Portfolio Management Flashcards
Exchange Traded Funds (ETFs)
Creation/Redemption: Investors can bring/redeem from authorized participants (AP) by exchanging basket of ETF stocks for one ETF share. This process keeps the ETF prices in line with the underlying stock prices to ensure that no arbitrage opportunities are present
Tracking Error is std dev of daily tracking difference annualized, caused by fees and taxes
ETF Bid/Ask Spreads are positively related to underlying spreads, risk premium, and AP’s profit margin, while being negatively related to secondary market volume of ETF trading
ETF Premium or Discount % = (ETF Price - NAV)/NAV, caused by time zone differences and stale pricing
ETF costs are trading costs and management fees, trading costs are driven by liquidity of the ETF (average volume traded) and management fees are set by AP. Short term investors want low trading costs as they are in and out, long term investors want low management fees as they will buy and hold
Risks for ETFs are counterparty risk and fund closures
ETFs allow for rebalancing/sector tracking trades/active management and alternative weightings in an ETF to bet on one aspect of the ETF more than the other aspects
Arbitrage Pricing Theory & Multifactor Model Types
Arbitrage Pricing Theory: Equilibrium in a portfolio, each return comes with its own risk and your portfolio total return is driven by the factors of that portfolio, three assumption:
- Unsystematic Risk can be diversified away
- Returns are generated by a factor model
- No arbitrage opportunity exists
Expected Return = Risk Free Rate + Sum of (Factor Sensitivities * Factor Risk Premium)
Portfolio will be exposed to a number of factors, all which come with their own risk premiums, the expected return you have will depend on the level of factor sensitivities that you have
Multifactor Models
- Macroeconomic Factors: Returns are explained by surprises/shocks in macro factors
- Fundamental Factors: Returns are explained by firm specific multiples/attributes
- Statistical Factors: Stats are used to predict returns, the problem with these models are they are pure numbers and don’t interpret the economy great
Active Risk & Return, Information Ratio, Portfolio Types
Active Return = Return Portfolio - Return Benchmark
Active risk is the std dev of active return overtime and its determined by active factor tilt and active asset selection
Active Risk^2 = Active Factor Risk + Active Specific Risk
Information Ratio = Active Return/Active Risk = Return Portfolio - Return Benchmark / std dev (Return Portfolio - Return Benchmark), risk is the risk that you don’t hit your returns
Higher information ratio means you are getting more return for every unit of risk that you are taking on which is a good thing
Multifactor Models breakdown factors into risk/return
Specific Factor Return = (Beta Portfolio - Beta Benchmark) * Return, this will give you the factor return for a specific factor in a portfolio
Active Specific Risk = (Weight Portfolio - Weight Benchmark)^2 * Variance, get yours weight difference, square it and multiple by variance
Factor portfolios focus on 1 single factor to track with all other factors being weighed at 0
Tracking portfolios will look to replicate index factors like S&P 500 to have the same exposures
Multifactor models allow for specific risk taking while diversifying other risks away
Value at Risk (VaR), Estimation Methods (Parametric, Historical, Montecarlo), Advantages & Disadvantages of VaR & VaR Extensions (CVaR, IVaR, MVaR, Relative VaR)
Value at Risk (VaR): Estimate minimum loss that will occur given a probability
5% VaR of 1 million means that 5% of the time you will loss at least 1 million and it could be more
VaR Estimation Methods:
Parametric: Uses variance and covariance
Historical: Uses historical values for risk factors over a lock back period
Montecarlo: Runs a bunch of scenarios to get a possible distribution of factors
Advantages of VaR: Widely accepted, simple, expresses risk as singular number, good for comparion
Disadvantages of VaR: Subjective to time period uses, sensitive to assumptions, can be manipulated or misstated with a few bad assumptions, focuses only on left tail
VaR Extensions:
Conditional VaR (CVAR): Expected loss given that a VaR event has occured (you are in the bottom tail)
Incremental VaR (IVaR): Estimated VaR change given a specific size change in portfolio
Marginal VaR (MVaR): Estimated VaR change given a position change in portfolio
Relative VaR: VaR difference between portfolio and benchmark
Sensitivity and Scenario Analysis with VaR
Sensitivity Analysis: Estimates change in security given one small risk value change
Scenario Analysis: Estimates change in value given specific set of risk factors changing (multiple factors)
- Sensitivity measures single factor, scenario measures multiple factors, but neither gives probabilities of occurrence, need VaR to give those probabilities and use all 3 together
Stress Test on a portfolio to determine solvency/survivability, gives a complete view at how risk factors affect but not exact probabilities, VaR gives probabilities, sensitivity & scenario give connections
Scenario can use historical or hypothetical but will never get a situation exactly right
Risk Measures (Beta, Duration, Convexity, Delta) & Industry Risks
Measures of Risk:
Beta = Equity Risk
Duration = Interest Rate Risk
Convexity = Change in Duration
Delta = Option Risk
Gamma = Change in Delta
Vega = Option Volatility Risk
Market Risk can be adjusted by changing portfolio holdings and trying to focus on the risks you feel best to handle
Risk level will never be 0, you want to manage the risks that you can and get away from risks you can’t handle, only take on the risks that you can handle
Industry Risks:
Banks: Asset/Liab mismatch, market risk, leverage, duration
Asset Manager: Return volatility and probability of absolute loss/relative loss to benchmark matter
Pension Funds: Asset/Liab mismatch, volatility of surplus because you don’t want it to randomly go down a ton one day when you need to pay
Property and Causality: Market Risk, VaR of capital (need to be able to make payments), insurance risk
Life Insurance: Market risk, asset/liab mismatch, surplus going down alot at once
Stop loss will close a position when it reaches a certain point, position limit will limit the total % one position can be in a portfolio, scenario limit will limit the downside of a scenario (example: if this happens we sell and its real bad we would sell at this point)
Backtesting (Steps & Problems) & Scenario Simulation, Historical, Monte Carlo
Backtesting uses historical data to evaluate whether an investment would have produced excess return
- 3 Steps: Design Strategy (Pick goal, rules, parameters)
Historical Investment Simulation (Assemble portfolio, rebalance overtime)
Analyze Output (Compute performance, risk/return, rebalance overtime)
- Rolling Window Backtesting: Move backtesting window with time, simulate real world investing
-Backtesting Problems: Survivorship Bias (Using only data that has survived overtime)
Lockahead Basis (Using info that wouldn’t be available like 4Q financials at 1/1)
Data Snooping (Picking models that backtest well, need to design model than test)
Scenario analysis (Looks at portfolio in different scenarios like high volatility or recession)
Stress Testing (will be scenario but extremes)
Historical Simulation (picks observations at random from history setting things to equal probability)
Monte Carlo (Distribution calibrated using historical data)
When correlated factors use multivariate model to account for correlation
Sensitivity analysis fits factors for skewness and kurtosis
Economics and Investment Markets
Market Value of Assets: Based on future DCFs and discount rate, if more risky than discount rate will be higher. Market prices are based on current expectations, changes in expectations will be what changes market prices
Short Term Interest Rates: Interest rates are GDP indicator, upward sloping means that economic expansion is expected and long term rates are higher to cool potential inflation, inversing interest rates means recession may be on the way
Breakeven Inflation Rate = Yield of non inflation index bonds - yield of inflation index bonds
- Can be predicted off of expected inflation and risk premium for inflation uncertainty
Credit Spreads will be up in bad times (junk bonds will need to yield more to get investment) and down in good times. This causes lower quality/junk bonds to outperform high quality bonds in good times
Noncyclical industries are less volatile than cyclical ones in both credit spreads and earnings, cyclical industries depend on phase of the economy (do people have money to spend on nonessential things)
Equities are cyclical so poor consumption hedge (if consumption down than equities will also go down), which makes the risk premium on equities positive
Commercial Real Estate valuation depends on income, quality of tenant, and terminal value and discount rate depends on uncertainty in terminal value and the fact its illiquid
Active Return, Sharpe Ratio, Info Ratio
Value added = active return = active portfolio return - benchmark return
- Active return of security = △ weight from benchmark * return
- Active return has asset allocation (how much you allocate to a sector vs another) and security selection/weighting (how much you weigh securities/change any weights)
Sharpe Ratio is every unit of return for portfolio above the risk free rate per unit of portfolio risk
Sharpe Ratio = Return Portfolio - Risk Free Rate / std dev of portfolio
Information Ratio (Higher the better) = IR = Active Return / Active Risk = Return Portfolio - Return Benchmark/ std dev portfolio - std dev benchmark
Unconstrained Portfolio Optimal Risk = σ*A = Info Ratio / Sharpe Ratio Benchmark * Std dev benchmark
Sharpe Ratio Portfolio = sqrt (Sharpe Ratio Benchmark^2 + Info Ratio Portfolio^2)
Info Ratio can be altered by cash/leverage in portfolio (you can actively take on less risk by holding cash), Sharpe can not
For unconstrained portfolio info ratio is unaffected by active weights because both active risk and return increase/decrease proportionally
Fundamental Law of Portfolio Management & Strengths/Weakness
Info Ratio Components: Information Coefficient (Managers skill), Breadth (Number of active independent bets), Transfer Coefficient (degree of constraint on managers active management between 0 and 1, will be 1 if unconstrained)
IR = TC * IC * sqrt(BR) = Transfer Coefficient * Information Coefficient * sqrt(Breadth)
Expected Active Return = TC * IC * sqrt(BR) * Active Risk = IR * Active Risk
Investors will always go for highest info ratio and combine active portfolio with benchmark to get optimal level of risk for the investor
Info Coefficient = 2 * (% correct) -1, so if right 60% of the time than (2 * .6) - 1 =.2 which is really good, most good ICs are .05 or .1
Fundamental law is good to measure IR, decide timing, securities, sector rotation, however need to be aware of bias in Info Coefficient Calc and true independence in Breath Calc (need to make sure only each independent bet is counted)
Trading Costs and Electronic Markets
Explicit costs are brokerage fees/taxes, stuff you see in your trade
Implicit costs are bid-ask spread, opportunity costs, stuff you don’t see in your trade
VWAP (Volume Weighted Average Price) transaction cost = Trade size * (Benchmark - Trade) for sell side and Trade size * (Trade - Benchmark) for buy side
Implementation Shortfall is value lost from decision to trade to trade being executed, price may have been more attractive when you decided but it took 10 seconds to enter and price changed
Market Fragmentation is when same security is traded in multiple markets, liquidity aggregation (superbook) or smart order routing are used to prevent market fragmentation
Electronic traders are anyone who trades electronically
Latency is speed that a trade is completed, want low latency to complete fastest and get best price available
Low Latency lets you get best prices, leapfrog (small good trades), flicker quote to see if there are hidden orders
Risks of electronic trading are malevolent orders to manipulate markets like wash trading, spoofing, bluffing, squeezing, gunning the market into bad trades. Other risk are fat fingering a trade and runaway algorithms that crash market.
Real time surveillance and monitoring help cut down on market manipulation and detect it quick
