Portfolio Management Flashcards
Multi-factor models
- Macroeconomic models; returns explained by surprises (GDP, interest rates, inflation, etc.)
- Fundamental factor models; explained by factors (P/E ratio, market cap, small, value, etc)
- Statistical factor models; variance and covariance explain models
Stock Price Sensitivity
(P/Es - P/Em) / Std of P/E
Arbitrage Pricing Theory (APT) Purpose and Assumptions
Purpose: Describes the equilibrium relationship between expected returns and systematic risk
Think: factor * sensitivities
Assumptions
- Unsystematic can be diversified away
- No arbitrage opportunities
Active Return
Rp - Rb
OR
IR * active risk
Active Standard Deviation
Purpose: is the standard deviation of the active return
Sq rt [(Rp-Rb)² / n - 1
Information ratio (IR)
Purpose: active return per unit of active risk. Measures manager’s consistency
R = (Rp - Rb) / Std(p) -Std(b)
OR
IR = IC * √BR
Note: It is affect by leverage
Active specific risk
Active specific risk = (Wp - Wb)² * residual risk²
Tracking vs Factor Portfolio
Tracking portfolio; tracks an index by matching the underlying factors
Factor Portfolio; looks at the sensitivity of one factor while setting all others to zero
Ex-Ante
Purpose: based on expectations (cannot be negative)
Formula: Return = ExpectedRp - ExpectedRb
Ex-Post
Ex-post: after the fact (can be negative)
Formula: Realized Return - benchmark return
Sharpe Ratio
Sharpe Ratio = Rp - Rf / Std Dev P
is unaffected by the addition of cash or leverage
Targeting Risk: Simple
To get the risk down you can just have cash
Std Dev of what you want / Std Dev of what you have
IR Analysis
The IR in unaffected by the aggressiveness of the active weights (return goes up but so does risk)
You can decrease risk by investing in the fund AND the benchmark
Can increase by shorting the by shorting benchmark and doubling down on the fund
Sharpe Ratio of an Active Portfolio
SRp² = SRb² + IR²
highest IR will produce the highest SR
Note: DONT FORGET TO TAKE THE SQUARE ROOT
Optimal active risk
Optimal active risk = (IR / SRb) * Std(b)
Total portfolio volatility
Total portfolio volatility = Std(b)² + Std(a)²
Std(a) = volatility of active return
Information coefficient (IC)
Measures manager skill
Ex-Ante: Expected correlation between active returns and forecast active returns (typcially small positive (<0.2)
Ex-post: IC measures actual correlation between active returns and forecast active returns
Breadth (BR)
Number of independent bets
Needs active returns correlated cross-sectionally and uncorrelated over time
Transfer Coefficient (TC)
Purpose: Correlation between actual active weights and optimal weights
TC = 1 for unconstrained portfolios
TC < 1 with constraints
Grinold (1994) Rule
Forecast of AR = IC * Std * S
S = scores
Fundamental Law
Basic Fundamental Law (unconstrained)
Full Fundamental Law (constrained)
Only difference is TC if they are constrained.
Fundamental Law:
IR
Expected Return
Expected active return
IR = (TC) * IC * √BR
ER = (TC) * (IC) √BR * Stdactive
Note: remove (TC) if uncontrained
Fundamental Law:
Optimal SR
Optimal Level of Active Risk
SRp² = SRb² + (TC)² * IR²
Stdactive = [TC * (IR/SRb)] * Stdb
Note: Remove (TC) if it is unconstrained
Conditional expected active return
CER = (TC) * (IC) * √BR * Stdactive
Clarke, de Silva, and Thorley
Ex-post decomposition of realized active return variance
Two Components:
Variation due to realized IC: TC²
Variation due to constraint induced noise: 1 - TC²
Example:
A (TC) of 0.8
64% (0.8²) of variation in performance is attributed to the realized IC
36% comes from constraint induced noise
IC of a market timer
IC = [2 * (# of bets correct/# of bets)] - 1
Example:
Dash is correct 53% of the time. Nunos makes monthly bets on 10 stocks. Has IC of 0.04. Calculate the # of bets Dash needs to make to match the IR of Nunos:
- Nunos IR = IC√BR = 0.04 * √10*12 = 0.438
- Dash IC = 2(% correct) - 1 which is 2(0.53) - 1 = 0.06
- Then solve for BR (this is where you can plug in the answers into the IC * √BR
Quarterly Information
If given quarterly standard deviations, you need to annualize. Multiply by the square root of 4
Marginal Utility
Consumption is higher during period of scarcity
Higher expected incomes =
- Consumption is lower
- Real rates are higher
Investors increase savings rate when
Expected returns are high
When uncertainly about future income increases
If GDP growth rates are high
- Investors expect higher income in the future
- Current consumption is preferred over future
- Rate of substitution will be low
- Interest rates high
Nominal Risk-Free Rates
r(short-term) = r + i
r(long-term) = r + i + rp
R = real risk free rate, i= inflation, rp = risk premium
Short-term, policy rates are positivity related to inflation gap and output gap
Gap is the difference between actual and expected
Traylor Rule
real rate + inflation + 0.5(inflation - target inflation) + 0.5(log of output - log of sustainable output)
YC and Business Cycle
S/t rates are low during recessions, long-term rates are high (due to expectations)
Positively sloped YC during recessions. Expectations are that things will go up
Inverted YC is indicative of late stages of economic expansions (indicator of recession)
Term Spread
Term Spread = yield on l/t bond - yield on s/t bond
Normal term spread is positive and attributable to the risk premium for uncertainty in inflation
Break-Even Inflation Rate (BEI)
BEI = nominal yield on default-free bond - real yield on default-free bond
THINK: treasury - TIP
BEI = i + rp
Credit Spread on Risky Bonds
credit spread = additional risk premium for credit risk
Increase during recessions, shrink during good times
When spread narrows, lower rated bonds outperform
When it widens, opposite occurs
THINK: of the value of bonds as the yield changes
Industry Sensitvity to Recessions
1, Cyclical industries are more sensitive (durable goods, consumer discretionary)
2, Customer stapes/nondiscretionary are more stable
3, Value performs well during recession
- Growth performs well during economic expansions
Factors Affecting Ability to Take Risk
- Spending needs
- l/t wealth target
- Financial strength
- Liabilities
Return objectives
Desired return (stated by client)
Required return (determined by l/t goals)
Must be consistent with risk objective
Return/Risk Tolerance for Different Client Types
Investor Return Requirement Risk Tolerance
Defined Benefit Sufficient to fund pension Depends on plan
Endowment/ Cover spending avg or above avg
foundation
Life Insurance Function of policy holder Regulations so below avg
Investment Constraints
Purpose: factors that limit available investment choices
- Liquidity: cash outflows > income
- Time horizon: time period for the portfolio
l/t is more than 10 years
- Taxes
- Legal/regulatory: external constraints
- Unique circumstances
