Taylor Rule

r = policy neutral rate + 0.5(exp - trend GDP growth) + 0.5(exp - acceptable inflation)

H-Model

for emerging economies

Fed Model

- EY > treasury yield, ratio > 1 - undervalued
- EY < treasury yield, ratio < 1 - overvalued

CONS: ignores ERP, ignores earnings growth, compares real variable (EY) to nominal value (treasury yield)

Yardeni Model

compares theoretical EY to acutal EY

- EY > fair value yield - undervalued
- EY < fair value yield - overvalued

CONS: assumed r, d varies over time, earnings estimates can be wrong

Q Models

MV/ replacement cost

q > 1 - overvalued

q < 1 - undervalued

CAPE

cyclically adjusted P/E ratio

CAPE > historical avg - overvalued

CAPE < historical avg - undervalued

10 yr avg earnings captures effects of business cycle and inflation

Credit Risk

risk counterparty will default; based on changes in spread

- %Δ value = - D (Δs)
- currency swap CR highest closet to maturity
- int rate or eqty swap CR highest in middle of life

HHI

HHI = Σ market share^{2}

effective # stocks = 1/ HHI

Mean Variance Optimization

optimizer to set AA, min tracking error, max returns; identify corner portfolios

+: considers correlations

-: doesn’t consider BM variance (need to factor into constraints); based on hist values

M^{2}

r_{f} + σ_{mkt} * SR

Myopic Loss Aversion

overemphasizing ST potential losses, underemphasizing LT potential gains > risk premium too high

Life Insurance

- bond like HK, insure against mortality risk
- not needed for equity like HK b/c higher risk HK

Corner Portfolios

- on efficient frontier
- move weight from 0% to X% or X% to 0%
- GMVP is starting port (doesn’t always follow 2)

Hedging Foreign Markets

- hedge foreign market risk only: earn Rf
_{for}+ R_{FX} - hedge FX risk only: earn Rf
_{dom}- Rf_{for}

Effective Beta

%Δ value of portfolio / %Δ value of index

FV of Portfolio AT

Expected Annual Return

D/P - Δs + i + g + ΔP/E

Strategic AA

- portfolio’s general AA, under “normal” conditions
- based on capital market exp and inv obj/ constraints
- LT time horizon
- neg: GIGO

Tactical AA

- exploit perceived capital market arbitrage opp
- based on ST cap market exp
- temporarily deviating from a portfolio’s LT SAA
- neg = volates linear reg assumptions

Return on Leverage

R_{lev} + borrowed/ equity * (R_{lev} - R_{bor})

Return

- coupon yield
- %Δ price
- manager exp → -DΔy + 1/2C(Δy)
^{2} - credit loss
- curr g/l

Immunization

- PVA = PVL
- min structural risk
- single liab = min convexity
- multiple liab = C
_{A}> C_{L}

Duration Gap

- gap = BPV
_{A}- BPV_{L }- BPV = D * V * 0.0001

- # contracts = gap/ BPV
- BPV
_{fut}= BPV/ CF - BPV
_{swap}= BPV_{rec}- BPVpaid

- BPV

Active Return

IC * √BR * σ_{Ra} * TC

IC = corr btwn factor and HPR

TC = degree of constraints

Duration Matching

balance price and reinvestment risk

- inc yield = ↓ price, ↑ reinv value
- dec yield = ↑ price, ↓ reinv value

Portfolio Construction

- full replication = dec tracking error (need fewer sec)
- optimization = dec tracking error, high turnover
- stratified samping = dec turnover, high tracking error

Active Share

diff btwn portfolio and benchmark; want higher active share b/c paying for active management

0.5 Σ |W_{p} - W_{b}|

Active Risk

tracking error b/c factor exposure and idiosyncratic risk

√ [( Σ R_{A}^{2 })/ ( T - 1 )]

Variance in Portfolio from Asset

- contribution of asset to portfolio var
- Σ w
_{i }w_{j }cov_{ij}

- Σ w
_{}contribution of asset to portfolio var (considering index)- ( w
_{p}- w_{b}) cov

- ( w

β

systematic risk; value equity and FI sec

ρ_{i,m} σ_{i }/ σ_{m}

Covariance

(Econ)

β_{1 }* β_{2 }* σ^{2}

ERP

(Econ)

σ_{p} * SR_{M} * corr + premiums

Information Ratio

Active Return/ Active Risk

Asset Class Characteristics

- homogeneous
- mutually exclusive
- diversifying
- contain most of the inv universe
- liquid

Monte Carlo Simulation

- multi-period - incorporate changes (rebalancing, distributions, taxes)
- include path dependency
- visualization of potential outcomes
- doesn’t follow normal distribution

Convexity

- stable curve = sell convexity
- long callable/ putable bonds
- long MBS
- short call/ put options

Benchmark Characteristics

- specified in advance
- appropriate
- measurable
- unambiguous
- relective of manager’s style
- accountable
- investable