Asset Allocation Approaches

- Asset-Only: manage risk/ return of assets
- Liability-Relative: manage assets in relation to liabilities
- Goals-Based: manage subportfolios to meet goals

Factor Portfolio

isolate systematic risk exposure

Risk Budgeting

where/ how much risk to take

- specify how risk is distributed regardless of expected returns
- how much additional risk the investor is willing to take relative to benchmark

Rebalancing

when to rebalances to benchmark; calendar or percentage-range based

drift corridor width based on

- transaction costs (+)
- risk tolerance (+)
- correlation w/ porfolio (+)
- volatility of portfolio (-)

Mean Variance Optimization

- approach to determining AA
- lowest standard deviation for a given level of expected return
- constraints: budget, no non-neg weights, client constraints
- find optimal weights: max utility, efficient frontier, min return, max SD

MVO Criticisms

- GIGO
- concentrated AA
- diversification
- ignores liabilities
- single period
- ignores skewness/ kurtosis of returns

MVO Improvements

- reverse opt - derive weights from expected return of global market port
- Black-Litterman model - reverse opt adjusted for investor exp
- add more constraints
- resample MVO - Monte Carlo Sim; less extreme weights, includes all asset classes
- include skewness/ kurtosis in utility function; use an asymmetric definition of risk (conditional VAR)

Utility Maximization Equation

U_{m} = E(r) - 0.5 * λ * Var

Roy’s Safety First Criterion

probability of portfolio exceeing min threshold return (want highest)

SF ratio = [E(RP) - R_{L }]/ σ_{P}

R_{L} = min level of portfolio return

Sharpe Ratio

excess return per unit of risk (want highest)

( R_{m }- R_{f} )/ σ_{m }

ERP_{m} / σ_{m}

Illiquid Assets and MVO

- calc MVO w/o illiquid assets classes, include in portfolio w/ set specific allocations for illiquid assets
- calc MVO w/ illiquid assets
- calc MVO w/ illiquid asset classes, include in portfolio w/ alt inv indexes

Incorporating Client Risk Pref in AA

- specifying additional constraints
- specifying a risk aversion factor for the investor
- monte carlo simulation

Factor-Based AA

multi-factor regression to derive return w/ MVO

- use risk factors instead of asset classes
- corr btwn factors typically lower than corr btwn asset classes

Contribution to Total Risk

MCTR (marginal): β_{ac}*σ_{p}

ACTR (abs): w*MCTR

opt allocation: excess return/ MCTR for each asset class = portfolio Sharpe Ratio

ALM

asset liability management

- surplus optimization (pension funds)
- hedging/ return-seeking approach (insurance companies, overfunded pensions) > mimics the liabilities it’s funding (fully hedge = conservative)
- integrated asset-liability approach (banks)

Strategic AA

- reflects desired systematic risk exp
- set target weights for portfolio
- longer-term capital market expectations to inc portfolio value

Tactical AA

use perceived short-term opportunities in the market to inc portfolio value; inc risk

- discretionary vs systematic (value or momentum)

TAA Performance Evaluation

- compare Sharpe Ratio to SAA
- compare realized risk/ return to SAA efficient frontier
- calc info ratio/ t-stat of excess returns relative to SAA
- attribution analysis to determine excess return

Mark to Market

PV of any g/l that would be realized if the forward contract was closed early w/ an offsetting contract position

Value = (g or l)/ ( 1 + LIBOR^{n-t })

Put Option

right to sell the underlying sec if P < X

gains value delta closer to -1, loses value delta closer to 0

Call Option

right to buy the underlying sec if X < P

gains value delta closer to 1, loses value delta closer to 0

Domestic Currency Return

R_{DC} = R_{FC} + R_{FX} + R_{FC}*R_{FX}

R_{DC} = ( EV - BV )/ BV

Domestic Currency Risk

σ^{2}_{RC} = σ^{2}_{RC} + σ^{2}_{RF} + 2σ_{RC}σ_{RF}ρ_{(RFC,RFX)}

corr = pos = inc volatility of returns

coor = neg = dec volatility of returns

Currency Management Strategies

- passive hedging: benchmark
- discretionary hedging: benchmark w/ slight deviation
- active curr management: greater deviation from benchmark
- currency overlay: seperate manager for currency

Influences on Whether to Fully Hedge Currency Position

- time horizon
- risk aversion
- liquidity needs
- FX bond exposure
- hedging costs
- opportunity costs

Economic Fundamentals

assumes LT currency value will converge w/ fair value

inc value of currency

- undervalued relative to FV
- inc in FV
- higher real or nom int rates
- lower inflation
- dec risk premium

Technical Analysis

- past price data can predict future
- patterns repeat: overbought/ sold reverse, support/ resistance levels, moving avg
- don’t need to know value of currency, just where it will trade

Carry Trade

borrow lower int rate currency (developed), invest proceeds in higher int rate currency (developing)

RISK: higher int rate durrency depreciates by more than the diff in spot rates

Covered Interest Rate Parity

F = S ( 1 + i_{p })/ ( 1 + i_{b}_{ })

Volatility Trading

profit from changes in volatility

expect inc volatility: long straddle (call, put in the money), long strangle (call, put out of the money)

Vega

change in value of option b/c change in volatility of underlying

inc volatility = inc value of options = inc price

Roll Yield

roll yield = hedged curr return = F/S - 1

hedge = locks in forward price

- S > F; i
_{B}< i_{P}: long B = pos roll yield > yes hedge - S < F; i
_{B}> i_{P}: long B = neg roll yield > no hedge

Hedging

- dynamic - change hege to cover additional exp
- depens on trans costs, risk aversion

- discretionary - imperfect hedge uj
- hedge long curr exp = sell forward

Hedging Types

- cross hedge: hedge w/ proxy deriv (not perfectly corr)
- macro hedge: hedge portfolio w/ deriv based on basket of curr
- MVHR: min var hedge ratio: reg to find % to hedge, min volatility of R
_{DC}