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Concepts
Elements of Portfolio
Managements

Description
Portfolio Management Process and Investment Policy Statement
1
...
) and micro factors (sector, industry and security-specific
consierations)
2
...
Determining an asset allocation strategy
- Evaluate securities as how they might fit into a portfolio that meets the objectives and constraints of the investor
- Implement and execute the portfolio decision
4
...
Monitoring dynamic investor objectives and capital market conditions : Continuously monitor both investor and marketplace characteristics for significant changes that require
adjustments in the portfolio

Portfolio perspective

- Equity pricing models : based on principle that only systematic risk is priced
- Basic principle of New Prudent Investor Rule : diversification is expected of porfolio managers as a method to reduce risk
- Should analyse risk-return tradeoff of the portfolio as a whole (instead of individual investments), because unsystematic risk can be diversified away by combining investments into a
portfolio
- Systematic risk : result of economic fundamentals (GDP growth, unexpected inflation, consumer confidence, unanticipated changes in credit spreads, business cycle)

Steps of the portfolio managment
process

Step 1 : Planning - analyse of objectives and constraints, developing IPS, determining investment strategy, selecting appropriate asset allocation
Step 2 : Execution
Step 3 : Feedback

Role and elements of investent
policy statement

Roles of IPS:
- Be readily implemented by current and future investment adviser
- Promote long-term discipline for portfolio decisions
- Protect against short-term shifts in strategy when either market environments or protfolio performance cause panic or overconfidence
Elments of IPS
- Client description → common understanding of the client's situa on
- Purpose of the IPS, including policies, objectives, goals, restrictions and limitations
- Identify duties and responsibilitis of involved parties
- Formal statements of objectives and constraints
- Calendar schedule for portfolio performance and IPS review
- Asset allocation ranges and statements regarding flexibility and rigidity when formulating / modifying strategic asset allocation
- Guidelines for portfolio adjustments and rebalancing

Impacts of capital market
expectations and investment time
horizon on strategic asset
allocation

Strategic asset allocation : combine IPS and capital market expectations → LT target weigh ng for asset classes included in the por olio
- Need for flexibility → allow for temporary tac cal asset alloca on in response for changes in ST capital market expecta ons
3 common approaches of strategic asset allocation :
- Passive investment strategies : not response for changes in expectations (e
...
: Indexing, buy-and-hold invesment)
- Active investment strategies : attempt to capitalise on differences between a portfolio manager's beliefs about security valuations and market value → more responsive for changing
expectations
- Semi-active / risk-controlled active / enhanced index strategies : hybrids of passive and active strategies
...
If por olio's risk-return differ significantly from investor's
objectives → need to be reviewed
Investment time horizon influenc investor's asset allocation
...
Risk objectives : factors associated with investor's willingness and ability to take risk
- Factors that affect ability to take risk
+ Required spending needs
+ Long-term wealth target
+ Financial strength
+ Liabilities
- 2 classes of risk objective measurement
+ Absolute risk objective (e
...
: standard deviation of total return)
+ Relative risk objectves (e
...
: deviation from an underlying index, tracking risk)
2
...
Ability to take risk

Below average ability to take risk

Above average ability to take risk

Below average willingness to take risk

Below average tolerance

Education / Resolution required

Above average willingness to take risk

Below average tolerance

Above average tolerance

Investment constraints

Investment constraints : factors restricting / limiting the universe of available investment choices
5 main clase of constraints:
1
...
Time horizon constraints (internal) : time periods over which a portfolio is expected to generate returns to meet specific future needs
3
...
Legal and regulatory factors (external) : specify which investment classes are not allowed or dictating any limitations places on allocations to partivular investment classes
5
...
Individual investor

Return requirement

Risk tolerance

Depend on life-cycle stage and financial position

Depend on life-cycle stage and financial position

2
...
Defined contribution pension plan

Depend on life-cycle stage of beneficiaries

4
...
Life insurance companies

Function of policyholder reserve rate

6
...
Banks

Function of cost of funds

Depend on risk tolerance of beneficiaries
Generally average or above average
Below average, due to significant regulatory constraints
Below average, due to significant regulatory constraints
Depend on business model and financial strength

Investment time horizon

Longer investment time horizon → Higher ability to take risk
Investment horizon of 10+ years : returns will average over economic and market cycles → greater alloca on to equi es
Short term horizon : uncertainty about returns and the inability to fix for poor results → select low-risk (predictable) securi es

Required ethical conduct for
managing investment portfolios

Portfolio managers must meet highest standards of ethical conduct , embodied by the CFA Institute Code and Standards of Practice

Concepts
Arbitrage Pricing Theory

Description
An Introduction to Multifactor Models
Arbitrage Pricing Theory : alternative to CAPM, linear model, with multile systematic risk factors priced by the market
Assumptions :
1
...
Returns are generated using a factor model
3
...
Macroeconomic factor model : asset returns are explained by surprises in macroeconomic risk factors (e
...
: GDP, interest rate, inflation)
- Factor surprises = Realised value - Predicted value
2
...
Statistical factor models

Macroeconomic factor model

Example :
𝑅 =𝐸 𝑅 +𝛽, ×𝐹

+𝛽, ×𝐹

+𝜀

Which:
𝐹
= 𝑠𝑢𝑟𝑝𝑟𝑖𝑠𝑒 𝑖𝑛 𝐺𝐷𝑃 𝑟𝑎𝑡𝑒
𝐹 = 𝑠𝑢𝑟𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 𝑐𝑟𝑒𝑑𝑖𝑡 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑠𝑝𝑟𝑒𝑎𝑑
𝜀 = 𝑓𝑖𝑟𝑚 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑠𝑢𝑟𝑝𝑟𝑖𝑠𝑒

𝛽 , = 𝐺𝐷𝑃 𝑠𝑢𝑟𝑝𝑟𝑖𝑠𝑒 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝐴𝑠𝑠𝑒𝑡 𝑖
𝛽 , = 𝐶𝑟𝑒𝑑𝑖𝑡 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑠𝑝𝑟𝑒𝑎𝑑 𝑠𝑢𝑟𝑝𝑟𝑖𝑠𝑒 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝐴𝑠𝑠𝑒𝑡 𝑖

Priced risk factors : only systematic factors are priced
Factor sensitivities :
- Different assets → different factor sensi vi es
- Can be estimated by regressing historical asset returns on the corresponding historical macroeconomic factors
Fundamental factor model

Example :
𝑅 = 𝑎 +𝛽, ×𝐹

/

+𝛽, ×𝐹

+𝜀

Which :
𝐹 / = 𝑟𝑒𝑡𝑢𝑟𝑛 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑃⁄𝐸 𝑓𝑎𝑐𝑡𝑜𝑟
𝐹
= 𝑟𝑒𝑡𝑢𝑟𝑛 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑚𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟
𝑃⁄𝐸 − 𝑃⁄𝐸
𝛽 , = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑠𝑒𝑑 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 𝑡𝑜 𝑃⁄𝐸 𝑓𝑎𝑐𝑡𝑜𝑟 =
𝜎 ⁄
𝑆𝐼𝑍𝐸 − 𝑆𝐼𝑍𝐸
𝛽 , = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑠𝑒𝑑 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 𝑡𝑜 𝑆𝐼𝑍𝐸 𝑓𝑎𝑐𝑡𝑜𝑟 =
𝜎
𝑎 = 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
𝜀 = 𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑛𝑜𝑡 𝑒𝑥𝑝𝑙𝑎𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 𝑚𝑜𝑑𝑒𝑙
𝜎 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
Differences between
Macroeconomic factor model vs
...
Sensitivities

- Regression slope estimates

- Calculated directly from the attribute

2
...
Intercept term

- Stock's expected return

- Regression intercept necessary to make the unsystematic risk of the
asset = 0

Active return : difference in returns between a managed portfolio and its benchmark

𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝑅 − 𝑅
Active risk (aka tracking error / tracking risk) : standard deviation of active return

𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑖𝑠𝑘 = 𝑡𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟 = 𝜎
Information ratio : standardised average active return to demonstrate manager's consistency in generating active return

𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 =

Return attribution

𝑅 −𝑅
𝜎

Active return = Factor return + Security selection return
- Factor return : arising from exposing to factor different from benchmark

𝐹𝑎𝑐𝑡𝑜𝑟 𝑟𝑒𝑡𝑢𝑟𝑛 =

𝛽

,

−𝛽

,

×λ

- Security selection return : arising from different weighting of specific factor from the benchmark
Risk attribution

𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑖𝑠𝑘 = 𝐴𝑐𝑡𝑖𝑣𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 𝑟𝑖𝑠𝑘 + 𝐴𝑐𝑡𝑖𝑣𝑒 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑟𝑖𝑠𝑘
- Active factor risk : related to factor sensitivities compared to benchmark (e
...
: underweight / overweight particular industries relative to portfolio's benchmark)
- Active specific risk related to individual asset's weighting in the portfolio vs
...
g
...
Passive management : construct a tracking portfolio → match same set of factor with a predetermined benchmark
model
2
...
Ruled-based or algorithmic active management (alternative indices) : use rules to change factor exposures when constructing portfolios → introduce biases in the por olio rela ve to
value-weighted benchmark indices
Carhart model

𝐸 𝑅 = 𝑅 + 𝛽 × 𝑅𝑀𝑅𝐹 + 𝛽 × 𝑆𝑀𝐵 + 𝛽 × 𝐻𝑀𝐿 + 𝛽 × 𝑊𝑀𝐿
RMRF = Return on value weighted equity index - Risk-free rate
SMB = Avg
...
return on large cap stocks
HML = Avg
...
return on low book-to-market stocks
WML = Avg
...
return on past losers

Potential benefits of multifactor
model

- Enable investors to zero on risks that they have comparative advantage in bearing , and avoild risk that they are incapable of absorbing
- If the actual asset returns are better described by multifactor models → help investors to select more efficient por olios

Concepts

Description

Value at Risk

Measuring and Managing Market Risk
Value at Risk (VaR) : measure downside risk of a portfolio
...
g
...
Parametric method (variance-covariance method)
- Use the estimated variances-covariances of each security to estimate (1) mean return and (2) standard deviation of returns of the portfolio
- Often assuming normal distribution

𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝜎

=𝑊

×𝜎

+𝑊

×𝜎

+ 2 × 𝑊 × 𝑊 × 𝐶𝑜𝑣

,

2
...
Monte Carlo simulation
- Based on an assumed probability distribution for each risk factor
- Must make assumption about the correlations between risk factors
Advantages / Disadvantages of VaR Advantages

Disadvantages

- Simple, easy to explain
- Allow comparison of riskiness of different portfolios, asset classes, trading operations
- Enable risk budgeting (allocation of capital, given a maximum amount of VaR exposure of
the organisation)
- Accept by global banking regulators as a measure of financial risk
- Can be verify by backtesting
- Provide probability of loss

- Require many assumptions, and can be significantly affected by these assumptions
- Actual returns distributions frequently have "fatter tails" than normal distribution → tend to
underestimate the probability of extreme outcomes
- Liquidity often falls significantly when asset prices fall → VaR might underes mate the
actual cost when liquidating under extreme price pressure
- Correlation increase during financial distress → overes mate diversifica on benefit /
underestimate magnitude of potential losses
- Many risk aspects are not quantified / included in VaR
- Focus only on downside risk

Extensions of VaR

1
...
Incremental VaR (IVaR) : change in VaR, due to change in portfolio allocation
3
...
Ex ante tracking error (relative VaR) : measure VaR of the difference between return on a portfolio and return on its benchmark

Sensitivity analysis

Sensitivity analysis : estimate the change in portfolio value, given a small change in one risk factor
Use of sensitivity analysis :
- Show the vulnerability of a portfolio to a variety of risk factors → excessive exposure can be hedged
Disadvantages :
- Do not provide probabilities and size of expected changes in risk factors and portfolio value

Scenario analysis

Scenario analysis : estimate the change in portfolio value, given a set of significant change in multiple risk
- Historical scenario : use set of changes in risk factors that have actually occurred in the past
- Hypothetical scenario : use any set of changes in risk factors
Use of scenario analysis :
- Show the vulnerability of a portfolio to a set of events / changes in correlations
Disadvantges :
- Do not provide probabilities of expected changees in risk factors and portfolio value

Stress testing / Reverse stress
testing

Stress testing :
- Based on ensitivity analysis / Scenario analysis
- Use extreme changes to estimate the effect on portfolio value
Reverse stress testing : identify scenarios that lead to business failure
...
Equity risk
- Beta
rate risk / Option risk / Market risk
2
...
Option risk

- Delta
- Gamma
- Vega

- Sensitivity to overall market returns
- Sensitivity to change in yield
- Sensitivity to change in duration
- sensitivity to change in underlying asset price
- Sensitivity to change in delta
- Sensitivity to change in underlying asset price volatility

Risk measured used by banks, asset 1
...
Traditional (long-only) asset managers
- Used risk measures :
+ Sensitivity analysis of interest risk and market risk
+ Historical and hypothetical scenario analysis ; Option risk
+ Active share (difference between weight of a security in the portfolio and its weight in the benchmark)
+ Ex-post tracking error (measure of portfolio's tracking error relative to benchmark portfolio over a lookback period) ; Ex-ante tracking error (estimate of potential underperformance
of current portfolio)
- Concerned risks : Return volatility ; probability distribution of absolute losses or losses relative to benchmark
3
...
Defined benefit pension funds
- Used risk measures : VaR for surplus (assets - liabilities) ; estimated of hedged exposure and unhedged exposure of the fund
- Concerned risks : Mismatch between assets and liabilities ; volatility of surplus
5
...
Life insurers
- Used risk measures : sensitivity analysis for market risk factor s for both investment portfolio and annuity liabilities ; scenario analysis for both nonmarket and market risk factors
- Concerned risks : market risks to the investment portfolio and liabilities ; assets - liabilities mismatch ; scenarios that lead to large decreases in the surplus

Constraints / Risk budgeting

Constraints :
- Too restrictive → reduce profitability
- Not restrictive → financial distress, corporate reorganisa on , bankruptcy
- Restriction @ business-unit level → may be to restric ve → not take into account diversifica on / offse ng posi ons across business units
Risk budeting :
- Step 1 : Determine acceptable total risk for an organisation
- Step 2 : Allocate that risk to different activities, strategies, asset classes to generate max return for the risk taken
Position limits : Max allocation (currency amounts or portfolio %) allowed for individual securities, asset classes, investment in a single country, etc
...
Real risk-free discount rate
2
...
Risk premium for the uncertainty of CF
Value of an asset change if:
- change in forecasted CF, or
- Change in any component of discount rate

Roles of expectations and changes Market participants receive new information → revise ming and amounts of expected future CF → change valua on
...
real ST interest rates

With no inflation, default-free bond has to compensate investor for foregoing current consumption
Real risk-free interest rate derives from inter-temporal rate of substitution (represent investor's trade-off between real consumption now and real consumption in the future)

𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑢𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑐𝑜𝑛𝑠𝑢𝑚𝑖𝑛𝑔 1 𝑢𝑛𝑖𝑡 𝑖𝑛 𝑡ℎ𝑒 𝑓𝑢𝑡𝑢𝑟𝑒 𝑢
=
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑢𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑜𝑓 1 𝑢𝑛𝑖𝑡 𝑢
Investor always prefers current consumption over future consumption → 𝑢 > 𝑢 → 𝑚 < 0
(*) Note
- ↑ u lity of current consuming rela ve to future consuming → ↑ real interest rate
- Diminishing marginal utility of wealth : ↓ marginal u lity of consump on as ↑ wealth ; ↑ marginal u lity of consump on during scarcity periods
- ↑ expected future income → ↓ marginal u lity of future consump on rela ve to current consump on → ↑ interest rate
- Better expected future economy → ↑ expected future income → ↑ current consump on + ↓ savings
- Worse expected future economy → ↓ expected future income → ↓ current consump on + ↑ savings
- ↑ expected return → ↑ savings
- ↑ uncertainty of future income → ↑ savings
𝑖𝑛𝑡𝑒𝑟 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 = 𝑚 =

Risky cashflow and risk premium

Ulitity of consumption and GDP
growth rate

Short-term nominal risk-free
interest rate

Uncertain underlying CF → ↑ risk premium for the uncertainty
- Price of a risk-free, inflation-indexed, zero-coupon bond that will be sold prior to maturity
𝐸 𝑃
𝑃 =
+ 𝑐𝑜𝑣 𝑃 , 𝑚
1+𝑅
- Covariance between the expected future price of the bond and the inter-temporal rate of substitution can be viewed as a risk premium
- High forecasted GDP growth → ↑ expected future income → ↓ u lity of future consump on → ↓ inter-temporal rate of subs tu on → ↓ savings + ↑ interest rate
→ real interest rate is positively correlated with real GDP growth rates
- Interest rate is positively correlated with the expected volatility in GDP growth due to higher risk premium
Nominal risk-free interest rate include premium for expected inflation - π

𝑟

= 𝑅+𝜋

Which:
𝑟 = 𝑆𝑇 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑅 = 𝑟𝑒𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝜋 = 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑜𝑟 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛
Long-term nominal risk-free
interest rate

Compared to short-term nominal risk-free interes rate, Long-term nominal risk-free interest rate also bear uncertainty about actual inflation

𝑟

=𝑅+𝜋+𝜃

Which :
𝑟 = 𝐿𝑇 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝜃 = 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑜𝑟 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦
Term spread = θ = yield of LT bond - yield of ST bond (usually > 0)
Required rate of return for credit
risky bonds

Credit risky bond has additional premium for scredit spread (credit risk premium)
Credit risk premium = yield of credit risky bond - yield of default free bond of the same maturity
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑓𝑜𝑟 𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘𝑦 𝑏𝑜𝑛𝑑𝑠 = 𝑅 + 𝜋 + 𝜃 + 𝛾

Which :
𝛾 = 𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚
- Economic downturn → default rate increase + Revovery rate decrease → Credit spread increase ;
- Economic expansion → credit spread decrease
Required rate of return for equity

Equity has additional premium for additional risk premium relative to risky debt

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑓𝑜𝑟 𝑒𝑞𝑢𝑖𝑡𝑦 = 𝑅 + 𝜋 + 𝜃 + 𝛾 + κ
Which :
κ = 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑡𝑜 𝑟𝑖𝑠𝑘𝑦 𝑑𝑒𝑏𝑡
λ = 𝑒𝑞𝑢𝑖𝑟𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝛾 + κ
- Consumption hedging property : asset that provide higher payoff during economic downturns → reduce risk premium on an asset → higher value
- Equity price are higher during expansion → not effec vely hedge against bad consump on outcomes → posi ve equity risk premium
Required rate of return for real
estate investment

Characteristics of real estate investments :
- Bond-like : due to steady rental income
- Equity-like : due to uncertainty of value of property at the end of the lease term
- Illiquidity

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑓𝑜𝑟 𝑟𝑒𝑎𝑙 𝑒𝑠𝑡𝑎𝑡𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝑅 + 𝜋 + 𝜃 + 𝛾 + κ + φ
Which:
𝜑 = 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚
- Commercial property values are cyclical, with positive correlation with values of other asset classes → poor hedge against bad consump on outcomes → required risk premium is
relatively high (close to risk premium required for equity investments)

Taylor rule

Central bank set policy rate to:
(1) maintain price stability, and
(2) achieve max sustainable level of employement
Taylor rule link central bank policy rate to economic condition
Central bank can:
- Making appropriate changes to policy rate → moderate the business cycle
- Not making appropriate changes to policy rate → magnify the cycle

𝑟 = 𝑅 + 0
...
5 × 𝑦 − 𝑦 ∗
Which:
𝑅 = 𝑛𝑒𝑢𝑡𝑟𝑎𝑙 𝑟𝑒𝑎𝑙 𝑝𝑜𝑙𝑖𝑐𝑦 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝜋 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒
𝜋 ∗ = 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑏𝑎𝑛𝑘 𝑠 𝑡𝑎𝑟𝑔𝑒𝑡 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒
𝑦 = 𝑙𝑜𝑔
...
𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑏𝑎𝑛𝑘 𝑠 𝑡𝑎𝑟𝑔𝑒𝑡 𝑠𝑢𝑠𝑡𝑎𝑖𝑛𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑝𝑢𝑡

Business cycle and yield curve slope - Recession → low policy rate
- Economy come out of recession → improve expecta on about GDP growth and infla on → higher long-term rate → posi ve sloped yield curve
- Expectation of decline in GDP growth → lower long-term rate → nega ve sloped yield curve (inverted yield curve)
Factors that affect yield spread
between non-inflation-adjusted
and inflation-adjusted indexed
bonds

Break-even inflation (BEI) = yield on non-inflation-indexed bond - yield on inflation-indexed bond = expected inflation ( π) + inflation uncertainty (θ)

Affect of product market on credit - Credit spread differ among sectors and over time
quality
- Differences in credit spread are due to difference in product industry and financial leverage
- Credit spreads forissuers in cyclical sector increase significantly during economic downturns compared to issuers in non-cyclical sector
Effects of business cycle on ST and Cyclical industries → more sensi ve to business cycle phase → revenue and earnings rise and fall with rate of economic growth
LT eanings and growth expectations Defensive & Non-cyclical industries → not sensi ve to business cyce phase → stable earnings and revenue thoughout business cycle

Cyclical effects o valuation
multiples

- Increase in expected future earnings growht → increase price mul ple (P/E, P/B) :
- Decrease in components of required rate of return (real risk free rate, expected inflation, risk premium) → increase in price mul ple

Different investmetn strategies

1a
...
Value stocks :
- Low P/E, high dividend yields
- Mature market, stable earnings
- Perform well during recession

Use of economic analysis in sector
rotation strategies

2a
...
Large-cap stocks : Lower volatility
There are periods during which 1 sector outperforms the other
→ Generate superior returns if able to rotate out underperforming sector and into be er perforing sector right before the change in performance
Economic analysis help in understanding and forecasting the relationship between equity market performance of different sectors and business cycle → enhance sector rota on strategy

Concepts
Active return

Description
Analysis of Active Portfolio Management
Active return : value added by active management
- Ex-ante active return : difference between expected return of active portfolio and expected return of benchmark
𝐸 𝑅 =𝐸 𝑅 −𝐸 𝑅
- Ex-post active return : difference between actual return of active portfolio and actual return of benchmark
Active weights : difference between security's weight in an active portfolio and its weight in the benchmark → determine the ac ve return

𝐸 𝑅

= ∑𝑤

𝐸 𝑅

=𝐸 𝑅

,

×𝐸 𝑅
−𝐸 𝑅

and

,

= ∑𝑤

Which:
∆𝑤 = 𝑎𝑐𝑡𝑖𝑣𝑒 𝑤𝑒𝑖𝑔ℎ𝑡 = 𝑤

,

,

−𝑤

×𝐸 𝑅

= ∑𝑤

𝐸 𝑅
,

− ∑𝑤

,

×𝐸 𝑅

,

×𝐸 𝑅

,

,

= ∑ ∆𝑤 × 𝐸 𝑅

,

Sharpe ratio (SR)

Sharpe ratio (SR) : excess return per unit of risk (standard deviation)
𝑅 −𝑅
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 𝑆𝑅 =
𝜎
(*) Sharpe ratio is unaffected by additional cash or leverage in the portfolio (similar effect on both numerator and denominator)

Information ratio (IR)

Information ratio (IR) : active return per unit of active risk (standard deviation of active returns)
𝑅 −𝑅
𝑅
𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑡𝑢𝑟𝑛
𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 𝐼𝑅 =
=
=
𝜎
𝜎
𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑖𝑠𝑘

Important notes on Sharpe ratio
(SR) and Information ratio (IR)

- IR is usually ex-ante
...
A er fee, IR o en < 0
- Fund with zero systematic risk : use risk-free rate as benchmark → IR = SR
- IR changes with additional of cash / use of leverage
- For unconstrained portfolio : IR is unaffected by the aggressiveness of the active weight (similar effect on both numerator and denominator)
- Combine actively managed portfolio with benchmark portfolio : IR of combined portfolio = IR of original actively managed portfolio
...
Information coefficient (IC) : expected risk-weighted correlation between active returns vs
...
Transfer coefficient (TC) : correlation between actual active weights vs
...
Breadth (BR) : number of independent active bets per year
Fundamental law of active portfolio Grinold rule : compute expected active return based on IC, active risk and standardised score
1
...
Calculation of expected value added by active management :

𝐸 𝑅

= ∑ ∆𝑤 × 𝜇

3
...
Constrained portfolio (TC < 1) : Calculation of Information ratio (IR), Sharpe ratio, Active return and optimal level of active risk :

𝐼𝑅 = 𝑇𝐶 × 𝐼𝐶 × 𝐵𝑅
𝐸 𝑅 = 𝑇𝐶 × 𝐼𝐶 × 𝐵𝑅 × 𝜎
𝐼𝑅 ∗
𝜎 = 𝑇𝐶 ×
×𝜎
𝑆𝑅
𝑆𝑅

=

𝑆𝑅

+ 𝑇𝐶 × 𝐼𝑅 ∗ < 𝑆𝑅

𝐼𝑅 ∗ = 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑢𝑛𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜

=

𝑆𝑅

Ex-post performance measurement Calculation of realised value added, using ex-post information coefficient
𝐸 𝑅 |𝐼𝐶
= 𝑇𝐶 × 𝐼𝐶
× 𝐵𝑅 × 𝜎
Actual return of active portfolio = condition expected return + noise term

𝑅 = 𝐸 𝑅 |𝐼𝐶

+ 𝑁𝑜𝑖𝑠𝑒

+ 𝐼𝑅 ∗

Use of information ratio in select
investment manager and level of
active risk

Portfolio theory conclusion : investors will choose a combination of risk-free asset and optimal risky portfolio, with weight based on risk tolerance
Optimal risky portfolio : portfolio with highest Sharpe ratio
Portfolio with highest Information ratio → por olio with highest Sharpe ra o
→ Ac ve por olio with highest Informa on ra o is the op mal ac ve por olio

𝐸 𝑅 = 𝐼𝑅 × 𝜎
→ higher IR → higher expected ac ve return
Market timing

Market timing : bet on direction of the market
Information coefficient of market timers is based on proportion of correct calls
𝐼𝐶 = 2 × % 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 − 1

Sector rotation

Sector rotation : investment strategy involving the movement of money from one industry sector to another in an attempt to beat the market
1
...
Annualised active risk and active return : annual active risk and active return, based on number of breadth
𝐴𝑛𝑛𝑢𝑎𝑙𝑖𝑠𝑒𝑑 𝑎𝑐𝑡𝑖𝑣𝑒 𝑟𝑖𝑠𝑘 = 𝜎 = 𝜎 × 𝐵𝑅
𝐴𝑛𝑛𝑢𝑎𝑙𝑖𝑠𝑒𝑑 𝑎𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝐸 𝑅 = 𝐼𝐶 × 𝐵𝑅 × 𝜎
Strengths and limitations of
fundamental law of active
management

Strengths : can be used to evaluate a range of active strategies
Limitations : poor inputs estimates lead to incorrect evaluation
- Ex-ante measurement of skill : Information coefficient (IC) is estimate of accuracy of active manager's forecast → manager tends to overes mate their ability to outperform the market
- Independence : breadth should be truly independent decisions that active managers makes
...
g
...
Execution algorithms : execute large orders with minimal price impact and without notice from other market participants (by breaking large order into smaller pieces)
2
...
Volume-weighted average price (VWAP) - Algorithms :
- Consider a security's historical trading patterns over a typical day
- Split large order into pieces sized proportionally to this historical distribution → larger pieces are executed during mes of the day when there are more trading
2
...

3
...
Statistical arbitrage : identify securities that historically move together but have diverged recently → buy 1 security + sell the other to realise profit when they eventually converge
a
...
Index arbitrage : seek temporary price performance differences between securities and their sector
c
...
Spread trading : take long and short position in 2 closely-related futures contracts e
...
:
- Intra-market spread : long 1 contract month + short another contract month for the same futures (long nearer futures + short later futures)
- Inter-market spread : Long futures in 1 market + Short same futures on another market
- Inter-exchange spread : Long futures in 1 exchange + Short same futures on another exchange
- Multilegged inter-exchange spreads :
+ Crack spread : crude oil vs petroleum products
+ Spark spread : electricity from gas-fired power plant vs
...
soybean oil futures vs
...
Mean reversion : when price of a security drift away from its recently historical mean → price will likely to move toward that mean
f
...
g
...
Liquidity aggregation and smart order routing :
- Market fragmentation → different price and liquidity of an idividual security across market
- Liquidity aggregation → gain full picture of liquidity over mul ple trading venues → direct each order to market that has the best price and liquidity
3
...
Trading on the news : trade, near-instantaneously and without human intervention, based on reaction to breaking news
5
...
Real-time pre-trade risk firewall
- Continuously calculate risk exposures on trading positions being taken → block trades that would exceed the risk limits
- Block errorneous trades (e
...
: fat finger trades - trade @ irrational price / quantity)
- Protect brokers that offers clients "sponsored access" to broker's exchange membership
2
...
E
...
:
1
...
Front running : trader has advance knowledge of a large buy order → trades slightly earlier than that order to profit from the price movement created by that large transac on
3
...
Fictitious orders : submit fictitious orders to move market price / force other algorithms to make unwise trades
- Quote stuffing : submit a large number of orders into the market and immediately cancels them → distract other market par cipants → give the origina ng algorithm opportunity to
trade ahead of others + take advantage of mispricing from the false order
- Layering : algorithm places genuine orders on one side of the market and layers of fake orders on the other side of the market → induce market par cipants to trade with the genuine
order
- Spoofing : place orders between the bid and ask price and cancel these trades before they execute → create fake pessimism / op mism about the security
5
...
Trader collusion : multiple traders work together to sway markets in a favorable direction to them

Positive & Negative impacts of
Algorithmic and High-frequency
trading

Positive impacts

Negative impacts

1
...
Increase liquidity via the high-frequency trading firms' willingness to buy and sell
securities
3
...
Tighter bid-ask spreads
5
...
Promote open and competitive markets
7
...


1
...
Mangnification of market movements by continue to execute instruction in situation that
may make human trader to pause
3
...

4
...
Out-of-control algorithms : if a trading algorithm was not tested adequately, or face a
scenario that was not programmed to deal with → may go wild and place illogical orders →
large loss for the firm
6
...
Slowed markets due to excessive orders
8
...
Unequal access to information : algorithmic programs are expensive to develop and
implement → smaller and individual investors have unequal access to informa on



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