Option-Implied Information in Asset Allocation Decisions · · 2012-12-133 Data needs and procedures ... implied covariance implied factor beta diversi cation ... Selection Using

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


it’sall about

objective

approach

foreknowledge


· · · + · · ·

returnreturnrelative return

riskvolatilityskewnesskurtosis

big riskdrawdown/ crash sizecrash probability


and for the future...

crystal ball?

probably not



source of information

history of returns

valuation assumptions

option prices


using

history of returns:

backward-looking

slow-moving

assumes future = past


using

valuationassumptions:

both too unrealistic and artificial

danger of over-fitting

expected performance only


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


most efficient in predicting future risk

variancesimplied variancepremium-corrected implied variance

factor exposureimplied covarianceimplied factor beta

diversificationaverage implied correlationaverage premium-corrected implied correlation


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

rule 1:it is better to have fewer parameters


rule 2:formula variation is not that important

data quality is important


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”


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


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)


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


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


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


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

Bottom line

option prices contain foreknowledgeuse them

to

win

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

Option-Implied Information in Asset Allocation Decisions · · 2012-12-133 Data needs and procedures ... implied covariance implied factor beta diversi cation ... Selection Using

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