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Title: CFA Level 3 - Portfolio Management and Wealth Planning
Description: I create this summary of knowledge for CFA level 3 2019 June exam. Hope this can help you. Please note that this may not cover all syllabus, and does not guarantee for your pass, which requires dedication, hardwork and consistency. In case having trouble with any part, please refer to CFA notebook/Schwesser

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Concepts

Description

Economic balance sheet

Introduction to asset allocation
1
...
Nonfinancial assets and liabilities = extended assets and liabilities
Examples :
    ‐  human capital : PV of expected earnings
    ‐ PV of pension income
    ‐ PV of expected intellectual properties royalties
    ‐ PV of expected underground resources
3
...
Asset‐only approaches : asset allocation decision 100% based on investor's assets
    ‐ Objectives : max the expected return per unit of risk
    ‐ Should consider investor constraints + risk tolerance
    ‐ Risk concept : asset class risk + create effective asset class combination
    ‐ Risk measure : standard deviation of portfolio, relative risk to a benchmark (tracking error), downside risk (VAR, semivariance, maximum drawdown)
2
...
Goals‐based approaches : asset allocation for subportfolios, that help investor to achieve the lifestyle/aspirational financial objectives
    ‐ Need to specify : (1) type of CF needed, (2) time horizons, (3) evel of risk tolerance (probability of achieving certain goal)
    ‐ Risk concept : unable to achieve financial goals
    ‐ Portfolio risk = weighted sum of risk of each goal

Allocation by asset classes

Asset classes : group of assets with similar characteristics
3 main super asset classes : (1) capital assets (bond, equity) ; (2) consumable / transformable assets (commodities) ; (3) store‐of‐value assets (currency, art)
Criteria to specify asset classes :
    ‐ Same asset class → similar a ributes (both descrip ve and sta s cal)
    ‐ Assets cannot be classified in more than 1 asset class
    ‐ Asset classes should cover all investable assets
    ‐ Asset classes should contain mostly liquid assets

Use of risk factors in asset
allocation

Investor selects asset classes based on desired exposure to common risk factors (volatility, liquidity, inflation, interest rate, duration, FX, default)
Factor‐based asset allocation : Risk factor may be overla across multiple asset classes → should focus on risk factor by iden fying risk factors + desired exposure to each
Limitation : cannot directly invest in all risk factors

Strategic asset allocation

Strategic asset allocation : combine market expectations with investor's risk, return and constraints
Steps in select strategic asset allocation :
    ‐ Step 1 ‐ Determine objectives : how investor use these assets? What investor want to achieve? What is the liabilities/goals? How to measure the objectives?
    ‐ Step 2 ‐ Determine risk tolerance : What is the sensitivities to risk? How to measure risk?
    ‐ Step 3 ‐ Determine time horizon
    ‐ Step 4 ‐ Determine constraints : tax situation? Social, environmental or governance considerations? Legal, regulatory, political considerations?
    ‐ Step 5 ‐ Select aset allocation approach : asset‐only / liability‐relative / goals‐based
    ‐ Step 6 ‐ Specify asset classes
    ‐ Step 7 ‐ Develop potential asset allocation
    ‐ Step 8 ‐ Test the results of potential asset allocation : to see if results align with objectives and risk tolerance for chosen horizon
    ‐ Step 9 ‐ Repeat step 7 + 8 untill discover optimal asset allocation

Global market portfolio

Global market portfolio :
    ‐ all available risky assets (global equity, global fixed income, global real estates, etc
...
g
...
Tactical asset allocation : active management strategy, seek for additional risk and return (alpha) to take advantes of ST opportunities
    ‐ Deviation should be restricted by risk budgets / rebalancing
    ‐ Reasons for deviation : forecasted asset class valuation, business cycle state, stock price momentum
    ‐ Trade off between potential outperformance vs tracking error
    ‐ Limitation : additional trading + monitoring cost; additional capital gain taxes
2
...
Passive management : investor insight / expectations does not impact portfolio composition
2
...
excess return
    ‐ tax status of investor

Risk budgeting

Risk budgeting : specify how risk should be distributed among portfolio assets without regad to asset expected returns
Active risk budgeting : how much additional risk investor willing to take compared to benchmark
    ‐ for asset classes allocation : active risk is deterimined by strategic asset allocation vs
...
asset class benchmark

Rebalancing

Benefits :
    ‐ maintain portfolio's risk and return characteristics as specified in IPS
    ‐ provide discipline
Drawbacks :
    ‐ related tax liability
    ‐ transaction costs

Rebalancing approaches

Calendar rebalancing

Percentage‐range rebalancing

Definition

Rebalance the portfolio to its strategic allocation on predetermined, regular Manager set a tolerance band / corridors (±5%) that are considered optimal
basis (monthly, quarterly)
...
If any asset class goes outside of that corridor, the
volatility
portfolio is rebalanced

Benefits

No need for constant monitoring

Costs

Subject to hard movement between rebalancing dates

Minimize the degree that asset classes can violate their allocation corridor
Increase time and expenses of constantly monitoring and trading

Considerating when setting
corridors

1
...
Risk tolerance : Less risk‐averse investor → wider corridor
3
...
Momentum : believe that current trend will continue → wider corridor ; believe in mean reversion → ghter rebalancing
5
...
Derivatives : If derivatives could be used in rebalancing → lower transac on costs, lower taxes, execute quicker and easier → ghter corridor
7
...
Volatility : higher volatility asset → ghter corridor

Concepts

Description

Mean‐variance optimisation

Principles of asset allocation
Mean‐variance optimisation (MVO) : identify portfolio allocations that maximise return for every level of risk
Assumptions : assume investors are risk adverse → prefer more return for for same level of risk
Approach to find the most efficient portfolio :
𝑈𝑡𝑖𝑙𝑖𝑡𝑦 𝑚𝑎𝑥𝑖𝑚𝑖𝑠𝑎𝑡𝑖𝑜𝑛 : 𝑈
𝐸 𝑅
0
...

    ‐ Average λ = 4
Common constraints :
    ‐ Budget constraints/Utility constraint : Sum of weights of all asset classes = 100%
    ‐ Non‐negativity constraint : Weight of each asset class is between 0% and 100%
Criticisms of MVO

Improve inputs quality ‐
Reverse optimisation

1
...
Concentrated asset allocation : MVO often identifies efficient portfolios that are highly concentrated in a subset of asset classes, and zero allocation to others → lowest standard
deviation does not mean diversification
3
...
Risk diversification : MVO diversify asset allocation across asset classes, but may not diversify source of risk
5
...
Single‐period framework : ignore interim CF / serial correlatio of asset returns from each period → ignore poten al costs/beneﬁts of rebalancing
Inputs
‐ Assumed optimal asset allocations
‐ Variances
‐ Covariances (Correlation)
‐ Risk aversion factor

Reverse MVO
‐ Maximise utility

Inputs
‐ Revised optimal asset allocations
‐ Portfolio expected return

MVO
‐ Maximise utility

Output

Output
‐ Implied returns
‐ Variances
‐ Covariances
(Correlations)

Advantages :
    ‐ Adress criticism #4 ‐ Risk diversification : Already reflect highly diversified portfolio
    ‐ Address criticism #1 ‐ GIGO : Improve return estimtes
Improve inputs quality ‐
Black Litterman model

Black Litterman model : extension of reverse optimisation, with implied returns are adjusted to reflect investor's view of future returns
Inputs
‐ Assumed optimal asset allocations
‐ Variances
‐ Covariances (Correlation)
‐ Risk aversion factor

Reverse MVO
‐ Maximise utility

Output

Black Litterman

Inputs
‐ Revised optimal asset allocations
‐ Portfolio expected return

MVO
‐ Maximise utility

Output
‐ Adjusted implied returns
‐ Variances
‐ Covariances
(Correlations)

Improve inputs quality ‐
Add more constraints

Adding more constraints : to include / exclude certain asset classes
Examples :
    ‐ Specifiy a fixed allocation to one or more assets (e
...
: human capital, nontradable assets)
    ‐ Set asset allocation range for asset class
    ‐ Set upper limit allocated for asset class to address liquidity issues
    ‐ Specify relative allocation between 2 or more classes
    ‐ Include constraints to require allocation to assets that hedge the liability in liability‐relative setting

Improve inputs quality ‐
Resampled MVO

Step 1 : Best estimates of expected returns, sigma, correlation → MVO → Eﬃcient fron er of Op mal alloca ons
Step 2 : Monte Carlo simulations to generate random variations for inputs around initial estimtes → Eﬃcient fron er + asset alloca on for each point in the fron er
Step 3 : Average simulated efficient frontier + asset allocation

Improve inputs quality ‐
Non‐normal distributions
(Skewness and Kurtosis)

Directly incorporate skewness / kurtosis in utility function, using asymmetric definition of risk (Value‐at‐Risk) instead of variance

Incorporate human capital and
residential real estate to MVO
framework

1
...
Residential real estate
    ‐ Can be add to individual's portfolio
    ‐ Risks and returns inputs are estimated using residential real estate property index for that specific region
    ‐ Add residential real estate → increase individual's capacity to take on addi onal risk
    ‐ Constraints : % allocated to residential real estate = current value of residential real estate / total portfolio value

Use of Monte Carlo simulation and 1
...
Guide investors to identify their risk tolerance level by showing the range and likelihood of possible outcomes, with various assumptions
Liquidity considerations in asset
allocation

Less‐liquid asset classes require liquidity return premium
Issue with less liquid asset classes in MVO :
    ‐ Few indexes available to track illiquid investments → harder to ﬁnd data to es mate return, risk and correla on
    ‐ Not investable as passive alternative
    ‐ Risk‐return characteristics of each specific real estate, private equity is different from other assets in its asset class
Solutions :
    ‐ Exclude illiquid asset classes when MVO, but use them to meet separate target asset allocation
    ‐ Include illiquid asset classes in MVO ; generate inputs from the specific investments
    ‐ Include illiquid asset classes in MVO ; use highly diversified asset class inputs
...
Specify additional constraints (e
...
: limit allocations to risky asset classes ; ceiling on portfolio risk)
2
...
Use Monte Carlo to show various wealth outcomes from assuming allocations with different levels of risk

Use of investment factors in asset Investor could define the opportunity as set of factors (e
...
: market exposure, size, valuation, momentum, liquidity, duration, credit, volatility)
allocation
Factors are zero‐dollar investment portfolio, which long the better performing attribute + short underperforming attribute
Example :
    ‐ Zero‐dollar portfolio long small stocks + short large stocks
    ‐ Zero‐dollar portfolio long value + short growth
Factors are not highly correlated with each other and other portfolio → improve risk‐return tradeoﬀ from op mal por olio + expands eﬃcient fron er
Characteristics of liabilities that
are relevant to asset allocation

1
...
g
...
g
...
Legal vs Quasi‐legal :
    ‐ Legal liabilities : obligations defined in a legal agreement
    ‐ Quasi‐legal liabilities : not legal obligated, but CF are expected to occur in future, which are essential to the mission of the institution
3
...
Liability value vs size of sponsoring organisation :
    ‐ large liability compared with the size of sponsoring organisation → necessary to be accounted in asset alloca on decision
    ‐ small liability : could be ignored
5
...

6
...
Regulations affecting the determination of liability value

Approaches to liability‐relative
asset allocation

1
...
Surplus volatility = measure of risk
∆𝐴𝑠𝑠𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 ∆𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒
𝑅
𝑆𝑢𝑟𝑝𝑙𝑢𝑠 𝑟𝑒𝑡𝑢𝑟𝑛
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑎𝑠𝑠𝑒𝑡 𝑣𝑎𝑙𝑢𝑒
𝑈

𝑅

0
...
2‐portfolio approach : separate asset portfolio into (1) hedging portfolio and (2) return‐seeking portfolio
    ‐ Hedging portfolio : created using CF matching / duration matchig / immunisation
    ‐ Modified approaches :
        + partially hedge liabilities + allocate more capital to return‐seeking portfolio
        + increase allocation to hedging portfolio
    ‐ Limitations :
        + Funding ratio < 0 → diﬃcult to create a hedging por olio that fully hedges the liabili es
        + May not be able to hedge certain kinds of risk (earthquakes)
3
...

Size of investment = PV of future goal discounted @ expected return of that module

Others approaches

1
...
60/40 split : maintain asset allocation @ 60% stocks / 40% bonds
3
...
Risk parity
    ‐ Each asset class contribute same amount of total portfolio risk → achieve diversiﬁca on
    ‐ Critic : focus only on risk, ignore return
5
...
Larger fund

Asset Allocation with Real‐world Constraints
‐ Lack expertise + governance structure to invest in complex strategies
‐ Difficult to achieve diversification
‐ Local legislation may restrict investors with a given level of capital / experience to invest in some assets
→ Could use commingled accounts (money pools from group of investors) to get an adequate size to diversify
‐ Have access to greater management expertise in governance capacity → able to apply complex strategies
‐ Able to invest in assets with high minimum investment requirements → higher level of diversiﬁca on
‐ Benefit from economic of scale (cost savings of internal management ; better negotiating power → be er management fee; higher alloca on to alterna ve
investments)

‐ May unable to take advantage of asset classes that lack the capacity to absorb large amount of funds
...
Too large fund

Additional constraints ‐ Liquidity
needs

Additional constraints ‐ Time
horizon

1
...
Sovereign Wealth funds, Endowments, Pension plans, Foundations

Longer time horizons + Lower liquidity

3
...
Life and Auto insurance

Low liquidity due to predictability of claims

5
...
Definitions :
    ‐ liability / goals to be funded at a future date
    ‐ Time horizon should be defined by each liability / goal
    ‐ Time progress → mix of assets / liabili es should change
2
...
Main consideration :
Insurance companies
    ‐ maintain enough capital to meet policyholders' claim
    ‐ factors that affect financial strength metrics :
        + Risk based capital measures
        + Liquidity
        + Yield levels
        + Credit rating
        + Potential to liquidate assets to meet claims
2
...
Main consideration : compare risk (risk of funding cost > a given threshold) vs return (PV of expected contribution) → decide op mal combina on
Pension funds
2
...
g
...
Common characteristics :
    ‐ Interest income : tax @ higher rate
    ‐ Dividend : tax @ lower rate
    ‐ Capital gain : tax @ lower rate; capital losses could be offset with capital gain
    ‐ Certain investments accounts may be tax deferred / tax exempt
2
...
Portfolio rebalancing
    ‐ Must balance the need to maintain strategic asset allocation vs ability to avoid tax
    ‐ Tax reduce volatility → taxable por olio should be rebalanced less frequently
𝑅𝑒𝑏𝑎𝑙𝑎𝑛𝑐𝑖𝑛𝑔 𝑟𝑎𝑛𝑔𝑒 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑅𝑒𝑏𝑎𝑙𝑎𝑛𝑐𝑖𝑛𝑔 𝑟𝑎𝑛𝑔𝑒 𝑝𝑟𝑒𝑡𝑎𝑥/ 1 𝑡
4
...
Ways to adjust unrealised gain/loss from market value :
    ‐ Assume assets are sold today → subtract unrealised gain/loss from current market value
    ‐ Assume assets are sold in the future → discount tax liability @ asset's a er tax return
    ‐ Assume assets are sold in the future → discount tax liability @ a er tax risk free rate
6
...
Change in goals
    ‐ For business : change in business cycle (e
...
: business downturn → increase CF needs)
    ‐ For individual : change in personal circumstances (e
...
: change in employment status, marriage status → change willingness + ability to take risk)
2
...
Change in beliefs
    ‐ Reasons :
        + Change in personnel of investment committee
        + Change in economic environment
        + Change at predetermined date without detailed reexamination (e
...
: target‐date mutual fund adjust asset allocation based on investors's age)

Tactical asset allocation

1
...
Objective :
    ‐ Increase risk‐adjusted returns by exploit ST opportunities (assume ST returns are predictable)
    ‐ Success depends on market timing, not security selection
    ‐ Consider constraints specified in IPS, but not specific liabilities/goals
3
...
benchmark of SAA
    ‐ Deviation size limited to a range around the allocation
    ‐ May have an allowable range of predicted volatility / tracking error budget vs
...
Evaluation :
    ‐ Compare TAA's Sharpe ratio vs SAA's Sharpe ratio
    ‐ Calculate information ratio / t‐stat of excess realised returns vs
...
Drawbacks :
    ‐ Additional trading costs and tax
    ‐ Increase risk
    ‐ Reduce diversification

Approaches to Tactical asset
allocation

1
...
More put purchase → increase vola lity ; more call purchase → decrease vola lity
2
...
Value approach : earn excess return of value stocks over growth stocks
    ‐ Value equities : identified using dividends yield / CF yields
    ‐ Value currencies : identified using ST interest rate difference
    ‐ Value commodities : identified using roll yield
    ‐ Value fixed income : udentified using yield spread over risk free rate
4
...
Loss aversion : dislike same loss > like same gain
    ‐ Solution : goal‐based investing (high priority goal is funded with less risky assets, and vice versa)
2
...
Mental accounting : separate assets/ liabilities to different groups based on subjective criteria → subop mal asset alloca on + less chance to meet goals
    ‐ Solution : goal‐based investing
4
...
Framing bias : the way information is presented affect the decision
    ‐ Solution : provide full range of relevant information
...
g
...
Availability bias : personal experience is more influenced in decision making
7
...
Home bias : over allocate in domestic securities → missing opportuni es in interna onal securi es

Investment governance

Effective framework should include :
    ‐ Clear ST + LT objectives
    ‐ Logical allocation of responsibility for asset allocation decisions based on skills and workload
    ‐ Process for develop + approve IPS
    ‐ Process for develop + approve strategic asset allocation
    ‐ Framework to monitor  + report performance relative to specified goals / objectives
    ‐ Periodic audits

Concepts

Description

Price Currencies /
Base Currencies

Base currencies : denominator of the exchange rate
Price currencies : numerator of the exchange rate

Currency Management ‐ Introduction

* Buy / Sell : to buy /sell the base currencies
Bid / Asked price

Bid/Asked price : difference is dealer's profit margin

Spot vs
...
Advantages :
    ‐ In short run, currency could fluctuate extremely → could exploit ineﬃcient pricing to increase por olio return
2
...
Passive hedging :
    ‐ Rule based
    ‐ Match currency exposure with the benchmark
    ‐ Require periodic balancing
    ‐ Goal : eliminate currency risk relative to benchmark
2
...
g
...
Active currency management :
    ‐ Moderate deviation from benchmark
    ‐ Manager is expected to generate positive incremental portfolio return from managing currency exposure
    ‐ Goal : earn incremental income (alpha), not reduce risk
4
...
Strategic Diversification Issues :
    ‐ LT currency volatility < ST currency volatility → ↓ need to hedge currency
    ‐ Positive correlation between foreign asset return and return from foreign currency → higher return vola lity → higher need for currency hedge
    ‐ Bond portfolio has higher positive correlation between asset return and currency return than equity portfolio → higher need for currency hedge in bond por olio
    ‐ Hedge ratio : varies by manager preferences
2
...
Short time horizon → hedge
2
...
Client with no concern of opportunities costs → hedge
4
...
Significant foreign currency bond exposure → hedge
6
...
Client with doubt of benefits of discretionary management →  hedge

Active strategies ‐ Economic
fundamentals

1
...
Factors that increase value of currency in ST :
    ‐ Currency is undervalued relative to fundamental value
    ‐ Currency with highest rate in increase of fundamental value
    ‐ Currency with higher real / nominal interest rates
    ‐ Currency with lower inflation
    ‐ Currency with decreasing risk premium

Active strategies ‐ Technical
analysis

1
...
Not necessary to know its fundamental value
2
...
Definition : borrow @ lower interest rate currency + invest @ higher interest rate currency
2
...
In fact :
    ‐ Higher interest rate currency depreciation < predicted by UIRP → carry trade earns proﬁt
    ‐ Small % of time (e
...
: hyperinflation, economic crisis), higher interest rate currency depcreciate much more than predicted in UIRP → carry trade suﬀer large loss

Active strategies ‐ Volatility
trading

1
...
Term :
    ‐ Delta : change in option price due to change in underlying value
    ‐ Vega : change in option price due to change in volatility of underlying
3
...
Definition : gain/loss on forward / future if spot price is unchanged at expiration
2
...
Relationship between forward premium / discount, initial difference in interest rate and roll yield :
Forward price > Spot price ; Interest base < Interest price

Forward price < Spot price ; Interest base > Interest price

Long Base currency forward
(Short price currency forward)

Negative roll yield → higher hedging cost → discourage hedging

Positive roll yield →  lower hedging cost → encourage hedging

Short Base currency forward
(Long price currency forward)

Positive roll yield → lower hedging cost → encourage hedging

Negative roll yield → higher hedging cost → discourage hedging

Strategies to reduce hedging costs 1
...
Buy at‐the‐money (ATM) put option (protective put) :
    ‐ Eliminate all downside risk, but retain upside potential
    ‐ Highest initial cost, but no opportunity cost
3
...
Collar : long OTM put + short OTM call
    ‐ OTM put : provide some downside protection + cost less than ATM put
    ‐ OTM call : generate premium income → decrease ini al cost; but limit upside poten al
5
...
Seagull spread : put spread + Short OTM call (Long OTM put + Short further OTM put + Short OTM call)
    ‐ Less initial cost than put spread, but limit upside potential
Cross hedge /
Macro hedge /
Minimum‐variance hedge ratio

1
...
g
...
Macro hedge :
    ‐ Address portfolio‐wide risk factors than risk of individual portfolio assets
    ‐ Use derivative contract based on fixed basket of currencies → not precisely match the currency exposure, but less costly
3
...
Low trading volume in emerging market → larger bid/ask spread
...

‐ Higher cost to exit than to enter in economic crises
‐ Transactions between 2 emerging market currencies are more costly, since few dealers make direct market between currencies of small markets
‐ Emerging currencies return distributions are non‐normal, with higher probabilities of extreme events + negative skew of returns
‐ Higher yield → large forward discouns → nega ve roll yield
‐ Contagion : Correlation of emerging currencies shift to +1
...
Risk governance should be (1) transparent, (2) create clear accountability, (3) cost efficient, (4) effective in achieving
desire outcomes
    ‐ Decentralised risk governance system : Each unit is responsible to execute
        + Benefit : place risk management on hand of those closest to each part of the organisation
    ‐ Centralised risk governance system (Enterprise risk management ‐ ERM) : 1 central unit is responsible to execute
        + Benefit : place responsibility on senior management + offer economies of scale
Steps to manage risk effectively :
    ‐ Identify each exposed risk factor
    ‐ Quantify each factor in measurable terms
    ‐ Add all exposed risk in a single total measure of firm‐wide risk
    ‐ Identify how each risk contributes to firm‐wide risk
    ‐ Systematically report the risks
    ‐ Support allocation of capital / risk to each unit of the firm
    ‐ Monitor compliance with allocated capital / risk limits

Financial risks /
Nonfinancial risks

1
...
→   e to market supply / demand
    ‐ Credit risk : Counterparty / debtor fail to make promised delivery
    ‐ Liquidity risk : possible loss from inability to liquidate a position quickly at fair price : Indicators include :
        + Bid‐ask spread : apply for small transactions only
        + Average / Typical trading volume
2
...
Analytical VaR : based on normal distribution + one‐tail confidence intervals
𝑉𝑎𝑅
𝑅 𝑧 𝜎
𝑉
𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝑉𝑎𝑅 ∶
𝐷𝑖𝑣𝑖𝑑𝑒 𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝑏𝑦 12

𝑊𝑒𝑒𝑘𝑙𝑦 𝑉𝑎𝑅 ∶
𝐷𝑖𝑣𝑖𝑑𝑒 𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝑏𝑦 52

𝐷𝑎𝑖𝑙𝑦 𝑉𝑎𝑅 ∶
𝑅𝑒𝑡𝑢𝑟𝑛 0

    ‐ Advantages :
        + Single number → Easy to understand
        + Allow modelling correlations of risks
        + Can apply for shorter / longer time periods
    ‐ Disadvantages : mostly related to assumption that returns are normally distributed
        + May have skewed return
...
Short op on → nega ve skew
        + May have higher number of extreme return events than normal distribution → fat tails
2
...
Many securities changfe characteristics over time
3
...
after events
    ‐ Limitations :
        + Outputs are as goods as inputs and assumptions
        + Change event sequences → diﬀerent results
    ‐ Stylised scenarios : specific risk factors includes :
        + Parallel yield curve shift
        + Change in steepness of yield curve
        + Parallel yield curve shift + change in steepness of yield curve
        + Change in yield curvve volatility
        + Change in equity index value
        + Change in equity index volatility
        + Change in value of key currency (vs USD)
        + Change in FX rate volatility
        + Change in swap spread in G7 + Switzerland
    ‐ Actual extreme events : measure impact of major past events
    ‐ Hypothetical events : measure impact of event not previously occurred
Stressing models :
    ‐ Factor push analysis : push factors to most disadvantages
    ‐ Maximum loss optimisation : use mathematical + computer model find worst combination
    ‐ Worst cast scenario

Credit risk

Current credit risk : amount of payment due
Potential credit risk : credit risk related to payment due in the future
Credit VaR : expected loss due to default at a given probability during a given period
1
...
Swap :
    ‐ Current credit risk : at each payment exchange date
    ‐ Potential credit risk : throughout its life
    ‐ If both parties are required to make payments → both par es will bear credit risk
    ‐ If netting of payment → only party with gain will bear credit risk
    ‐ Swap near maturity → decrease remaining number of payments → decrease credit risk
3
...
Options : only long option face credit risk
5
...
capital and risk allocated (Return on Capital, Return on VaR)
Additional methods for managing market risk :
    ‐ Position limit
    ‐ Liquidity limit : set nominal limit = % of typical trading volumes
    ‐ Performance stopout : Absolute $ limit for loss to a position over a certain period
...
g
...
Notional / Nomial / Monetary position limits
2
...
Internal and regulatory capital requirements : Requirement from management / regulators to have a specified amount of capital to minimise probability of bankruptcy
4
...
Foundation phase : accumulate wealth via job + savings, seeking education, building business
    ‐ Long time horizon
    ‐ Often have little wealth (except who inherit wealth) → reduce ability to take risk
2
...
) also rise
    ‐ Max savings + wealth accumulation → higher ability to take risk
3
...
Distribution phase : assets > reasonable level of needs → begin distribu ng assets to others (gi s, inheritance, dona on)

Traditional finance /
Behavioral finance

1
...
Behavioral finance :
    ‐ Loss aversion :
        + Gain : choose certainty option
        + Loss : choose uncertainty option, hoping to avoid loss
    ‐ Biased expectations : overconfident in predicting the future (e
...
: focus o outlier events, let 1 asset represent another asset)
    ‐ Asset segregation : view asset in isolation, not consider effect of correlation with other assets
...
Cautious investors : risk adverse + base decisions on feelings
    ‐ Drefer safe, low volatility investment, little potential for loss
    ‐ Difficult to advise
    ‐ Do not like to make investment decision → miss investment opportuni es
    ‐ Low turnover portfolio
2
...
Individualistic investors : less risk adverse + base decision on thinking
    ‐ Do their own research
    ‐ Face contradict information → Spend me to reconcile the diﬀerence
    ‐ Confident in their ability to make investment decisions + ability to achieve LT investment objectives
4
...
g
...
g
...
Trust : to transfer wealth to future generation
    ‐ Revocable trust :
        + Grantor retain ownership
        + Grantor control over assets
        + Grantor is responsible for taxes
    ‐ Irrevocable trust :
        + The trust has ownership
        + Assets is considered to be transferred to future generations
        + The trust is responsible for taxes
2
...
g
...
Ability to take risk : how much volatility / losses the portfolio can withstand and still meet clients' required expenditure
...
Willingness to take risk : subjective, determined via analysis of psychological profile + facts

Return objective

Return objective has to be consistent with risk objective and constraints
Return objective needs to be specified between : nominal / real / pretax / post tax
Required return : necessary to meet high‐priority goal (e
...
: living expenses, children education, healthcare)
Desired return : to meet other secondary goals
Calculation of return :
    ‐ Step 1 : Calculate real, post tax return
    ‐ Step 2 : Nominal, post tax return = Real, post tax return + Inflation
    ‐ Step 3 : Nominal, pre‐tax return = Nominal, post tax return / (1 ‐ tax rate)

Strategic asset allocation

Strategic asset allocation (SAA) : mix of asset classes to meet return / risk objectives + consistent with constraints
Consideration when choosing portfolio :
    ‐ Step 1 : eliminate portfolio that violate constraints
        + Excess cash equivalent
        + Insufficient cash equivalent to meet appropriate liquidity needs
        + Hold / Fail to hold assets specified in constraints
    ‐ Step 2 : eliminate portfolio that violate specified risk objective (max shortfall risk, standard deviation)
    ‐ Step 3 : eliminate portfolio that generate insufficient return
    ‐ Step 4 : eliminate portfolio with inappropriate asset classes weighting
        + 60 equity / 40 fixed‐income for average investor
...
Return over time does not solely depend on the starting value of the period, but also depend on future addition / withdrawals
    ‐ Can consider points along timeline (Do savings need to be increased, Can early retire, must retire later)
Disadvantages :
    ‐ Only as goods as the inputs
    ‐ Based on return historical data
...
Taxes on income : paid by individuals / corporations on income (wages, interest, dividends, capital gain)
2
...
Tax on consumption :
    ‐ sales taxes : paid by customers
    ‐ VAT : paid at each intermediate production step, ultimately borne by consumer

Marginal tax rate

Marginal tax rate : highest tax rate applied

Accrual tax

Accrual taxes : periodic (annual) tax, calculated based on income
𝐹𝑉

𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

1

𝑟

1

𝑡

Tax drag : measure the impact of tax
𝑇𝑎𝑥 𝑑𝑟𝑎𝑔 $
𝑇𝑎𝑥 𝑑𝑟𝑎𝑔 %

𝑔𝑎𝑖𝑛 𝑤𝑖𝑡ℎ 𝑛𝑜 𝑡𝑎𝑥𝑒𝑠 𝑔𝑎𝑖𝑛 𝑤𝑖𝑡ℎ 𝑡𝑎𝑥𝑒𝑠
𝑇𝑎𝑥 𝑑𝑟𝑎𝑔 $
𝐺𝑎𝑖𝑛 𝑤𝑖𝑡ℎ 𝑛𝑜 𝑡𝑎𝑥𝑒𝑠

Observation :
    ‐ n > 1 → periodic tax payment reduce beneﬁt of tax‐free compounding over me → tax drag % > tax rate
    ‐ Time horizon increase → adverse eﬀect increase
    ‐ Higher rate of return → adverse eﬀect increase
    ‐ Increase both time horizon and rate of return → further increase adverse eﬀect
Deferred capital gains tax

Capital gain tax : tax on gain in value of asset, paid when asset is sold → can realise pretax compounding of return → lower tax drag
𝐹𝑉
𝐵

𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
1 𝑟
𝐶𝑜𝑠𝑡 𝑏𝑎𝑠𝑖𝑠
𝐴𝑠𝑠𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑠𝑡𝑎𝑟𝑡 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑

1

𝑡

𝑡

𝐵

Observation :
    ‐ Tax paid at end of time horizon → No lost of compounding of return
    ‐ Increase of time horizon / rate of return → increase tax drag
    ‐ Relationship between tax drag % and tax rate is depend in B
        + No initial unrealised gain/loss → B=1 → tax drag % = tax rate
        + Initial unrealised gain → B<1 → tax drag % > tax rate
        + Initial unrealised loss → B>1 → tax drag % < tax rate
Wealth tax

Wealth tax : tax on total asset value, not return
𝐹𝑉

𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

1

𝑟

1

𝑡

Observation :
    ‐ Wealth tax rate is much smaller than other taxes, since it is calculated based on total asset value
    ‐ Increase time horizon → tax drag increase
    ‐ Increase rate of return → tax drag $ increase, but tax drag % decrease
Blended taxation

Portfolio may subject to multiple taxation methods, with different tax rate, including :
    ‐ Interest, Dividend ‐ accrual tax
    ‐ Realised gain + unrealised gain ‐ capital gain tax
Effective tax rate on unrealised gain :
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑜𝑛 𝑢𝑛𝑟𝑒𝑎𝑙𝑖𝑠𝑒𝑑 𝑔𝑎𝑖𝑛

𝑇∗

𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑒𝑛𝑑 𝑣𝑎𝑙𝑢𝑒

or
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑜𝑛 𝑢𝑛𝑟𝑒𝑎𝑙𝑖𝑠𝑒𝑑 𝑔𝑎𝑖𝑛
𝐹𝑉
Accrual equivalent return /
Accrual equivalent tax rate

𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

1

𝑟

𝑇∗

𝑡
𝑇∗

1

1
𝑇∗

𝑈𝑛𝑟𝑒𝑎𝑙𝑖𝑠𝑒𝑑 𝑔𝑎𝑖𝑛
𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒

1

𝐵

𝑡

Accrual equivalent return : Annual after tax rate of return, which after compounded, equal to after tax future value (after considering all tax issues)
𝑅

𝐹𝑉
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

1

Accrual equivalent tax rate : tax rate, that if applied to pretax return, equal to accrual equivalent return
𝑅
𝑅
𝑟
1 𝑡
→𝑡
1
𝑟
Tax location

𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑡𝑎𝑥 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠

𝑟𝑒𝑡𝑢𝑟𝑛 𝑝𝑜𝑟𝑡𝑖𝑜𝑛
𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑒𝑎𝑙𝑖𝑠𝑒𝑑 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒

1
...
Tax exempt accounts (TEA) :
    ‐ After tax funds are deposited
    ‐ No tax is due on returns / withdrawal
𝐹𝑉
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
1 𝑟
3
...

    ‐ If the decendent leaves no will / the will is invalid → assets are distributed by the court
    ‐ All legal costs are borne by decendent's assets
    ‐ To avoid probate, use : joint ownership with rights of survivorship, living trusts, retirement plans, life insurance, etc
...
Input value and assumptions :
    ‐ Distribution amount (recurring + one‐off)
    ‐ Inflation rate
    ‐ Asset class returns + correlations
    ‐ Return distributions
    ‐ Tax rates
    ‐ Other relevant factors
2
...
Advantages :
    ‐ Show the interaction between distribution and return sequence
    ‐ Show probability that portfolio value = 0 based on different retirement start date + distribution %

Generation skipping

Generation skipping : transfer wealth from first generation directly to third generation → avoid double tax (tax once, instead of twice)
...
Education : Gain knowledge / skills via education
    ‐ Minimal emphasis on savings / risk management
2
...
Career development : Expand job skills + increase upward mobility
    ‐ Increase financial obligations (e
...
: children college)
    ‐ Can build FC + Retirement savings over time
4
...
Preretirement :
    ‐ Continue to accumulate FC
    ‐ Decreasing investment risk
    ‐ Start tax planning for retirement
6
...
Late retirement :
    ‐ Highly unpredictive, might face longevity risk
    ‐ Increase health care expenses
    ‐ Decrease ability to make decisio

Economic Balance sheet

Economic balance sheet :
    ‐ Assets = FC + HC
    ‐ Liabilities = Financial Liabilities + Consumption + Bequest goals
Goals : to better planning of resources to meet remaining life goals

Risk for individuals

Risk types

Insurance method

Description

1
...
Premature death risk

Life insurance

‐ Substantial at early career stage (due to loss of significant amount of HC)
‐ Survivor might need to consume FC early

3
...
Property risk

Property insurance

‐ Risk of sudden loss on value of property (due to fire, flood, accident) and related unexpected needs (temporary living +
transportation expenses, lost of imcome)
‐ May lead to consome FC early

5
...
Heakth risk

Health insurance

‐ risk of loss of FC to pay for illness / injury expenses
‐ May reduce / eliminate ability to work
‐ May increase future expenses / decrease future life expectancy

Life insurance ‐ terminology

Benefit / Face amount : future payout
Premium : insurance cost
Cash value : amount can be withdrawed before payout → decrease payout
Paid up : date when insurance is fully paid → no more premiums required
Limitation : Payout restriction amount
Contestability period : period for insurer to investigate / deny payment of the claims
Policy owner : Person who pay the premium
Beneficiaries : Receiver of payout
Premium schedule : Amount + frequency of payouts
Riders : Additional terms
Modifications : Allowable changes

Life insurance ‐ types

1
...
Permanent insurance : last fot life of insured
    ‐ Whole life :
        + Fixed annual payment
        + Stop paying premiums → cancel the policy
    ‐ Universal life :
        + Premiums : can be changed to change the amount / growth rate of insurane
        + Can stop paying premiums without cancel the policy, as long as the cash value and earnings are sufficient to pay for the cost of insurance each period
3
...
Mortality estimates :
    ‐ Mortality table : reflect past experience + future mortality projections (based on age, health, gender, lifestyle)
    ‐ Goal : avoid adverse selection , avoid undercharge for risks assumed
2
...
Load :
    ‐ Gross premium = Load + Net premium
    ‐ To cover company's operating cost (e
...
: sales commission, cost of medical test)

Life insurance ‐ Pricing

Method 1 ‐ Net payment cost index : assume individual dies at end of horizon + cash value is not considered
    ‐ Step 1 : Calculate FV of premiums paid ‐ at start of the year
    ‐ Step 2 : Calculate FV of dividends ‐ at end of the year
    ‐ Step 3 : FV of insurance = Step 1 ‐ Step 2
    ‐ Step 4 : Annuitize FV of insurance for annual cost (calculate yearly payments) ‐ at start of the year
    ‐ Step 5 : Assume 1 insurance policy value = $1,000
...
Divide the annual cost to number of insurance policy employed to calculate the cost per $100 of insurance per year

Annuities ‐ Description and
terminology

Annuities : one‐time premium payment for fixed payout received for the life of annuitant
Terminology :
    ‐ Insurer : collect premium + make payout
    ‐ Annuitant : receve payout
    ‐ Owner : pay the premium + purchase the annuity
    ‐ Beneficiary : receive remaining of the contract at death of annuitant

Annuities ‐ Types

1
...
Immediate annuities : immediate payout
    ‐ Immediate variable annuities : payout is indexed to performance of some assets
    ‐ Immediate fixed annuities : fixed payout

Annuities ‐ Advantages /
Disadvantages of fixed and
variable

Annuities ‐ Alternative

1
...
Flexibility

‐ Fixed : payouts cannot be changed
‐ Variable : payouts are linked to performance of reference assets ; may allow withdrawal of funds at market value less surrender fee

3
...
Mortality credits

‐ Gain from individuals who die early (earn less payout) offset with loss from individual who die later (earn more payout)

5
...
Inflation

‐ Variable : return tie to appreciating asset (stock market) → provide LT inﬂa on protec on
‐ Fixed : No inflation protection (except buying riders, design fixed annuities with payout that increase by a predetermined amount)

7
...
annuities :
    ‐ Longer than average age expectancy → annui es
    ‐ Want lifetime income → annui es
    ‐ Don't want to leave assets to others → annui es
    ‐ More conservative → annui es
    ‐ No guaranteed income (pension) → annui es

Risk management decision matrix Characteristic of loss

Occurs regularly

Infrequent

Very severe

Risk avoidance

Risk transfer (insurance)

Not severe

Risk reduction (actions to reduce Risk retention
the amount of loss)

Human capital

Characteristics : complex
    ‐ Couple : each member's HC normally not perfectly correlated (+1) with each other → couple HC is less risky than if same amount were earned by only 1 member
    ‐ One member has less geographically mobile career skils → couple HC is at risk if the other member must moved
    ‐ 1 member is not working, but can return to work if needed → lower risk of couple' HC
    ‐ HC is normally less risky than FC → FC lted toward riskier assets

Risk management strategies

    ‐ Determine appropriate amount of systematic risk via asset allocation
    ‐ Reduce non‐systematic risks via :
        + Asset allocation
        + Isurance (transfer risks)

Concepts
Pension ‐ terminology

Description
Managing Institutional Investor Portfolio
1
...
Plan surplus  = plan assets ‐ plan liabilities
...
Accumulated benefit obligations (ABO) : Total PV of current pension liabilities
4
...
Total future liability = PBO + PV of liability to current employees from their service from now to retirement
6
...
Active lives : number of currently employeed participants

Defined benefits /
Defined contributions

1
...
salary, number of years worked)
    ‐ Employer bears investment risk → Employer must increase funding to the plan in case of poor investment performance
2
...
Plan surplus : greater surplus → more ability to suﬀer poor results without increase funding → higher risk tolerance
2
...
Common risk exposure between sponsor and pension fund : higher correlation between firm profitability and value of plan assets →  lower risk tolerance
4
...
Workforce characteristics :
    ‐ Lower average age of workforce → longer me horizon → higher risk tolerance
    ‐ Higher (retired lives/active lives) ratio → require higher liquidity → lower risk tolerance

Defined benefits plan ‐ Return
objectives

Goal : generate return sufficient to cover pension liabilities
Specific return requirement : depend on risk tolerance and constraints

Defined benefits plan ‐ Constraints 1
...
Time horizon : affected by :
    ‐ Plan is terminating → me horizon = termina on date
    ‐ Ongoing plan → me horizon depends on characteris cs of plan par cipants
3
...
Legal and regulatory factors : follow regulations of Employee Retirement Income Security Act (ERISA)
5
...
Pension investment returns vs Company's operating returns :
    ‐ Favor low correlation → minimise the need for increase contribu ons during period of poor performance
    → Avoid invest in sponsor company / same industry
2
...
Expenses)

Coporate sponsor

5% of assets
(exc
...
33%
of assets
None

Public sponsored organisation

Grants to :
General public (include large
‐ Educational purposes
donor)
‐ Religious purposes
1
...
Return : need to preserve real purchasing power → Min return = required payout + fund expenses + expected inﬂa on

Foundation ‐ Constraints

1
...
Liquidity : to meet the required spending rate
3
...
Legal and regulatory : follow regulations of Uniform Management Institutionl Funds Act (UMIFA)
5
...
Simple spending rule :
𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔

𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒

𝑀𝑉

2
...
Geometric spending rule : provide some smoothing, but less weight to older periods
𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔
Endowments ‐ Objectives

𝑆𝑚𝑜𝑜𝑡ℎ𝑖𝑛𝑔 𝑟𝑎𝑡𝑒

𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔

1

𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛

1

𝑆𝑚𝑜𝑜𝑡ℎ𝑖𝑛𝑔 𝑟𝑎𝑡𝑒

𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒

𝑀𝑉

1
...
Factor aﬀec ng risk tolerance :
    ‐ No smoothing rule → lower risk tolerance
...
Return : Total return = spending rate + expenses + expected inflation rate

Endowments ‐ Constraints

1
...
Liquidity : to cover emergency needs + current spending → low
3
...
Legal and regulatory :
    ‐ Adopt Uniform Management Institutional Fund Act (UMIFA)
    ‐ Cannot be used for private individuals
5
...
Whole life / Ordinary life :
    ‐ receive premium over multiple years + pay payoff amount at death of policy holder
    ‐ Include cash value / policyholder could borrow the cash value
    ‐ Cash value build up at crediting rate
    ‐ Need to increase crediting rate to attract customers → need higher return from the por olio
    ‐ Policy features + Volatile interest rate → diﬃcult to predict dura on + me horizon
2
...
Variable life, universal life, variable universal life :
    ‐ Same as whole life, but the cash value build up is linked to investment returns
    ‐ Less likely to trigger cash withdrawals
    ‐ Increase need to earn higher return to retain + attract customers

Life insurance company ‐
Objectives

1
...
Risk :
    ‐  Valuation risk : interest rate risk
        + Mismatch between assets duration and liabilities duration → Highly vola le surplus
    ‐ Reinvestment risk : Accumulated portfolio value depend on the ability to reinvestment rate of coupon received
    ‐ Cash flow volatility : life insurance company has low tolerance for delays of collecting income from investment activities
    ‐ Credit risk : ability of the issuers to pay interest + principal when due
        + Require credit analysis to determine the potential
        + Manage via diversification
3
...
Liquidity : key issues :
    ‐ Disintermediation risk : policyholders are more likely to withdraw cash value during period of high interest rate → Shorter dura on + Higher liquidity reserves
    ‐ Asset marketability risk : large portions of the portfolio is illiquid
2
...
Taxes :
    ‐ Return up to actuarial assumed rate : tax free
    ‐ Return above actuarial assumed rate : taxable
4
...
return instead of eligible investments
    ‐ Specified valuation methods → limit the ability to focus on MV and total por olio return
5
...
Risk : Key considerations :
    ‐ CF characteristics : erratic + unpredictable → low risk tolerance
    ‐ Common stock‐to‐surplus ratio changes
...
Return : non‐life insurance companies ignores the expected return on investment portfolio when setting price for insurance policies
...
Underwriting / Profitability cycle :
    ‐ Profitable → pay taxes → shi to taxable bonds to tax‐exempt bonds
    ‐ Profitable → lower policy premium to a ract customers → Increase claims on policy → business turn to losses → increase demand to liquidate assets to meet claims → sell tax‐
exempt bonds + increase premium to restore profitability

Non‐life insurance ‐ Constraints

1
...
Liquidity : higher + less predictable → large holdings of marketable, money market assets
3
...
Taxes : taxable
5
...
Operating :
    ‐ Liabilities : take deposits → Short‐term
    ‐ Assets : make loan → long‐term + illiquid
    → make prodit on the spread
    → mismatch in dura ons, liquidity and quality between assets and liabili es
2
...
Purpose of the investment portfolio :
    ‐ Manage total balance sheet interest rate risk by adjust the duration of assets to match duration of liabilities
    ‐ Maintain liquidity to offset with less liquid loan assets → heavily invest in government securi es
    ‐ Increase income with interest earned
    ‐ Manage credit risk by holding high quality securities to offset loan assets' higher risk

Banks ‐ Objectives

1
...
Risks are measured by :
    ‐ VaR
    ‐ Leverage‐adjusted duration gap (LADG)
𝐿𝐴𝐷𝐺

𝐷

𝐷

𝑀𝑉 𝑜𝑓 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
𝑀𝑉 𝑜𝑓 𝐴𝑠𝑠𝑒𝑡𝑠

LADG = 0 → equity is unaﬀected by changes in interest rate
LADG > 0 → interest rate up , equity down
LADG < 0 → interest rate up , equity up
2
...
Liquidity : affected by deposit withdrawals, loan demand and regulations → short + liquid
2
...
Taxes : taxable
4
...
Investment companies :
    ‐ Intermediates institutional investor that pool + invest money for group of investors
    ‐ Returns are passed to investors
    ‐ Invest in accordance with their prospectus
2
...

3
...
Liquidity : minimal costs and timely trading
    ‐ Allow traders with information can trade more frequently →  price is more eﬃcient ; Allow corpora ons to raise capital more cheaply, quickly
...
Transparency : correct + updated trade and market information (pre‐trade and post‐trade) without significant expenses or delay
3
...
Quote‐driven markets : traders deal with dealers, at dealer's bid/ask price
    ‐ Dealer maintain inventory of securities + post bid / ask price
    ‐ Dealer provide liquidity (dealers willing to holds illiquid securities)
    ‐ Close‐book market : dealer' offering of securities is closed to average investors →  must trade via broker
2
...
Electronic crossing networks : Orders are batched and matched at fixed points in time during the day at average of bid / ask quotes
            + Low commission + No bid/ask spread →  low trading costs
            + If insufficient activity →  trade may not be ﬁlled / par ally ﬁlled
            + No identity of counterparty / counterparty's trade size
            + No price discovery
        b
...
Automated auctions : trade continuously thoughout the day, execute based on set of rules
            + No identity of counterparty
            + Provide price discovery
3
...
Hybrid markets : combine features of Quote‐driven markets, Order‐driven markets and Brokered markets

Volume‐weighted Average Price

Volume‐weighted Average Price  (VWAP) : weighted average of execution price
    ‐ Weight = proportion of trading volume within the day
Advantages :
    ‐ Easy to understand
    ‐ Simple to calculate
    ‐ Can be applied quickly to enhance trading decisions
    ‐ Appropriate for small trades
Disadvantages :
    ‐ Not appropriate for large trades (large trades significantly affect VWAP →  compare the trade to itself)
    ‐ Can be game by traders (wait until late in the day to execute trade : price moving down →  buy only ; price moving up →  sell only)
    ‐ Do not take into account delayed / unfilled orders
    ‐ Do not take into account market movements / trade volume

Implementation shortfall

Implementation shortfall (IS) : to measure transaction costs
    IS = Gain/Loss of a hypothetical portfolio which trade is fullu executed with no cost ‐ Gain/Loss of actual portfolio
Key terms :
    ‐ Decision price (DP) : market price of the security when the order is initiated (initiated when market is closed →  DP = previous day's closing price)
    ‐ Execution price (EP) : Price that the trade is executed
    ‐ Revised benchmark price (BP*) : Market price of the next day, if the order is not completed within the day
...
Transaction costs are affected by :
    ‐ Security liquidity (trading volume, market cap, spread, price)
    ‐ Size of trade relative to liquidity
    ‐ Trading style : more aggressive →  higher costs
    ‐ Momentum : buy stock costs more when the trend is upward
    ‐ Risk
Advantages :
    ‐ Compare actual trading costs vs
...
Liquidity‐motivated trader

Convert securities to cash, and vice versa

Prefer quick trade →  prefer market order

4
...
Information‐motivated trader
2
...
Liquidity at any cost

Time‐sensitive information

Quick execution

High trading costs
May leak information if traded via broker

2
...
Need trustworthy agent

N/A

Use broker's skill to reduce cost

High commission
May leak information of trade intention

4
...
Low‐cost whatever the liquidity Passive trader / Value‐motivated trader

Algorithmic trading

Algorithmic trading : use automated, quantitative systems to trade, based on rules, benchmarks and constraints
...
Logical participation strategies
    a
...
Implementation shortfall strategies : use Implementation shortfall to minimise market impact and opportunity cost (missed trade)
        ‐ Higher risk aversion → immediate execu on, accept greater market impact + minimise opportunity cost
        ‐ Lower risk aversion → pa ent trading, to lower market impact, but risk of higher opportunity cost
2
...
Hunter strategies : adjust order size to take advantage of change in market liquidity
    b
...
Smart routing : monitor multiple markets + order in the most liquid market

Choice of trading strategy

Driven by 3 factors :
1
...
Bid‐ask spread
3
...
Require diligence and dedication to the process

Evaluate trading procedures

CFA Institute's Trade Management Guidelines : to achieve best execution + max portfolio value for clients
3 parts of the Guidelines :
1
...
Disclosures : Firm should help client to assess firm's ability to provide best execution by periodically disclosing to clients about :
    ‐ general informaion about their trading techniques, markets, brokers
    ‐ conflicts of interest related to trading
3
...
Otherwise, no one wants to take the opposite side of the trade
Development of complex trading techniques + decline in commissions → increase opportunity + tempta on to act unethically
Buy‐side trader have fiduciary duty to max client's portfolio value

Concepts

Description

Evaluating Portfolio Performance
Performance evaluation ‐ Purpose Fund sponsor's perspective : provide feedbank + control mechanism → improve investment policy's eﬀec veness
    ‐ Show where is effective / ineffective in the policy and allocation
    ‐ Direct management to areas of value added / lost
    ‐ Quantify the results of active management / other policy decisions
    ‐ Indicate where other additional strategies can be successfully aplied
    ‐ Feedback on application of policies in IPS
Investment manager's perspective : feedbak and control mechanism by comparing actual returns with benchmark → inves gate the eﬀec veness of investment process
Performance evaluation ‐
Components

1
...
Performance attribution : determine sources of performance
3
...
Time Weighted Rate of Return (TWRR) :
    ‐ Calculate each subperiod's return
    ‐ Compound subperiod's return to calculate TWRR
    ‐ Require fund market value on the date of each external CF
𝑇𝑊𝑅𝑅

1

𝑟

1

𝑟

⋯

1

𝑟

1

2
...
g
...
MWRR

1
...
MWRR is only affected by subperiod returns, not timing of external CF
2
...
TWRR shows what returns on assets if no external CF occured
4
...
Specific in advance : known to investment manager + sponsor, specified at the beginning of evaluation period
2
...
Measurable : value + return can be determined on a resonably frequent basis
4
...
Reflective of manager's current investment opinion : Manager has current knowledge/expertise in securities in the benchmark
6
...
Investable : Can replicate the benchmark

Performance measurement ‐
Types of benchmark

Types

Description

Advantages

Disadvantages

1
...
Manager universe ‐ Benchmark = Median manager / funds (from
universe of manager / funds)

‐ Measurable

‐ Subject to survivorship bias (underperforming
manager are removed from universe history)
‐ Impossible to identify median manager in advance →
also fail unambiguous property
‐ Median account differ between period → not
investable
‐ Cannot verify benchmark's appropriateness
‐ Sponsor has to rely on the validity of the universe

3
...
)

‐ Well recognised, easy to understand, widely available ‐ Manager's style may be different from the index's
‐ Unambiguous, investable, measurable, specified in
style
advance
‐ Appropriate if it reflects manager's approach

4
...
Factor‐model
based

‐ Benchmark portfolio = portfolio with exposures ‐ Useful in performance evaluation
to same systematic risk factors with investment ‐ Capture factor exposure that affect portfolio
performance
manager
‐ Example factors : market index, industry,
growth characteristics, company size, financial
strength
𝑟
𝑎 𝑏
𝐹
𝑏
𝐹
⋯ 𝑏
𝐹
𝜀

‐ Focus on factor exposure → not intui ve
‐ Data + Model may not available / expensive
‐ Different models give different output → ambiguous

6
...
Custom security‐ Reflect manager's security allocations and
based
investment process
Construction process :
‐ Step 1 : Identify key elements of manager's
investment process
‐ Step 2 : Select securities that consistent with
the process
‐ Step 3 : Weight the securities to reflect
manager's process
‐ Step 4 : Review + adust to replicate manager's
process and results
‐ Step 5 : Rebalance the benchmark on
predetermined schedule
Performance measurement ‐
Benchmarks testing

‐ Some style indices can have weightings in certain
securities / sectors larger than prudent
‐ Different definition of investment style → diﬀerent
benchmark

‐ Meet criteria of valid benchmark
‐ May be expensive
‐ Allow continual monitoring
‐ Cannot construct if lack transparency by manager
‐ Allow fund sponsor to allocate risk across investment
management teams

1
...
Indicators of low systematic bias :
    ‐ Regression correlation between portfolio and benchmark ≈ 1
    ‐ Style (S) and Value Added (A) are uncorrelated → Manager's ability to add value is not related to Style performance
    ‐ Style (S) and Excess earnings (E = P ‐ M) is positively correlated : Style outperforms the market → Por olio outperforms the market
2
...
Same systematic risk characteristics to portfolio
4
...
Low benchmark turnover
6
...
Diversity + Lack of transparency of hedge funds
Issues with benchmarks to hedge 2
...
Solu on is to use value added return
funds
𝑟
𝑟
𝑟
3
...
Some hedge funds have no defined style
→ Sharpe ra o is used as basis for comparing hedge fund manager
...
3 main inputs :
    ‐ Policy allocation : sponsor determine assets categories + weight + allocation of total fund among fund managers, based on risk tolerance, LT expectations and liabilities
    ‐ Benchmark portfolio returns : broad market index = benchmark for asset categories ; Narrowly focused index = benchmark for investment style
    ‐ Fund returns, valuations, external CF
2
...
Pure sector allocation : performance attributed to difference in sector weighting between portfolio and benchmark
    ‐ Assume manager holds same sectors as benchmark + same securities and securities weight in each sectors
𝑃𝑢𝑟𝑒 𝑠𝑒𝑐𝑡𝑜𝑟 𝑎𝑙𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛

𝑤

𝑊

,

𝑅

,

𝑅

,

2
...
Allocation/Selection interaction : joint effect of assigning weights to both sectors and individual securities
𝐴𝑙𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛

Equity performance attribution ‐
Fundamental factor models
attribution

𝑆𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛

𝑤

,

𝑤

,

𝑅

,

𝑅

,

Fundamental factor model : combine economic sector factors wth other fundamental factors (company size, growth characteristics, financial strength)
Step to construct factor model :
    ‐ Identify fundamental factors that generate systematic returns
    ‐ Determine portfolio and benchmark exposure to fundamental factors at the start of the period
    ‐ Determine manager's active exposure to each factor (Actual exposure ‐ Normal exposure)
    ‐ Determine active impact (added return due to active exposure)
→ Indicate source of por olio returns, manager's ability to me the market

Equity performance attribution ‐
Fundamental factor models vs
...
Changes in external interest rate environment : portfolio return due to shifts and twist in Treasury yield curve → beyond manager's control → not being evaluated
    ‐ Expected interest rate effect : portfolio return if interest rate changes in accordance to forward curve (as planned)
    ‐ Unexpected interest rate effect : portfolio return due to changes in forward rates (not as planned)
2
...
g
...
Active risk
𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑟
𝑟
𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜
𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑖𝑠𝑘
𝜎
Performance appraisal ‐
1
...
Alpha > 0 → Por olio Treynor > Market Treynor
Risk‐adjusted measures summary     ‐ Disadvantages : depend on beta and CAPM assumptions
        + assumption of single price risk rather than multifactor risk pricing
        + use market proxy (S&P500) to replicate the market
2
...
Superior Sharpe → Superior M2
3
...
Actual future results can be different due to manager's change in style and approach in the future
5
...
Create goal + best practice for calculation / presentation of investment performance → can compare performance of GIPS‐compliant ﬁrms in diﬀerent countries
2
...
Increase comparison of historical performance of firms → client can make educated decisions when hiring new managers
4
...
Encourage self‐regulation

GIPS ‐ Charateristics

1
...
Include requirements (have to follow) and recommendations (best practice, not required)
...
Only firms can claim compliance (not individuals)
4
...
Managers have to include all actual fee‐paying, discretionary portfolios with similar strategy/objective in composites
6
...
Since 1 Jan 2000 : only compliant data are presented
8
...
Accuracy of input data is critical to the accuracy of performane presentation
10
...
To fully explain the performance, firms are encouraged to present all relevant supporting information
12
...
Firms re encouraged to develop monitoring processes/controls to maintain GIPS compliance
14
...
Since 1 Jan 2011, comply with GIPS v
...
To clients : able to compare performance of firms in different countries, with different practices
2
...
Firm : Investment firm/Subsidiary/Division ; which is a distinct business entity to clients
2
...
A
...
A
...
(refer to GIPS valuation principal for details)
1
...
3 : Portfolio valuation frequency :
    ‐ Before 1 Jan 2001 : at least quarterly
    ‐ Since 1 Jan 2001 : at least monthly
    ‐ Since 1 Jan 2011 : at least monthly + on date of all large external CF
1
...
4 : Since 1 Jan 2010, firms must value portfolio at month‐end / last business day of the month
1
...
5 : Since 1 Jan 2005, must use trade‐date accounting (assets will be shown on the date of trade, not settlement date)
1
...
6 : Must use accrual accounting to accrue interest income
...
A
...
B
...
B
...
B
...
B
...
Beginning and ending balance must include income earned, realised gain/loss, unrealised gain/loss and accrued interest (for fixed income)
2
...

    ‐ Large external CF : External CF large enough that it may distort the computed return
    ‐ Prohibit more/less frequent valuation → prevent cherry picking
3
...
Return calculation must be gross of fee (after trading expenses, but before other fees)
    ‐ Bundle fee : include trading expenses + management fees + other fees
...
If firm control timing of external CF → use IRR instead of TWRR
RECOMMENDATIONS
2
...
1 : Returns should be calculated net of non‐reclaimable withholding taxes on dividend, interest and capital gains
...
A
...
A
...
A
...
A
...
g
...
A
...
A
...
A
...
Change in minimum asset level cannot be applied retrospec vely
3
...
10 : In case of receiving significant external CF :
    ‐ Method 1 : treat the external CF as new portfolio (not include in the composite)
...
B
...
A
...
The portfolio can be considered non‐disretionary in several specific situations (e
...
: most of the portfolio
must be in cash due to liquidity requirements ; portfolio has minimal tracking limits from index portfolio)

Dislosures

REQUIRED DISCLOSURES
4
...
2 : "firm" definition
4
...
16 : date, description and reason of redefinition of "firm" (if any)
4
...
3 + 4
...
10 + 4
...
11 : composite description , composite creation date , list of composite description available upon request
4
...
17 : date, description and reason of redefinition of composite
4
...
18 : changes in composite name
4
...
19 : minimum asset level + changes (if any)
4
...
4 : benchmark description
4
...
29 : if no appropriate benchmark exists → disclose why
4
...
30 : date, description and reason for changes in benchmarks
4
...
31 : If use custom benchmark/combination of multiple benchmark → disclose benchmark components, weights and rebalancing process
4
...
5 : when present gross‐of‐fee return : whether there is any fees are deducted other than trading expenses
4
...
6 : when present net‐of fee return :
    ‐ any fee are deducted other than trading expenses and management fee
    ‐ if model/actual management fees are used
    ‐ if returns are net of performance‐based fee
4
...
24 : If there is bundle fee → disclose what fees are included in the bundle fee
4
...
9 : fee schedule appropriate to compliant presentation
4
...
7 : currency used to present performance
4
...
8 : which measure of internal dispersion used
4
...
12 : policies for valuing portfolios, calculating performance, preparing compliant presentation
4
...
26 : Before 1 Jan 2010, disclose if ay portfolios were not valued @ month‐end/last business day of the month
4
...
27 : Since 1 Jan 2011, disclose the use of subjective unobservable inputs for portfolio valuation (if material)
4
...
28 : Since 1 Jan 2011, disclose if actual valuation hierachy is materially different from recommended hierachy by GIPS
4
...
13 : extent of leverage/derivatives/short position (if material) + sufficient frequency description and characteristics of instruments
4
...
14 : all significant events that would help client to assess compliant presentation
4
...
15 : before 1 Jan 2000 : must disclose periods of non‐compliance
4
...
20 : details of treatment of withholding tax on dividends, interest income and capital gains if material + whether benchmark is net of withholding tax (if available)
4
...
21 : Since 1 Jan 2011, disclose + describe material differences in FX rate/valuation sources used for portfolios in a composite + composite vs
...
A
...
A
...
A
...
A
...
A
...
A
...
A
...
B
...
B
...
B
...
B
...
B
...
B
...
B
...
B
...
A
...
A
...
A
...
A
...
A
...
A
...
A
...
A
...
B
...
B
...
B
...
B
...
B
...
B
...
B
...
B
...
B
...
A
...
A
...
A
...
A
...
A
...
A
...
b‐e :
    ‐ Firm must disclose internal valuation methods used + frequency of external valuation
    ‐ Sine 1 Jan 2011, disclose material changes in valuation method + disclose and explaint the difference in internal vs
...
A
...
A
...
A
...
A
...
A
...
a : firm must provide description of "discretion"
6
...
11 and 6
...
15 :
    ‐ Since 1 Jan 2006, GIPS‐compliant and GIPS noncompliant performance cannot be linked
    ‐ Before 1 Jan 2006, GIPS‐compliant and GIPS noncompliant performance can be linked, with disclosure
6
...
14 : Capital return + income return components must be disclosed, must sum to total return, must be clearly identified as gross/net‐of‐fees
6
...
16
...
A
...
b : % of composite assets valued using external valuator at end of each year
RECOMMENDATIONS
‐ Should disclose the accounting methods used
‐ Should disclose material differences in valuation for performance vs
...
CALCULATION METHODS
6
...
17 and 6
...
18 : must report since inception IRR (SI‐IRR) using at least quarterly rates of return
...
A
...
A
...

    ‐ Vintage year : (1) first year of fund contribution or (2) when all investors have committed to the contribution amount
B
...
A
...
A
...
A
...
PRESENTATION
6
...
24 and 6
...
26 : Must report benchmark SI‐IRR through each annual period end
...
Benchmark must
    ‐ Reflect mandate, objective, strategy of composite
    ‐ Have same period as composite
    ‐  Same vintage year as composite
6
...
25 : at end of reporting period, firm must disclose :
    ‐ Committed capital : capital amount investor must contribute
    ‐ Since‐inception paid‐in‐capital : capital amount has been contributed to date
    ‐ Distributions : amount paid back to investors
    ‐ Total value to since‐inception paid‐in‐capital (TVPI) = Total value ÷ Since‐inception paid‐in‐capital
                                                                                                     = (Residual value + Since‐inception distributions) ÷ Since‐inception paid‐in‐capital
    ‐ Since‐inception distributions to paid‐in‐capital (DPI) = Since‐inception distributions ÷ Since‐inception paid‐in‐capital
    ‐ PIC multiple = Paid‐in‐capital ÷ Committed capital
    ‐ Residual value to paid‐in‐capital (RVPI) = Residual value ÷ Paid‐in‐capital

Private equity

REQUIREMENTS
A
...
A
...
A
...
CALCULATION METHODOLOGY
7
...
3 and 7
...
4 : Annualised SI‐IRR
    ‐ Before 1 Jan 2011, SI‐IRR is calculated using daily/monthly CF
    ‐ Since 1 Jan 2011, SI‐IRR must be calculated using daily CF
...
A
...
A
...
A
...
COMPOSITE CONSTRUCTION
7
...
8 : Composite definitios must always stay consistent
7
...
9 : Primary funds must be included in at least 1 composite (defined by vintage year, investment strategy, mandate, objective)
7
...
10 : Fund of funds : must be included in at least 1 composite (defined by vintage year, investment strategy, mandate, objective)
D
...
A
...
A
...
A
...
A
...
A
...
A
...
A
...
A
...
A
...
A
...
PRESENTATION
7
...
21 : Since 1 Jan 2011, must present both netand gross‐of‐fees annualised SI‐IRR for each year since inception to liquidation
7
...
22 : Since 1 Jan 2011, fund of funds composites must present SI‐IRR of underlying investments grouped by vintage year (gross of fund of funds management fees)
7
...
23 : at end of reporting period, firm must disclose :
    ‐ Committed capital : capital amount investor must contribute
    ‐ Since‐inception paid‐in‐capital : capital amount has been contributed to date
    ‐ Distributions : amount paid back to investors
    ‐ Total value to since‐inception paid‐in‐capital (TVPI) = Total value ÷ Since‐inception paid‐in‐capital
                                                                                                     = (Residual value + Since‐inception distributions) ÷ Since‐inception paid‐in‐capital
    ‐ Since‐inception distributions to paid‐in‐capital (DPI) = Since‐inception distributions ÷ Since‐inception paid‐in‐capital
    ‐ PIC multiple = Paid‐in‐capital ÷ Committed capital
    ‐ Residual value to paid‐in‐capital (RVPI) = Residual value ÷ Paid‐in‐capital
7
...
24 :
    ‐ If there is benchmark → must present cumula ve annualised SI‐IRR of the benchmark for the same periods
    ‐ If there is no benchmark → must explain
7
...
25 : Benchmark must have same vintage year, investment objective, strategy and mandate as the composites
7
...
26 : Since 1 Jan 2011, fund of funds composites must show % of composite assets are direct investments
7
...
27 : Since 1 Jan 2011, fund of funds composites must show % of composite assets invested in fund investment vehicles
7
...
28 : Before 1 Jan 2006, may preent non‐compliant performance
RECOMMENDATIONS
7
...
1 to 7
...
3 :
    ‐ Valuation should be done at least quarterly
    ‐ Before 1 Jan 2011, SI‐IRR should be calculated using daily CF
    ‐ Should disclose + explain material differences between valuations used in performance reporting vs
...
If trading expenses cannot be separated from bundle wrap fee →  deduct en re bundle wrap fee
    ‐ Must disclose all fee in bundle wrap fees
    ‐ Must disclose % of composite assets are portfolios with bundle fee
Additional GIPS provisions :
    ‐ Include performance of WFSMAs in appropriate composites
...
Since 1 Jan 2006, non‐compliant results cannot be included
    ‐ Composite presentation must include results of all WFSMAs accounts with same style (regardless of sponsor)
    ‐ If there is a sponsor‐specific composite :
        + must disclose sponsor name
        + Wrap fee does not have to be deducted, but must be disclosed if not deducted
        + Must be labeled as only for the use of that sponsor (to prevent the sponsor to use that for marketing)
If WFSMAs ae included in composites containing non‐WFSMAs, and unalbe to separate trading expenses from sponsor's bundle fee →  decrease the reported performance of the
composite
If WFSMAs are included in WFSMA‐only composite →  cannot show other assets under management

Valuation principles

Valuation hierachy : in descending order of usage
...
GIPS recommend a single value
    ‐ Firm should rotate valuators every 3‐5 years
Private equity valuation principles :
    ‐ Valuation method must be the most appropriate for a particular investment, based on nature, facts and circumstances
    ‐ Should consider :
        + reliable appraisal data
        + comparable enterprise / transaction data
        + enterprise's stage of development
        + additional unique characteristics
Other requirements :
    ‐ If local laws/regulations conflict with GIPS →  follow local laws/regula ons + disclose the conﬂict
    ‐ Must disclose portfolio valuation policies and hierachy
    ‐ Since 1 Jan 2011, must disclose any subjective valuation if portfolio is significant portion of the composite
    ‐ Must disclose whether the actual hierachy used is different from GIPS recommended hierachy

GIPS advertising guidelines

All compliant advertisements must include :
1
...
How to obtain a compliant presentation / list of description of all composites
3
...
Description of composite being advertised
5
...
Whether performance is gross or net of management fees
7
...
If no benchmark →  explain
8
...
Extent and use of leverage / derivatives / short selling in detail
10
...
Ignore unrealised gain loss →  usually understate tax liability + overstate a er‐
tax returns
    ‐ Mark‐to‐liquidation method : assume all gains are taxed each period →  ignore value of tax deferral →  overstate ta liability + understate a er‐tax returns
After‐tax benchmark returns : if present after‐tax returns of portfolio → must present a er‐tax benchmark returns
...
g
...
Assumptions :
    ‐ Individuals are risk‐adverse
    ‐ Individuals have perfect information
    ‐ Individuals focus on maximising personal utility (Satisfaction)
    →  Investors is Rational Economic Man (REM) →  lead to eﬃcient markets (price reﬂect available relevant informa on)
2
...
Decision making process of REM can be explained using Bayes' formula
𝑃 𝐵|𝐴
P(A|B) = probability that A occurs given that B has occured
𝑃 𝐴|𝐵
𝑃 𝐴
𝑃 𝐵
P(B|A) = probability that B occurs given that A has occured
P(A) = unconditional probability that A occurs
P(B) = unconditional probability that B occurs
4
...
Utility is subjective, depend on unique preferences
    ‐ Risk : random variable, due to difference between actual outcomes vs
...
Uncertainty is not measurable → not included in tradi onal u lity maximisa on analysis
    ‐ Subjective analysis : extends decision theory to where probability cannot be objectively measured

Behavioural finance

Behavioural finance : Investors do not always make decisions to maximise utility

Behavioural finance ‐ Bounded
rationality

Bounded rationality :
    ‐ assume knowledge capacity limits
    ‐ No assumption of perfect information, no fully rational decision making and consistent utility maximisation
    → Outcomes : oﬀer suﬃcient sa sfac on, but op mal

Prospect theory

1st phase  ‐ Editing : options are edited using simple decision rules to make preliminary analysis
    ‐ Codification : code the options as gain/loss + probability to each outcome (based on selected point)
    ‐ Combination : combine outcomes with identical values → simplify the outcomes
    ‐ Segregation : separate expeted return into risk‐free and risky component of return (75% earn $100 + 25% earn $150 = 100% earn $100 + 25% earn extra $50)
    ‐ Cancellation : remove common outcomes in all options
→ may lead to isolation effect : focus on 1 factor/outcome while ignore others
Note : Sequence of editing can lead to different decisions
2nd phase ‐ Evaluation : investor place values on options (weighted ; probability‐weighted outcome) to determine expected utility
𝑣
𝑤
𝑣
⋯
𝑢𝑡𝑖𝑙𝑖𝑡𝑦 𝑤
𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑤𝑒𝑖𝑔ℎ𝑡𝑠 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒 𝑋 𝑎𝑛𝑑 𝑋
𝑝 𝑎𝑛𝑑 𝑝
𝑣 𝑣𝑎𝑙𝑢𝑒 𝑎𝑠𝑠𝑖𝑔𝑛𝑒𝑑 𝑡𝑜 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑤 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑤𝑒𝑖𝑔ℎ𝑡𝑖𝑛𝑔
    ‐ w : reflect trend of individuals to overreact to small probabilities / underreact to large probabilities
    ‐ utility value function : based on changes, not level
    ‐ Result utility value function : S‐shaped and asymmetric → decline in value for a given loss > increase in value for a same gain
    ‐ most investors are risk averse when presented with likely gains (not take a bet with equal chance of $100 gain or $70 loss)
    ‐ most investors are risk seekers when preseted wth likely losses (choose a bet with equal chance of $100 loss or $20 loss instead of sure loss of $50)
    ‐ explaim why investors over‐concentrate in high‐risk and low‐risk investments, but not medium‐risk investments

Traditional finance perspective ‐
Efficient market hypothesis

1
...
Supports :
a
...
Semi‐strong efficient :
    ‐ Majority of professional mutual fund manages have negative alpha (negative excess returns) → consistent with semi‐strong form
    ‐ Stock split leads to increase in dividends → increase economic value
...
Challenges :
    ‐ Funamental anomalies : studies show that
        + value stock with lower P/E, P/B and P/S , higher E/P, B/P and dividend yield outperform growth stocks
        + abnormal return for small‐cap stoks
        → violate both seni‐strong form and strong form
    ‐ Technical anomalies : studies show that
        + ST moving average above (below) LT moving average → buy (sell) signals
        + Stock rise above resistance level → buy signal ; stock price frop below support level → sell signal
        → violate all 3 form of EMH
    ‐ Calendar anomalies : stocks have abnormally high returns in Jan, last day of each month, and first 4 days of each month → violate all forms of EMH

Behavioural finance perspective

1
...
Behavioral asset pricing :
    ‐ Discount rate = risk free rate + fundamental premium + Sentiment premium
    ‐ Sentiment premium : additional premium based on individual's opinion
3
...
Each layer has different expected return and risk
...
Risk‐averse → larger number of assets in each layer
    ‐ Investor believes they have advantage information → more concentrated posi on
    ‐ Loss‐averse investors → larger cash posi on to avoid having to sell at loss to meet liquidity needs
    → Overall por olio : diversiﬁed, but sub‐op mal (no considera on to correla on between stocks/layers)
4
...
No adapt → no survive
    ‐ Assumption : investors satisfice, rather than max
...
Change in competitive environment → change in market risk premium
        + Active management and find arbitrage opportunities + add value
        + No strategy would work all the time
        + Adapt + innovate is must have to continue success
        + Suvivors change + adapt

Concepts
Cognitive errors vs
...
Cognitive errors : bias from reasoning, due to (1) lack of understanding proper statistical analysis techniques, (2) error in information processing, (3) faulty reasoning, and (4)
memory errors
    ‐ Belief perseverance biases : desire to stick with previous decision
    ‐ Processing errors biases : error in information analysis
Emotional biases : bias from feelings
Description
Consequences
investor fails to change that view based ‐ Unwilling/Slow to update a view → hold investment
on new available information
for too long
‐ Hold investment to avoid stress of updating view

Detection
‐ Beware of their own bias

2
...
Representativeness

The past will persist + new information is
classified based on past experience
‐ Base rate neglect : not consider the
probability of initial classification
‐ Sample‐size neglect : initial
classification based on overly small /
unrealistic data sample

‐ Believe that new information is more important +
have excessive turnover
‐ Make decision based on simple rules of thumb ;
classification with no thorough analysis ; attach too
much/too little importance to new information

‐ Better understanding the laws of probability and
statistical analysis

4
...
Hindsight bias

Remember selective memory of past
‐ Overestimate ability to correctly predict events →
events/actions (remember correct views reinforce overconfidence bias
+ forget errors)
‐ Overly criticise performance of others

1
...
Anchoring &
Adjustment bias

‐ Question "do I really remember what I
predicted/recommended?"
‐ maintain + review records to determine past
errors/successes

Description
Consequences
Detection
Investor make decision based on the old, ‐ Investors stay anchored to an initial estimate, not adjust for ‐ Question "Am I dependent on previous price?"
anchoring views (instead of new views new information
based on new information)

2
...
total return consistent with
investor's risk objectives/constraints

3
...
intrinsic value

4
...
Loss‐aversion bias

Implication of biases on
Investment Policy and Asset
Allocation

Description
More pain from a loss than pleasure from an
equal gain

Consequences
Detection
‐ Feeling more pain from a loss than pleasure from an equal ‐ Maintain disciplined process based on
gain
future prospects of investment
‐ Avoid pain of loss by : (1) hold to losers too long, or (2) sell
winners too quickly
‐ Continue to hold assets that decrease in value + loss value →
incur too much risk
‐ If incline in value → take excess risk in hope for recovering
‐ Allow framing reference point to determine if a position is a
gain or loss
‐ Treating money made from trading differently than other
funds → take excess risk with this money
‐ Myopic loss aversion : ST risk of stocks leads to excessively
high equity risk premium

2
...
Self‐control bias

Investor lack self‐discipline, prefer immediate
pleasure over LT goals

‐ Create appropriate investment plan +
‐ Insufficient savings to fund retirement needs
budget → achieve suﬃcient savings
‐ Take excess risk to compensate for insufficient savings
‐ Overemphasis on income‐producing assets to meet ST needs

4
...
Endowment bias

Asset feels more special/valuable once it is
owned

‐ Fail to sell inappropriate asset → inappropriate asset
allocation
‐ Hold familiar securities since they provide some comfort

‐ Start a discipline diversification program
‐ Question : "Would you make same
investment with new money today?"

6
...
Goal‐based investing (GBI)
    ‐ Set the relative importance of client's goals
        + Essential needs/obligations (living expenses) → meet with layer of low risk investment
        + Desired outcomes (annual donation) → meet with layer of medium risk investment
        + Low prority aspirations (leave the portfolio to foundation at death) → meet with layer of high risk investment
    ‐ Consistent with loss‐aversion : more important goals → less risky assets + less poten al loss
2
...
lifestyle → low standard of living risk (SLR) → could aﬀord deviate from op mal por olio
    ‐ Cognitive biases → easier to moderate → can have less devia on from op mal por olio
    ‐ Emotional biases → harder to moderate → may have to be adapted → less eﬃcient por olio
    ‐ Setting range of accepted deviations from optimal allocation
        + Low SLR + Emotional biases → can adapt with large devia on
        + High SLR + Cognitive biases → biases have to be addressed + moderated to achieve near op mal asset alloca on (small devia on)
        + Other cases : combination of adapt and moderate

Concepts

Description

Behavioural finance and Investment processes
Classify investors into personality Classify investors into personality types : embed behavioural biases in IPS
types
1
...
Bailard, Biehl, Kaiser (BBK) 5‐way model :

3
...
Adviser understand LT financial goals of clients and their reasons → enhance rela onship as client feels adviser truly understand him and his needs
2
...
Adviser acts as client expects : adviser understands client + his motivation → know what ac ons to perform + what info to provide + required frequency of contact
4
...
Investor's respond are affected by wording of questions
    ‐ Questionnaire should be revised annually
2
...
Status quo bias : As investor age, his optimal portfolio mis will shift
...
Naive diversification : investor equally divide their fund among groups of securities
    ‐ Conditional naive diversification : investors select a small number of funds + allocate fund equally
    ‐ Motivation : avoid regret by not missing best performer
3
...
Excessive trading :
    ‐ Reasons :
        + Overconfidence
        + Self‐selection
        + Disposition effect : sell winners + hold losers
5
...
Lead to the use portfolios (e
...
target fund) which work around the bias
portfolio management process
2
...
Tiered investments (that investor understand) are better than traditional optimal portfolio (that investor do not
understand and follow)

Effect of behavioural factors on
analyst's forecast

1
...
The way management presents information :
    ‐ Reasons :
        + Framing : digest same information differently, depend on how it is presented
        + Anchoring & adjustment : Anchor to previous forecast
        + Availability bias : data that is easier to recall  → more weight
        + Self‐attribution bias : salary and bonus are based on operating results → more likely to overstate results
        + Recalculate earnings
    ‐ Solutions :
        + Focus on verifiable, comparable quantitative data rather than subjective information
        + Check that the information is framed properly
        + Recognise appropriate starting point for data
3
...
g
...
Gambler's fallacy means that if there is a streak of head, gamblers starts to feel an
increased chance of tail)
    ‐ Solutions :
        + incorporate new information
        + apply Bayes's formula
        + seek contradict information
        + get promt feedbacks

Effect of behavioural factors on
investment committee

1
...
Solutions :
    ‐ Comprise people with different background
    ‐ Comprise members who are not afraid of express different opinion
    ‐ Committee chair should encourage members to speak out
    ‐ Mutual respect for all members

Impact of behavioral biases on
market

1
...
g
...
Momentum effect :
    ‐ Can last up to 2 years, before reverse back to mean
    ‐ Reasons : due Herding : follows a large groups/trend
...
Financial bubbles & crashes
    ‐ Bubbles / Crashes : an extended period of time that prices are 2 standard deviations from the mean
    ‐ Reasons :
        + Overconfidence : underestimate risk + concentrate the portfolios
        + Confirmation bias
        + Self‐attribution bias
        + Regret aversion : does not want to miss the trend
        + Disposition effect : more willing to sell winners + hold losers
4
...
Growth
    ‐ Farma and French : value stock outperform growth stock ; Small cap stocks outperform large cap, due to higher risk exposure of companies with particular size and B/V ratio (not
reflect in the pricing model)
    ‐ Other studies : due to behavioural biases
        + Halo effect : companies with favorable attributes (good record of growth + price performance) → good investment + con nued high expected return → good buy
        + Home bias : investor favor domestic securities

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