Portfolio Management Flashcards
Macroeconomic factor model
In a macroeconomic factor model, the factors are surprises in macroeconomic variables, such as inflation risk and GDP growth, that significantly explain returns.
ai represent the expected return.
b1F1 + b2F2 are returns resulting from factor surprises.
While the error term represents the asset specific risk
Fundamental factor model
Attributes of Stocks or companies
Example Bv/MV, Market Cap, EPS
Company Fundamental Factor
Part of fundamental factor models - Internal company performance
Earnings growth, Financial leverage
Company Share Related Factor
Part of fundamental factor models - Valuation measure - Factors related to share price
EPS, B/MV
What is categorized as an Macroeconomic factor
Sector/Industry
Sector or industry membership factors fall under this heading. Various models include such factors as CAPM beta, other similar measures of systematic risk, and yield curve level sensitivity—all of which can be placed in this category.
If all factors are equal to their expected value (Macroeconomic Factor Models)
All factors are equal to zero (Actual - Expected)
Application of Multifactor Models
Return Attribution
Risk Attribution
Portfolio Construction
Strategic portfolio decisions
Return Attribution
Relative to a benchmark
Fundamental models are favored
Attribute active return Rp - Rb
Investment Mandate
How we should perform relative to a benchmark
Actual Investment Style
How we actually invest
Active Risk
Standard deviation of the actual returns
Standard deviation (Return of portfolio - Return of benchmark)
Active risk is also known as tracking error
Risk attribution of absolute returns
Sharpe Ratio
Risk attribution of relative returns
Information Ratio (IR)
IR = (Rp - Rn) / Sd Ra
IR = (Rp - Rb) / Tracking error
Tracking error = Sd of (Rp - Rb)
Portfolio construction: Passive management
Replicate benchmark factors exposure on a much smaller set of securities
In managing a fund that seeks to track an index with many component securities, portfolio managers may need to select a sample of securities from the index. Analysts can use multifactor models to replicate an index fund’s factor exposures, mirroring those of the index tracked.
Portfolio construction: Active management
Use multifactor model to predict alpha or construct portfolio with a desired risk
Many quantitative investment managers rely on multifactor models in predicting alpha (excess risk-adjusted returns) or relative return (the return on one asset or asset class relative to that of another) as part of a variety of active investment strategies. In constructing portfolios, analysts use multifactor models to establish desired risk profiles.
Portfolio construction: Rule based Active management
Overweight or underweighted specific factors
These strategies routinely tilt toward such factors as size, value, quality, or momentum when constructing portfolios. As such, alternative index approaches aim to capture some systematic exposure traditionally attributed to manager skill, or “alpha,” in a transparent, mechanical, rules-based manner at low cost. Alternative index strategies rely heavily on factor models to introduce intentional factor and style biases versus capitalization-weighted indexes
The 3 assumptions of Arbitrage Pricing Theory (APT)
- A factor model describes assets returns.
- With many assets available - investors can form well diversified portfolios that can eliminate asset specific risk.
- No arbitrage can exist among well diversified portfolios (All are priced correctly)
Additional information ..
Expected returns are a linear function of the risk of the asset with respect to a set of risk factors.
Explains the returns in equlibrium.
APT does not indicate the identity or even the number of risk factors.
SMB
Small Minus Big: Average return on 3 small cap portfolio minus 3 average return big cap portfolios
Small cap factor
HML
High Minus Low: Average return on 2 high Bv/Mv Portfolio minus Average return on 2 low BV/MV portfolios
Value factor
WML
Winners Minus Losers: Past 12 month winners (top 30%) minus bottom 12 months losers (bottom 30%)
Momentum factor
Creation Basket
List of securities ETF manager wants to own, disclosed everyday.
A list of requiered in-kind securities published each day by the ETF Sponsor.
Serves as the portfolio for determining the intrinsic NAV of the ETF
Tracking error
Annual standard deviation of daily return differences of ETF and index.
Sources of tracking error for ETFs
Fees and expenses
Representative sampling / optimization
Depository Receipts and ETFs
Index change
Fund accounting practice
Regulatory and tax requirements
Asset management operations
Spreads & Their Relationships - On going order flows
Negatively related: As more order flows (volume) go through the narrower spreads.
Spreads & Their Relationships - Actual Costs
Positively related: As the costs increases, the wider the spreads
Spreads & Their Relationships - Competition
Negatively related: As competition increases, the narrower the spreads
ETF share price > Intraday N.A.V.
Trading at a premium.
AP buys the creation basket in exchange for new ETF shares (Creation units).
The new shares are then sold on open market for a profit.
Sells ETF shares - Buys creation basket
ETF share price < Intraday N.A.V.
Trading at a discount
ETF shares are trading at a discount - Creation basket is at a premium
Buys ETF shares and sells the redemption basket
Redemption Basket
List of securities the ETF manager wants to sell.
The basket of securities the AP (Authorized Participant) receives when it
redeems the ETF shares is called the redemption basket.
Surprise in a macroeconomic model is defined as
Actual - Forecasted
Information Ratio (IR)
The higher the information Ratio, the better
Formula: (Rp - Rb) / Sdv (Rp-Rb)
Mean Active return / Tracking error
Active return / Active Risk
An advantage of statistical factor models
They make minimal assumptions. However, the interpretation of statistical factors is generally more difficult than the interpretation of macroeconomic and fundamental factor models.
Assumption of CAPM
Perfect competition - Frictionless and can borrow a the RfR
Rational, mean-variance optimizer
Perfect information (same variance and covariance matrix)
Arbitrage opportunity in regards to Factor model questions
We want to earn a Risk Free Rate of return.
We want a zero factor exposure
Sell anything that is too high / overprices
Whatever we short - we will have a factor exposure of whatever we short (we have the Beta of the security we short), which means we have to long/invest assets that gives us the same factor (beta) exposure thus have a net factor of zero.
When is the sensitivity determined in a Fundamental and Macro Factor model?
Fundamental factor model: Sensitivity (beta) is determined first
Macro factor model: Sensitivity (beta) is determined last
What is the intercept of a Factor model
Expected return
Which type of factor model is most directly applicable to an analysis of the style orientation (Growth vs Value)
Fundamental Factor Models
Company specific factor, therefore we want fundamental factor models
Suppose an active equity manager has earned an active return of 110 basis points, of which 80 basis points is the result of security selection ability. Explain the likely source of the remaining 30 basis points of active return.
Active return = Active factor risk + Security selection
110 = x + 80
The remaining 30 BSP comes from active factor risk
What is the information ratio of an index fund that effectively meets its investment objective?
Zero
because IR = (Rp - Rb) / Sdv (Rp - Rb)
If it meet its investment objective, hence performed equally to its bench mark, then there is no difference between portfolio and benchmark
What are the two types of risk an active investment manager can assume in seeking to increase his information ratio?
Active risk + Security specific risk (Security selection)
This is apart of risk attribution for multifactor models
Active risk = Standard deviation of (Rp - Rb)
Active risk
Standard deviation of (Rp - Rb)
Active factor risk
Return of portfolio (Rp)
Asset Specific Risk / Security Selection
Return on Benchmark
What is the purpose of VaR
Value at Risk is to capture market risk.
Equity prices
Commodity prices
Forex
Interest rates
Does not tell about about average loss
How to interpret a one day 95% VaR
95% confidence that we will NOT lose more than … per day
with 95% probability, we will experience a maximum loss of …
How to interpret 5% VaR
The 5% minimum loss of a portfolio over a 1 day period
or…
A expected loss of … to occure every 20 days (depend on duration)
3 different ways to estimate VaR
Parametric method
Historical simulation method
Monte Carlo Simulation
Explain Parametric Method
Variance - Covariance method
Begins with risk decomposition of the portfolio holdings
Assumes return distribution for risk factor is normal distributed
We need expected returns and standard deviation of portfolio
Calculate VaR for parametric method
[Expected return - Z* Portfolio standard dev]*(-1) * Pv
Z = Standard deviation number
Pros and Cons of parametric method
Pro: Simple and straightforward
Con: VaR is very sensitive to expected returns and standard deviation
Difficult to use of portfolio contains options since it threatens normality. Options have a non normal payoff function.
Historical simulation method
We set / construct a portfolio with fixed weights
We measure portfolio return over the observed period
We then rank the portfolio returns from smallest to largest
We then use percentile to find 1,5,10 % VaR
- I we have 500 observation, and we want to find 5% VaR, the 25th observation os our 5% VaR
Brief characteristics of historical simulation method
Not constrained by normality assumption
Estimates VaR based on what actually happened
Can handle any kind of financial instruments
Monte Carlo Simulation
Not constrained by any distribution - We can define the distribution
Avoids complexity of parametric method when portfolio has many risk factors
Calculating VaR is the same as historical method
Conditional VaR - CVaR
Relies on a particular VaR measure - Average loss greater than our particular VaR measure.
average loss on the condition that VaR > Cut off
Informs us about average loss
Typically obtained by backtesting
Also known as Expected tail loss or expected shortfall
Incramental VaR - IVaR
How VaR will change if a position size changes relative to the remaining position.
example:
SPY - 80 % weight - > 90% weight
LWC - 20 % weight -> 10% Weight
VaR 2,407,503 -> 2,733,722
IVaR = 2,733,722 - 2,407,503 = 326,192
Marginal VaR - MVaR
Conceptually the same to IVaR, but reflects the effects of a very small change in a position - 1 unit change in position.
Relative VaR - Ex Ante tracking error
The degree to which the performance of a given portfolio might deviate from a benchmark.
Portfolio vs Benchmark
What is Sensitivity risk measure
Examines how performance responds to a single change in an underlying risk factor.
Remember; How SENSITIVE a FACTOR is to a change
What is scenario risk measure
Estimates the portfolio returns that would result from a hypothetical change in the market or historical events.
Scenario = What if something was different
Sensitivity and Scenario vs VaR
VaR: measure of loss and probability of large loss
SS: Change in the value of an asset in response tp a change in something else
VaR: Uses market returns from a look back period
SS: Uses market returns from a specific unrepresentative time period