Option-Implied Information in Asset Allocation Decisions Grigory Vilkov Goethe 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 wise commander to achieve things beyond the reach of ordinary men, is foreknowledge....foreknowledge cannot be elicited from spirits; it cannot be obtained inductively from experience, nor by any deductive calculation. Knowledge can only be obtained from other men. Sun Tzi
Option Markets and Information for Investment Decisions it s all about objective approach foreknowledge
Option Markets and Information for Investment Decisions return return relative return + risk volatility skewness kurtosis big risk drawdown/ crash size crash probability
Option Markets and Information for Investment Decisions and for the future... crystal ball? probably not
Option Markets and Information for Investment Decisions
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 valuation assumptions : both too unrealistic and artificial danger of over-fitting expected performance only
Option Markets and Information for Investment Decisions using option prices forward-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 timing stock cross-section implied correlation variance risk premium implied volatility implied skewness variance risk premium implied volatility
Option-implied quantities vs. needs of portfolio manager most efficient in predicting future risk variances factor exposure diversification implied variance premium-corrected implied variance implied covariance implied factor beta average implied correlation average premium-corrected implied correlation
Option-implied quantities vs. needs of portfolio manager most efficient in predicting future crashes (big risks) crash timing crash size nothing works well enough! tail loss measure implied correlation tail loss measure implied skewness
Data needs and procedures rule 1: it is better to have fewer parameters
Data needs and procedures rule 2: formula variation is not that important data quality is important
Data needs and procedures volatility/ skewness/ kurtosis non-parametric model-free methods (e.g., BKM 03) with interpolation and flat extrapolation 0.45 observed implied volatility 0.44 Implied Volatility 0.43 0.42 interpolated implied volatility extrapolated implied volatility 0.41 0.4 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Strike/Spot just compute option prices and plug them into a formula
Data needs and procedures implied correlation ρ Q ij,t }{{} = ρ P ij,t }{{} implied correlation historical correlation index variance {}}{ (σ Q Index,t )2 = how to compute? + ρ t (1 ρ P ij,t) }{{} risk premium sum of weighted individual covariances { }}{ w i,t w j,t σ Q ( ) i,t σq j,t ρ P ij,t + (1 ρ P ij,t) ρ t i,j identify ρ t and compute ρ Q ij,t from definition
Data needs and procedures tail loss measure Implied Volatility 0.45 0.44 0.43 0.42 0.41 observed implied volatility threshold option 0.4 0.7 0.8 0.9 1 1.1 1.2 Strike/Spot select threshold moneyness level h calibrate two 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 x t r f t,t+ t +θ t x t (r m t,t+ t r f t,t+ t ) }{{} managed portfolio return select θ t optimally on 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 1.5 1 Market Weight 0.5 0 0.5 Long market Short market S&P500 Price Jan97 Jan98 Jan99 Jan00 Jan01 Jan02 Jan03 Jan04 Jan05 Jan06 Jan07 Jan08 Jan09 Jan10 Oct10
Empirical results: market return predictability implied correlation: most useful signal performance of the managed portfolio vs. market 150 S&P500 Managed portfolio Cumulative Return, % 100 50 stability: visually clear return: about 3 Sharpe ratio: about 10 0 Jan97 Jan00 Jan03 Jan06 Jan09 Oct10
Empirical results: stock return predictability stock returns w mean-variance problem max E[R] w 0 w ˆΣw with characteristic-adjusted mean returns ) E[R i ] = E[R benchmark ] (1 + δ x i x i - 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 min w 0 w ˆΣw with implied variance-based covariance matrix ˆΣ = diag(implied volatility) ˆΩ diag(implied volatility) portfolio variance: 10 to 20% lower
Empirical results: covariance/beta predictability implied factor betas Q σ β Q i,factor = i N w j σj Q ρ Q ij j=1 (σ Q factor )2 with implied volatilities σ Q and correlations ρ Q ij
Empirical results: covariance/beta predictability relation between market risk and return 11% Historical Option Implied Realized Return 9% 7% 5% 3% 1 2 3 4 5 Quintile Portfolios
Empirical results: covariance/beta predictability reason for observed risk-return relation? bias by predicting future market betas Prediction Error 0.5 0.25 0 0.25 Historical 0.5 1 Option Implied 2 3 4 Quintile Portfolios 5 regression tendency clear bias in historical betas historical beta high/low realized beta is low/high need to revise low volatility investing?
Empirical results: crash predictability implied crash beta use tail loss measure ( conditional negative return beyond a threshold ) compute perception of crash size relative to market crash β crash = Cov(TLM market,tlm industry ) Var(TLM market )
Empirical results: crash predictability banking sector crash beta XLF Financial Crash Beta SP 500 Index Level 1600 2 01 Oct 2008 23 Oct 2009 1400 1.5 1200 1 25 Nov 2008 13 Feb 2009 28 Dec 2009 1000 0.5 0 800 19 Apr 2009 0.5 600 Jan07 Jan08 Jan09 Jan10 Oct10
Bottom line option prices contain foreknowledge use 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-Implied Correlations, Review of Financial Studies, 25(10) DeMiguel, Plyakha, Uppal, and Vilkov, 2012, Improving Portfolio Selection Using Option-Implied Volatility and Skewness, Journal of Financial 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 and the Price of Correlation Risk, working paper Rehman and Vilkov, 2008, Risk-Neutral Skewness: Return Predictability and Its Sources, working paper Vilkov and Xiao, 2012, Option-Implied Information and Predictability of Extreme Returns, working paper Grigory Vilkov Option-Implied Information in Asset Allocation 12 December 2012 32 / 32