Portfolio Management Flashcards
What is the correlation between (sensitivity of corporate bond’s spread to changes in business cycle) to (that business’ level of cyclicality)
Positive
Sources of Tracking Error
1) Fees and expenses
2) Representative sampling/optimization
3) ADRs
4) Fund accounting practices
5) Regulatory and tax requirements
6) Asset manager operations
Holding period cost (%)
Round-trip trade cost (%) + Management fee for period (%) + bid-offer spread on purchase/sale
Standardized Beta
- utilized in fundamental factor models
- the value of the attribute for the asset minus the average value of the attribute across all stocks divided by the standard deviation of the attribute’s values across all stocks
- (value of attribute k for asset i - average value of attribute k) / standard deviation of the values of attribute k
Active Return
return on a portfolio minus the return on the portfolio’s benchmark
Active risk
The standard deviation of active returns
Tracking Error
- also called tracking risk and can be referred to as active risk
- sample standard deviation * (R(p) - R(b))
Information Ratio
- tool for evaluating mean active returns per unit of active risk
- IR = (R(p) - R(b)) / TE
Active risk squared
- variance of active return
- s^2 * (R(p) - R(b))
- Active factor risk + active specific risk
Active factor risk
The contribution to active risk squared resulting from the portfolio’s different-from-benchmark exposures relative to factors specified in the risk model
Active specific risk
- also called security selection risk
- Measures the active non-factor or residual risk assumed by the manager
3 Types of Multifactor models
1) Macroeconomic factor models
2) Fundamental factor models
3) Statistical factor models
- statistical methods are applied to a set of historical returns to determine portfolios that explain historical returns in one of two sense, factor analysis models and principal-components models
Factor Analysis Models
Factors are the portfolios that best reproduce historical return covariances
Value at risk (VaR)
The minimum loss that would be expected a certain percentage of the time over a certain period of time given the assume market conditions
How many standard deviations below expected value is 5% VAR
1.65
How many standard deviations below expected value is 1% VAR
2.33
1 Standard Deviation below expected value is what % VAR
16%
Steps to estimate VaR using parametric method
1) multiply portfolio standard deviation by the number of standard deviations that correspond to the VaR
2) subtract the step 1 from daily expected return
3) take the absolute value of step 2
4) Multiple step 3 by portfolio value
Steps to estimate annual parametric VaR
1) find the corresponding annual std (daily std * sqrt(250)) and expected return (daily expected return * 250)
2) multiple annual std by number of standard deviations corresponding to the VaR
3) subtract that value from the annual expected return calculated in step 1
4) take absolute value of that figure
5) multiple that figure by the total portfolio value
Historical simulation method of VaR
uses the current portfolio and reprices it using the actual historical changes in the key factors experienced during the lookback period
- does not use expected return, standard deviation, or correlations
Conditional VaR
The weighted average of all loss outcomes in the return distribution that exceed the VaR loss
- answers the question, “How much can i expect to lose if VaR is exceed?”
- more comprehensive than VaR
- referred to as expected tail loss or expected shortfall
Incremental VaR (IVaR)
A measure of the incremental effect of an asset on the VaR of a portfolio by measuring the difference between the portfolio’s VaR while including a specified asset and the portfolio’s VaR with that asset eliminated
Marginal VaR (MVaR)
A measure of the effect of a small change in a position size on portfolio VaR
Delta
relationship between the option price and the underlying price
Gamma
2nd order, how sensitive delta is to change in the value of underlying
Vega
1st order, the change in the value of the derivative based off a change in the value of volatility
Pass/fail test
Stress tests used by companies that use leverage
Reverse stress testing
user identifies key risk exposures in the portfolio and subjects those exposures to extreme market movements
How often are securities in an ETF disclosed
daily
Creation basket
list of required in-kind securities published each day by the ETF sponsor
When an authorized participant transacts to create or redeem ETF shares, the related costs are borne by who
transacting shareholders
Smallest contributor to tracking error
Changes to the underlying index securities
Fund-Closure Risk
Risk that an ETF may shut down due to regulations, competition, and corporate action
Expectations-related risk
Risk that some ETF investors may not fully understand how more complex ETFs will perform
3 Assumptions of APT
1) A factor model describes asset returns
2) There are many assets, so investors can form well-diversified portfolios that eliminate asset-specific risk
3) No arb opportunities exist among well-diversified portfolios
Expected return when using macroeconomic factor model
the intercept (when all model factors take on a value of zero)
which of the factor models make minimal assumptions
statistical factor models
Two components of portfolio’s active return
factor tilt and security selection
What are the factors in macroeconomic factor model
surprises in macroeconomic data
In which model are standardized betas used
Fundamental factor models
Diversification reduces which part of a portfolio’s risk
active specific risk, the portfolio with the lowest active specific risk is the most diversified
Delta range of long call options
0 to 1
Delta range of short call options
0 to -1
Delta range of long put options
0 to -1
Delta range of short put options
0 to 1
Surplus at risk
application of VAR that estimates how much the assets might underperform liabilities with a given confidence level, usually over a year
Ex post vs ex ante tracking error
If tracking error is measured historically, it is ex post
If tracking error is predictive, it is ex ante
gross exposure
measures the combination of long and short exposures and can be an important metric in the management of hedge fund exposure
scenario limit
limit on the estimated loss for a given scenario, which if exceeded, would require corrective action in the portfolio
relative Var
measure of the degree to which the performance of the portfolio might deviate from its benchmark, ex ante tracking error
bootstrapping
random sampling with replacement
inverse transformation
method of random observation generation, often used in simulation
what do you do when returns from various factors are correlated in monte carlo simulation
specify a multivariate distribution rather than modeling each factor or asset on a standalone basis
impact of increase in income on marginal utility of consumption
decreases marginal utility of consumption
impact of increase in income on required risk premium
decreases required risk premium
Correlation (positive/negative) between real short-term interest rates and real GDP growth
Positive
correlation (positive/negative) between real short-term interest rates and volatility of real GDP growth
positive
the covariance between a risk-averse investor’s inter-temporal rate of substitution and the expected future price of a risky asset is, positive/negative/zero
negative
what are positive output gaps usually associated with
economic growth beyond sustainable capacity
break even inflation rate
The difference between the yield on a zero-coupon, default-free nominal bond and on a zero-coupon default free real bond of the same maturity
data snooping
practice of determining a model by extensive searching through a dataset for statistically significant patterns
p hacking
same thing as data snooping
inter-temporal rate of substitution
ratio of the marginal utility of consumption n periods in the future to the marginal utility of consumption today
utility derived from an additional unit of consumption in bad economic times
relatively high, because current income and consumption is low
asset that has relatively high returns when marginal utility of consumption is high provides a hedge against bad times…risk premium? price? required rate of return?
negative risk premium, high price, low required rate of return
shape of the yield curve for default free government bonds during a recession
steepen
correlation of returns to short-dated bonds to bad times vs. long-dated bonds
more negatively correlated with bad times than are returns to long-dated bonds
The information coefficient, links which two factors together
Forecasted active returns with realized active returns
how to measure consistency of active return
IR, Active Return/Active Risk
relationship between sharpe ratio and information ratio
SR^2 (portfolio) = SR^2 (benchmark) + (TC^2) * IR^2 (fund)
Information ratio of the unconstrained optimal portfolio
(transfer coefficient) * (information coefficient) * (sq(breadth))
IC * Sq(Breadth)
TC = 1
Transfer coefficient
Measures the degree to which the investor’s forecasts are translated into active weights
The correlation between any set of active weights and forecasted active returns
Expected active portfolio return
E(R(a)) = IC*Sq(breadth)
Expected Active Return
Managed portfolio return - benchmark return
Active risk of the managed portfolio
square root of the sum of active weights times the active volatility squared for each security
Unconstrained portfolio optimal active risk
std(p) = TC* (IR / SR(b) )*std(b)
Information coefficient of a market timer
IC = 2*(% correct) - 1
Limitations of the fundamental law
1) Bias in measurement of the ex-ante IC
2) Lack of independence while measuring the breadth of an active strategy
2 Broad categories of trading algorithsm
1) Execution algorithms
2) High-frequency algorithms
Execution algorithms
Break a large order, typically placed by institutions, into smaller pieces which are then placed strategically over time to minimize negative price risk
High-frequency algorithms
Rules for trading on real-time market data that a computer uses to pursue profit opportunities
Referring to rapidly updated information sources
Types of Execution Algorithms
1) Volume-weighted average price (VWAP)
2) Implementation shortfall
3) Market participation
VWAP algorithm
split an order into pieces sized proportionally to the security’s historical trading pattern over a day
Implementation shortfall algorithm
continually adjust the speed at which a trade executes as market conditions change to try to minimize difference between decision price and final execution price
market participation algorithms
slice larger orders into smaller pieces that are then entered in the market at a pace that matches the pace of overall trading of the security
Types of high frequency trading algorithms
1) Statistical arb
2) Liquidity aggregation and smart order routing
3) Real-time pricing
4) Trading on news
5) Genetic tuning
Statistical arb algo
Used to trade securities that historically have moved together
1) Pairs trading
2) Index arb
3) Basket trading
4) Spread trading
5) Mean reversion
6) Delta-neutral strategies
Liquidity aggregation/smart order routing
Sending each order to the market that has the best combination of price and liquidity (smart order routing) or by spreading the order over several trading venues (liquidity aggregation)
Genetic Tuning
a self-evolving system that tests many different strategies, implements profitable strategies, and kills off money-losers
Two methods of using algos to mitigate trading risks
1) Real-time trade risk firewalls
2) Back-testing and market simulation
Real-time trade risk firewalls
Constantly calculate risk exposures on trades to ensure that risk limits are not exceeded. Trades that would exceed limits are blocked
Backtesting and market simulation
Testing algos to see how they would perform in response to various offline scenarious or historical data
Value added from security selection
(Portfolio return - benchmark return) *portfolio allocation
Value added from asset allocation
(Portfolio weight - benchmark weight) * Benchmark return
Impact on information ratio when the aggressiveness of the active weights of an unconstrained portfolio is increase/decreased
No change
Impact on the sharpe ratio by the addition of cash or leverage in a portfolio
No change
Information ratio of a closet index
indeterminate, small, and often negative due to management fees
highest attainable sharpe ratio of an actively managed portfolio
SR(p)^2 = SR(b)^2 + IR^2
What does the information coefficient measure
IC measures an investment manager’s ability to forecast returns
Active share
measure of the percentage of the portfolio that differs from the benchmark
exact replications of indexes have active share of 0
completely different will be 1
Index tracking
The one-day difference in returns between the ETF fund and the underlying index
First step of a VAR calculation
convert the et of holdings in the portfolio into a set of exposures to risk factors
When are indicated NAVs for ETFs calculated by the exchange
during the day
All else equal, saving today for one year will how impact marginal utility of consumption
increase marginal utility of consumption today
With respect to ETF’s, what is a soft closure
a change in investment strategy
Realized value added through active management is a function of the correlation between what
what the portfolio manager implements through active weights and the portfolio’s realized active returns
Information coefficient represents the correlation between what
What the portfolio manager forecasts for active return and the portfolio’s realized active returns
Transfer coefficient represents the correlation between what
Optimal active weights and actual active weights
Full fundamental Law
TC * IC * Sq(BR) * Active Risk
Who absorbs the costs of transacting securities for the ETF
the authorized participant
Which source of tracking error contributes to overperformance in an ETF
securities lending
Portfolio construction is completed in which step of the backtesting process
Historical investment simulation
Who uses maximum drawdown as a risk measure
Hedge fund
What kind of model is the Carhart 4-factor model
fundamental factor
In which model are factor sensitives estimated first
fundamental factor models
iNAVs
Intraday “fair value” estimates of an ETF share based on its creation basket composition for that day
What is the use of ETFs in portfolio rebalancing
maintain exposure to target weights
Which part of the macroeconomic factor model is asset-specific risk specified by
error term
Neutral Rate of interest
Short-term interest rate + targeted rate of inflation
