FRM Part I Book 4: Valuation and risk models (2015 SchweserNotes)

301 Pages·12.378 MB·English

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I
F R M Part B ook 4:
VALUATION AND RlSK MODELS
Reading Assignments and Learning Objectives 5
Valuation and Risk Models
VaR Methods 13
49: Quantifying Volatility in VaR Models 24
50: Putting VaR to Work 45
51: Measures of Financial Risk 59
52: Stress Testing 71
53: Principles for Sound Stress Testing Practices and Supervision 80
54: Binomial Trees 93
55: The Black-Scholes-Merton Model 110
56: Greek Letters 128
57: Prices, Discount Factors, and Arbitrage 148
58: Spot, Forward, and Par Rates 164
59: Returns, Spreads, and Yields 182
60: One-Factor Risk Metrics and Hedges 198
61: Multi-Factor Risk Metrics and Hedges 215
62: Assessing Country Risk 228
63: Country Risk Assessment in Practice 239
64: External and Internal Ratings 249
65: Capital Structure in Banks 259
66: Operational Risk 271
Self-Test: Valuation and Risk Models 284
Formulas 291
Appendix 296
Index 299
©2014 Kaplan, Inc. Page 3
FRM 2015 PART I BOOK 4: VALUATION AND RISK MODELS
©2014 Kaplan, Inc., d.b.a. Kaplan Schweser. All rights reserved.
Printed in the United States of America.
ISBN: 978-1-4754-3111-7
PPN: 3200-6168
Required Disclaimer: GARP® does not endorse, promote, review, or warrant the accuracy of the products or
services offered by Kaplan Schweser of FRM® related information, nor does it endorse any pass rates claimed
by the provider. Further, GARP® is not responsible for any fees or costs paid by the user to Kaplan Schweser,
nor is GARP® responsible for any fees or costs of any person or entity providing any services to Kaplan
Schweser. FRM®, GARP®, and Global Association of Risk Professionals™ are trademarks owned by the
Global Association of Risk Professionals, Inc.
These materials may not be copied without written permission from the author. The unauthorized duplication
of these notes is a violation of global copyright laws. Your assistance in pursuing potential violators of this law is
greatly appreciated.
Disclaimer: The SchweserNotes should be used in conjunction with the original readings as set forth by
GARP®. The information contained in these books is based on the original readings and is believed to be
accurate. Ffowever, their accuracy cannot be guaranteed nor is any warranty conveyed as to your ultimate exam
success.
Page 4 ©2014 Kaplan, Inc.
Reading Assignments and
Learning Objectives
The following material is a review of the Valuation and Risk Models principles designed to
address the learning objectives set forth by the Global Association of Risk Professionals.
Reading Assignments
Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and
Operational Risk: The Value at Risk Approach (Oxford: Blackwell Publishing, 2004).
49. “Quantifying Volatility in VaR Models,” Chapter 2 (page 24)
50. “Putting VaR to Work,” Chapter 3 (page 45)
Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley &
Sons, 2005).
51. “Measures of Financial Risk,” Chapter 2 (page 59)
Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk,
3rd Edition (New York: McGrawHill, 2007).
52. “Stress Testing,” Chapter 14 (page 71)
53. “Principles for Sound Stress Testing Practices and Supervision” (Basel Committee on
Banking Supervision Publication, May 2009). (page 80)
John Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson
Prentice Hall, 2014).
54. “Binomial Trees,” Chapter 13 (page 93)
55. “The Black-Scholes-Merton Model,” Chapter 15 (page 110)
56. “Greek Letters,” Chapter 19 (page 128)
Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons,
2011).
57. “Prices, Discount Factors, and Arbitrage,” Chapter 1 (page 148)
58. “Spot, Forward, and Par Rates,” Chapter 2 (page 164)
59. “Returns, Spreads, and Yields,” Chapter 3 (page 182)
60. “One-Factor Risk Metrics and Hedges,” Chapter 4 (page 198)
61. “Multi-Factor Risk Metrics and Hedges,” Chapter 5 (page 215)
©2014 Kaplan, Inc. Page 5
Book 4
Reading Assignments and Learning Objectives
Daniel Wagner, Managing Country Risk: A Practitioner’s Guide to Effective Cross-Border
Risk Analysis (Boca Raton, FL: Taylor & Francis Group, 2012).
62. “Assessing Country Risk,” Chapter 3 (page 228)
63. “Country Risk Assessment in Practice,” Chapter 4 (page 239)
Arnaud de Servigny and Olivier Renault, Measuring and Managing Credit Risk
(New York: McGraw-Hill, 2004).
64. “External and Internal Ratings,” Chapter 2 (page 249)
Gerhard Schroeck, Risk Management and Value Creation in Financial Institutions
(New York: Wiley, 2002).
65. “Capital Structure in Banks,” Chapter 5 (page 259)
John Hull, Risk Management and Financial Institutions, 3rd Edition (Boston: Pearson
Prentice Hall, 2012).
66. “Operational Risk,” Chapter 20 (page 271)
Page 6 ©2014 Kaplan, Inc.
Book 4
Reading Assignments and Learning Objectives
Learning Objectives
49. Quantifying Volatility in VaR Models
After completing this reading, you should be able to:
1. Explain how asset return distributions tend to deviate from the normal distribution,
(page 24)
2. Explain reasons for fat tails in a return distribution and describe their implications,
(page 24)
3. Distinguish between conditional and unconditional distributions, (page 24)
4. Describe the implications of regime switching on quantifying volatility, (page 26)
5. Explain the various approaches for estimating VaR (page 27)
6. Compare and contrast different parametric and non-parametric approaches for
estimating conditional volatility, (page 27)
7. Calculate conditional volatility using parametric and non-parametric approaches,
(page 27)
8. Explain the process of return aggregation in the context of volatility forecasting
methods, (page 37)
9. Describe implied volatility as a predictor of future volatility and its shortcomings,
(page 37)
10. Explain long horizon volatility/VaR and the process of mean reversion according to
an AR(1) model, (page 38)
50. Putting VaR to Work
After completing this reading, you should be able to:
1. Explain and give examples of linear and non-linear derivatives, (page 45)
2. Describe and calculate VaR for linear derivatives, (page 47)
3. Describe the delta-normal approach to calculating VaR for non-linear derivatives,
(page 47)
4. Describe the limitations of the delta-normal method, (page 47)
5. Explain the full revaluation method for computing VaR. (page 51)
6. Compare delta-normal and full revaluation approaches for computing VaR.
(page 51)
7. Explain structural Monte Carlo, stress testing and scenario analysis methods for
computing VaR, identifying strengths and weaknesses of each approach, (page 51)
8. Describe the implications of correlation breakdown for scenario analysis, (page 51)
9. Describe worst-case scenario (WCS) analysis and compare WCS to VaR. (page 53)
51. Measures of Financial Risk
After completing this reading, you should be able to:
1. Describe the mean-variance framework and the efficient frontier, (page 59)
2. Explain the limitations of the mean-variance framework with respect to
assumptions about the return distributions, (page 61)
3. Define the Value-at-Rsk (VaR) measure of risk, describe assumptions about return
distributions and holding period, and explain the limitations of VaR. (page 62)
4. Define the properties of a coherent risk measure and explain the meaning of each
property, (page 63)
5. Explain why VaR is not a coherent risk measure, (page 64)
6. Explain and calculate expected shortfall (ES), and compare and contrast VaR and
ES. (page 64)
©2014 Kaplan, Inc. Page 7
Book 4
Reading Assignments and Learning Objectives
7. Describe spectral risk measures, and explain how VaR and ES are special cases of
spectral risk measures, (page 65)
8. Describe how the results of scenario analysis can be interpreted as coherent risk
measures, (page 65)
52. Stress Testing
After completing this reading, you should be able to:
1. Describe the purposes of stress testing and the process of implementing a stress
testing scenario, (page 71)
2. Contrast between event-driven scenarios and portfolio-driven scenarios, (page 72)
3. Identify common one-variable sensitivity tests, (page 72)
4. Analyze drawbacks to scenario analysis, (page 73)
5. Distinguish between unidimensional and multidimensional scenarios, (page 73)
6. Compare and contrast various approaches to multidimensional scenario analysis,
(page 74)
7. Define and distinguish between sensitivity analysis and stress testing model
parameters, (page 75)
8. Explain how the results of a stress test can be used to improve risk analysis and risk
management systems, (page 75)
53. Principles for Sound Stress Testing Practices and Supervision
After completing this reading, you should be able to:
1. Describe the rationale for the use of stress testing as a risk management tool.
(page 80)
2. Describe weaknesses identified and recommendations for improvement in:
• The use of stress testing and integration in risk governance
• Stress testing methodologies
• Stress testing scenarios
• Stress testing handling of specific risks and products (page 81)
3. Describe stress testing principles for banks regarding the use of stress testing and
integration in risk governance, stress testing methodology and scenario selection,
and principles for supervisors, (page 81)
54. Binomial Trees
After completing this reading, you should be able to:
1. Calculate the value of an American and a European call or put option using a one-
step and two-step binomial model, (page 93)
2. Describe how volatility is captured in the binomial model, (page 100)
4. Explain how the binomial model can be altered to price options on: stocks with
dividends, stock indices, currencies, and futures, (page 100)
3. Describe how the value calculated using a binomial model converges as time periods
are added, (page 103)
55. The Black-Scholes-Merton Model
After completing this reading, you should be able to:
1. Explain the lognormal property of stock prices, the distribution of rates of return,
and the calculation of expected return, (page 110)
2. Compute the realized return and historical volatility of a stock, (page 110)
3. Describe the assumptions underlying the Black-Scholes-Merton option pricing
model, (page 113)
Page 8 ©2014 Kaplan, Inc.
Book 4
Reading Assignments and Learning Objectives
4. Compute the value of a European option using the Black-Scholes-Merton model on
a non-dividend-paying stock, (page 114)
5. Identify the complications involving the valuation of warrants, (page 120)
6. Define implied volatilities and describe how to compute implied volatilities from
market prices of options using the Black-Scholes-Merton model, (page 120)
7. Explain how dividends affect the early decision for American call and put options,
(page 119)
8. Compute the value of a European option using the Black-Scholes-Merton model on
a dividend-paying stock, (page 116)
9. Describe the use of Black’s Approximation in calculating the value of an American
call option on a dividend-paying stock, (page 119)
56. Greek Letters
After completing this reading, you should be able to:
1. Describe and assess the risks associated with naked and covered option positions,
(page 128)
2. Explain how naked and covered option positions generate a stop loss trading
strategy, (page 129)
3. Describe delta hedging for an option, forward, and futures contracts, (page 129)
4. Compute the delta of an option, (page 129)
5. Describe the dynamic aspects of delta hedging, (page 132)
6. Define the delta of a portfolio, (page 135)
7. Define and describe theta, gamma, vega, and rho for option positions, (page 136)
8. Explain how to implement and maintain a gamma neutral position, (page 136)
9. Describe the relationship between delta, theta, and gamma, (page 136)
10. Describe how hedging activities take place in practice, and describe how scenario
analysis can be used to formulate expected gains and losses with option positions,
(page 142)
11. Describe how portfolio insurance can be created through option instruments and
stock index futures, (page 143)
57. Prices, Discount Factors, and Arbitrage
After completing this reading, you should be able to:
1. Define discount factor and use a discount function to compute present and future
values, (page 151)
2. Define the “law of one price,” explain it using an arbitrage argument, and describe
how it can be applied to bond pricing, (page 153)
3. Identify the components of a U.S. Treasury coupon bond, and compare and
contrast the structure to Treasury STRIPS, including the difference between
P-STRIPS and C-STRIPS. (page 155)
4. Construct a replicating portfolio using multiple fixed income securities to match
the cash flows of a given fixed income security, (page 156)
5. Identify arbitrage opportunities for fixed income securities with certain cash flows,
(page 153)
6. Differentiate between “clean” and “dirty” bond pricing and explain the implications
of accrued interest with respect to bond pricing, (page 157)
7. Describe the common day-count conventions used in bond pricing, (page 157)
©2014 Kaplan, Inc. Page 9
Book 4
Reading Assignments and Learning Objectives
58. Spot, Forward, and Par Rates
After completing this reading, you should be able to:
1. Calculate and interpret the impact of different compounding frequencies on a
bond’s value, (page 164)
2. Calculate discount factors given interest rate swap rates, (page 165)
3. Compute spot rates given discount factors, (page 167)
4. Interpret the forward rate, and compute forward rates given spot rates, (page 169)
5. Define par rate and describe the equation for the par rate of a bond, (page 171)
6. Interpret the relationship between spot, forward and par rates, (page 172)
7. Assess the impact of maturity on the price of a bond and the returns generated by
bonds, (page 174)
8. Define the “flattening” and “steepening” of rate curves and describe a trade to
reflect expectations that a curve will flatten or steepen, (page 174)
59. Returns, Spreads, and Yields
After completing this reading, you should be able to:
1. Distinguish between gross and net realized returns, and calculate the realized return
for a bond over a holding period including reinvestments, (page 182)
2. Define and interpret the spread of a bond, and explain how a spread is derived from
a bond price and a term structure of rates, (page 184)
3. Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing,
(page 184)
4. Compute a bond’s YTM given a bond structure and price, (page 184)
5. Calculate the price of an annuity and a perpetuity, (page 188)
6. Explain the relationship between spot rates and YTM. (page 189)
7. Define the coupon effect and explain the relationship between coupon rate, YTM,
and bond prices, (page 190)
8. Explain the decomposition of P&L for a bond into separate factors including carry
roll-down, rate change and spread change effects, (page 191)
9. Identify the most common assumptions in carry roll-down scenarios, including
realized forwards, unchanged term structure, and unchanged yields, (page 192)
60. One-Factor Risk Metrics and Hedges
After completing this reading, you should be able to:
1. Describe an interest rate factor and identify common examples of interest rate
factors, (page 198)
2. Define and compute the DV01 of a fixed income security given a change in yield
and the resulting change in price, (page 199)
3. Calculate the face amount of bonds required to hedge an option position given the
DV01 of each, (page 199)
4. Define, compute, and interpret the effective duration of a fixed income security
given a change in yield and the resulting change in price, (page 201)
5. Compare and contrast DV01 and effective duration as measures of price sensitivity,
(page 203)
6. Define, compute, and interpret the convexity of a fixed income security given a
change in yield and the resulting change in price, (page 204)
7. Explain the process of calculating the effective duration and convexity of a portfolio
of fixed income securities, (page 206)
Page 10 ©2014 Kaplan, Inc.
Book 4
Reading Assignments and Learning Objectives
8. Explain the impact of negative convexity on the hedging of fixed income securities.
(page 207)
9. Construct a barbell portfolio to match the cost and duration of a given bullet
investment, and explain the advantages and disadvantages of bullet versus barbell
portfolios, (page 208)
61. Multi-Factor Risk Metrics and Hedges
After completing this reading, you should be able to:
1. Describe and assess the major weakness attributable to single-factor approaches
when hedging portfolios or implementing asset liability techniques, (page 215)
2. Define key rate exposures and know the characteristics of key rate exposure factors
including partial ‘01s and forward-bucket ‘01s. (page 216)
3. Describe key-rate shift analysis, (page 216)
4. Define, calculate, and interpret key rate ‘01 and key rate duration, (page 217)
5. Describe the key rate exposure technique in multi-factor hedging applications;
summarize its advantages/disadvantages. (page 218)
6. Calculate the key rate exposures for a given security, and compute the appropriate
hedging positions given a specific key rate exposure profile, (page 218)
7. Relate key rates, partial ‘01s and forward-bucket ‘01s, and calculate the forward
bucket ‘01 for a shift in rates in one or more buckets, (page 220)
8. Construct an appropriate hedge for a position across its entire range of forward
bucket exposures, (page 221)
9. Apply key rate and multi-factor analysis to estimating portfolio volatility.
(page 222)
62. Assessing Country Risk
After completing this reading, you should be able to:
1. Identify characteristics and guidelines leading to effective country risk analysis.
(page 228)
2. Identify key indicators used by rating agencies to analyze a country’s debt and
political risk, and describe challenges faced by country risk analysts in using external
agency ratings, (page 229)
3. Describe factors which are likely to influence the political stability and economic
openness within a country, (page 231)
4. Apply basic country risk analysis in comparing two countries as illustrated in the
case study, (page 232)
63. Country Risk Assessment in Practice
After completing this reading, you should be able to:
1. Explain key considerations when developing and using analytical tools to assess
country risk, (page 239)
2. Describe a process for generating a ranking system and selecting risk management
tools to compare the risk among countries, (page 240)
3. Describe qualitative and quantitative factors that can be used to assess country risk.
(page 242)
4. Describe alternative measures and indices that can be useful in assessing country
risk, (page 243)
©2014 Kaplan, Inc. Page 11