CFA 2018 Level 2 Portfolio Management

(1)

Portfolio Management

Level 2 -- 2017

(2)

Topic weight:

Study Session 1-2 Ethics & Professional Standards 10 -15% Study Session 3 Quantitative Methods 5 -10%

Study Session 4 Economics 5 -10%

Study Session 5-6 Financial Reporting and Analysis 15 -20% Study Session 7-8 Corporate Finance 5 -15% Study Session 9-11 Equity Investment 15 -25% Study Session 12-13 Fixed Income 10 -20%

Study Session 14 Derivatives 5 -15%

Study Session 15 Alternative Investments 5 -10% Study Session 16-17 Portfolio Management 5 -10% Weights: 100%

(3)

Brief Introduction

Content:

Ø SS 16: Process, Asset Allocation, and Risk Management üReading 47: The Portfolio Management Process and The

Investment Policy Statement

(4)

Content:

Ø SS 17: Economic Analysis, Active Management, and Trading üReading 50: Economics and Investment Markets

üReading 51: Analysis of Active Portfolio Management

üReading 52: Algorithmic Trading and High-Frequency

Trading

(5)

考纲对比:

Ø 与2016年相比，2017年的考纲变化比较大。

ü 新增Reading 49: Measuring and Managing Market Risk；

ü 新增Reading 52: Algorithmic Trading and High-Frequency

Trading。

(6)

Brief Introduction

成功了，可以高兴但不可狂妄；

(9)

Portfolio Management Process and IPS

Tasks:

Ø

Describe

the steps of the portfolio management

process;

Ø

Explain

the role and elements of the investment

policy statement;

Ø

Define and distinguish

investment objectives and

(10)

Portfolio perspective

Ø Focus on the aggregate risk-return tradeoff of all the

investor’s holdings: the portfolio.

üIf we evaluate the prospects of each asset in isolation, we

will likely misunderstand the risk and return prospects of the investor’s total investment position-our most basic concern.

(11)

Steps of portfolio management process

Ø Planning

üIdentifying and specifying the investor’s objectives and

constraints;

üCreating the investment policy statement (IPS); üForming capital market expectations;

üCreating the strategic asset allocation.

(12)

Steps of portfolio management process (Cont.)

Ø Execution

üSpecifying the investment strategy and asset allocation;

üSpecifying the security selection;

üPortfolio constructions and revisions. Ø Feedback

üMonitoring and rebalancing; üPerformance evaluation.

(13)

Definition of IPS

Ø An IPS is a written planning document that governs all

investment decisions for the client.

Role of IPS

Ø The IPS serves as the governing document for all investment

decision-making.

(14)

Elements of IPS

Ø A brief client description;

Ø Purpose of of establishing IPS;

Ø Duties and investment responsibilities of parties involved; Ø Statement of investment goal, objectives and constraints; Ø Schedule for review of investment performance and IPS; Ø Performance measures and benchmarks to be used; Ø Considerations for strategic asset allocation;

Ø Investment strategies and investment styles; Ø Guidelines for portfolio rebalancing.

(15)

Investment objectives and constraints

üTime horizon constraints üTax constraints

üLegal and regulatory factors üUnique circumstances

(16)

Risk objectives

Ø Types of risk objective:

üAbsolute (e.g. std dev.) vs. relative (e.g. tracking risk);

üDownside risk (e.g. VaR).

Ø The risk objective limits how high the investor can set the

return objective.

(17)

Risk objectives

Ø Risk tolerance: combination of ability and willingness to

take risk:

willingness Ability

Below average Above average

Below average Below average _{risk tolerance} Resolution_needed

Above average Below average _{risk tolerance} Above average

(18)

Risk objectives

Ø Factors that affect ability to accept risk: üRequired spending needs

üLong-term wealth target üFinancial strength

üLiabilities

(19)

Investment objectives (Cont.)

Ø Return objective

üTypes of return objective:

• Nominal return vs. real return;

• Pre-tax return vs. after-tax return;

• Desired return vs. required return.

üTotal return perspective:

• Consider both income and capital gain.

üReturn objective must be consistent with risk objective.

(20)

Investment time horizons

Ø Investors may have short or long investment horizons, or

some combination of the two when multiple investment goals are identified.

Ø The longer the time horizon the more risk the investor can

take.

üInvestors may allocate a greater proportion of funds to

risky assets when they address long-term as opposed to short-term investment objectives.

(21)

Investment time horizons (Cont.)

Ø With a focus on risk, even investors with a long-term

objective may limit risk taking because of sensitivity to the possibility of substantial interim losses.

Ø The investment policy must be designed to accommodate all

time horizons in a multistage horizon case (Short-, medium-, and long-term goals).

(22)

Strategic asset allocation

Ø Combine the IPS and capital market expectations to

formulate target weightings on acceptable asset classes.

üTactical asset allocation is allowed for temporary shifts.

(23)

Strategic asset allocation (cont.)

Ø Forecasts of risk-return characteristics are required for asset

classes that are included in the investor’s portfolio so that the expected risk-return profiles is well understood;

Ø An investor with a shorter investment time horizon will

often choose a strategic asset allocation that is relatively less risky, with a smaller allocation to equities.

(24)

Ethical responsibilities of portfolio manager

Ø Ethical conduct is the foundation requirement for managing

investment portfolios.

üThe portfolio manager must keep foremost in mind that he

or she is in a position of trust, requiring ethical conduct towards the public, client, prospects, employers,

employees, and fellow workers.

(25)

Ø Importance: ☆

Ø Content:

ü Portfolio management process; ü Role and elements of IPS;

ü Investment objectives; ü Investment constraints.

Ø Exam tips:

(26)

Arbitrage Pricing Theory (APT)

Tasks:

Ø

Describe

APT, including its underlying assumptions;

Ø

Determine

whether an arbitrage opportunity exists

with APT model;

Ø

Calculate

the expected return on an asset with APT

(27)

Review: CAPM

Ø

üThe expected returns (required return) of assets vary only

by their systematic risk as measured by beta (β);

üExpected return (required return) obtained from the

CAPM is used for assets valuation by investors and capital budgeting to determine economic feasibility of projects .

i f i m f

E R =R

[

]



β [E(R -

R ]

)

Arbitrage Pricing Theory (APT)

(28)

Review: assumptions of CAPM

Ø Investors are risk averse, utility-maximizing, rational

individuals;

Ø Markets are frictionless, including no cost and no taxes; Ø Investor plan for the same single holding period;

Ø Investor have homogeneous expectations or beliefs; Ø All investments are infinitely divisible;

Ø Investors are price takers.

(29)

Arbitrage pricing model

Ø A linear model with multiple systematic risk factors.

üβ_p,j = the sensitivity of the portfolio to factor j;

üλ_j = the expected risk premium for risk factor j; or the risk

premium for a pure factor portfolio for factor j.

• A portfolio with sensitivity of 1 to factor j and sensitivity of 0 to all other factors;

• Also called factor risk premium.

P F P,1 1 P,2 2 P,k k

E(R ) = R + β (λ ) + β (λ ) +...+ β (λ )

(30)

Assumptions of APT

Ø A factor model describes asset returns;

Ø There are many assets, so investors can form well-diversified

portfolios that eliminate asset specific risk;

Ø No arbitrage opportunities exist among well-diversified

portfolios.

(31)

Arbitrage pricing model (Cont.)

Ø APT provides an expression for the expected return of asset

assuming that financial markets are in equilibrium;

Ø APT makes less assumptions than CAPM and does not

identify the specific risk factors as well as the number of risk factors.

üCAPM can be regarded as a special case of APT with only

one risk factor (market risk factor).

(32)

Example

Ø Calculate the expected return for a portfolio with following

information using the APT model. The risk free rate is 5%. Risk factor 1 Risk factor 2

Factor betas 1.8 0.9

Factor risk premiums 1.5% 2%

Answer:

Ø E(R) = 5% + 1.8*1.5% + 0.9*2% = 9%.

(33)

Arbitrage opportunity

Ø An opportunity to conduct an arbitrage: earn an expected

positive net profit without risk and with no net investment of money.

üIf two portfolios with identical risk factors and factor

sensitivities have different return, there is an arbitrage opportunity.

(34)

Example

Ø Suppose we use a one-factor APT model to evaluate assets,

and we observe the following information, identify the arbitrage opportunity.

Portfolio Expected Return Factor Sensitivity (Beta)

A 0.075 0.5

B 0.07 0.4

C 0.08 0.45

(35)

Answer:

Ø We can create a portfolio D with 50% A and 50% B:

Portfolio Expected Return Factor Sensitivity _(Beta)

A 7.5% 0.5

B 7.0% 0.4

C 8.0% 0.45

D

(0.5A+0.5B) 7.25% 0.45

(36)

Answer (Cont.):

Ø As Portfolio D (0.5A+0.5B) has the same factor sensitivity as

Portfolio C but a different expected return, then an arbitrage opportunity exists: Portfolio C is undervalued.

üBy buying Portfolio C and short-selling Portfolio D, we

expect to earn a riskless 0.75% return.

(37)

Ø Importance: ☆☆☆

Ø Content:

ü APT model and its consumptions; ü Arbitrage with APT model;

ü Asset return with APT model. Ø Exam tips:

ü _{常考点1：APT模型的consumption和interpretation；}

(38)

Multifactor Models: Introduction

Tasks:

Ø

Describe and compare

macroeconomic factor

(39)

Multifactor models

Ø Macroeconomic factor model

üRisk factors: surprises in macroeconomic variables.

• E.g.: GDP, interest rate, inflation, credit spreads, etc.

Ø Fundamental factor model

üRisk factors: attributes of stocks or companies.

• E.g.: P/B ratio, P/E ratio, earning growth rate, etc.

Ø Statistical factor model

üUse statistical methods to explain asset returns.

(40)

Macroeconomic factor models

Ø R_i = a_i + b_i1F₁ + b_i2F₂ + ... + b_iKF_K + ε_i

üR_i = the return to asset i;

üa_i= the expected return to asset i;

üF_k = the surprise in the factor k, k = 1, 2, ..., k;

• Difference between realized value and predicted value.

üb_ik = the sensitivity of the return on asset i to a surprise in

factor k, k = 1, 2, ..., k;

üε_i = an error term.

Ø Example: R_i = E(R_i) + b_i1F_INFL + b_i2F_GDP + ε_i

(41)

Fundamental factor models

Ø R_i = a_i + b_i1F₁ + b_i2F₂ + ... + b_iKF_K + ε_i üR_i = the return to asset i;

üa_i= regression intercept necessary to make the

unsystematic risk of asset equal to zero;

üF_k = return associated with the factor k, which are asset

attributes that are important in explaining cross-sectional differences in stock prices;

üb_ik = standardized beta of attributes of the asset.

ik Value of attribute k for asset i- Average _(v value of attribute k

b =

σ alues of attribute k)

(42)

Macroeconomic vs. Fundamental factor models

Ø Interpretation of factors

üMacroeconomic factor models: surprises in the

macroeconomic variables;

üFundamental factor models: return associated with asset

attributes.

Ø Interpretation of factor sensitivities

üMacroeconomic factor models: regression slope estimate;

üFundamental factor models: standardized beta.

(43)

Macroeconomic vs. Fundamental factor models (Cont.)

Ø Interpretation of intercept term

üMacroeconomic factor models: the asset’s expected return

based on market expectations (e.g. APT);

üFundamental factor models: regression intercept.

(44)

Macroeconomic vs. Fundamental factor models (Cont.)

Ø Data processing

üMacroeconomic factor models: develop the factor (surprise)

series first and then estimate the factor sensitivities through regressions;

üFundamental factor models: specify the factor sensitivities

(attributes) first and then estimate the factor returns through regressions.

(45)

Statistical factor models

Ø These models make minimal assumptions but the factors are

difficult to interpret economically, in contrast to macroeconomic models and fundamental models.

(46)

Ø Content:

ü Macroeconomic factor models; ü Fundamental factor models;

ü Statistical models. Ø Exam tips:

ü _{很总要的考点，主要考概念题，特别是}

Macroeconomic factor models和Fundamental factor

(47)

Multifactor Models: Application

Tasks:

Ø

Explain

sources of active risk and

interpret

tracking

risk and the information ratio;

Ø

Describe

uses of multifactor models and

interpret

(48)

Applications of multifactor models

Ø Performance attribution

üReturn attribution

üRisk attribution

Ø Portfolio construction

Ø Strategic portfolio decisions

(49)

Return attribution

Ø Multifactor models can be used to attribute portfolio return

to different factors.

üActive return = R_P - R_B

• RP = portfolio return

• RB = benchmark return

(50)

Return attribution (Cont.)

üActive return = Factor return + Security selection return

• Factor return: return earned by taking different factor exposures compared to the benchmark;

• Security selection return: earned by allocating different weights to securities compared to the benchmark.





β : factor sensitivity for i factor in the active portfolio;

β : factor sensitivity for i factor in the benchmark portfolio; λ : factor risk premium for factor i.

(51)

Risk attribution

Ø Active risk: the standard deviation of active returns.

Active risk = σ(Rp – RB)

• Also refers to tracking risk, or tracking error.

Ø Information ratio (IR): standardized average active return.

(52)

Risk attribution (Cont.)

Ø The active risk of a portfolio can be separated to two parts:

Active risk squared = Active factor risk + Active specific risk

üActive factor risk: the active risk resulting from the

portfolio’s different-from-benchmark factor exposures;

üActive specific risk: the active non-factor or residual risk

assumed by the manager, resulting from the portfolio’s different-from-benchmark weighting for specific securities.

• Also refers to security selection risk.

(53)

Example:

Ø Decomposition of active risk squared:

(54)

Example (Cont.):

Ø Decomposition of active risk squared (re-stated by %):

(55)

Example (Cont.):

Ø Conclusions:

üPortfolio A assumed substantial active industry risk,

whereas Portfolio B was approximately industry neutral relative to the benchmark.

üBy contrast, Portfolio B had higher active bets on the style

factors representing company and share characteristics.

(56)

Example (Cont.):

üPortfolio C assumed more active factor risk related to the

style factors, but B assumed more active specific risk. It is also possible to infer from the greater level of B’s active specific risk that B is somewhat less diversified than C.

üPortfolio D appears to be a passively managed portfolio,

judging by its negligible level of active risk. Its risk exposures very closely match the benchmark.

(57)

Portfolio construction

Ø Multifactor models permit the portfolio manager to make focused bets or to control portfolio risk relative to the benchmark’s risk.

üPassive management: selecting a sample of securities from

the index, replicating an index fund’s factor exposures, and mirroring those of the index tracked;

üActive management: predicting alpha or relative return, or

establish a specific desired risk profile for a portfolio.

(58)

Example:

Ø The following table shows the risk factors and the factor

sensitivities for the portfolios:

(59)

Example (Cont.):

Ø A portfolio manager wants to place a bet that real business

activity will increase. Which portfolio is most appropriate and what position should be chosen?

Answer: B

Ø Portfolio B is the factor portfolio for business cycle risk

because it has a sensitivity of 1 to business cycle risk and a sensitivity of 0 to all other risk factors. The manager should take a long position in Portfolio B.

(60)

Example (Cont.):

Ø A portfolio manager wants to hedge an existing positive

(long) exposure to time horizon risk. Which portfolio is most appropriate and what position should be chosen?

Answer: D

Ø Portfolio D is the factor portfolio for time horizon risk

because it has a sensitivity of 1 to time horizon risk and a sensitivity of 0 to all other risk factors. The manager should take a short position in Portfolio D.

(61)

Strategic portfolio decisions

Ø By introducing more risk factors, multifactor models enable

investor gain from taking more/less exposures to risks that they have a comparative advantage/disadvantage;

Ø By considering multiple sources of systematic risk,

multifactor models allow investors to achieve better-diversified and possibly more efficient portfolios.

LOS 48.g; Describe (☆☆)

(62)

Ø Content:

ü Applications of multifactor models:

• Return attribution and risk attribution;

• Portfolio construction;

• Strategic portfolio decisions.

Ø Exam tips:

(63)

Value at Risk (VaR)

Tasks:

Ø

Compare

the parametric, historical simulation, and

Monte Carlo simulation methods for estimating

VaR;

Ø

Describe

advantages, limitations and extension of

(64)

Value at Risk (VaR)

Ø The minimum loss that would be expected a certain

percentage of the time over a certain period of time given the assumed market conditions.

Ø Example: the 5% VaR of a portfolio is €2.2 million over a

one-day period.

üInterpretation: the minimum loss that would be expected

to occur over one day 5% of the time is $2.2 million.

(65)

Methods to estimate VaR

Ø Parametric (variance–covariance) method Ø Historical simulation method

Ø Monte Carlo simulation method

(66)

Parametric method

Ø Assumes that the return distributions for the risk factors in

the portfolio are normal;

Ø Uses the expected return and standard deviation of return

for each risk factor to estimate the VaR.

üVaR(X%) = E(R) - Z_X%×σ

üVaR(X%)_dollar= [E(R) - Z_X%×σ]×asset value

(67)

Parametric method (Cont.)

Ø Advantage:

üSimple and straightforward.

Ø Disadvantage:

üIts estimates will only be as good as the estimate of the

parameter (mean, variance, covariance).

üThe usefulness is limited when normality assumption is not

reasonable.

• E.g.: when the investment portfolio contains options.

(68)

Historical simulation method

Ø Re-prices the current portfolio given the returns that

occurred on each day of the historical lookback period and sort the results from largest loss to greatest gain.

Ø Example: you have accumulated 100 daily returns for your

$100M portfolio. After ranking the returns from highest to lowest, you identify the lowest six returns: -0.0011, -0.0019, -0.0025, -0.0034, -0.0096, -0.0101.

üVaR_daily(5%)= 0.19% or $190,000

(69)

Historical simulation method (Cont.)

Ø Advantage:

üNo normality or any other distribution assumption;

• Available to estimate the VaR for portfolio with options.

ü Based on what actually happened, so it cannot be

dismissed as introducing impossible outcomes.

(70)

Historical simulation method (Cont.)

üNo certainty that a historical event will re-occur, or that it

would occur in the same manner or with the same likelihood as represented by the historical data.

• If data in the lookback period is more volatile, VaR will be

over-estimate;

• If data in the lookback period is less volatile, VaR will be

under-estimate.

(71)

Value at Risk (Cont.)

Ø Both parametric and historical simulation methods has a

shortage that all observations are weighted equally.

üImprovement: giving more weight to more recent

observations and less weight to more distant observations.

(72)

Monte Carlo simulation method (Cont.)

Ø The user develops his own assumptions about the statistical

characteristics of the distribution and uses those

characteristics to generate random outcomes that represent hypothetical returns to a portfolio.

(73)

Monte Carlo simulation method (Cont.)

Ø Advantage:

üIt can accommodate virtually any distribution, and can

accurately incorporating the effects of option positions or bond positions with embedded options.

üComplex

üAssumptions of inputs are critical for accuracy of estimates.

(74)

Advantages of VaR

Ø Simple concept

Ø Easily communicated concept

Ø Provides a basis for risk comparison Ø Facilitates capital allocation decisions

Ø Can be used for performance evaluation

Ø Reliability can be verified

Ø Widely accepted by regulators

(75)

Limitations of VaR

Ø Subjectivity

Ø Underestimating the frequency of extreme events

Ø Failure to take into account liquidity Ø Sensitivity to correlation risk

Ø Vulnerability to trending or volatility regimes

Ø Misunderstanding the meaning of VaR Ø Oversimplification

Ø Disregard of right-tail events

(76)

Extensions of VaR

Ø Conditional VaR (CVaR): the average loss that would be

incurred if the VaR cutoff is exceeded.

üAlso named expected tail loss or expected shortfall.

Ø Incremental VaR (IVaR): the difference in VaR between the

“before” and “after” VaR if a position size is changed relative to the remaining positions.

(77)

Extensions of VaR (Cont.)

Ø Marginal VaR (MVaR): the change in VaR for a small change

in a given portfolio holding.

ü Strictly, MVaR is the slope of VaR-weight curve for a

security in the portfolio;

ü Approximately, MVaR is the change in VaR for a $1 or 1%

change in the position for a security in the portfolio.

(78)

Extensions of VaR (Cont.)

Ø Relative VaR: a measure of the degree to which the

performance of a given investment portfolio might deviate from its benchmark.

üAlso named ex ante tracking error.

(79)

Ø Content:

ü Definition and interpretation of VaR; ü Method to estimate VaR:

• Parametric method; historical simulation method, Monte Carlo simulation method.

ü Advantages, limitations, and extensions of VaR. Ø Exam tips:

(80)

Sensitivity and Scenario Risk Measures

Tasks:

Ø

Describe

sensitivity risk measures and scenario risk

measures;

Ø

Describe

advantages and limitations of sensitivity

risk measures and scenario risk measures;

(81)

Sensitivity risk measures

Ø Examine how portfolio value responds to a small change in a single risk factor.

Scenario risk measures

Ø Provides an estimate of the impact on portfolio value of a

set of significant change in multiple risk factors.

(82)

Sensitivity risk measures

Ø Equity exposure measures: Beta (β)

CAPM: E(Ri) = RF + βi[E(RM) – RF]

üAssets with betas more (less) than 1 are considered more

(less) volatile than the market as a whole.

(83)

Sensitivity risk measures (Cont.)

Ø Fixed-income exposure measures: duration and convexity. üGiven a bond priced at P and yield change of ΔY, the rate of

return or percentage price change for the bond is approximately given as follows:

 

2

ΔP_{= -Duration ΔY + Convexity ΔY}1

P  2  

(84)

Sensitivity risk measures (Cont.)

Ø Options risk measures: Delta (Δ), Gamma (Γ), Vega (Λ), etc. üDelta: sensitivity of option price against the underlying

asset price;

üGamma: sensitivity of option delta against the underlying

asset price;

üVega: sensitivity of option price against underlying asset

price volatility.

(85)

Sensitivity risk measures (Cont.)

Ø Advantage: can inform a portfolio manager about a

portfolio’s exposure to various risk factors to facilitate risk management.

üIf too much/less risk exposure to a risk factor, the manager

can modify the exposure accordingly.

(86)

Sensitivity risk measures (Cont.)

Ø Limitations:

üCan only be used to estimate the effects of small changes

in risk factors.

• Even combination of first-order and second-order effects only provide approximation for large changes in risk

factors.

üTwo portfolios with same sensitivity risk measures can have

different risk due to different volatility of risk factors.

• E.g.: two fixed income portfolios with same duration but different yield volatilities.

(87)

Scenario risk measures

Ø Historical scenario approach: use a set of changes in risk

factors that have actually occurred in the past.

üE.g.: change of risk factors in financial crisis.

Ø Hypothetical scenario approach: use a set of hypothetical

change in risk factors, not just those that have happened in the past.

üStress tests: examine the impact on portfolio of a scenario

of extreme changes of risk factors.

(88)

Scenario risk measures (Cont.)

Ø Scenario analysis can be regarded as the final step in the risk

management process, after performing sensitivity analysis.

üScenario analysis can provide additional information on a

portfolio's vulnerability to changes of risk factors or the correlations between risk factors.

üStress tests can determine the size of change on a certain

risk factor that could compromise the sustainability of the investment.

(89)

Scenario risk measures (Cont.)

Ø Advantage:

üScenario risk measures focus on extreme outcomes, but

not bound by either recent historical events or

assumptions about parameters or probability distributions.

üScenario analysis is an open-ended exercise that could look

at positive or negative events, although its most common application is to assess the negative outcomes.

• Stress tests intentionally focus on extreme negative events.

(90)

Scenario risk measures (Cont.)

Ø Limitations:

ü Historical scenarios are not going to happen in exactly the

same way again; and hypothetical scenarios may incorrectly specify how assets will co-move.

üHypothetical scenarios are difficult to create and maintain.

• It is very difficult to know how to establish the

appropriate limits on a scenario analysis or stress test.

(91)

Scenario risk measures (Cont.)

Ø Limitations:

üThe more extreme the scenario, and the farther from

historical experience, the less likely it is to be found believable by management of a company or a portfolio.

(92)

VaR vs. Sensitivity vs. Scenario risk measures

Ø VaR provides a probability of loss, and is a downside risk

measures;

Ø Sensitivity risk measures provide estimates of relative

exposure to different risk factors but no estimate of probabilities, and are not downside risk measures;

Ø Scenario risk measures provide estimates of effect to

simultaneous changes of multiple risk factors, but no estimate of probability.

(93)

VaR vs. Sensitivity vs. Scenario risk measures

Ø They are best used in combination because no one measure

has the answer, but all provide valuable information that can help risk managers understand the portfolio and avoid

unwanted outcomes and surprises.

(94)

Choices of risk measures

Ø The choices of risk measures by an organization is mainly

decided by the types of risks it faces, the regulation that govern it, and whether it uses leverage.

üBanks

üAsset managers üPension funds üinsurers

(95)

Banks

Ø Banks need to balance a number of competing aspects of

risk to manage their business and meet the expectations of equity investors/analysts, bond investors, credit rating

agencies, depositors, and regulatory entities.

Ø The typical risk measures used by banks: üSensitivity measures;

üScenario analysis and stress tests; üLeverage risk measures;

üVaR .

(96)

Asset managers

Ø Traditional asset managers: focus on relative risk measures. üPosition limits, sensitivity measures, scenario analysis,

active share, VaR.

Ø Hedge funds managers: focus on absolute return.

üSensitivity measures, leverage, VaR, scenario analysis,

drawdown.

(97)

Pension funds

Ø The risk management goal for defined benefit pension funds

is to be sufficiently funded to make future payments to pensioners.

Ø The typical risk measures used by pension funds:

üSensitivity measures, surplus at risk.

(98)

Risk measures and capital allocation

Ø Capital allocation: the practice of allocating capital to fund

its various business units or activities, ensure sufficient

resource in areas in which it expects the greatest reward and has the greatest expertise.

Ø Risk measures must be introduced when limit the overall risk and allocate risk across the activities or business units by

risk budgeting.

(99)

Constraints in market risk management

Ø Risk budgeting: determining the overall risk appetite, and

then allocated to sub-activities or business units.

Ø Position limits: the maximum currency amount or

percentage of portfolio value allowed for specific asset or asset class.

Ø Scenario limits: limits on expected loss for a given scenario. Ø Stop-loss limits: require an investment position to be

reduced or closed out when losses exceed a given amount over a specified time period.

LOS 49.k; Explain (☆)

(100)

Ø Content:

ü Sensitivity risk measures vs. scenario risk measures; ü Advantages and limitations of the risk measures;

ü Choice of risk measures;

ü Constraints in market risk management.

Ø Exam tips:

(101)

Economics and Investment Markets (1)

Tasks:

Ø

Explain

the notion that to affect market values;

Ø

Explain

the role of expectations in market valuation;

Ø

Explain

the relationship between the long-term

growth rate and the real short-term interest rates;

(102)

Present value model (DCF model)

Ø The value of any asset can be calculated as the present value

of its expected cash flows.

ür: the discount rate

r = R + π + RP

• R: real risk-free rate;

• π: expected inflation;

• RP: risk premium.

Economics and Investment Markets (1)

(103)

Present value model (Cont.)

Ø If a economic factor affects an asset’s market value, it must

affect one or more of the following:

üThe timing and/or amount of the expected cash flows;

üOne or more of the discount rate components: default-free

interest rate, expected inflation, and risk premiums.

• Risk premiums are not only determined by the risk magnitude, but also the investor’s perception of risk.

(104)

Role of expectation

Ø Asset values depend on the expectation of future cash flows,

which is based on current information that may be relevant to forecasting future cash flows.

Ø Asset values may need to be adjusted due to the fact that

the unanticipated information arise, as the current asset values only reflect the expected information.

(105)

Inter-temporal rate of substitution (ITRS)

Ø The ratio of the marginal utility of consuming 1 unit in the

future (Ut) to the marginal utility of consuming 1 unit today

(U0), denoted by mt.

üm_t is always less than 1 because investor always prefer

current consumption over future consumption (U0 > Ut).

(106)

Real risk free rate

Ø Assuming a zero coupon, inflation-indexed, risk-free bond

with par value of $1, its price should be: P0 = mt

Ø So, the real risk-free rate (unannualized) is:

üThe higher the U₀ relative to U_t, the lower the m_t, the

(107)

GDP growth vs. real risk free rate

Ø Real risk free rate is positively related to GDP growth rate; üHigher GDP growth rate → higher future income → lower

Ut relative to U0 (diminishing marginal utility of wealth) →

lower mt → higher real risk free rate.

• E.g.: China, India.

Ø Real risk free rate is also positively with the volatility of the

growth rate due to higher “risk premium”.

(108)

Inflation vs. nominal risk-free interest rate (r)

Ø In terms of nominal risk-free interest rate, the effects of

inflation should be considered:

üPremium for expected inflation (π);

üRisk premium for uncertainty about actual inflation (θ). Ø The uncertainty for short-term inflation is negligible:

rshort-term = R + π

Ø For long term securities, risk premium for uncertainty of

inflation need to be included: rlong-term = R + π + θ

(109)

Inflation vs. nominal risk-free interest rate (Cont.)

Ø Break-even inflation rate (BEI): the yield difference between

a non-indexed risk-free bond and the inflation-indexed risk-free bond with the same maturity;

üThe BEI captures the effects of inflation on yield:

BEI = π + θ

(110)

Business cycle vs. policy rate

Ø Central banks can mitigate the business cycle by adjusting

the policy rate, the Taylor Rule addresses the central bank’s policy rate to business cycle.

r = R

n

+

π

+ 0.5(

π

–

π

*

) + 0.5(Y-Y

*

)

ü

r: central bank policy rate implied by the Taylor Rule;

ü

R

_n

: neutral real policy interest rate;

ü

π

: current inflation rate;

π

*

: target inflation rate;

üY: log of actual real GDP; Y*_{: log of target real GDP.}

(111)

Ø Content:

ü Market valuation and discount rate;

ü Inter-temporal rate of substitution and real risk free rate;

ü GDP growth vs. real risk free rate;

ü Inflation vs. nominal risk-free interest rate;

ü Business cycle vs. policy rate.

Ø Exam tips:

(112)

Economics and Investment Markets (2)

Tasks:

Ø

Explain

how business cycle affects the slope of the

term structure of interest rates, and asset’s market

valuation;

Ø

Describe

the factors that affect yield spreads,

(113)

Business cycle vs. slope of yield curve

Ø During the recession, the slope of yield curve will increase; üCentral bank tends to lower the policy rate;

üInvestors expect higher future GDP growth and higher

long-term rates as economic growth recovers.

Ø During the recession, short-term bonds generally perform

better than long-term bonds.

(114)

Business cycle vs. slope of yield curve (Cont.)

Ø Later stages of expansion often have negatively sloped

(inverted) yield curve.

üTypically, high inflation and high short-term interest rate; üLow long-term rates due to expectations of decreasing

inflation and GDP growth.

Ø During the expansion, long-term bonds generally perform

better than short-term bonds.

(115)

Business cycle vs. credit spreads

Ø Credit spreads: the yield difference between a credit risky

bond and a default-free bond with same maturity. Yield for credit risky bond = R + π + θ + γ

üγ: credit spread, or risk premium for credit risk.

(116)

Business cycle vs. credit spreads (Cont.)

Ø Credit spreads tends to narrow in times of robust economic growth, when defaults are less common.

üCredit risky (lower-rated) bonds will perform better than

default-free (higher-rated) bonds.

Ø Credit spreads tend to rise in times of economic weakness,

as the probability of default rises.

üDefault-free (higher-rated) bonds will perform better than

credit risky (lower-rated) bonds.

(117)

Characteristics of market vs. credit quality

Ø During economic downturn, the spread on the consumer

cyclical sector rises more dramatically than it do for corporate bonds in the consumer non-cyclical sector.

Ø Issuers that are profitable, have low debt interest payments,

and that are not heavily reliant on debt financing will tend to have a high credit rating.

(118)

Business cycle vs. earning growth expectations

Ø Booming economy tends to lead to a rise of the earning

growth expectations; recession tends to lead to a decline of the earning growth expectations.

Ø Earning growth rate tend to be relatively stable throughout

the business cycle for defensive or non-cyclical industries.

(119)

Business cycle vs. equity risk premium

Ø The equity risk premium is typically higher than credit risk

premium because equity is more risky than debt. Yield for equity = R + π + θ + λ

üλ: equity risk premium (λ > γ).

Ø Consumption-hedging property: providing higher payoff

during economic downturns.

üAssets with more consumption-hedging property will be

more highly valued and have less risk premium.

(120)

Business cycle vs. equity risk premium (Cont.)

Ø Investors will demand a higher equity risk premium because

the consumption-hedging properties of equities are poor.

üEquities tend not to pay off in bad times.

(121)

Business cycle vs. valuation multiples

Ø Valuation multiples are positively related to expected

earning growth rate, and negatively related to required rate of return.

Required rate of return = R + π + θ + λ

Ø Valuation multiples tend to rise during periods of economic

expansion and fall during recessions.

(122)

Business cycle vs. style strategy

Ø Value strategy vs. growth strategy

üA value strategy performs well during recession, while

growth strategy performs well during expansion.

Ø Capitalization

üSmall-cap stocks tend to underperform large-cap stocks in

difficult economic conditions.

• Less diversified business(earning streams);

• More difficulties in raising funds;

• Higher risk premium demanded by investors relative to large-cap stock due to higher volatility.

(123)

Business cycle vs. rotation strategies

Ø During economic expansion:

üRotating into growth stocks when they are expected to

outperform value stocks;

üRotating into small-cap stocks when they are expected to

outperform large-cap stocks;

üRotating into cyclical stocks when they are expected to

outperform countercyclical stocks.

(124)

Business cycle vs. commercial real estate investment

Ø Commercial real estate investment have the following

characteristics:

üBond-like characteristics: steady rental income stream, like

cash flows of bonds;

üEquity-like characteristics: uncertain value of the property

at the end of the lease term;

üIlliquidity.

Ø Yield for commercial real estate = R + π + θ + λ + φ üφ: risk premium for illiquidity.

(125)

Business cycle vs. commercial real estate investment

Ø Investors will demand a high risk premium for commercial

real estate investment due to weak consumption-hedging properties.

üCommercial property value tend to decline in bad times.

(126)

Ø Content:

ü Business cycle vs. slope of yield curve; ü Business cycle vs. credit spreads;

ü Business cycle vs. equity risk premium; ü Business cycle vs. investment style;

ü Business cycle vs. commercial real estate investment.

Ø Exam tips:

(127)

Value Added by Active Management

Tasks:

Ø

Describe

how value added by active management

is measured;

Ø

Calculate and interpret

the information ratio and

(128)

Measures of value added

Ø Active return

üR_P: return of actively managed portfolio; üR_B: return of benchmark portfolio;

üR_i: return of security i;

üΔw_i = w_P,i – w_B,i, active weights;

• Sum of active weights for all securities equal to zero;

• Over-weighted: positive; under-weighted: negative.

üR_A,i = R_i – R_B, active security return.

N N

A P B i i i A,i i=1 i=1

R = R - R =



Δw R =



Δw R

(129)

Measures of value added (Cont.)

Ø Ex-anti active return: based on expected return;

Ø Ex-post active return: based on realized return.

(130)

Measures of value added (Cont.)

Ø For portfolio with multiple asset classes, active return can

be decomposed to two sources:

üActive asset allocation: active weights of asset classes

against benchmark portfolio;

üSecurity selection: active weights of security within asset

classes.

(131)

Review: sharp ratio (SR)

Ø Sharp ratio measure the total risk-adjusted value added, and

calculated as excess return per unit of risk.

üSharp ratio is unaffected by the addition of cash or leverage

because excess return and risk will change proportionally.

p f P

R - R SR =

σ

(132)

Information ratio (IR)

Ø Information ratio measure the relative risk-adjusted value

added, and calculated as mean active returns per unit of active risk.

üEx-anti IR: based on expected return;

üEx-post IR: based on realized return.

• Can be used for performance evaluation: the higher, the better.

(133)

Sharp ratio Information ratio

Total risk-adjusted value added Relative risk-adjusted value _added

Unaffected by the addition of

cash or use of leverage Affectedcash or use of leverage by the addition of

Affected by the aggressive

active weight Unaffectedactive weight by the aggressive Two ratios would be equal if the benchmark is risk-free asset

Sharp ratio vs. information ratio

(134)

Information ratio (IR)

Ø Information ratio can be used for investment manager

selection:

üManager with higher IR is preferred; üHigher IR also means higher SR.

Ø Information ratio can also be used to determine the

expected active return for a given target level of active risk. E(RA) = IR * σA

(135)

Ø Importance: ☆☆

Ø Content:

ü Definition of active return;

ü Sharp ratio vs. information ratio.

Ø Exam tips:

(136)

The Fundamental Law

Tasks:

Ø

State and interpret

the fundamental law of active

portfolio management;

Ø

Describe

the practical strengths and limitations of

(137)

The fundamental law of active management

Ø The fundamental law is a framework for thinking about the

potential value added through active portfolio management;

üThe most common use is the description and evaluation of

active management strategies.

Ø The law itself is a mathematical relationship that relates the

expected information ratio of an actively managed portfolio to a few key parameters.

(138)

The fundamental law of active management (Cont.)

Ø The correlation triangle

(139)

The fundamental law of active management (Cont.)

Ø Realized value added is the sum of the products of active

weights and realized active returns.

üThe value of this sum is ultimately a function of the

correlation coefficient between the active weights, Δwi,

and realized active returns, RA,i. (base of the triangle)

üThe correlation can be examined by the correlations on the

two vertical legs:

• Information coefficient (IC);

• Transfer coefficient (TC).

(140)

Information coefficient (IC)

Ø Correlation between the forecasted active returns, μ_i, and

the realized active returns, RA,i;

üA measure of manager’s forecasting accuracy (also called

signal quality).

• Ex-ante IC: must be positive;

• Ex-post IC: either positive or negative.

(141)

Transfer coefficient (TC)

Ø Correlation between the forecasted active returns, μ_i, and

(142)

Transfer coefficient (Cont.)

Ø Measures the degree to which the investor’s forecasts are translated into active weights, or the extent to which constraints reduce the expected value added of the investor’s forecasting ability.

üFor portfolios without any constraints, TC equals to 1;

üFor portfolios with constraints, TC < 1.

(143)

Breadth (BR)

Ø The number of independent active decisions make per year

by the investor in constructing the portfolio.

ü“Independent” in this context means that the active

decisions should not be based on highly correlated (or identical) information sets;

üA measure of how much efforts the manager has put into. Ø E.g.: if a manager takes active position in 10 securities per

month, then BR = 10*12 =120.

(144)

The fundamental law of active management (cont.)

Ø For actively managed portfolios, the full fundamental law is

expressed in the following equation:

üFor portfolio without any constraints, TC = 1.

A A

IR = (TC)(IC) BR E(R ) = (TC)(IC) BRσ

A A

IR = (IC) BR E(R ) = (IC) BRσ

(145)

Market timing

Ø Market timing: simply bets on the market direction; Ø Information coefficient for market timing:

IC = 2*(%correct) - 1

üIf the manager is correct 50% of the time, IC = 0.

üThis formula is also applicable to evaluate IC of active

sector rotation strategies.

(146)

Limitations of the fundamental law

Ø Limitation: poor input estimates lead to incorrect evaluation. üUncertainty in ex-ante measurement of skill.

• IC is difficult to justify due to existence of the bias, various asset segments, or different time periods.

üAssumption of independence of active decisions.

• The number of individual assets is not an adequate

measure of strategy breadth (BR) when the active returns between individual assets are correlated.

(147)

Ø Content:

ü The fundamental law of active management:

• Information coefficient (IC);

• Transfer coefficient (TC);

• Breadth (BR).

ü Limitations of the fundamental law.

Ø Exam tips:

(148)

Algorithmic Trading and High-Frequency Trading

Tasks:

Ø

Distinguish

between execution algorithms and

high-frequency trading algorithms;

(149)

Definition of algorithmic trading

Ø Algorithmic trading is “using a computer to automate a

trading strategy.”

ü In almost all cases, algorithms encode what traders can do

but with far higher speed.

(150)

Categories of trading algorithms

Ø Execution algorithms: break down large orders and execute

them over a period of time.

üThe goal is to minimize the impact that a large order has in

the market and to achieve a benchmarked price.

(151)

Categories of trading algorithms (Cont.)

Ø High-frequency trading (HFT) algorithms: refers to the

tracking of high-frequency streams of data, making decisions based on patterns in those data that indicate possible

trading opportunities, and automatically placing and managing orders to capitalize on those opportunities.

üThe goal is to earn profit.

(152)

Execution algorithms vs. HFT algorithms

Ø Execution algorithms

üHow to trade;

üThe goal is to minimize market impact and try to ensure a

fair price.

Ø High-frequency trading (HFT) algorithms:

üHow to trade; when to trade; and even what to trade. üThe goal is to earn profit.

(153)

Types of execution algorithms

Ø Volume-weighted average price (VWAP):

üUses the historical trading volume distribution for a

particular security over the course of a day and divides the order into slices, proportioned to this distribution.

Ø Implementation shortfall:

üDynamically adjusts the schedule of the trade in response

to market conditions to minimize the difference between the price at which the buy or sell decision was made and final execution price.

(154)

Types of execution algorithms (Cont.)

Ø Market participation algorithms:

üSlices the order into segments intended to participate on a

pro-rata basis with volume throughout the course of the execution period.

(155)

Types of HFT algorithms

Ø Statistical arbitrage

üPairs trading

üIndex arbitrage üBasket trading

üSpread trading

üMean reversion

üDelta neutral strategies

(156)

Types of HFT algorithms (Cont.)

Ø Liquidity aggregation and smart order routing Ø Real-time pricing of instruments

Ø Trading on news Ø Genetic tuning

(157)

Trading algorithms for market fragmentation

Ø Market fragmentation refers to that the same security is

traded in multiple financial markets, this phenomenon

creates the potential for price and liquidity disparities across different markets.

Ø Algorithmic methods can be used to address this issue, such

as liquidity aggregators and smart order routing.

(158)

Trading algorithms for market fragmentation (Cont.)

Ø Liquidity aggregators offer a global-ordered view of liquidity

for each instrument regardless of which trading market offers the liquidity.

Ø Smart order routing sends the orders to the relevant

markets with the best combination of liquidity and price.

(159)

Trading algorithms for risk management

Ø Real-time pre-trade risk firewall:

üContinuously calculate risk exposures on the trades to

ensure that risk limits are not exceeded.

üTrades exceeding limits are blocked.

Ø Back testing and market simulation:

üTesting algorithms to see how they perform under various

scenarios, including historical data and invented scenarios.

(160)

Trading algorithms for regulatory oversight

Ø Regulators around the world have recognized that real-time

market monitoring and surveillance allows rapid action to prevent or minimize any market impact.

Ø Suspicious trading includes: üInsider trading

üFront running üPainting the tape üFictitious orders üWash trading üTrader collusion

(161)

Positive impact of algorithmic trading

Ø Minimized market impact of large trades Ø Lower cost of execution

Ø Improved efficiency in certain markets

Ø More open and competitive trading markets

Ø Improved and more efficient trading venues

(162)

Negative impact of algorithmic trading

Ø Fear of an unfair advantage

Ø Acceleration and accentuation of market movements

Ø Gaming the market Ø Increased risk profile

Ø Algorithms gone wild

Ø Potential for market denial-of-service-style attacks Ø Additional load on trading venues

Ø Increased difficulty of policing the market

(163)

Ø Content:

ü Definition and categories of algorithmic trading; ü Applications of algorithmic trading;

ü Positive and negative impact of algorithmic trading. Ø Exam tips: