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9 Portfolio Management
2023年CFA二级投资组合管理科目，概念较多，其中multifactor models计算要重点掌握
编辑于2023-10-12 12:42:47- 相似推荐
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Portfolio Management
Exchange-Traded Funds: Mechanics and Applications
ETF mechanics
Definition: An exchange-traded fund(ETF)is a type of fund that involves a collection of securities, and often tracks an underlying index
特点: Unlike open-end mutual funds, ETFs are traded on secondary markets
The creation and redemption process: Primary market: over=the-counter(OTC) basis between authorized participants (APs), and the ETF issuer(sponsor)
The AP creates new ETF shares by transacting in kind with the ETF issuer
APs transfer securities to (for creations) or receive securities from (for redemptions) the ETF issuer, in exchange for ETF shares
List of securties
Creation basket: the list of securities specific to each ETF
Redemption basket: the basket of securities the AP receives when it redeems the ETF shares
Creation units: the size of transaction between the AP and the ETF manager, usually 50,000 shares of the ETF
Trading and settlement
US settlement: T+2 settlement process works for majority of ETF transactions
European trading and settlement
Understanding ETFs
Expense ratio
ETFs generally charge lower fees than mutual funds because
ETF providers do not have to keep track of individual investor accounts
Nor do ETF issuers bear the costs of communicating directly with individual investors
Index-based portfolio management, used by most ETFs, does not require the security and macroeconomic research carried out by active managers
The actual costs to manage an ETF vary, depending on
Portfolio complexity
Issuer size (economies of scale apply)
The competitive landscape
Index tracking
Daily difference: using the one-day difference in returns between the fund, as measured by its NAV, and its index
Periodic tracking: tracking error is defined as the standard deviation of differences in daily performance between the index and the fund tracking the index, and a reported tracking error number is typically for a 12-month period
Sources of tracking error
Fees and expenses
Representative sampling/optimization
Depositary receipts and other ETFs
Index changes
Tax issues
Two tax-based evaluations
The investor must consider the likelihood of an ETF distributing capital gains to shareholders
The investor must consider what happens when the investor sells the ETF
The issue of capital gains distributions affects all investors in taxable accounts
ETFs are said to be "tax fair" and “tax efficient” because they have certain advantages over traditional mutual funds regarding capital gains distributions
Tax fairness: An investor sells ETF shares to another investor in the secondary market. Thus, the selling activities of individual investors in the secondary market do not require the fund to trade out of its underlying positions. If an AP redeems ETF shares, this redemption occurs in kind. In markets where redemptions in kind are allowed, this is not a taxable event
Tax efficiency: By choosing shares with the largest unrealized capital gains—that is, those acquired at the lowest cost basis—ETF managers can use the in-kind redemption process to reduce potential capital gains in the fund
Other distributions: Other events, such as security dividend distributions, can trigger tax liabilities for investors but the treatment varies by region
ETF trading costs
ETF bid-ask spread
定义: Represents the market makers price for taking the other side of the ETF transaction
The drivers of ETF bid-ask spread
The market structure
Liquidity of the underlying securities held
The amount of ongoing order flow in the ETF
The market structure
Fixed-income securities, which trade in a dealer market, tend to have much wider bid-ask spreads than large capitalization stocks
The bid-ask spread of an ETF holding stocks traded in other markets and time zones is influenced by whether the markets for the underlying stocks are open during the hours in which the ETF trades
Liquidity of the underlying securities held
The amount of ongoing order flow in the ETF
Daily share volume
The amount of competition among market makers for that ETF
The actual costs and risks for the liquidity provider
ETF bid–ask spreads are generally less than or equal to the combination of the following
± Creation/redemption fees and other direct trading costs, such as brokerage and exchange fees
+ Bid–ask spreads of the underlying securities held in the ETF
+ Compensation to market maker or liquidity provider
+Market maker's desired profit spread, subject to competitive forces
− Discount related to the likelihood of receiving an offsetting ETF order in a short time frame
Premiums and discounts
At the end of the trading day, each ETF has an end-of-day NAV at which shares can be created or redeemed and with which the ETF's closing price can be compared
During the trading day, exchanges disseminate ETF iNAVs, or "indicated" NAVs; iNAVs are intraday "fair value" estimates of an ETF share based on its creation basket composition for that day
The calculation for end-of-day and intraday premiums/discounts
End-of-day ETF premium or discount (%) = (ETF price − NAV per share) / NAV per share
Intraday ETF premium or discount (%) = (ETF price − iNAV per share) / iNAV per share
Premiums/discounts are driven by a number of factors
Time differences
Differences in exchange closing times between the underlying and the exchange where the ETF trades
Some underlying like bonds do not trade on an exchange, no true "closing prices" are available for valuing the bonds in a portfolio
Stable pricing
Total costs of ETF ownership
Round-trip trading cost (%) = (One-way commission%×2) + (0.5×Bid–ask spread%)×2 = Two-way commission% +Bid–ask spread
Holding period cost (%) = Round-trip trade cost (%) + Management fee for period (%)
ETF risks
Counterparty risk
Settlement risk
Security lending
Fund closures
Regulations
Competition
Corporate actions
Fund closures-soft closures
Creation and redemption halts
Change in investment strategy
Investor-related risk
ETFs in portfolio management
Portfolio efficiency
Portfolio liquidity management
Minimizing potential cash drag
Transacting the ETF may incur lower trading costs and be easier operationally than liquidating underlying securities or requesting funds from an external manager
Portfolio rebalancing
Portfolio completion strategies
Transition management: to the process of hiring and firing managers—or making changes to allocations with existing managers—while trying to keep target allocations in place
For very large asset owners, they may be able to negotiate lower fees for a dedicated separately managed account (SMA) or find lower-cost commingled trust accounts that offer lower fees for large investors
Asset class exposure management
Core exposure to an asset class or sub-asset class
Tactical strategies
Active and factor investing
Factor (smart beta) ETFs
Risk management
Alternatively weighted ETFs
Discretionary active ETFs
Dynamic asset allocation and multi-asset strategies
Using Multifactor Models
Background and uses of multifactor models
CAPM
CAPM model: E(Ri)=Rf + βi[E(RM)-Rf]
CML
Security market line (SML)
Arbitrage pricing theory
Introduction
APT introduced a framework that explains the expected return of an asset (or portfolio) in equilibrium as a linear function of the risk of the asset (or portfolio) with respect to a set of factors capturing systematic risk
APT provides an expression for the expected return of asset i assuming that financial markets are in equilibrium
APT is similar to the CAPM, but the APT makes less strong assumptions
Assumptions
Security returns can be described by a factor model
There are sufficient securities to diversify away idiosyncratic risk (unsystemati risk)
Well-functioning security markets do not allow for the persistence of arbitrage opportunities
公式
βp,k = the sensitivity of the portfolio to factor k
λ k = the factor risk premium for factor k
Pure factor portfolio: a portfolio with sensitivity of 1 to factor k and sensitivity of 0 to all other factors
Multifactor models
Macroeconomic factor model
Macroeconomic factor: interest rates, inflation risk, business cycle risk, and credit spreads
公式
Ri: the return to asset i
E(Ri): the expected return to asset i
biK: the sensitivity of the return on asset i to a surprise in factor K(K= 1, 2, . . ., K)
FK: the surprise (the difference between realized value and predicted value) in the factor K. (K= 1, 2, . . ., K)
εi: an error term
应用
We might assume that the returns for a particular stock are correlated with surprises in inflation rates and surprises in GDP growth
Fundamental factor model
Fundamental factor: book-value-to-price ratio, market capitalization, the price-to-earnings ratio, and financial leverage
公式
αi: intercept term
biK: an asset's sensitivity to a factor K is expressed using a standardized beta
Comparison
Statistical factor model
方法: Statistical methods are applied to historical returns of a group of securities to extract factors that can explain the observed returns of securities in the group
Advantage: make minimal assumptions
Disadvantage:the interpretation of statistical factors is generally difficult in contrast to macroeconomic and fundamental factors
Applications of multifactor models
Factor models in return attribution
The return on a portfolio, RP, can be viewed as the sum of the benchmark's return, RB , and the active return = RP − RB
Active return=the return from factor tilts + security selection
The first component
The second component: security selection
Factor models in risk attribution
Active risk squared = Active factor risk + Active specific risk
Factor models in portfolio construction
Passive management: Analysts can use multifactor models to replicate an index fund's factor exposures, mirroring those of the index tracked
Active management: In constructing portfolios, analysts use multifactor models to establish desired risk profiles
Factor models in strategic portfolio decisions: A multifactor approach can help investors achieve better-diversified and possibly more-efficient portfolios
Measuring and Managing Market Risk
Introduction and understanding value at risk
Definiton: Value at risk(VaR) is the minimum (maximum) loss that would be expected a certain percentage of the time over a certain period of time given the assumed market conditions
特点
VaR can be measured in either currency units or in percentage terms
A VaR statement references a time horizon
VaR associated with a given probability
Assumed market conditions
Estimating VaR
Parametric method
Percentage VaR=|μt- Zα × σ| or |Zα × σ|
Dollar VaR= |(μt- Zα × σ)×asset value| or |Zα × σ×asset value |
VaR for a portfolio which contains two assets
VaR for normal distribution
Z-value under certain confidence level
Historical simulation method
方法: Uses the current portfolio and reprices it using the actual historical changes in the key factors experienced during the lookback period
Advantage: do not have any distribution assumption andcan accommodate options
Disadvantages
All observations are weighted equally (Ghost effect)
There can be no certainty that a historical event will re-occur or that it would occur in the same manner or with the same likelihood as represented by the historical data
Monte Carlo simulation
方法: The user develops his own assumptions about the statistical characteristics of the distribution and uses those characteristics to generate random outcomes that represent hypothetical returns to a portfolio with the specified characteristics
Advantages
Monte Carlo simulation does not need to be constrained by the assumption of normal distributions
More flexible than parametric and historical simulation method
Disadvantages
Must first decide how many random values to generate and there is no industry standard (garbage in, garbage out)
The more values we use, the more reliable our answers are but the more time-consuming the procedure becomes
Advantages, limitations and extensions of VaR
Advantages
Simple concept
Easily communicated concept
Provides a basis for risk comparison
Facilitates capital allocation decisions
Can be used for performance evaluation
Reliability can be verified
Widely accepted by regulators
Limitations
Subjectivity
Underestimating the frequency of extreme events
Failure to take into account liquidity
Sensitivity to correlation risk
Vulnerability to trending or volatility regimes
Misunderstanding the meaning of VaR
Oversimplification
Disregard of right-tail events
Extensions of VaR
Conditional VaR (CVaR)/expected tail loss/ expected shortfall
The expected (average) loss of all the portfolio returns in the worst α% cases
Incremental VaR (IVaR): Can capture how the portfolio VaR will change if a position size is changed relative to the remaining positions
Marginal VaR (MVaR): Reflect the impact of a small change in a given portfolio
Ex-ante tracking error (relative VaR): A measure of the degree to which the performance of a given investment portfolio might deviate from its benchmark
Other key risk measures
Sensitivity risk measures: Sensitivity measures examine how performance responds to a single change in an underlying risk factor
Equity exposure measures: Beta (β)
Fixed-income exposure measures: duration and convexity
Options risk measures: duration and convexity
Scenario risk measures
Historical scenarios: Measure the portfolio return that would result from a repeat of a particular period of financial market history
Hypothetical scenarios
定义: Describe a market event that has not occurred in the past but people believes has some probability of occurring in the future
Stress tests: apply extreme negative stress to a particular portfolio exposure
Reverse stress testing: used to design an effective hypothetical scenario, it is necessary to identify the portfolio's most significant exposures
Comparison
Market risk management
Risk budgeting
Position limits
Scenario limits
Stop-loss limits
Capital allocation
Applications of risk measures
Banks
Liquidity gap
VaR
Leverage
Sensitivities
Economic capital
Scenario analysis
Traditional asset managers
Position limits
Sensitivities
Liquidity
Scenario analysis
Redemption risk
Ex-ante tracking error
VaR
Hedge fund managers
Sensitivities
Leverage
VaR
Scenarios
Drawdown
Insures
The market risk management measures in the property and casualty lines of business
Sensitivities and exposures
Economic capital and VaR
Scenario analysis
The market risk management measures in the life portfolio
Sensitivities and exposures
Asset and liability matching
Scenario analysis
Backtesting and Simulation
Backtesting
Objectives: Backtesting approximates the real-life investment process by using historical data to assess whether a strategy would have produced desirable results
Process
Step 1: strategy design
Investment Universe
Return Definition
Rebalancing Frequency and Transaction Cost
Start and End Date
Step 2: historical investment simulation
The portfolio construction process depends primarily on the investment hypothesis under consideration, the investment manager's capabilities and style, and the client's investment mandate for which the potential strategy is relevant
To simulate rebalancing, analysts typically use rolling windows
Step 3: analysis of backtesting output
Not only the average return of the portfolio but also the risk profile (e.g., volatility and downside risk) should be cared
Analysts often use metrics such as the Sharpe ratio, the Sortino ratio, volatility, and maximum drawdown (the maximum loss from a peak to a trough for an asset or portfolio)
Common problems
Survivorship bias
解决: Point-in-time data
表现: Low-volatility anomaly: stocks with low volatility tend to outperform high-volatility stock
Look-ahead bias
原因: using information that was unknown or unavailable during the historical periods over which the backtest is conducted
Survivorship is a type of look-ahead bias
Data snooping (p-hacking)
Historical scenario analysis
定义: Historical scenario analysis is a type of backtesting that explores the performance and risk of an investment strategy in different structural regimes and at structural breaks
方法: Examine the benchmark and risk parity factor portfolios with respect to these two regimes—recession versus expansion and high volatility versus low volatility
Simulation analysis
The step of simulation
Step 1:Determine what we want to understand: target variable
Step 2: Specify key decision variables
Step 3: Specify the number of trial (N) to run.
Step 4: Define the distributional properties of the key decision variables
Step 5: Use a random number generator to draw N random numbers for each key decision variable
Step 6: For each set of simulated key decision variables, computethe value of the target variable
Step 7: Repeat the same processes from step 5 and 6 until completing the desired number of trials (N)
Step 8: Calculate the typical metrics, such as mean return, volatility, Sharpe ratio and the various downside risk metrics (maximum drawdown)
Historical simulation
Historical simulation incorporates randomness by randomly drawing returns from historical data rather than following each period chronologically
Random sampling with replacement (bootstrapping) is often used in investment research
The problem with historical time-series data is that there is only one set of realized data to draw from, but most financial variables are not stationary
Monte Carlo simulation
An important issue with historical simulation is that the data are limited to historical observations, which may not represent the future, and this deficiency can be addressed with Monte Carlo simulation
The advantage and disadvantage
Ad: highly flexible
Dis-ad: complex and computationally intensive
步骤
Specify a function form for each key decision variable
Considerations for the functional form of the statistical distribution
Sensitivity analysis
Definition: a technique for exploring how a target variable is affected by changes in input variables (e.g., the distribution of asset or factor returns)
作用: We should conduct a sensitivity analysis by fitting our factor return data to a different distribution and repeating the MonteCarlo simulation accordingly
Economics and Investment Markets
Framework for the economic analysis of financial markets
The present value model
原理: The value of any asset can be computed as the present value of its expected future cash flows discounted at an appropriate riskadjusted discount rate
Components of discount rate
Default-free interest rate
Expected inflation
Risk premium
Expectations and asset values
The discount rate
Real default-free interest rates
The choice to invest today involves the opportunity cost of not consuming today, and this trade-off is measured by the marginal utility of consumption
The marginal utility of consumption of investors diminishes as their wealth increases
Inter-temporal rate of substitution
always les than 1 because investor always prefer current consumption over future consumption)
关系: In "good" ("bad") economic times, the utility derived from an additional unit of consumption today will be relatively low (high)
The current price (0) of a zero-coupon, inflation-indexed, risk-free bond(TIPS: treasury Inflation-Protected Securities) that will pay $1 at time t can be expressed as: P0= mt
关系
Real risk-free interest rate is positively related to GDP growth rate
GDP growth rate is forecasted to be high
Future income will be higher
The utility of consumption in the future (Ut) will be lower(diminishing marginal utility of wealth)
mt will be lower
Real risk-free interest rate will be higher
Interest rates are positively correlated with the expected volatility in GDP growth due to higher risk premium
Short-term nominal interest rates
实例: Treasury bills (T-bills) are very short-dated nominal zero-coupon government bonds
特点
Very heavily influenced by the inflation environment and inflation expectations over time
Influenced by real economic activity (saving and investment decisions of households)
Affected by the central bank's policy rate (fluctuate around the neutral policy rate)
Taylor rule
作用: help rate setters gauge whether their policy rate is at an "appropriate" level
公式:R = R(neutral) + θ + 0.5 (θ − θ∗) + 0.5 (Y − Y∗)
R: central bank policy rate implied by the Taylor rule
R(neutral): neutral real policy interest rate
θand θ∗: current inflation rate and central bank's target inflation rate, respectively
Y and Y*: log of current growth of GDP and log of central bank's target growth of GDP, respectively
Long-term nominal interest rates
假设: Investors are risk averse and thus need to be compensated for taking on risk and the uncertainty related to future inflation
The effect of inflation
Premium for expected inflation
Risk premium for inflation uncertainty
Break-even inflation rate(BEI)
定义: The difference between the yield of a non-inflation-indexed risk-free bond and the yield of an inflationindexed risk-free bond of the same maturity
BEI = π+ θ
θ :expected inflation
π :risk premium for uncertainty in inflation
Slope of yield curve
During the recession
The slope of yield curve will increase because
Central bank tends to lower the policy rate
Investors expect higher future GDP growth and higher long-term rates as economic growth recovers
Short-term bonds generally perform better than long-term bonds
During the expansion
Negatively sloped (inverted) yield curve
Long-term bonds generally perform better than short-term bonds
Credit spread
During the expansion, long-term bonds generally perform better than short-term bonds
Credit spreads tends to narrow in times of robust economic growth, when defaults are less common
Credit risky (lower-rated) bonds will perform better than default-free (higher-rated) bonds
Credit spreads tends to rise in times of economic weakness as the probability of default rises
Default-free (higher-rated) will perform better than credit risky (lower-rated) bonds
Industry sector and company specific factors
Some industrial sectors are more sensitive to the business cycle than others
Issuers that are profitable , have low debt interest payments, and that are not heavily reliant on debt financing will tend to have ahigh credit rating
Equity risk premium
λ: equity risk premium
k: additional risk premium relative to risky debt for an investment in equities
Consumption-hedging property
Consumption-hedging property describe the feature that may provide high payoff during economic downturns
The consumption-hedging properties for equities are poor
Investment strategy
Growth stocks
Strong earnings growth
High P/E and low dividend yield
Have low (or no) positive earnings
Value stocks
Operates in more mature markets with a lower earnings growth
Low P/E and high dividend yield
Capitalization
Small-cap stocks tend to underperform large-cap stocks in difficult economic conditions
Higher risk premium demanded by investors to invest in small-cap stocks relative to large-cap stock due to higher volatility
Commercial real estate investment
特点
Bond-like characteristics : steady rental income stream, like cash flows of bonds
Equity-like characteristics : uncertain value of the property at the end of the lease term
Illiquidity
Discount rate
risk premium for illiquidity
Analysis of Active Portfolio Management
Active management and value added
Measuring value added
Active weights
Active security returns
Decomposition of value added
方法: The total value added as the sum of the active asset allocation decisions and the weighted sum of the value added from security selection
公式组成
Active asset allocation
Security selection
Comparing risk and return
Sharpe ratio
公式
影响因素
The Sharpe ratio is unaffected by the addition of cash or leverage in a portfolio
Sharpe ratio is affected by the change of aggressive active weight
Information ratio
公式
类型
Ex-anti IR: based on expected return
Ex-post IR: based on realized return
影响因素
The information ratio is unaffected by the aggressiveness of active weights
The information ratio is unaffected by taking positions in benchmark portfolio
The information ratio is affected by the addition of cash or the use of leverage (前提: benchmark 不能选取无风险资产)
Constructing optimal portfolios
The optimal portfolio: The active portfolio with the highest (squared) information ratio will also have the highest (squared) Sharpe ratio
The optimal amount of active risk
The fundamental law
The correlation triangle
各项计算
Information coefficient (IC)
公式
作用: A measure of manager's forecasting accuracy (also called signal quality)
Ex-ante IC: must be positive
Ex-post IC: either positive or negative
Transfer coefficient (TC)
公式
Optimal active weights
特点
For portfolios without any constraints, TC = 1
For portfolios with constraints, TC < 1
Breadth (BR): The number of independent active bets taken per year
The fundamental law of active management
Full fundamental law
If portfolio without any constraints, TC=1
Market timing
IC = 2 ∙ (%correct) − 1
If the manager is correct 50% of the time, IC=0
Limitations: Poor input estimates lead to incorrect evaluation
Trading Costs and Electronic Markets
Pre
Trading cost
Explicit trading costs: direct cost trading, include brokerage, taxes, and fees
Implicit costs: include the bid-ask spread, market or price impact costs, opportunity costs, and delay costs (or slippage)
Dealer quotes
Bid-ask prices: the prices at which dealers will buy/sell specified quantities of a security
Bid ask spread: the difference between the ask price and the bid price
Best(inside,market) bid-ask spread: the spread between the best ask (lowest) price and the best bid (highest) price in a market
Mid-quote price: (ask + bid)/2
Electronic markets
作用
The exchanges use electronic systems to arrange trades by matching orders submitted by buyers with those submitted by sellers
Traders use electronic systems to generate the orders that the exchanges process
The two types of systems are co-dependent
Costs of trading
Implicit costs
Bid-ask spread
Market impact (or price impact)
Delay cost (or slippage): the cost of an adverse price movement during the lag in executing a large trade
Opportunity cost: arises from unfilled orders or failed trading opportunities
Implicit costs estimates
Effective spread
公式
The effective spread
For buy orders: 2 × (trade price - midquote price)
For sell orders: 2 × (midquote price - trade price)
The effective spread trading cost estimate
For buy orders: trade size × (trade price - midquote price)
For sell orders: trade size × (midquote price - trade price)
Limitations
It does not take into account the price impact cost
Not account for slippage or delay costs
Not capture the opportunity cost of a trade
Volume-weighted average price (VWAP)
For buy orders: trade size × (trade VWAP - VWAP benchmark)
For sell orders: trade size × (VWAP benchmark - trade VWAP)
implementation shortfall
Implementation shortfall measures the total cost of implementing an investment decision by capturing all explicit and implicit costs
Implementation shortfall = paper value - actual value
Electronic markets
Market fragmentation: trading the same instrument in multiple venues
Types of electronic traders
Electronic news traders: analyze high-speed news feeds and submit market orders (as opposed to limit orders) based on the analysis
Electronic dealers: these post bid and offer prices to profit from the spread
Electronic arbitrageurs: these round-trade in multiple markets seeking to exploit price discrepancies.
Electronic front runners: identify when large number of orders will fill on the same side of the market
Electronic quote matchers: try to exploit the option values of standing orders
Low-latency traders
定义: The elapsed time between the occurrence of an event and a subsequent action that depend on that event
Comparative advantages
Take advantage of market opportunities before others do
Receive time precedence that would allow them to trade sooner when offering liquidity to others
Ensure order cancellation when they no longer want to fill the order
Characteristics
Hidden orders
Leapfrog
Flickering quotes
Electronic trading risks
The HFT Arms Race: the competition among high-frequency traders has created an "arms race" in which each trader tries to be faster than the next
Costs form barriers to entry can create natural monopolies
Systemic risk
Runaway algorithms
Fat finger errors
Overcharge orders (demand liquidity significantly higher than what is available in the market)
Malevolent orders (created to specifically manipulate the market)