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Option-Implied Informationin
Asset Allocation Decisions
Grigory VilkovGoethe University Frankfurt
12 December 2012
Grigory Vilkov Option-Implied Information in Asset Allocation 12 December 2012 1 / 32
Agenda for today
1 Option markets and information for investment decisions
2 Option-implied quantities vs. needs of portfolio manager
3 Data needs and procedures
4 Empirical results and consequences for asset allocation
• Return predictability
• Risk predictability
• Big risk predictability
5 Summary and Conclusions
Option Markets and Information for Investment Decisions
...what enables the wisecommander to achieve thingsbeyond the reach of ordinarymen, is foreknowledge....foreknowledge cannot beelicited from spirits; itcannot be obtainedinductively fromexperience, nor by anydeductive calculation.Knowledge can only beobtained from other men.Sun Tzi
Option Markets and Information for Investment Decisions
it’sall about
objective
approach
foreknowledge
Option Markets and Information for Investment Decisions
· · · + · · ·
returnreturnrelative return
riskvolatilityskewnesskurtosis
big riskdrawdown/ crash sizecrash probability
Option Markets and Information for Investment Decisions
and for the future...
crystal ball?
probably not
Option Markets and Information for Investment Decisions
source of information
history of returns
valuation assumptions
option prices
Option Markets and Information for Investment Decisions
using
history of returns:
backward-looking
slow-moving
assumes future = past
Option Markets and Information for Investment Decisions
using
valuationassumptions:
both too unrealistic and artificial
danger of over-fitting
expected performance only
Option Markets and Information for Investment Decisions
using
option pricesforward-looking
immediate response
meets all requirements:
return: market and stocks
risk: moments of return
big risk: size and probability
term: exact multiple maturities
how: non-/parametric
but: may be too noisy
Option-implied quantities vs. needs of portfolio manager
most efficient in predicting future returns
market timingimplied correlationvariance risk premiumimplied volatility
stock cross-sectionimplied skewnessvariance risk premiumimplied volatility
Option-implied quantities vs. needs of portfolio manager
most efficient in predicting future risk
variancesimplied variancepremium-corrected implied variance
factor exposureimplied covarianceimplied factor beta
diversificationaverage implied correlationaverage premium-corrected implied correlation
Option-implied quantities vs. needs of portfolio manager
most efficient in predicting future crashes (big risks)
crash timingnothing works well enough!tail loss measureimplied correlation
crash sizetail loss measureimplied skewness
Data needs and procedures
volatility/ skewness/ kurtosisnon-parametric model-free methods (e.g., BKM’03)
with interpolation and flat extrapolation
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.40.4
0.41
0.42
0.43
0.44
0.45
Strike/Spot
Imp
lied
Vo
lati
lity
← observed implied volatility
← interpolated implied volatility
↓ extrapolated implied volatility
just compute option prices and plug them into a “formula”
Data needs and procedures
implied correlationρQij ,t︸︷︷︸
implied correlation
= ρPij ,t︸︷︷︸historical correlation
+ ρt × (1− ρPij ,t)︸ ︷︷ ︸risk premium
how to compute?
index variance︷ ︸︸ ︷(σQIndex ,t)
2 =
sum of weighted individual covariances︷ ︸︸ ︷∑i ,j
wi ,twj ,tσQi ,tσ
Qj ,t
(ρPij ,t + (1− ρPij ,t)× ρt
)identify ρt and compute ρQij ,t from definition
Data needs and procedures
tail loss measure
0.7 0.8 0.9 1 1.1 1.20.4
0.41
0.42
0.43
0.44
0.45
Strike/Spot
Imp
lied
Vo
lati
lity
← observed implied volatility
← threshold option
selectthreshold moneyness level h
calibratetwo parameters from OTM puts
compute
expected loss beyond h
tail loss measure = expected loss / current price
Empirical results: market return predictability
market return
use signal variable xt
r ft,t+∆t +θt ×xt × (rmt,t+∆t − r ft,t+∆t)︸ ︷︷ ︸managed portfolio return
select θt optimallyon each day t using rolling window
(maximize average utility of gross return)
Empirical results: market return predictability
implied correlation: most useful signal
market portfolio weight vs. market dynamics
Jan97 Jan98 Jan99 Jan00 Jan01 Jan02 Jan03 Jan04 Jan05 Jan06 Jan07 Jan08 Jan09 Jan10 Oct10
−0.5
0
0.5
1
1.5
Mar
ket W
eigh
t
Long marketShort marketS&P500 Price
Empirical results: market return predictability
implied correlation: most useful signal
performance of the managed portfolio vs. market
Jan97 Jan00 Jan03 Jan06 Jan09 Oct100
50
100
150
Cum
ulat
ive
Ret
urn,
%
S&P500Managed portfolio
stability: visually clear
return: about×3
Sharpe ratio: about×10
Empirical results: stock return predictability
stock returns
mean-variance problem maxw≥0w>E [R ]√
w>Σw
with characteristic-adjusted mean returns
E [Ri ] = E [Rbenchmark ]×(
1 + δ × xi)
xi - value of characteristic for a stock i , δ - adjustment intensity
Empirical results: stock return predictability
implied skewness: most useful characteristic(model-free implied skewness, call-put volatility spread)
with 500 stocks being S&P500 components
return: about×1.2 to 1.4
Sharpe ratio: about×2 to 3
negative effect: high turnover
Empirical results: variance predictability
stock variance
minimum-variance problem minw≥0 w>Σw
with implied variance-based covariance matrix
Σ = diag(implied volatility)× Ω× diag(implied volatility)
portfolio variance: 10 to 20% lower
Empirical results: covariance/beta predictability
implied factor betas
βQi ,factor =
σQi
N∑j=1
wjσQj ρ
Qij
(σQfactor )2
with implied volatilities σQ and correlations ρQij
Empirical results: covariance/beta predictability
relation between market risk and return
1 2 3 4 5 3%
5%
7%
9%
11%
Quintile Portfolios
Rea
lize
d R
eturn
Historical
Option−Implied
Empirical results: covariance/beta predictability
reason for observed risk-return relation?
bias by predicting future market betas
1 2 3 4 5−0.5
−0.25
0
0.25
0.5
Quintile Portfolios
Pre
dic
tion E
rror
Historical
Option−Implied
regression tendency→ clear bias in historical betas
historical beta high/low→ realized beta is low/high
need to reviselow volatility investing?
Empirical results: crash predictability
implied crash betause
tail loss measure(“conditional negative return beyond a threshold”)
computeperception of crash size relative to market crash
βcrash =Cov(TLMmarket ,TLMindustry )
Var(TLMmarket)
Empirical results: crash predictability
banking sector crash beta
Jan07 Jan08 Jan09 Jan10 Oct10−0.5
0
0.5
1
1.5
2
← 01−Oct−2008
← 25−Nov−2008
← 13−Feb−2009
← 19−Apr−2009
← 23−Oct−2009
← 28−Dec−2009
600
800
1000
1200
1400
1600XLF Financial Crash BetaSP 500 Index Level
References
The results and ideas above are based on the following papers(which can be found on www.vilkov.net)
• Buss and Vilkov, 2012, Measuring Equity Risk with Option-ImpliedCorrelations, Review of Financial Studies, 25(10)
• DeMiguel, Plyakha, Uppal, and Vilkov, 2012, Improving PortfolioSelection Using Option-Implied Volatility and Skewness, Journal ofFinancial and Quantitative Analysis, forthcoming
• Driessen, Maenhout and Vilkov, 2009, The Price of Correlation Risk:Evidence from Equity Options, Journal of Finance, 64 (3)
• Driessen, Maenhout, and Vilkov, 2012, Option-Implied Correlations andthe Price of Correlation Risk, working paper
• Rehman and Vilkov, 2008, Risk-Neutral Skewness: Return Predictabilityand Its Sources, working paper
• Vilkov and Xiao, 2012, Option-Implied Information and Predictability ofExtreme Returns, working paper
Grigory Vilkov Option-Implied Information in Asset Allocation 12 December 2012 32 / 32