2014 Issued by MLC Investments Limited (MLC) ABN 30 002 641 661 AFSL 230705 This information is general and doesn t take
More informationCoupon Bonds and Zeroes
Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zero-coupon bonds Bond replication No-arbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semi-annual compounding
More informationInvestigating Use of Beta Coefficients for Stock Predictions
University of Akron: Ohio s Polytechnic University IdeaExchange@UAkron Honors Research Projects The Dr. Gary B. and Pamela S. Williams Honors College Spring 2015 Investigating Use of Beta Coefficients
More informationAsset Liability Management for Insurance Companies
e-learning and reference solutions for the global finance professional Asset Liability Management A comprehensive e-learning product covering Global Best Practices, Strategic, Operational and Analytical
More informationWhat is Value at Risk?
VALUE AT RISK (VAR) What is the most I can lose on this investment? This is a question that almost every investor who has invested or is considering investing in a risky asset asks at some point in time.
More informationHow To Invest In Stocks And Bonds
Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationOne Period Binomial Model
FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 One Period Binomial Model These notes consider the one period binomial model to exactly price an option. We will consider three different methods of pricing
More informationAVANTGARD Treasury, liquidity risk, and cash management. White Paper FINANCIAL RISK MANAGEMENT IN TREASURY
AVANTGARD Treasury, liquidity risk, and cash management White Paper FINANCIAL RISK MANAGEMENT IN TREASURY Contents 1 Introduction 1 Mitigating financial risk: Is there an effective framework in place?
More informationFinancial risk management
Financial risk management Topic Gateway Series No. 47 1 Prepared by Jasmin Harvey and Technical Information Service February 2008 About Topic Gateways Topic Gateways are intended as a refresher or introduction
More informationFinancial Risk Management Exam Sample Questions/Answers
Financial Risk Management Exam Sample Questions/Answers Prepared by Daniel HERLEMONT 1 2 3 4 5 6 Chapter 3 Fundamentals of Statistics FRM-99, Question 4 Random walk assumes that returns from one time period
More information