CFA 2018 Level 2 Portfolio Management
7 months ago
2017 年CFA二级培训项目 Portfolio Management 讲师：周琪Topic Weightings in CFA Level II Session NO. Content Weightings
Study Session 1-2 Ethics & Professional Standards 10-15
Study Session 3 Quantitative Methods 5-10
Study Session 4 Economic Analysis
5-10 Study Session 5-6
Financial Statement Analysis 15-20 Study Session 7-8
Corporate Finance 5-15
Study Session 9-11 Equity Analysis
15-25 Study Session 12-13 Fixed Income Analysis 10-20 Study Session 14
Derivative Investments 5-15 Study Session 15 Alternative Investments 5-10
Study Session 16-17 Portfolio Management 5-10
SS16: Portfolio Management:
Process, Asset Allocation, and Risk Management Framework Portfolio Management
R47 The portfolio Management Process and the Investment Policy Statement • R48 An introduction to multifactor models R49 Measuring and Managing Market Risk SS17: Economic Analysis, Active
Management, and Trading
R50 Economics and investment markets R51 Analysis of active portfolio management R52 Algorithmic Trading and
Investment Policy Statement
1. Portfolio Perspective
2. Investment Objectives and ConstrainsFramework
4. Management investment portfoliosPortfolio Perspective
Portfolio Perspective: focus on the aggregate of all the investor’s holdings the portfolio Harry Markowitz → Modern Portfolio Theory (MPT) Some pricing models
such as CAPM, APT, ICAPM, etc → these pricing models are all based on the principle that systematic risk is
priced → should analyze the risk-return tradeoff of the portfolioPortfolio Management
Steps the planning step
Identifying and Specifying the Investor’s
Objective and Constraints
Creating the Investment Policy Statement Forming Capital Markets Expectations Creating the Strategic Asset Allocation the execution step Tactical Asset Allocation Security Selection/Composition
the feedback step Monitoring and Rebalance Performance EvaluationInvestment Objectives and Constrains
Investment objectives relate to what the investor wants to accomplish with the portfolio Objectives are mainly concerned with risk and return considerations
Risk measurement - Value at risk (VaR) Willingness to Take Risk
Ability to Take Risk Below Average Above Average
Below Average Below-average risk tolerance
Resolution needed Above Average Resolution needed
Above-average risk toleranceInvestment Objectives and Constrains
Some specific factors that affect the ability to accept risk
Required spending needs Long-term wealth target Financial strengths/Liabilities Health/Age
Some specific factors that affect the willingness to accept risk
Return objective Habit Historical Trading CharacterInvestment Objectives and Constrains
Return measurement such as: total Return; absolute Return; return relative to the
real returns inflation-adjusted
benchmark’s; return nominal returns;
returns ; pretax returns; post-tax returns
Return desire and requirement is that level of return stated by the client, including
how much the investor wishes to receive from the portfolio required return represents some level of return that must be
achieved by the portfolio, at least on an average basis to meet the
target financial obligationsInvestment Objectives and Constrains
Investment constrains Investment constrains are those factors restricting or limiting the universe of available investment choices.
Types Liquidity requirement: a need for cash of new contributions or savings at a specified point in time.
Time horizon: the time period associated with an investment objective (short term, long term, or a combination of the two).
Tax concerns: tax payments reduce the amount of the total return. Legal and regulatory factors: external factors imposed by governmental, regulatory, or oversight authorities to constrain investment decision- making.
Unique circumstances: internal factors , an individual investor’s portfolio choices may be constrained by circumstances focusing on health needs, support of dependents, and other circumstances unique to the particular individual.IPS Definition a written planning document that governs all investment decisions for the client Main roles Be readily implemented by current or future investment advisers. Promote long-term discipline for portfolio decisions. Help protect against short-term shifts in strategy when either market environments or portfolio performance cause panic or overconfidence.IPS
Elements A client description that provides enough background so any competent investment adviser can give a common understanding of the client’s situation.
The purpose of the IPS with respect to policies, objectives, goals, restrictions, and portfolio limitations. Identification of duties and responsibilities of parties involved. The formal statement of objectives and constrains . A calendar schedule for both portfolio performance and IPS review. Asset allocation ranges and statements regarding flexibility and rigidity when formulating or modifying the strategic asset allocation. Guidelines for portfolio adjustments and rebalancing.IPS
Three approaches for investment strategy
Passive investment strategy approach: portfolio composition does not react to changes in expectations, an example in indexing Active approach : involves holding a portfolio different from a benchmark or comparison portfolio for the purpose of producing positive excess risk-adjusted returns
Semiactive approach : an indexing approach with controlled use of weights different from benchmarkCME and Strategic Asset allocation
Capital market expectations
The manager’s third task in the planning process is to form capital market expectations. Long-run forecasts of risk and return characteristics for various asset classes form the basis for choosing portfolios that maximize expected return for given levels of risk, or minimize risk for given levels of expected return.
Strategic Asset allocation
the final step in the planning stage, combines the IPS and capital market expectations to formulate weightings on acceptable asset
classesManagement investment portfolios
ethical conduct as a requirement for managing investment portfolios
the investment professional who manages client portfolio well meets both standards of competence and standards of conduct the appropriate standard of conduct is embodied by the CFA
Institute Code and Standards
1. Arbitrage Pricing Theory (APT)
2. Multifactor ModelFramework
Macroeconomic Factor Model • Factor Sensitivities for a Two-Stock
Fundamental Factor • Standardized beta
3. Statistical Factor models
4. Application ：Return Attribution
5. Application: Portfolio ConstructionArbitrage Pricing Theory (APT)
asset pricing model developed by the arbitrage pricing theory
Assumptions A factor model describes asset returns There are many assets, so investors can form well-diversified portfolios that eliminate asset-specific risk
No arbitrage opportunities exist among well-diversified portfolios
) ( ... ) ( ) ( ) ( ,
2 2 , 1 1 ,
P k k P P F P R R E
Arbitrage Pricing Theory (APT)
The factor risk premium (or factor price, ) represents the expected return in
excess of the risk free rate for a portfolio with a sensitivity of 1 to factor j and a sensitivity of 0 to all other factors. Such a portfolio is called a pure factor portfolio for factor j.
The parameters of the APT equation are the and the
risk-free rate factor
(the factor sensitivities are specific to individual
risk-premiums investments).Arbitrage Pricing Theory (APT)
Arbitrage Opportunities The APT assumes there are no market imperfections preventing investors from exploiting arbitrage opportunities
extreme long and short positions are permitted and mispricing will disappear immediately all arbitrage opportunities would be exploited and eliminated immediatelyExample- Arbitrage Pricing Theory (APT)
Suppose that two factors, surprise in inflation (factor 1) and surprise in
GDP growth (factor 2), explain returns. According to the APT, an arbitrage opportunity exists unless
E R ( ) R β (λ )+β (λ )
P F p,1 1 p,2
2 Well-diversified portfolios, J, K, and L, given in table.
Portfolio Expected return Sensitivity to Sensitivity to GDP inflation factor factor J
1.1 E R ( )
1.0 λ +1.5λ F J
β +0.06β K F P
2 p,1 p,2
0.5 E R ( ) 0.07 0.02 λ +1.0λ
E R ( ) 0.11 R
1.3 λ +1.1λ L FMultifactor Model
Multifactor models have gained importance for the practical business of portfolio management for two main reasons.
multifactor models explain asset returns better than the market model does.
multifactor models provide a more detailed analysis of risk than does a single factor model.Types of Multifactor Models
Macroeconomic Factor Fundamental factor models Statistical factor models Mixed factor models
Some practical factor models have the characteristics of more than one of the above categories. We can call such models mixed factor models.Macroeconomic Factor Model
Macroeconomic Factor assumption: the factors are surprises in macroeconomic variables that significantly explain equity returns
Surprise = actual value – predicted (expected) value
, b i2
… … … … … … … … … … … … … … …
Regression (time series) Return F
R E R b F b F
2 ( ) i i i GDP i QS i
i = firm-specific surprise which not be explained by the model.
= return for asset i E(R
exactly formula for return of asset i Where: R
= GDP surprise sensitivity of asset i b
= surprise in the credit quality spread b
= surprise in the GDP rate F
)= expected return for asset i F
= credit quality spread surprise sensitivity of asset i εMacroeconomic Factor model
Suppose our forecast at the beginning of the month is that inflation will be
0.4 percent during the month. At the end of the month, we find that inflation was actually 0.5 percent during the month. During any month, Actual inflation = Predicted inflation + Surprise inflation In this case, actual inflation was 0.5 percent and predicted inflation was
0.4 percent. Therefore, the surprise in inflation was 0.5 - 0.4 = 0.1 percent.Macroeconomic Factor model
Slope coefficients are naturally interpreted as the factor sensitivities of the asset.
A factor sensitivity is a measure of the response of return to each unit of increase in a factor, holding all other factors constant.
The term ε is the part of return that is unexplained by expected return or
the factor surprises. If we have adequately represented the sources of common risk (the factors), then ε must represent an asset-specific risk. For a
stock, it might represent the return from an unanticipated company-specific event.
Factor Sensitivities for a Two-Stock Portfolio
Suppose that stock returns are affected by two common factors: surprises in inflation and surprises in GDP growth. A portfolio manager is analyzing the returns on a portfolio of two stocks, Manumatic (MANM) and Nextech (NXT), The following equations describe the returns for those stocks, where the factors F . and F , represent the
surprise in inflation and GDP growth, respectively:
R 0.09 1 F
1 F MANM
R 0.12 2 F
4 F NXTOne-third of the portfolio is invested in Manumatic stock, and two- thirds is invested in Nextech stock. Formulate an expression for the return on the portfolio. State the expected return on the portfolio. Calculate the return on the portfolio given that the surprises in inflation and GDP growth are 1 percent and 0 percent, respectively, assuming that the error terms for MANM and NXT both equal 0.5 percent.
Factor Sensitivities for a Two-Stock Portfolio
Correct Answer 1 :
The portfolio's return is the following weighted average of the returns to the two stocks: Rp = (1/3)(0.09) + (2/3)(0 .12) + [(1/3)(- I) (2/3)(2)] F + [(1/3)(1) + (2/3)(4)]F + (1/3) ε + (2/3) ε
+ INFL GDP MANM NXT
= 0.11 + 1 F + 3F + (1/3) ε + (2/3) ε
Correct Answer 2 :
The on the portfolio is 11 percent, the value of
expected return the in the expression obtained in Part 1. intercept
Correct Answer 3 :
Rp = 0.11 + 1 F + 3F + (1/3) ε + (2/3) ε = 0.11 +
1(0.01) + 3(0) + (1/3)(0.005) + (2/3)(0.005) = 0.125 or 12.5 percentFundamental Factor
i i i1 P/E i2 SIZE i R a b F b F
P E b e g b
… … … … … … … … … … … … … … …
(P/E) - P/E . . ij i
1 / Asset i's attribut value - average attribute value (attribute value)
No economic interpretation
Regression (cross sectional data) Return bStandardized beta
Suppose, for example, that an investment has a dividend yield of
3.5 percent and that the average dividend yield across all stocks being considered is 2.5 percent. Further, suppose that the standard deviation of dividend yields across all stocks is 2 percent.
The investment's sensitivity to dividend yield is (3.5% - 2.5%)/2% = 0.50, or one-half standard deviation above average.Standardized beta
The scaling permits all factor sensitivities to be interpreted similarly, despite differences in units of measure and scale in the variables. The exception to this interpretation is factors for binary variables such as industry membership. A company either participates in an industry or it does not.
The industry factor sensitivities would be 0 - 1 dummy variables; in models that recognize that companies frequently operate in multiple industries, the value of the sensitivity would be 1 for each industry in which a company operated.Statistical Factor models
Statistical factor models
In a statistical factor model, statistical methods are applied to historical returns of a group of securities to extract factors that can explain the observed returns of securities in the group. In statistical factor models, the factors are actually portfolios of the
securities in the group under study and are therefore defined by portfolio weights. Two major types of factor models are factor analysis models and principal components models.
Factor analysis models best explain historical return covariances. Principal components models best explain the historical return variances.
Advantage and Disadvantage Major advantage: it make minimal assumptions.
Major weakness: the statistical factors do not lend
themselves well to economic interpretationArbitrage Pricing Theory (APT)
The relation between APT and multifactor models
APT Multifactor models Characteristics
pricing model that explains the variation across assets’ expected returns
regression that explains the variation over time in returns for one asset
Assumptions equilibrium-pricing model that assumes no arbitrage opportunities ad hoc (i.e., rather than being derived directly from an equilibrium theory, the factors are identified empirically by looking for macroeconomic variables that best fit the data)
Intercept risk-free rate
derived from the APT equation in macroeconomic factor modelArbitrage Pricing Theory (APT)
Comparison CAPM and APT
All investors should hold some APT gives no special role to the combination of the market portfolio, and is
market far more
. than CAPM. Asset returns
portfolio and the risk-free asset flexible
Assumptions To control risk, less risk averse follow a multifactor process, investors simply hold more of the allowing investors to manage market portfolio and less of the , rather than
several risk factors risk-free asst. just one.
Investor’s unique circumstances may drive the investor to holdThe risk of the investor’s portfolio portfolios titled away from the
conclusions is determined solely by the market portfolio in order to resulting portfolio beta . hedge or speculate on multiple risk factors.Application ：Return Attribution
Multifactor models can help us understand in detail the sources of a manager’s returns relative to a benchmark.
Active return = R − R
p B With the help of a factor model, we can analyze a portfolio manager’s active return as the sum of two components
The first component is the product of the portfolio manager’s factor tilts (overweight or underweight relative to the benchmark factor sensitivities) and the factor returns; we call that component the return from factor tilts.
The second component of active return reflects the manager’s skill in individual asset selection (ability to overweight securities that outperform the benchmark or underweight securities that underperform the benchmark); we call that component security selection.Application ：Return Attribution
Active return=factor return + security selection return
k - factor return pk k
=factor sensitivity for the kth factor in the active portfolio
=factor sensitivity for the kth factor in the benchmark portfolio bk
=factor risk premium for factor k
Security selection: Security selection return=active return
– factor return
The security selection return is then the residual difference between active return and factor return.Application ：Risk Attribution
Definition: the standard deviation of active returns Exactly formula: 2
( R R ) Pt Bt active risk s
( ) R R P B t
Information Ratio Definition: the ratio of mean active return to active risk Purpose: a tool for evaluating mean active returns per unit of active risk Exact formula:
R R P B
(R R ) P BExample: Information ratioTo illustrate the calculation, if a portfolio achieved a mean return of 9 percent during the same period that its benchmark earned a mean return of 7.5 percent, and the portfolio's tracking risk was 6 percent, we would calculate an information ratio of (9% - 7.5%)/6% = 0.25. Setting guidelines for acceptable active risk or tracking risk is one of the ways that some institutional investors attempt to assure that the overall risk and style characteristics of their investments are in line with those desired.Application ：Risk Attribution
We can separate a portfolio's active risk squared into two components: Active factor risk is the contribution to active risk squared resulting from the portfolio's
exposures relative to factors specified in the risk model.
2 P B Active risk squared = s (R R )
Active specific risk or asset selection risk is the contribution to active risk squared resulting from the portfolio's active weights on individual assets as those weights interact with assets' residual risk. Active risk squared = Active factor risk + Active specific risk Example
Steve Martingale, CFA, is analyzing the performance of three actively managed mutual funds using a two-factor model. The results of his risk decomposition are shown below: Questions:
Active Factor Active
Specific Active Risk
Which fund assumes the highest level of active risk? Which fund assumes the highest percentage level of style? Which fund assumes the lower percentage level of active specific risk?
Squared Fund Size Factor Style Factor Total Factor Alpha
Correct Answer :
The table below shows the proportional contribution of various resources of active risk as a proportion of active risk squared.
The Gamma fund has the highest level of active risk(6.1%). Note that active risk is the square root of active risk squared(as given).
The Alpha fund has the highest exposure to style factor risk as seen by 56% of active risk being attributed to differences in style.
The Alpha fund has the lowest exposure to active specific risk(15%)as a proportion of total active risk.
Active Factor Active
Risk Fund Size Factor Style Factor Total Factor
Alpha 29% 56% 85% 15% 4.7% Beta 20% 5% 25% 75% 4.0%
Gamma 47% 0% 48% 52% 6.1%Application: Portfolio Construction
Passive management. Analysts can use multifactor models to match an index fund's factor exposures to the factor exposures of the index tracked. Active management. Many quantitative investment managers rely on multifactor models in predicting alpha (excess risk-adjusted returns) or relative return (the return on one asset or asset class relative to that of another) as part of a variety of active investment strategies.
In evaluating portfolios, analysts use multi-factor models to understand the sources of active managers' returns and assess the risks assumed relative to the manager's benchmark (comparison portfolio).
Rules-based active management (alternative indexes). These strategies routinely tilt toward factors such as size, value, quality, or momentum when constructing portfolios.Application: Portfolio Construction
The Carhart four-factor model (four factor model)
1 RMRF+ β
2 SML+ β
3 HML+ β
According to the model, there are three groups of stocks that tend to have higher returns than those predicted solely by their sensitivity to the market return:
Small-capitalization stocks: SMB=Return of Small – Return of Big Low price-to book- ratio stocks, commonly referred to as ―value‖ stocks, HML (BV/P) Stocks whose prices have been rising, commonly referred to as
―momentum‖ stocks: WML=Return of Winner – return of Loser
1. Understanding VaR
2. The Confidence IntervalsFramework
3. Analytical (variance-covariance) method
4. Historical Method
5. Monte Carlo Simulation Method
6. Extensions of VaR
7. Other Key Risk Measures
8. Applications of Risk Measures
9. Using Constraints in Market Risk ManagementUnderstanding VaR
VaR states at some probability (often 1 % or 5%) the expected loss during a specified time period. The loss can be stated as a percentage of value or as a nominal amount. VaR always has a dual interpretation.
A measure in either currency units (in this example, the euro) or in percentage terms.
A minimum loss. A statement references a time horizon: losses that would be expected to occur over a given period of time.Understanding VaR
Analysis should consider some additional issues with VaR:
The VaR time period should relate to the nature of the situation. A traditional stock and bond portfolio would likely focus on a longer monthly or quarterly VaR while a highly leveraged derivatives portfolio might focus on a shorter daily VaR.
The percentage selected will affect the VaR. A 1% VaR would be expected to show greater risk than a 5% VaR.
The left-tail should be examined. Left-tail refers to a traditional probability distribution graph of returns. The left side displays the low or negative returns, which is what VaR measures at some probability. But suppose the 5% VaR is losing $ 1.37 million, what happens at 4%, 1%, and so on? In other words, how much worse can it get?
Understanding VaR Example
Given a VaR of $12.5 million at 5% for one month, which of the following statements is correct? A. There is a 5% chance of losing $12.5 million over one month.
B. There is a 95% chance that the expected loss over the next month is less than $12.5 million.Estimating VaR
3 methods to estimate VaR:
Analytical method (variance-covariance/delta normal method) Historical method Monte Carlo methodUnderstanding VaR
The analytical method (or variance-covariance method) is based on the normal distribution and the concept of one-tailed confidence intervals. Example: Analytical VaR
The expected annual return for a $1 00,000,000 portfolio is 6.0% and the historical standard deviation is 12%. Calculate VaR at 5% significance.
A CFA candidate would know that 5% in a single tail is associated with 1.645, or approximately 1.65, standard deviations from the mean expected return. Therefore, the 5% annual VaR is:
p p VaR R z
V 6% 1.65 12% $100, 000, 000 $13,800, 000
The Confidence Intervals
68% confidence interval is
90% confidence interval is 95% confidence interval is 99% confidence interval is [ 1.65 , 1.65 ]
[ 1.96 , 1.96 ] [ 2.58 , 2.58 ] [ , ]
Probability μ μ+σ μ-σ
μ+1.96σ μ-2.58σ 68% 95% 99%
μ-1.96σ μ-2.58σFor the Exam: 5% VaR is 1.65 standard deviations below the mean
1% VaR is 2.33 standard deviations below the mean. VaR for periods less than a year are computed with return and standard deviations expressed for the desired period of time.
For monthly VaR, divide the annual return by 12 and the standard deviation by the square root of 12. Then, compute monthly VaR.
For weekly VaR, divide the annual return by 52 and the standard deviation by the square root of 52. Then, compute weekly VaR.
For a very short period (1-day) VaR can be approximated by ignoring the return component (i.e., enter the return as zero). This will make the VaR estimate worse as no return is considered, but over one day the expected return should be small.Example
The expected annual return for a $1 00,000,000 portfolio is 6.0% and the historical standard deviation is 12%. Calculate weekly VaR at 1%.
The number of standard deviations for a 1% VaR will be 2.33 below the mean return.
The weekly return will be 6%/52 = 0.1154%. The weekly standard
deviation will be 12%/52 = 1 .6641% VaR = 0.1154% -2.33(1 .6641%) = -3.7620%
Which of the following statements is not correct? A. A 1% VaR implies a downward move of 1%.
B. A one standard deviation downward move is equivalent to a 16% VaR.
C. A 5% VaR implies a move of 1.65 standard deviations less than the expected value.Analytical (variance-covariance) method
Advantages of the analytical method include: Easy to calculate and easily understood as a single number. Allows modeling the correlations of risks. Can be applied to shorter or longer time periods as relevant. Disadvantages of the analytical method include: Assumes normal distribution of returns.
Some securities have skewed returns. Variance-covariance VaR has been modified to attempt to deal with skew and options in the delta-normal method.
Many assets exhibit leptokurtosis (fat tails). The difficulty of estimating standard deviation in very large portfolios.Historical MethodAdvantages of the historical method include: Very easy to calculate and understand. Does not assume a returns distribution. Can be applied to different time periods according to industry custom. The primary disadvantage of the historical method is the assumption that the pattern of historical returns will repeat in the future (i.e., it is indicative of future returns).Example
You have accumulated 100 daily returns for your $100,000,000 portfolio. After ranking the returns from highest to lowest, you identify the lower five returns:
0.0019, -0.0025, -0.0034, -0.0096, -0.0101 Calculate daily VaR at 5% significant using the historical method.Answer:
Since these are the lowest five returns, they represent the 5% lower tail of the ―distribution‖ of 100 historical returns. The fifth lowest return (- 0.0019) is the 5% daily VaR. We should ay there is a 5% chance of a daily loss exceeding 0.19%, or $190,000.Monte Carlo Simulation Method
A computer program simulates the changes in value of the portfolio through time based on:
a model of the return-generating process; and an assumed probability distribution for each variable of interest
A Monte Carlo output specifies the expected 1-week portfolio return and standard deviation as 0.00188 and 0.0125, respectively. Calculate the 1-week value at risk at 5% significance.
VaR R ( )( ) z
V P P = 0.00188 1.65(0.0125) ($100, 000, 000)
0.018745($100, 000, 000) $1,874,500Monte Carlo Simulation Method
The primary advantage of the Monte Carlo method is also its primary disadvantage.
It can incorporate any assumptions regarding return patterns, correlations, and other factors the analyst believes are relevant. For some portfolios it may be the only reasonable approach to use. That leads to its downside: the output is only as good as the input assumptions. This complexity can lead to a false sense of overconfidence in the output among the less informed. It is data and
computer intensive which can make it costly to use in complex situations (where it may also be the only reasonable method to use).Advantages and Limitations of VaR
Advantages Simple concept. Easily communicated concept. Provides a basis for risk comparison. Facilitates capital allocation decisions. Can be used for performance evaluation. Reliability can be verified.
Widely accepted by regulators.Advantages and Limitations of VaR
Limitation Subjectivity. Underestimating the frequency of extreme events. Failure to take into account liquidity. Sensitivity to correlation risk. Vulnerability to trending or volatility regimes. Misunderstanding the meaning of VaR.
Oversimplification. Disregard of right-tail events.Extensions of VaRConditional VaR (CVaR):the average loss that would be incurred if the VaR cutoff is exceeded. CVaR is also sometimes referred to as the expected tail loss or expected shortfall. Incremental VaR (IVaR): how the portfolio VaR will change if a position size is changed relative to the remaining positions. Marginal VaR (MVaR): it is conceptually similar to incremental VaR in that it reflects the effect of an anticipated change in the portfolio, but it uses formulas derived from calculus to reflect the effect of a very small change in the position. ex ante tracking error, also known as relative VaR : a measure of the degree to which the performance of a given investment portfolio might deviate from its benchmark.Other Key Risk Measures
Sensitivity Equity Expos