6. Portfolio Management Flashcards
HPR (ETF)
HPR = Round Trip Trade Cost + Mgmt Fee
Tracking Error (Formula)
TE = StDev (ETF-Index) anualizado
Impacted by Fees, Expenses, Subsample, Use of aluguel. Index Rebalance.
Authorized Participant
Large Institutional Entity allowed to create/redeem ETF shares
Securities < ETF share
- Buy basket
- Create ETF shares
- AP sells ETF shares @ higher value
Securities > ETF share
- Redeem ETF shares
- Gets basket
- AP sells securities @ higher value
Arbitrage Gap w/ ETFs
Buy low, sell high (between NAV price and ETF share). It must consider operational costs.
ETF settlement
T+2 days
Expense Ratio
Amount by which ETF should underperform its benchmark index
Tax Fairness ETF (Concept)
Tax for those who redeem only
ETF Sponsor
Publishes In-King ETF basked and creates/redeem shares for APs
Multifactor Models (Types)
- Macro (Surprises) - Estimated after
- Fundamental (Stock Specific Betas) - Assumed before
- Statistical (Complex to interpret, fewer assumptions)
VaR (Concept)
- Minimum loss for X% of the time 5%: 1,65 (normal 90%) 2,5%: 1,96 (normal 95%) 1%: 2,33 (normal 98%) 0,5%: 2,56 (normal 99%)
Parametric Var (Formula)
VaR = [ E(Rp) - (t crítico * stdev portfolio)] * -1 * Notional
From daily to anual: E(Rp) * 250
From daily to anual: stdev portfolio * Raiz de 250
VaR (Daily, Annual, Weekly)
Daily/Annual: 250 days
Weekly: 52 weeks
Monthly: 12 months
Conditional VaR (Concept)
Average loss, given that loss has exceeded VaR
Incremental VaR (Concept)
Δ Var Adicional per Unit of Increase in Exposure
Marginal VaR (Concept)
Δ Var Adicional por +1% de exposição
Relative VaR (Concept)
Undeperformance of at least X% em relação a um benchmark
VaR Methods (List)
- Parametric
- Historical Simulation (all observations equally weighted)
- Monte Carlo (não assume Distr. Normal)
Scenario Risk Measures (List)
- Historical Scneario = Stress Test or Reverse (plot desired exposure and check scenario focused on affecting these top exposures
- Hypothetic = Simulation. You determine the assumptions.
- Sensitivity = Combine with simulation and check Δ Output given change in ONE variable.
Backtesting and Simulation (Steps)
- Strategy Design (hypothesis, goal, key parameters)
- Historical Simulation (Generate portfolios)
- Analysis of Output (Calculate metrics)
- Roll windows test (Test recent 12 months, generate outputs, compare with the Month 13, walk forward)
Backtest Strategies
- Benchmark Portfolio (BM): Same weight per factor of risk. Select 4 factors with 0,25 weight each.
- Risk Parity (RP): Same risk per factor selected. Choose Total Risk and divide equally for the 4 factors above. Estimula a diversificação.
Biases in Investment Calculations
- Survivorship Bias (survivor stocks = higher returns)
- Look Ahead Bias (data not available in the day of analysis)
- Data snooping: Caçar significância estatística onde não tem
Interest Rate (Economics & Investment Market FORMULA)
Interest = [1 / m (t,s) ] - 1
scenario: good future ↑ (e vice-versa) = juro maior
↓ m = willingness to trade dinheiro hoje por amanhã
↓ u = utilidade grana no futuro
m (t, s) - formula
m (t, s) = u (t+s) / u (t)
m = willingness to trade
u = utilidade marginal do dinheiro
ambos baixos ↓ qdo a economia for promissora
Taylor Rule (Formula)
Taylor Rule: I + θ + 0,5 (θ - θ) + 0,5 (y - y)
(θ - θ) = inflation - expected inflation
(y - y) = output gap = actual - potential
Break Even Inflation (Bey Formula)
BEY = (R nominal - Rreal) p/ bond de curtíssimo prazo zero coupon
Teoricamente é o preço da incerteza da inflação.
Correlation between Interest Rate and Economy
Short Term = Monetary Policy (explica 1/3 dos Yields). Resto é Inflação.
Long Term = Real Growth
E (Ractive) - Formula
E (Ra) = E (Rp) - E (Rbenchmark)
Alpha (α) - Formula
α = Rp - β(Rbenchmark)
Ractive - Formula
Ractive = ∑ Δwi (Ri - Rbenchmark)
Ractive = AA + SS
Ractive = ∑ Δwclasse*Rclasse +∑ Wstockspecific *Ractive
Sharpe Ratio (Formula)
SRP = (Rp - Rf)/σ portfolio
Add Cash, não impacta
Information Ratio (Formula)
IR = (Rp - Rbenchmark) / σativo
IR = Ractive / σativo
Add Agressividade (Δwi), não impacta
Breadth (Formula)
BR = N / [1 + (N-1)correlation]
or BR = N if no correlation between decisions
N = number of estimates
Basic Law (Unconstrained Portfolio)
IR = IC * √BR * σativo
IC entre -1 e +1
Full Law (Unconstrained Portfolio)
E (Ractive) = TC * IC * √BR * σativo = (IR * σativo)
σativo (Formula)
1) σativo = E (Ractive) / IR
Manipulação da fórmula de Information Ratio
2) σativo* = TC * (IR / SRB) * σbenchmark
Fórmula = TC * IRB * risco
Relação Quadrado (Fórmula)
SRpˆ2 = SRbˆ2 + (TC * IRˆ2)
Information Coefficient (Formula)
IC = Correl ( Ri/σi; μi/σi)
IC = Acertos - Erros
Retorno e Forecast
Transfer Coefficient (Formula)
TC = Correl (μi/σi; Δwi*σi)
Forecast e Implementação do Peso Ativo
Value Added (Concept)
Relação entre wi (Peso Ativo) e Ri (Retorno do Ativo)
Ex-Post Performance (Formula)
Ractive = E (Ractive | IC Return) + Noise
IC Return = TCˆ2
Se TC = 0.6, logo 36% da variância (σ^2) do Ractive virá do Information Coefficient (IC)
Noise = (1 - TCˆ2) = 64% resíduo
Implementation Shortfall
Paper Portfolio - Actual Portfolio
Paper = (Actual Value - Decision Value) realizei Actual = (Quanto vale - Quanto Custou) Gastei ao implementar
Effective Spread (Formula)
Buy = [Size * (Trade Price - Bid-Ask/2)] * 2 Sell = Inverte os lados do parêntesis
VWAP (Formula)
Buy = Size * (Trade VWAP - VWAP Benchmark) Sell = Inverte os lados do parêntesis
Preço médio das ordens executadas
Buy = Quero que VWAP meu < VWAP bench Sell = Quero que VWAP meu > VWAP bench
