Copyright Bionic Turtle LLC. This document can only be used by customers of Bionic Turtle, LLC. 2009 FRM Foundations 1a (1 of 2) • Hosted by David Harper CFA, FRM, CIPM • Published April 20, 2008 Brought to you by bionicturtle.com This tutorial is for paid members only. You know who you are. Anybody else is using an illegal copy and also violates GARP’s ethical standards.
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Copyright Bionic Turtle LLC. This document can only be used by customers of Bionic Turtle, LLC.
2009 FRM Foundations 1a (1 of 2)
• Hosted by David Harper CFA, FRM, CIPM
• Published April 20, 2008
Brought to you bybionicturtle.com
This tutorial is for paid members only. You know who you are. Anybody else is using an illegal copy and also violates GARP’s ethical standards.
Copyright Bionic Turtle LLC. This document can only be used by customers of Bionic Turtle, LLC.
Foundations 1.a Agenda (Note order of study guide)
• Jorion Value at Risk (VaR) – Chapter 1
• Amenc Portfolio Theory – Chapter 4
• Grinold Active Portfolio Management – Chapter 7
2
2009 FRM Foundations 1 (Readings 1, 2 & 3)
• 1.a.1. Introduction to VaR
• 1.a.2. CML & SML
• 1.a.3. CAPM
• 1.a.4. RAPMs
• 1.a.5. APT (trivial version, Grinold)
Related Learning Spreadsheets
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Copyright Bionic Turtle LLC. This document can only be used by customers of Bionic Turtle, LLC.
Define what a derivative contract is and how it differs from a security
• Jorion: “A position in a forward contract is equivalent to the same notional amount invested directly in the spot market, leveraged by cash so that there is zero initial investment”
• This is the essence of financial engineering: funded positions in cash market can be “replicated” with synthetically unfunded positions … for example
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Define what a derivative contract is and how it differs from a security Investor sells credit default swap (CDS) and deposits cash into default-free money market: synthetically long the bond
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Define value at risk (VaR) and describe how it is used in risk management VaR summarizes the worst loss over a target horizon that will not be exceeded with a given level of confidence (Jorion p 17).
“Under normal market conditions, the most the portfolio can lose over a month is about $3.6 million at the 99% confidence level”
“Under normal market conditions, the most the portfolio can lose over the target horizon is $X or %Y at the selected confidence level.”
A VaR statement requires two user choices:horizon and confidence; e.g., 1 day 99%, 10-day 95%, …
These exclusions are often tested. Note that operational risk is not really “all other risks.” In other words: Credit + Market + Operational < Total Risk! Also, keep in mind strategic risk is not an operational risk!
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Operational risk…
• Operational risk > Best Protection?
– “The best protection against operational risks consists of redundancies of systems, clear separation of responsibilities with strong internal controls, and regular contingency planning”
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Describe Capital Asset Pricing Model (CAPM), list underlying assumptions; explain implications, contributions & limitations.
Security Market Line (SML) says the excess expected return on a security is a linear function of beta (the security’s sensitivity to the market risk premium)
0%
5%
10%
15%
20%
25%
0.00 1.00 2.00 3.00
Exp
ect
ed
Ret
urn
Beta
SECURITY MARKET LINE (SML)
Riskless rate 4.00%
Market portfolio, M PercentAsset A 56.82%Asset B 43.18%E[return] of marketportfolio M
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Describe Capital Asset Pricing Model (CAPM), list underlying assumptions; explain implications, contributions & limitations.
• CAPM
• Beta (i) is asset’s sensitivity to movements in the market:
– Beta is the covariance of the return of the security with the return of the market portfolio divided by () the variance of the return of the market portfolio:
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Describe Capital Asset Pricing Model (CAPM), list underlying assumptions; explain implications, contributions & limitations
• Investors can borrow and lend at the risk-free rate without limit (unlimited lending and borrowing)
• Information is simultaneously free to all All investors have the same forecast return, variance and covariance expectations for all assets (perfect, costless information)
• Perfect markets with neither taxes and nor transaction costs. All assets are infinitely divisible
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Richard Grinold. Chapter 7
64
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Describe limitations and deficiencies in the CAPM.
• The CAPM is based on the notion that the market portfolio is
– Mean/variance-efficient and
– Fully invested: “Even if the CAPM is true in some broader context of a worldwide portfolio, it cannot be valid in the restricted single-market world in which it is ordinarily applied.”
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2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
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Describe limitations and deficiencies in the CAPM.
• All of the other assumptions underlying the CAPM can be challenged “adding additional wounds”– Mean/ variance preferences,
– Identical expectations of mean and variance,
– No taxes or transactions costs,
– No restrictions on stock positions
• The most grievous of these is the requirement that all participants know every stock's expected excess return. – “Thus we would suspect that the CAPM can be only
approximately true. It provides a guideline that should be neither ignored nor taken as gospel.”
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2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
Dubious
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Define and describe the components of the Arbitrage Pricing Theory (APT) model.
• The APT maintains that the expected excess return on any stock is determined by that stock's factor exposures and the factor forecasts associated with those factors.
,
1
K
n n k k n
k
r X b u
,
1
{ }K
n n n k k
k
f E r X m
67
2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
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Define and describe the components of the Arbitrage Pricing Theory (APT) model.
• The factor forecast is simply the sum of [exposure k factor k]
• The excess return contains an unexplained specific (idiosyncratic) return
,
1
K
n n k k n
k
r X b u
,
1
{ }K
n n n k k
k
f E r X m
68
2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
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Calculate a security’s expected excess returns using the APT model and interpret the results.
Factor Forecasts 2.00% 2.50% -1.50% 0.00% 6.00%
Standardized Exposures (Factor Loadings, Sensitivities or Betas) APT-
2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
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APT
CAPM
Discuss the relationship between APT and the CAPM.
• CAPM has one factor,K = 1.
• Stock's exposure to that factor is the stock's beta
• The expected return associated with thefactor is expected excess return on the market
( ) [ ( ) )]i F i M FE R R E R R
,
1
{ }K
n n n k k
k
f E r X m
(R ) [ ( ) )]excess i M FE E R R
,1 1{ }n n nf E r X m
{ }n nf E r ERP
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2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
• APT is generalized CAPM
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Describe the properties of a qualified model in the context of the APT.
• An APT factor model is qualified if and only if portfolio Q is diversified with respect to that factor model.
– Among all portfolios with the same factor exposures as portfolio Q, portfolio Q has minimum risk (No other portfolio with the same factor exposures is less risky than portfolio Q)
– Any factor model that is good at explaining risk should be qualified; i.e., not much specific risk
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2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
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Describe the difficulties involved with factor forecasting.
• “Fewer is not better:” ideally, we would like the factor model to contain more (several) factors
– But our ability to forecast additional factors is challenged
– Historical factors returns are not likely to extrapolate “out of sample” into the future
• But a saving grace: we hope/trust that factors may be more stable than that asset returns!
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2009 FRM. Foundations. 3. Grinold Active Portfolio. Chapter 7 (APT)
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Describe some of the methods typically used in factor forecasting.