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

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)