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
Constraints in measuring and managing market risk
Risk Budgeting
Position Limits
Scenario Limits
Stop-loss Limits
Explain the following constraint - Risk Budgeting
Total risk appetite allocated to sub activities
Explain the following constraint - Position Limits
A control on overconcentration
Explain the following constraint - Scenario Limits
A limit on the estimated loss for a gain scenario
Explain the following constraint - Stop-loss Limits
When a loss of a particular size occurs in a specific period - reduce or liquidate portfolio position.
Name the 3 factors that influence the types of risk measuers
- Degree of leverage
- Mix of risk factor exposure
- Accounting / Regulatory requirement
surplus at risk in regards to VaR
How assets might underperform to their liabilities.
Surplus at risk is an application of VaR; it estimates how much the assets might underperform the liabilities with a given confidence level, usually over a year.
Liquidity Gap
Relevant to the banks.
Liquidity between the assets and liabilities.
How quickly can I get cash for my assets to pay my liabilities?
Steps of Backtesting
- Strategy design
- Historical investment simulation
- Analysis of backtesting outputs
Strategy design in backtesting
Step 1
Specify the investment hypothesis and goal
Determine investment rules and process
Decide key parameters
Return definition
Rebalancing / reconstitution frequency
Start and end dates
Historical investment simulation in backtesting
Step 2
Construct a portfolio to be tested
- Strategy
- Portfolio securities
- Investment hypothesis
Make sure it is rebalanced on a predetermined frequency
Analysis of back-testing outputs in backtesting
Step 3.
Calculate portfolio statistics
Compute key metrics
What do we do in Historical investment simulation for Backtesting multifactor models?
Backtesting a multifactor strategy is similar to the method introduced earlier, but the rolling-window procedure is implemented twice, once at each portfolio “layer.”
Rolling window
- Once at the factor level
-Again at the factor portfolio level
Risk parity portfolio
A portfolio allocation scheme that weights stocks or factors based on a equal risk contribution.
High volatility factor: Lower weights
Low volatility factor: High weights
The sum of the total standard deviation of each factor / Number of factors
They usually perform better than the benchmark, hence why they’re leveraged.
Requires a complete variance-covariance matrix at each rebalacing date.
objective of backtesting
To understand the risk–return tradeoff of an investment strategy by approximating the real-life investment process.
Historical Scenario Analysis
Type of backtesting that explores the performance of an investment strategy in different structural regimes and breaks.
NOT THE SAME AS Historical simulation
Bootstrapping
Refers to random sampling with replacement, often used in historical simulation.
Random sampling with replacement, also known as bootstrapping, is often used in historical simulations because the number of simulations needed is often larger than the size of the historical dataset
What are the two types of analysis in Simulation analysis
Historical simulation and Monte Carlo simulation
Historical simulation differs from Monte Carlo Simulation
It assumes that sampling the returns from the actual data provides sufficient guidance about future asset returns.
What is another name for Random sampling with replacement
Bootstraping
What is Data snooping?
A form of statistical bias manipulating data or analysis to artificially get statistically significant results.
Also known as P-Hacking
According to CFA. Why are interest rates higher when future conditions are expected to be better
Because we delay consumption, our utility to consume, so we have to be compensated for the higher rate of return.
Good economics = Higher interest rates = Encourage people to save
As market conditions improve, bonds decrease in price, and the yield increases. Remember the inverse relationship.
What happens when income rises
Lower Risk aversion
Higher investments in risky assets
Low premiums for a given risk
One interpretation of an upward-sloping yield curve is that the returns to short-dated bonds are
One interpretation of an upward-sloping yield curve is that returns to short-dated bonds are more negatively correlated with bad times than are returns to long-dated bonds. This interpretation is based on the notion that investors are willing to pay a premium and accept a lower return for short-dated bonds if they believe that long-dated bonds are not a good hedge against economic “bad times.”
The covariance between a risk-averse investor’s inter-temporal rate of substitution and the expected future price of a risky asset is typically
Negative
Explain the relationship between Real short-term interest rates and GDP
Real short-term interest rates are positively related to both real GDP growth and the volatility of real GDP growth.
If GDP volatility is high, so too is the Real-Short term interest rates.
Break-even rate of inflation (BEI)
The difference between the nominal yield on a fixed-rate investment and the real yield (fixed spread) on an inflation-linked investment of similar maturity and credit quality.
Is composed of the expected rate of inflation plus a risk premium for the uncertainty of future inflation.
Explain WHY PE, CF, or other factors can increase in regards to the Economics and Investment Markets
One of the factors in the denominator, Real interest rates, inflation, expected inflation, credit risk decrease.
Default-free real interest rates tend to be relatively high in countries with high expected economic growth because investors
Increase current borrowing
Positive output gaps are usually associated with
Economic growth beyond sustainable capacit
One interpretation of an upward sloping yield curve is that the returns to short-dated bonds are
More negatively correlated with bad times than are returns to long-dated bonds.
This interpretation is based on the notion that investors are willing to pay a premium and accept a lower return for short-dated bonds if they believe that long-dated bonds are not a good hedge against economic “bad times.”
A decrease in the prices of AAA-rated corporate bonds during a recession would most likely be the result o
Increases in credit risk premiums
When will higher corporate rated bonds outperform lower rated corporate bonds.
During recession
Risk-averse investors demanding a large equity risk premium are most likely expecting their future consumption outcomes and equity returns to be
Positively correlated
If investors demand high equity risk premiums, they are likely expecting their future consumption and equity returns to be positively correlated. The positive correlation indicates that equities will exhibit poor hedging properties, because equity returns will be high (i.e., pay off) during “good times” and will be low (i.e., not pay off) during “bad times.” In other words, the covariance between risk-averse investors’ inter-temporal rates of substitution and the expected future prices of equities is highly negative, resulting in a positive and large equity risk premium. This is the case because in good times, when equity returns are high, the marginal value of consumption is low. Similarly, in bad times, when equity returns are low, the marginal value of consumption is high. Holding all else constant, the larger the magnitude of the negative covariance term, the larger the risk premium.
Are interest rates and marginal rate inter-temporal rate of substitution directly or inversely related
Inversely related
Higher Mt - Lower Interest rates
Lower Mt - Higher interest rates
Are future asset prices and marginal rate inter-temporal rate of substitution directly or inversely related?
Inversely related
Higher future asset prices -> Lower Mt - Higher interest rates
Lower future asset prices -> Higher Mt - Lower interest rates
Are future asset prices and interest rates directly or inversely related?
Directly related
Higher future asset prices = Higher interest rates
Lower future asset prices = Lower interest rates
Is GDP growth and volatility positively or negatively related to Real interest rates?
Positive correlated.
As GDP grows and interest rates grow, real interest rates increase.
Are short-term bond returns positively or negatively correlated to economic turbulence?
that returns to short-dated bonds are more negatively correlated with bad times than are returns to long-dated bonds.
This interpretation is based on the notion that investors are willing to pay a premium and accept a lower return for short-dated bonds if they believe that long-dated bonds are not a good hedge against economic “bad times.”
This interpretation is based on the notion that investors are willing to pay a premium and accept a lower return for short-dated bonds if they believe that long-dated bonds are not a good hedge against economic “bad times.”
Active weights
Difference between the weight of the security between the portfolio and the benchmark.
Δ portfolio - benchmark
What is the components / formula for asset allocation
(ΔWeight of stocks * Return benchmark stocks ) + (ΔWeight bonds * Returns benchmark bonds)
What is the components / formula for Security selection
(Portfolio weight stocks * Active return stocks) + (Portfolio bond weights * Active return bonds)
Where does active return come from?
Overweighing securities that will do better than benchmark, and underweighting stocks that will perform poorly than the benchmark
How to calculate cash in the Sharpe ratio?
- New desired standard deviation / previous standard deviation
σ₁ / σ₀ = Weight in portfolio = Wp
(1- Wp) = Cash
How to calculate weight in the Sharpe ratio?
New desired standard deviation / previous standard deviation
σ₁ / σ₀ = Weight in portfolio = Wp
The formula for combined return in Sharpe ratio
(Rp * Wp) + (1-Wp)*RfR
Does cash or leverage change the Sharpe ratio?
No, it does not.
Does cash or leverage change the Information Ratio?
Yes, it does!!
How can we change the risk in the Sharpe ratio?
With cash and leverage
But this does not change the Sharpe Ratio
How can we change the risk in the Information ratio?
Through the aggressiveness of active weights in the portfolio
We can change the risk by investing in the active portfolio and the benchmark portfolio
Property of active management theory
Implies that the active portfolio with the highest IR will also have the highest Sharpe Ratio
Optimal amount of active risk (Active risk) Formula
(Information Ratio * Standard deviation of benchmark) / Sharpe Ratio of benchmark
Optimal expected active return is a function of …
Forecasting ability
Breath
Active risk
The basic fundamental law formula
IC* √BR * σA = IR^* σA
The full fundamental Law formula
TC * IC* √BR * σA = IR^* σA
In regards to fundamental law, what if we assume all securities have the same standard deviation
Then, the correlation does not have to be risk-adjusted
What does it mean if we have a Transfer Coefficient = 1?
Unconstrained portfolio.
Our information ratio is invariant to changes in active risk
What is the relationship with IR and a constrained portfolio?
If we have constraint in our portfolio our information ratio drops
What is the alternative formula to calculate Sharpe Ratio if we have IR
SRP^2=(SRB^2+IR^2)
SRP=(SRB^2+IR^2)^0.5
What is the formula to determine a portfolio managers ability to achieve active return?
Information ratio.
Using Full fundamental law
IR=(TC)(IC)√BR
Basic Fundamental law
IR=(IC)*√BR
Does adding cash to the portfolio change the portfolio’s information ratio?
Yes it does!
The information ratio for a portfolio of risky assets will generally shrink if cash is added to the portfolio.
Does increasing the aggressiveness of active weights change the portfolio’s information ratio?
No it doesn’t !!
Because the diversified asset portfolio is an unconstrained portfolio, its information ratio would be unaffected by an increase in the aggressiveness of active weights.
Characteristics of A closet index
- Low active risk
- Sharpe Ratio close to benchmark
- Information ratio can be Inconclusive because of low active risk
- IR can be negative due to management fee
A closet index will have a very low active risk and will also have a Sharpe ratio very close to the benchmark.
A closet index’s information ratio can be indeterminate (because the active risk is so low) and is often negative due to management fees.
What does the Information coefficient measure?
The IC measures an investment manager’s ability to forecast returns
How can we measure which factor most influences our active returns?
Return from factor tilts = Sum of the absolute contribution to active return
= ∑[(Portfolio sensitivity) − (Benchmark sensitivity)] × (Factor return)
ETF Prices may be a less accurate reflection of fair value than NAV when…
The ETF is less actively traded.
ETF that trade infrequently may alos have large premiums or discount to NAV.
If the ETF has not traded in the hours leading up to the market close, NAV may have significantly changed during that time.
What is “stale pricing” in ETF
ETFs that trade infrequently may also have large premiums or discounts to NAV.
If the ETF has not traded in the hours leading up to the market close, NAV may have
significantly risen or fallen during that time owing to market movement.
The use of ETF in managers transition activity is meant to
Maintain interim benchmark exposure.
What is the purpose of maintain exposure to target weights in ETFs
The use of ETF for Portolio rebalacing.
How do we use ETF for portfolio completiton strategies
To fill gaps in stratigic exposure in a country or sector.
For liquid ETF, the bid-ask spread can be…
Can be significantly tighter than the spreads on the underlying.
Cash equitization/liquidity management
Minimize cash drag by staying invested in benchmark exposure
Portfolio Rebalacing
Maintain exposure to target weights
Portfolio Completion
Fill gaps in strategic exposure
Manager transaction activity
Maintain interim benchmark exposure during manager transitions.
What is iNAV of an ETF
Indicated NAV.
iNAV are intraday fair value estimates of an ETF share based on its creation basket composition for that day.
The amount of ETF shares created or redeemed is based on:
The quantities listed in the creation basket.
How is an ETF expected to perform relative to its benchmark
Underperform its benchmark by the ammount of its expense ratio.
Which costs of owning an ETF is more important for a long-term holder?
Managment fee and tracking errors.
Which costs of owning an ETF are more important to a shor-term trader?
Premium/Discount to NAV.
What is the iNAV based on?
Intraday FV estimation of an ETF is based on the ETFs creation basket composition for just that day.
Is credit spread a market risk sensitivity measure?
No it is not!!!
What is reverse stress testing?
Identifying a set of exposures and then determining what would stress thos risk factors.
What is the inter-temporal rate of substitution
Future utility / current utility
Utility consumption today (current utility) is always greater than future utility
Expected future economic condition: GOOD: Future utility and inter-temporal rate of substitution decreases.
Expected future economic condition: BAD: Future utility and inter-temporal rate of substitution increase.
The component of the discount rate that is most viable between asset class and another is the ..
Risk preimiums related to cash flow uncertainity.
The size of the risk premiums will vary among asset classes and the variation is largely resposnible for the distinction between one asset class and another.
What is the difference between the nominal and risk free interest rate?
Break-even inflation rate
Risky financial assets tend to display
High returns when the marginal value of consumption is low.
and
Low returns when the marginal value of consumption is high.
The relationshipbetween credit spreads and the business cycle is
Counter-cyclical
Credit spreads tend to widen in economic downturn and tend to shrink during economic expansion.
How will saving affect marginal utility of consumption in one year
Increase the marginal utility of consumption today.
What is Index Tracking?
Index Tracking is often evaluated using the one-day difference in returns between the fund, as
measured by its NAV and its Index.
