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Portfolio Management Level 2 – 2019 Instructor: Feng
1

Brief Introduction
Topic weights:
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
10 -15%
Study Session 7-8
Corporate Finance
5 -10%
Study Session 9-11
Equity Investment
10 -15%
Study Session 12-13
Fixed Income
10 -15%
Study Session 14
Derivatives
5 -15%
Study Session 15
Alternative Investments
5 -10%
Study Session 16-17
Portfolio Management
5 -15%
Weights: 100%
2

Brief Introduction
Contents:
➢ SS 16: Process, Asset Allocation, and Risk Management
✓Reading 46: The Portfolio Management Process and The Investment Policy Statement (☆)
✓Reading 47: An Introduction to Multifactor Models (☆☆☆) ✓Reading 48: Measuring and Managing Market Risk (☆☆☆)
3

Brief Introduction
Contents:
➢ SS 17: Economic Analysis, Active Management, and Trading
✓Reading 49: Economics and Investment Markets (☆) ✓Reading 50: Analysis of Active Portfolio Management
(☆☆☆)
✓Reading 51: Algorithmic Trading and High-Frequency
Trading (☆)
4

Brief Introduction
考纲对比:
➢ 与2018年相比,2019年的考纲没有变化。但权重从
5%~10% 提高到 5%~15%。
5

Brief Introduction
Level I vs. Level II:
➢ 初看关系不大,但跟Level I 的逻辑框架基本一致,还是 沿着组合管理的几个基本步骤,在一级的基础上进行了 更加深度的学习。
6

Brief Introduction
学习建议:
➢ 本门课程难度不大,但知识点比较杂,概念比较多; ➢ 章节之间比较独立,可以对重点章节重点学习;
➢ 适当做题,不需要刷题;
➢ 最重要的,认真、仔细的听课。
7

Brief Introduction
成功了,可以高兴但不可狂妄;
失败了,可以悲伤但无需绝望!
8

The Portfolio Management Process and The Investment Policy Statement
Portfolio Management Process and IPS
Tasks:
➢ Describe the steps of the portfolio management process;
➢ Explain the role and elements of the investment policy statement;
➢ Define and distinguish investment objectives and constraints.
9

Portfolio Management Process and IPS
Portfolio perspective
➢ Focus on the aggregate risk-return tradeoff of all the investor’s holdings: the portfolio.
✓If 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.
10

Portfolio Management Process and IPS
Steps of portfolio management process ➢ Planning
✓Identifying and specifying the investor’s objectives and constraints;
✓Creating the investment policy statement (IPS); ✓Forming capital market expectations; ✓Creating the strategic asset allocation.
11

Portfolio Management Process and IPS
Steps of portfolio management process (Cont.) ➢ Execution
✓Specifying the investment strategy and asset allocation; ✓Specifying the security selection;
✓Portfolio constructions and revisions.
➢ Feedback
✓Monitoring and rebalancing; ✓Performance evaluation.
12

Portfolio Management Process and IPS
Definition of IPS
➢ An IPS is a written planning document that governs all
investment decisions for the client.
Role of IPS
➢ The IPS serves as the governing document for all investment decision-making.
13

Portfolio Management Process and IPS
Elements of IPS
➢ A brief client description;
➢ Purpose of of establishing IPS;
➢ Duties and investment responsibilities of parties involved; ➢ Statement of investment goal, objectives and constraints; ➢ Schedule for review of investment performance and IPS; ➢ Performance measures and benchmarks to be used;
➢ Considerations for strategic asset allocation;
➢ Investment strategies and investment styles;
➢ Guidelines for portfolio rebalancing.
14

Portfolio Management Process and IPS
Investment objectives and constraints ➢ Investment objectives
✓Risk objective
✓Return objective
➢ Investment constraints
✓Liquidity constraints ✓Time horizon constraints ✓Tax constraints
✓Legal and regulatory factors ✓Unique circumstances
15

Portfolio Management Process and IPS
Risk objectives
➢ Types of risk objective:
✓Absolute (e.g. std dev.) vs. relative (e.g. tracking risk); ✓Downside risk (e.g. VaR).
➢ The risk objective limits how high the investor can set the return objective.
16

Portfolio Management Process and IPS
Risk objectives
➢ 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
17

Portfolio Management Process and IPS
Risk objectives
➢ Factors that affect ability to accept risk:
✓Required spending needs ✓Long-term wealth target ✓Financial strength ✓Liabilities
18

Portfolio Management Process and IPS
Investment objectives (Cont.) ➢ Return objective
✓Types of return objective:
• Nominal return vs. real return;
• Pre-tax return vs. after-tax return; • Desired return vs. required return.
✓Total return perspective:
• Consider both income and capital gain.
✓Return objective must be consistent with risk objective.
19

Portfolio Management Process and IPS
Investment time horizons
➢ Investors may have short or long investment horizons, or some combination of the two when multiple investment goals are identified.
➢ The longer the time horizon the more risk the investor can take.
✓Investors may allocate a greater proportion of funds to risky assets when they address long-term as opposed to short-term investment objectives.
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Portfolio Management Process and IPS
Investment time horizons (Cont.)
➢ 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.
➢ The investment policy must be designed to accommodate all time horizons in a multistage horizon case (Short-, medium-, and long-term goals).
21

Portfolio Management Process and IPS
Strategic asset allocation
➢ Combine the IPS and capital market expectations to formulate target weightings on acceptable asset classes.
✓Tactical asset allocation is allowed for temporary shifts.
22

Portfolio Management Process and IPS
Strategic asset allocation (cont.)
➢ 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;
➢ 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.
23

Portfolio Management Process and IPS
Ethical responsibilities of portfolio manager
➢ Ethical conduct is the foundation requirement for managing
investment portfolios.
✓The 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.
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Summary
➢ Importance: ☆ ➢ Content:
✓ Portfolio management process; ✓ Role and elements of IPS;
✓ Investment objectives;
✓ Investment constraints.
➢ Exam tips:
✓ 不是考试重点。
25

An Introduction to Multifactor Models
Arbitrage Pricing Theory (APT)
Tasks:
➢ Describe APT, including its underlying assumptions; ➢ Determine whether an arbitrage opportunity exists
with APT model;
➢ Calculate the expected return on an asset with APT
model.
26

Arbitrage Pricing Theory (APT)
Review: CAPM
➢E[Ri]=Rf +βi[E(Rm-Rf)]
✓The expected returns (required return) of assets vary only
by their systematic risk as measured by beta (β); ✓Expected return (required return) obtained from the
CAPM is used for assets valuation by investors and capital budgeting to determine economic feasibility of projects .
27

Arbitrage Pricing Theory
Review: assumptions of CAPM
➢ Investors are risk averse, utility-maximizing, rational individuals;
➢ Markets are frictionless, including no cost and no taxes;
➢ Investor plan for the same single holding period;
➢ Investor have homogeneous expectations or beliefs;
➢ All investments are infinitely divisible;
➢ Investors are price takers.
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Arbitrage Pricing Theory
Arbitrage pricing model
➢ A linear model with multiple systematic risk factors. E(RP)=RF +βP,1(λ1)+βP,2(λ2)+…+βP,k(λk)
✓βp,j = the sensitivity of the portfolio to factor j;
✓λj = the expected risk premium for risk factor j; or the risk
premium for a pure factor portfolio for factor j.
• Pure factor portfolio: a portfolio with sensitivity of 1 to
factor j and sensitivity of 0 to all other factors; • Also called factor risk premium.
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Arbitrage Pricing Theory
Assumptions of APT
➢ 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.
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Arbitrage Pricing Theory
Arbitrage pricing model (Cont.)
➢ APT provides an expression for the expected return of asset assuming that financial markets are in equilibrium;
➢ APT makes less assumptions than CAPM and does not identify the specific risk factors as well as the number of risk factors.
✓CAPM can be regarded as a special case of APT with only one risk factor (market risk factor).
31

Arbitrage Pricing Theory
Example
➢ 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:
➢ E® = 5% + 1.81.5% + 0.92% = 9%.
32

Arbitrage Pricing Theory
Arbitrage opportunity
➢ An opportunity to conduct an arbitrage: earn an expected positive net profit without risk and with no net investment of money.
✓If two portfolios with identical risk factors and factor sensitivities have different return, there is an arbitrage opportunity.
33

Arbitrage Pricing Theory
Example
➢ 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
34

Arbitrage Pricing Theory
Answer:
➢ 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
35

Arbitrage Pricing Theory
Answer (Cont.):
➢ 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.
✓By buying Portfolio C and short-selling Portfolio D, we expect to earn a riskless 0.75% return.
36

Summary
➢ Importance: ☆☆☆ ➢ Content:
✓ APT model and its assumptions; ✓ Arbitrage with APT model;
✓ Asset return with APT model.
➢ Exam tips:
✓ 常考点1:APT模型的assumption和interpretation; ✓ 常考点2:根据APT模型算资产回报。
37

An Introduction to Multifactor Models
Multifactor Models: Introduction
Tasks:
➢ Describe and compare macroeconomic factor models, fundamental factor models, and statistical factor models.
38

Multifactor Models: Introduction
Multifactor models
➢ Macroeconomic factor model
✓Risk factors: surprises in macroeconomic variables.
• E.g.: GDP, interest rate, inflation, credit spreads, etc.
➢ Fundamental factor model
✓Risk factors: attributes of stocks or companies.
• E.g.: P/B ratio, P/E ratio, earning growth rate, etc. ➢ Statistical factor model
✓Use statistical methods to explain asset returns.
39

Multifactor Models: Introduction
Macroeconomic factor models
➢ Ri = ai + bi1F1 + bi2F2 + … + biKFK + εi
✓Ri = the return to asset i;
✓ai = the expected return to asset i;
✓Fk = the surprise in the factor k, k = 1, 2, …, k;
• Difference between realized value and predicted value. ✓bik = the sensitivity of the return on asset i to a surprise in
factor k, k = 1, 2, …, k; ✓εi = an error term.
➢ Example: Ri = E(Ri) + bi1FINFL + bi2FGDP + εi
40

Multifactor Models: Introduction
Fundamental factor models
➢ Ri = ai + bi1F1 + bi2F2 + … + biKFK + εi
✓Ri = the return to asset i;
✓ai = regression intercept necessary to make the
unsystematic risk of asset equal to zero;
✓Fk = return associated with the factor k, which are asset
attributes that are important in explaining cross-sectional
differences in stock prices;
✓bik = standardized beta of attributes of the asset.
bik = Value of attribute k for asset i- Average value of attribute k σ(values of attribute k)
41

Multifactor Models: Introduction
Macroeconomic vs. Fundamental factor models ➢ Interpretation of factors
✓Macroeconomic factor models: surprises in the macroeconomic variables;
✓Fundamental factor models: return associated with asset attributes.
➢ Interpretation of factor sensitivities
✓Macroeconomic factor models: regression slope estimate; ✓Fundamental factor models: standardized beta.
42

Multifactor Models: Introduction
Macroeconomic vs. Fundamental factor models (Cont.) ➢ Interpretation of intercept term
✓Macroeconomic factor models: the asset’s expected return based on market expectations (e.g. APT);
✓Fundamental factor models: regression intercept.
43

Multifactor Models: Introduction
Macroeconomic vs. Fundamental factor models (Cont.) ➢ Data processing
✓Macroeconomic factor models: develop the factor (surprise) series first and then estimate the factor sensitivities through regressions;
✓Fundamental factor models: specify the factor sensitivities (attributes) first and then estimate the factor returns through regressions.
44

Multifactor Models: Introduction
Statistical factor models
➢ These models make minimal assumptions but the factors are difficult to interpret economically, in contrast to macroeconomic models and fundamental models.
45

Practice 1
Last year the return on Harry Company stock was 5 percent. The portion of the return on the stock not explained by a two- factor macroeconomic factor model was 3 percent. Using the data given below, what is Harry Company stock’s expected return.
46

Practice 1
A. 11% B. 15% C. 19%
Answer: A
5% = Expected return – 1.5*(Interest rate surprise) + 2*(GDP surprise) + Error term
= Expected return – 1.5*(2%) + 2*(–3%) + 3% So, the expected return = 5% + 3% + 6% -3% = 11%.
47

Summary
➢ Importance: ☆☆☆ ➢ Content:
✓ Macroeconomic factor models; ✓ Fundamental factor models;
✓ Statistical models.
➢ Exam tips:
✓ 很重要的考点,主要考概念题,特别是
Macroeconomic factor models和Fundamental factor model的解读与对比。
48

An Introduction to Multifactor Models
Multifactor Models: Application
Tasks:
➢ Explain sources of active risk and interpret tracking risk and the information ratio;
➢ Describe uses of multifactor models and interpret the output of analyses based on multifactor models.
49

Multifactor Models: Application
Applications of multifactor models
➢ Performance attribution ✓Return attribution ✓Risk attribution
➢ Portfolio construction
➢ Strategic portfolio decisions
50

Multifactor Models: Application
Return attribution
➢ Multifactor models can be used to attribute portfolio return to different factors.
✓Active return = RP - RB
• RP = portfolio return
• RB = benchmark return
51

Multifactor Models: Application
Return attribution (Cont.)
✓Active return = Factor return + Security selection return • Factor return: return earned by taking different factor
exposures compared to the benchmark;
Factor return = k (βP,i -βB,i )×λi i=1
βP,i: factor sensitivity for ith factor in the active portfolio;
βB,i: factor sensitivity for ith factor in the benchmark portfolio; λi: factor risk premium for factor i.
• Security selection return: earned by allocating different weights to securities compared to the benchmark.
52

Multifactor Models: Application
Risk attribution
➢ Active risk: the standard deviation of active returns.
Active risk = σ(Rp – RB)
✓ Also refers to tracking risk, or tracking error.
➢ Information ratio (IR): standardized average active return.
IR= RP-RB σ(RP -RB )
✓ A tool for evaluating mean active returns per unit of active risk.
53

Multifactor Models: Application
Risk attribution (Cont.)
➢ The active risk of a portfolio can be separated to two parts: Active risk squared = Active factor risk + Active specific risk
✓Active factor risk: the active risk resulting from the portfolio’s different-from-benchmark factor exposures;
✓Active 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.
54

Multifactor Models: Application
Example:
➢ Decomposition of active risk squared:
55

Multifactor Models: Application
Example (Cont.):
➢ Decomposition of active risk squared (re-stated by %):
56

Multifactor Models: Application
Example (Cont.):
➢ Conclusions:
✓Portfolio A assumed substantial active industry risk,
whereas Portfolio B was approximately industry neutral
relative to the benchmark.
✓By contrast, Portfolio B had higher active bets on the style
factors representing company and share characteristics.
57

Multifactor Models: Application
Example (Cont.):
✓Portfolio 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.
✓Portfolio D appears to be a passively managed portfolio, judging by its negligible level of active risk. Its risk exposures very closely match the benchmark.
58

Multifactor Models: Application
Portfolio construction
➢ Multifactor models permit the portfolio manager to make
focused bets or to control portfolio risk relative to the
benchmark’s risk.
✓Passive management: selecting a sample of securities from
the index, replicating an index fund’s factor exposures, and
mirroring those of the index tracked;
✓Active management: predicting alpha or relative return, or
establish a specific desired risk profile for a portfolio.
59

Multifactor Models: Application
Example:
➢ The following table shows the risk factors and the factor sensitivities for the portfolios:
60

Multifactor Models: Application
Example (Cont.):
➢ 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
➢ 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.
61

Multifactor Models: Application
Example (Cont.):
➢ 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
➢ 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.
62

Multifactor Models: Application
Strategic portfolio decisions
➢ By introducing more risk factors, multifactor models enable investor gain from taking more/less exposures to risks that they have a comparative advantage/disadvantage;
➢ By considering multiple sources of systematic risk, multifactor models allow investors to achieve better- diversified and possibly more efficient portfolios.
63

Summary
➢ Importance: ☆ ➢ Content:
✓ Applications of multifactor models:
• Return attribution and risk attribution;
• Portfolio construction;
• Strategic portfolio decisions.
➢ Exam tips:
✓ 不是考试重点。
64

Measuring and Managing Market Risk
Value at Risk (VaR)
Tasks:
➢ Compare the parametric, historical simulation, and Monte Carlo simulation methods for estimating VaR;
➢ Describe advantages, limitations and extension of VaR.
65

Value at Risk (VaR)
Value at Risk (VaR)
➢ The minimum loss that would be expected a certain
percentage of the time over a certain period of time given
the assumed market conditions.
➢ Example: the 5% VaR of a portfolio is €2.2 million over a
one-day period.
✓Interpretation: the minimum loss that would be expected
to occur over one day 5% of the time is $2.2 million.
66

Value at Risk
Methods to estimate VaR
➢ Parametric (variance–covariance) method ➢ Historical simulation method
➢ Monte Carlo simulation method
67

Value at Risk
Parametric method
➢ Assumes that the return distributions for the risk factors in the portfolio are normal;
➢ Uses the expected return and standard deviation of return for each risk factor to estimate the VaR.
✓VaR(X%) = E® - ZX%×σ
✓VaR(X%)dollar = [E® - ZX%×σ]×asset value
68

Value at Risk
Parametric method (Cont.) ➢ Advantage:
✓Simple and straightforward. ➢ Disadvantage:
✓Its estimates will only be as good as the estimate of the parameter (mean, variance, covariance).
✓The usefulness is limited when normality assumption is not reasonable.
• E.g.: when the investment portfolio contains options.
69

Value at Risk
Historical simulation method
➢ 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.
➢ 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.
✓VaRdaily(5%) = 0.19% or $190,000
70

Value at Risk
Historical simulation method (Cont.) ➢ Advantage:
✓No normality or any other distribution assumption;
• Available to estimate the VaR for portfolio with options.
✓Based on what actually happened, so it cannot be dismissed as introducing impossible outcomes.
71

Value at Risk
Historical simulation method (Cont.) ➢ Disadvantage:
✓No 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.
72

Value at Risk
Value at Risk (Cont.)
➢ Both parametric and historical simulation methods has a shortage that all observations are weighted equally.
✓Improvement: giving more weight to more recent observations and less weight to more distant observations.
73

Value at Risk
Monte Carlo simulation method (Cont.)
➢ 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.
74

Value at Risk
Monte Carlo simulation method (Cont.) ➢ Advantage:
✓It can accommodate virtually any distribution, and can accurately incorporating the effects of option positions or bond positions with embedded options.
➢ Disadvantage:
✓Complex
✓Assumptions of inputs are critical for accuracy of estimates.
75

Value at Risk
Advantages of VaR
➢ 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
76

Value at Risk
Limitations of VaR
➢ 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
77

Value at Risk
Extensions of VaR
➢ Conditional VaR (CVaR): the average loss that would be
incurred if the VaR cutoff is exceeded.
✓Also named expected tail loss or expected shortfall.
➢ Incremental VaR (IVaR): the difference in VaR between the “before” and “after” VaR if a position size is changed relative to the remaining positions.
78

Value at Risk
Extensions of VaR (Cont.)
➢ Marginal VaR (MVaR): the change in VaR for a small change
in a given portfolio holding.
✓ Strictly, MVaR is the slope of VaR-weight curve for a
security in the portfolio;
✓ Approximately, MVaR is the change in VaR for a $1 or 1%
change in the position for a security in the portfolio.
79

Value at Risk
Extensions of VaR (Cont.)
➢ Relative VaR: a measure of the degree to which the
performance of a given investment portfolio might deviate
from its benchmark.
✓Also named ex ante tracking error.
80

Practice 1
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.
C. The minimum loss that would be expected to occur over one month 5% of the time is $12.5 million
81

Practice 1
Answer: C
It is the only statement that accurately expresses the VaR.
A is incorrect because VaR does not give the likelihood of losing a specific amount. B is incorrect because VaR is not an expected loss—it is a minimum loss.
82

Summary
➢ Importance: ☆☆☆ ➢ Content:
✓ Definition and interpretation of VaR; ✓ Method to estimate VaR:
• Parametric method; historical simulation method, Monte Carlo simulation method.
✓ Advantages, limitations, and extensions of VaR. ➢ Exam tips:
✓ 常考点1:VaR的定义和解读,概念题;
✓ 常考点2:估计VaR值的方法对比,概念题。
83

Measuring and Managing Market Risk
Sensitivity and Scenario Risk Measures
Tasks:
➢ Describe sensitivity risk measures and scenario risk measures;
➢ Describe advantages and limitations of sensitivity risk measures and scenario risk measures;
➢ Explain constraints used in managing market risks.
84

Sensitivity and Scenario Risk Measures
Sensitivity risk measures
➢ Examine how portfolio value responds to a small change in a
single risk factor.
Scenario risk measures
➢ Provides an estimate of the impact on portfolio value of a set of significant change in multiple risk factors.
85

Sensitivity and Scenario Risk Measures
Sensitivity risk measures
➢ Equity exposure measures: Beta (β)
CAPM: E(Ri) = RF + βi[E(RM) – RF]
✓Assets with betas more (less) than 1 are considered more
(less) volatile than the market as a whole.
86

Sensitivity and Scenario Risk Measures
Sensitivity risk measures (Cont.)
➢ Fixed-income exposure measures: duration and convexity.
✓Given 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:
ΔP = -Duration  ΔY + 1  Convexity  (ΔY)2 P2
87

Sensitivity and Scenario Risk Measures
Sensitivity risk measures (Cont.)
➢ Options risk measures: Delta (Δ), Gamma (Γ), Vega (Λ), etc. ✓Delta: sensitivity of option price against the underlying
asset price;
✓Gamma: sensitivity of option delta against the underlying
asset price;
✓Vega: sensitivity of option price against underlying asset
price volatility.
ΔP =DeltaΔS+ 1Gamma(ΔS)2 +VegaΔV
2
call
88

Sensitivity and Scenario Risk Measures
Sensitivity risk measures (Cont.)
➢ Advantage: can inform a portfolio manager about a
portfolio’s exposure to various risk factors to facilitate risk
management.
✓If too much/less risk exposure to a risk factor, the manager
can modify the exposure accordingly.
89

Sensitivity and Scenario Risk Measures
Sensitivity risk measures (Cont.) ➢ Limitations:
✓Can 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.
✓Two 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.
90

Sensitivity and Scenario Risk Measures
Scenario risk measures
➢ Historical scenario approach: use a set of changes in risk
factors that have actually occurred in the past. ✓E.g.: change of risk factors in financial crisis.
➢ Hypothetical scenario approach: use a set of hypothetical change in risk factors, not just those that have happened in the past.
✓Stress tests: examine the impact on portfolio of a scenario of extreme changes of risk factors.
91

Sensitivity and Scenario Risk Measures
Scenario risk measures (Cont.)
➢ Scenario analysis can be regarded as the final step in the risk
management process, after performing sensitivity analysis. ✓Scenario analysis can provide additional information on a
portfolio’s vulnerability to changes of risk factors or the
correlations between risk factors.
✓Stress tests can determine the size of change on a certain
risk factor that could compromise the sustainability of the investment.
92

Sensitivity and Scenario Risk Measures
Scenario risk measures (Cont.) ➢ Advantage:
✓Scenario risk measures focus on extreme outcomes, but not bound by either recent historical events or assumptions about parameters or probability distributions.
✓Scenario 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.
93

Sensitivity and Scenario Risk Measures
Scenario risk measures (Cont.) ➢ Limitations:
✓ Historical scenarios are not going to happen in exactly the same way again; and hypothetical scenarios may incorrectly specify how assets will co-move.
✓Hypothetical 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.
94

Sensitivity and Scenario Risk Measures
Scenario risk measures (Cont.) ➢ Limitations:
✓The 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.
95

Sensitivity and Scenario Risk Measures
VaR vs. Sensitivity vs. Scenario risk measures
➢ VaR provides a probability of loss, and is a downside risk
measures;
➢ Sensitivity risk measures provide estimates of relative
exposure to different risk factors but no estimate of
probabilities, and are not downside risk measures;
➢ Scenario risk measures provide estimates of effect to
simultaneous changes of multiple risk factors, but no estimate of probability.
96

Sensitivity and Scenario Risk Measures
VaR vs. Sensitivity vs. Scenario risk measures
➢ 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.
97

Sensitivity and Scenario Risk Measures
Choices of risk measures
➢ 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.
✓Banks
✓Asset managers ✓Pension funds ✓insurers
98

Sensitivity and Scenario Risk Measures
Banks
➢ 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.
➢ The typical risk measures used by banks: ✓Sensitivity measures;
✓Scenario analysis and stress tests; ✓Leverage risk measures;
✓VaR .
99

Sensitivity and Scenario Risk Measures
Asset managers
➢ Traditional asset managers: focus on relative risk measures. ✓Position limits, sensitivity measures, scenario analysis,
active share, VaR.
➢ Hedge funds managers: focus on absolute return.
✓Sensitivity measures, leverage, VaR, scenario analysis, drawdown.
100

Sensitivity and Scenario Risk Measures
Pension funds
➢ The risk management goal for defined benefit pension funds is to be sufficiently funded to make future payments to pensioners.
➢ The typical risk measures used by pension funds: ✓Sensitivity measures, surplus at risk.
101

Sensitivity and Scenario Risk Measures
Risk measures and capital allocation
➢ 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.
➢ Risk measures must be introduced when limit the overall risk and allocate risk across the activities or business units by risk budgeting.
102

Sensitivity and Scenario Risk Measures
Constraints in market risk management
➢ Risk budgeting: determining the overall risk appetite, and
then allocated to sub-activities or business units. ➢ Position limits: the maximum currency amount or
percentage of portfolio value allowed for specific asset or
asset class.
➢ Scenario limits: limits on expected loss for a given scenario. ➢ Stop-loss limits: require an investment position to be
reduced or closed out when losses exceed a given amount over a specified time period.
103

Summary
➢ Importance: ☆ ➢ Content:
✓ Sensitivity risk measures vs. scenario risk measures; ✓ Advantages and limitations of the risk measures;
✓ Choice of risk measures;
✓ Constraints in market risk management.
➢ Exam tips:
✓ 不是考试重点。
104

Economics and Investment Markets
Economics and Investment Markets (1)
Tasks:
➢ Explain the notion that to affect market values; ➢ Explain the relationship between the long-term
growth rate and the real short-term interest rates; ➢ Explain how business cycle affects policy rates and
the slope of the term structure of interest rates.
105

Economics and Investment Markets (1)
Present value model (DCF model)
➢ The value of any asset can be calculated as the present value of its expected cash flows.
n CF P= i
i=1 (1+r)i
✓r: the discount rate r = R + π + RP
• R: real risk-free rate; • π: expected inflation; • RP: risk premium.
106

Economics and Investment Markets (1)
Present value model (Cont.)
➢ If a economic factor affects an asset’s market value, it must affect one or more of the following:
✓The timing and/or amount of the expected cash flows; ✓One 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.
107

Economics and Investment Markets (1)
Role of expectation
➢ 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.
➢ 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.
108

Economics and Investment Markets (1)
Inter-temporal rate of substitution (ITRS)
➢ 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 (Ut/U0).
✓mt is always less than 1 because investor always prefer current consumption over future consumption (U0 > Ut).
109

Economics and Investment Markets (1)
Real risk free rate
➢ Assuming a zero coupon, inflation-indexed, risk-free bond with par value of $1, its price should be:
P0 = mt
➢ So, the real risk-free rate (unannualized) is:
1-P 1 R= 0= -1
Pm 0t
✓The higher the U0 relative to Ut, the lower the mt, the higher the R.
110

Economics and Investment Markets (1)
GDP growth vs. real risk free rate
➢ Real risk free rate is positively related to GDP growth rate; ✓Higher 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.
➢ Real risk free rate is also positively with the volatility of the growth rate due to higher “risk premium”.
111

Economics and Investment Markets (1)
Inflation vs. nominal risk-free interest rate ®
➢ In terms of nominal risk-free interest rate, the effects of inflation should be considered:
✓Premium for expected inflation (π);
✓Risk premium for uncertainty about actual inflation (θ). ➢ The uncertainty for short-term inflation is negligible:
rshort-term = R + π
➢ For long term securities, risk premium for uncertainty of
inflation need to be included: rlong-term =R+π+θ
112

Economics and Investment Markets (1)
Inflation vs. nominal risk-free interest rate (Cont.)
➢ Break-even inflation rate (BEI): the yield difference between
a non-inflation-indexed risk-free bond and the inflation-
indexed risk-free bond with the same maturity; ✓The BEI captures the effects of inflation on yield:
BEI = π + θ
113

Economics and Investment Markets (1)
Business cycle vs. policy rate
➢ 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 = Rn + π + 0.5(π – π*) + 0.5(Y-Y*)
✓r: central bank policy rate implied by the Taylor Rule; ✓Rn: neutral real policy interest rate;
✓π: current inflation rate; π*: target inflation rate;
✓Y: log of actual real GDP; Y*: log of target real GDP.
114

Economics and Investment Markets (1)
Business cycle vs. slope of yield curve
➢ During the recession, the slope of yield curve will increase; ✓Central bank tends to lower the policy rate;
✓Investors expect higher future GDP growth and higher
long-term rates as economic growth recovers.
➢ During the recession, short-term bonds generally perform
better than long-term bonds.
115

Economics and Investment Markets (1)
Business cycle vs. slope of yield curve (Cont.)
➢ Later stages of expansion often have negatively sloped (inverted) yield curve.
✓Typically, high inflation and high short-term interest rate; ✓Low long-term rates due to expectations of decreasing
inflation and GDP growth.
➢ During the expansion, long-term bonds generally perform
better than short-term bonds.
116

Summary
➢ Importance: ☆ ➢ Content:
✓ Market valuation and discount rate;
✓ Inter-temporal rate of substitution and real risk free rate; ✓ GDP growth vs. real risk free rate;
✓ Inflation vs. nominal risk-free interest rate;
✓ Business cycle vs. policy rate.
✓ Business cycle vs. slope of yield curve;
➢ Exam tips:
✓ 不是考试重点。
117

Economics and Investment Markets
Economics and Investment Markets (2)
Tasks:
➢ Describe the factors that affect yield spreads, including credit spread.
118

Economics and Investment Markets (2)
Business cycle vs. credit spreads
➢ 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
✓γ: credit spread, or risk premium for credit risk.
119

Economics and Investment Markets (2)
Business cycle vs. credit spreads (Cont.)
➢ Credit spreads tends to narrow in times of robust economic
growth, when defaults are less common.
✓Credit risky (lower-rated) bonds will perform better than
default-free (higher-rated) bonds.
➢ Credit spreads tend to rise in times of economic weakness,
as the probability of default rises.
✓Default-free (higher-rated) bonds will perform better than
credit risky (lower-rated) bonds.
120

Economics and Investment Markets (2)
Characteristics of market vs. credit quality
➢ 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.
➢ 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.
121

Economics and Investment Markets (2)
Business cycle vs. earning growth expectations
➢ 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.
➢ Earning growth rate tend to be relatively stable throughout the business cycle for defensive or non-cyclical industries.
122

Economics and Investment Markets (2)
Business cycle vs. equity risk premium
➢ 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 ✓λ: equity risk premium (λ > γ).
➢ Consumption-hedging property: providing higher payoff during economic downturns.
✓Assets with more consumption-hedging property will be more highly valued and have less risk premium.
123

Economics and Investment Markets (2)
Business cycle vs. equity risk premium (Cont.)
➢ Investors will demand a higher equity risk premium because the consumption-hedging properties of equities are poor.
✓Equities tend not to pay off in bad times.
124

Economics and Investment Markets (2)
Business cycle vs. valuation multiples
➢ 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
➢ Valuation multiples tend to rise during periods of economic
expansion and fall during recessions.
125

Economics and Investment Markets (2)
Business cycle vs. style strategy ➢ Value strategy vs. growth strategy
✓A value strategy performs well during recession, while growth strategy performs well during expansion.
➢ Capitalization
✓Small-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.
126

Economics and Investment Markets (2)
Business cycle vs. rotation strategies ➢ During economic expansion:
✓Rotating into growth stocks when they are expected to outperform value stocks;
✓Rotating into small-cap stocks when they are expected to outperform large-cap stocks;
✓Rotating into cyclical stocks when they are expected to outperform countercyclical stocks.
127

Economics and Investment Markets (2)
Business cycle vs. commercial real estate investment
➢ Commercial real estate investment have the following characteristics:
✓Bond-like characteristics: steady rental income stream, like cash flows of bonds;
✓Equity-like characteristics: uncertain value of the property at the end of the lease term;
✓Illiquidity.
➢ Yield for commercial real estate = R + π + θ + λ + φ
✓φ: risk premium for illiquidity.
128

Economics and Investment Markets (2)
Business cycle vs. commercial real estate investment
➢ Investors will demand a high risk premium for commercial real estate investment due to weak consumption-hedging properties.
✓Commercial property value tend to decline in bad times.
129

Summary
➢ Importance: ☆ ➢ Content:
✓ Business cycle vs. credit spreads;
✓ Business cycle vs. equity risk premium;
✓ Business cycle vs. investment style;
✓ Business cycle vs. commercial real estate investment.
➢ Exam tips:
✓ 不是考试重点。
130

Analysis of Active Portfolio Management
Measures of Value Added by Active Management
Tasks:
➢ Describe how value added by active management is measured;
➢ Calculate and interpret the information ratio and contrast it to the Sharpe ratio.
131

Measures of Value Added by Active Management
Measures of value added ➢ Active return
➢ Information ratio
132

Measures of Value Added by Active Management
Active return (RA)
➢ R A = R P - R B =
i=1
Δw R = ii
Δw R
i A,i
NN


i=1
✓RP: return of actively managed portfolio; ✓RB: return of benchmark portfolio;
✓Ri: return of security i;
✓Δwi = wP,i – wB,i, active weights;
• Sum of active weights for all securities equal to zero;
• Over-weighted: positive; under-weighted: negative. ✓RA,i = Ri – RB, active security return.
133

Measures of Value Added by Active Management
Active return (Cont.)
➢ Ex-anti active return: based on expected return; ➢ Ex-post active return: based on realized return.
134

Measures of Value Added by Active Management
Active return (Cont.)
➢ For portfolio with multiple asset classes, active return can be decomposed to two sources:
✓Active asset allocation: active weights of asset classes against benchmark portfolio;
✓Security selection: active weights of security within asset
classes.
MM
RA= ΔwR + wR

j B,j

P,j A,j
j=1
j=1
• RA,j: active return of asset class j.
135

Measures of Value Added by Active Management
Information ratio (IR)
➢ Information ratio measure the relative risk-adjusted value
added, and calculated as mean active returns per unit of active risk.
IR = Active return = RActive = Rp - RB Activerisk σ(RActive) σ(Rp -RB)
✓Ex-anti IR: based on expected return; ✓Ex-post IR: based on realized return.
• Can be used for performance evaluation: the higher, the better.
136

Measures of Value Added by Active Management
Information ratio (IR)
➢ Information ratio can be used for investment manager selection:
✓Manager with higher IR is preferred;
✓Higher IR also means higher SR.
➢ Information ratio can also be used to determine the
expected active return for a given target level of active risk. E(RA) = IR * σA
137

Measures of Value Added by Active Management
Information ratio vs. Sharp ratio
➢ Review: Sharp ratio measure the total risk-adjusted value
added, and calculated as excess return per unit of risk.
SR= Rp -Rf σP
✓Sharp ratio is unaffected by the addition of cash or leverage because excess return and risk will change proportionally.
138

Measures of Value Added by Active Management
Sharp ratio vs. information ratio (Cont.)
Sharp ratio
Information ratio
Total risk-adjusted value added
Relative risk-adjusted value added
Unaffected by the addition of cash or use of leverage
Affected by the addition of cash or use of leverage
Affected by the aggressive active weight
Unaffected by the aggressive active weight
Two ratios would be equal if the benchmark is risk-free asset
139

Summary
➢ Importance: ☆☆ ➢ Content:
✓ Active return and information ratio;
✓ Information ratio vs. Sharp ratio. ➢ Exam tips:
✓ 常考点:information ratio的定义与计算。
140

Analysis of Active Portfolio Management
The Fundamental Law
Tasks:
➢ State and interpret the fundamental law of active portfolio management;
➢ Describe the practical strengths and limitations of the fundamental law of active management.
141

The Fundamental Law
The fundamental law
➢ The fundamental law is a framework for thinking about the potential value added through active portfolio management;
✓The most common use is the description and evaluation of active management strategies.
➢ The law itself is a mathematical relationship that relates the expected information ratio of an actively managed portfolio to a few key parameters.
142

The Fundamental Law
The fundamental law (Cont.)
➢ The correlation triangle
143

The Fundamental Law
The fundamental law (Cont.)
➢ Realized value added is the sum of the products of active weights and realized active returns.
✓The 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)
✓The correlation can be examined by the correlations on the two vertical legs:
• Information coefficient (IC); • Transfer coefficient (TC).
144

The Fundamental Law
Information coefficient (IC)
➢ Correlation between the forecasted active returns, μi, and the realized active returns, RA,i;
IC = Corr RA,i , μi  σ σ
ii
✓A measure of manager’s forecasting accuracy (also called
signal quality).
• Ex-ante IC: must be positive;
• Ex-post IC: either positive or negative.
145

The Fundamental Law
Transfer coefficient (TC)
➢ Correlation between the forecasted active returns, μi, and the active weights, Δwi;
TC = Corr( μi , Δw σ ) = Corr (Δwσ , Δw σ ) σii iiii
Δw
: = μi i σ2
i
i
, optimal active weights.
146

The Fundamental Law
Transfer coefficient (Cont.)
➢ 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.
✓For portfolios without any constraints, TC equals to 1; ✓For portfolios with constraints, TC < 1.
147

The Fundamental Law
Breadth (BR)
➢ The number of independent active decisions make per year by the investor in constructing the portfolio.
✓“Independent” in this context means that the active decisions should not be based on highly correlated (or identical) information sets;
✓A measure of how much efforts the manager has put into. ➢ E.g.: if a manager takes active position in 10 securities per
month, then BR = 10*12 =120.
148

The Fundamental Law
The fundamental law (cont.)
➢ For actively managed portfolios, the full fundamental law is expressed in the following equation:
IR = (TC)(IC) BR E(RA ) = (TC)(IC) BRσA
✓For portfolio without any constraints, TC = 1. IR = (IC) BR E(RA ) = (IC) BRσA
149

The Fundamental Law
Market timing
➢ Market timing: simply bets on the market direction;
✓Information coefficient for market timing: IC = 2*(%correct) - 1
✓If the manager is correct 50% of the time, IC = 0. ✓This formula is also applicable to evaluate IC of active
sector rotation strategies.
150

The Fundamental Law
Evaluation of active management strategies
➢ Example: Consider two active management strategies:
individual stock selection with a benchmark composed of 100 securities, and industrial sector selection with a benchmark of nine sectors. The active security returns are defined as residuals in a risk model and thus are essentially uncorrelated, and forecasts are independent from year to year. Suppose the individual stock investor is expected to exhibit skill as measured by an information coefficient of 0.05, while the industrial sector investor has a higher information coefficient of 0.15.
151

The Fundamental Law
Evaluation of active management strategies (Cont.)
➢ 1. Conceptually, what is the breadth (i.e., number of independent decisions per year) of each active management strategy?
➢ Solution:
Given that the active asset returns in each strategy are uncorrelated, and forecasts are independent from year to year, the breadth of the security selection strategy is BR = 100 and the breadth of the sector selection strategy is BR = 9.
152

The Fundamental Law
Evaluation of active management strategies (Cont.)
➢ 2. Calculate the expected information ratio for each strategy, under the assumption that each investor’s forecasts can be implemented without constraints.
➢ Solution:
The IC of the unconstrained security selection strategy is:
IR = (IC) BR = 0.05 100 = 0.5
The IC of the industrial sector selection strategy is:
IR = (IC) BR = 0.15 9 = 0.45
153

The Fundamental Law
Evaluation of active management strategies (Cont.)
➢ 3. Suppose the aggressiveness of each strategy is established by a portfolio active risk target of 3.0% per year. What is the expected active return to each strategy?
➢ Solution:
The expected active return to the unconstrained security selection strategy is 0.53.0% = 1.50%, while the expected active return of the industrial sector selection strategy is 0.453.0% = 1.35%.
154

The Fundamental Law
Evaluation of active management strategies (Cont.)
➢ 4. Under the more realistic assumption that the individual security selection strategy is constrained to be long only and has turnover limits, the transfer coefficient has a value of 0.60. What is constrained information ratio and expected active return of the security selection strategy?
➢ Solution:
The IC of the constrained security selection strategy is:
IR = (TC)(IC) BR = 0.60.05 100 = 0.3
The expected active return is 0.30*3.0% = 0.90%.
155

The Fundamental Law
Limitations of the fundamental law
➢ Limitation: poor input estimates lead to incorrect evaluation.
✓Uncertainty in ex-ante measurement of skill.
• IC is difficult to justify due to existence of the bias,
various asset segments, or different time periods. ✓Assumption 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.
156

Summary
➢ Importance: ☆☆☆ ➢ Content:
✓ The fundamental law of active management:
• Information coefficient (IC);
• Transfer coefficient (TC);
• Breadth (BR).
✓ Limitations of the fundamental law. ➢ Exam tips:
✓ 常考点:the fundamental law的计算公式。
157

Algorithmic Trading and High-Frequency Trading
Algorithmic Trading and High-Frequency Trading
Tasks:
➢ Distinguish between execution algorithms and high-frequency trading algorithms;
➢ Describe the application of algorithmic trading.
158

Algorithmic Trading and High-Frequency Trading
Algorithmic Trading and High-Frequency Trading
➢ Definition ➢ Categories ➢ Application
159

Definition
Definition of algorithmic trading
➢ Algorithmic trading is “using a computer to automate a trading strategy.”
✓ In almost all cases, algorithms encode what traders can do but with far higher speed.
160

Categories
Categories of trading algorithms
➢ Execution algorithms: break down large orders and execute
them over a period of time.
✓The goal is to minimize the impact that a large order has in
the market and to achieve a benchmarked price.
161

Categories
Categories of trading algorithms (Cont.)
➢ 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.
✓The goal is to earn profit.
162

Categories
Execution algorithms vs. HFT algorithms ➢ Execution algorithms
✓How to trade;
✓The goal is to minimize market impact and try to ensure a
fair price.
➢ High-frequency trading (HFT) algorithms:
✓How to trade; when to trade; and even what to trade. ✓The goal is to earn profit.
163

Categories
Types of execution algorithms
➢ Volume-weighted average price (VWAP):
✓Uses 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.
➢ Implementation shortfall:
✓Dynamically 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.
164

Categories
Types of execution algorithms (Cont.) ➢ Market participation algorithms:
✓Slices the order into segments intended to participate on a pro-rata basis with volume throughout the course of the execution period.
165

Categories
Types of HFT algorithms
➢ Statistical arbitrage ✓Pairs trading
✓Index arbitrage ✓Basket trading ✓Spread trading
✓Mean reversion ✓Delta neutral strategies
166

Categories
Types of HFT algorithms (Cont.)
➢ Liquidity aggregation and smart order routing ➢ Real-time pricing of instruments
➢ Trading on news
➢ Genetic tuning
167

Application
Trading algorithms for market fragmentation
➢ 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.
➢ Algorithmic methods can be used to address this issue, such as liquidity aggregators and smart order routing.
168

Application
Trading algorithms for market fragmentation (Cont.)
➢ Liquidity aggregators offer a global-ordered view of liquidity
for each instrument regardless of which trading market
offers the liquidity.
➢ Smart order routing sends the orders to the relevant
markets with the best combination of liquidity and price.
169

Application
Trading algorithms for risk management ➢ Real-time pre-trade risk firewall:
✓Continuously calculate risk exposures on the trades to ensure that risk limits are not exceeded.
✓Trades exceeding limits are blocked. ➢ Back testing and market simulation:
✓Testing algorithms to see how they perform under various scenarios, including historical data and invented scenarios.
170

Application
Trading algorithms for regulatory oversight
➢ Regulators around the world have recognized that real-time market monitoring and surveillance allows rapid action to prevent or minimize any market impact.
➢ Suspicious trading includes: ✓Insider trading
✓Front running
✓Painting the tape ✓Fictitious orders
✓Wash trading ✓Trader collusion
171

Application
Positive impact of algorithmic trading
➢ Minimized market impact of large trades
➢ Lower cost of execution
➢ Improved efficiency in certain markets
➢ More open and competitive trading markets ➢ Improved and more efficient trading venues
172

Application
Negative impact of algorithmic trading
➢ Fear of an unfair advantage
➢ Acceleration and accentuation of market movements ➢ Gaming the market
➢ Increased risk profile
➢ Algorithms gone wild
➢ Potential for market denial-of-service-style attacks
➢ Additional load on trading venues
➢ Increased difficulty of policing the market
173

Summary
➢ Importance: ☆ ➢ Content:
✓ Definition and categories of algorithmic trading;
✓ Applications of algorithmic trading;
✓ Positive and negative impact of algorithmic trading.
➢ Exam tips:
✓ 不是重要考点。
174

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