Ebook Option-Implied Correlation and Factor Betas Revisited
The notion of beta, as emanating from the seminal work of Sharpe (1964) and Lintner (1965), is the cornerstone of modern finance and one of the most important concepts in both theory and practice. It represents the stock return sensitivity to movements of the market and other factors and therefore its systematic risk. Wang (2003) and Ghysels and Jacquier (2006), among others, stress the importance of an accurate measurement and even more of an accurate prediction of individual stock betas. Many practical areas rely on betas portfolio and risk management, asset pricing, cost of capital estimation, and performance measurement. Investors will clearly benefit from a better beta forecast in applications like building a tracking portfolio with a targeted market beta, immunizing portfolios against economic factors, trading market neutral pairs, etc. Our objective is to use information from option prices to construct option-implied betas that are superior predictors for out-of-sample factor betas. Options are forward-looking instruments with fixed maturity, subsuming the market expectations about the foreseeable future, and hence we expect the proposed method to work better than the historical ones.
We make two important contributions. First, we propose a new efficient way to model the heterogenous implied correlations (HETIC) in two consistent versions. The full HETIC gives us the full correlation matrix for a given stock universe, and the reduced HETIC gives the vector of stock-factor correlations. The reduced version may be estimated for factors with traded options on them (e.g., market index), and is computationally very efficient. To get the implied correlation we add to the correlation predictor the correlation risk premium, and the latter is modeled for all stock-stock or stock-factor pairs as a function of one state variable. This function is positively related to the market volatility risk premium and negatively related to the individual stock volatility risk premiums.
Second, we show how to use option-implied second moments to compute forward looking betas under the risk-neutral measure Q for arbitrary factors that do not have traded options on them. This is not possible for the other option implied methods. Empirically, we deal with the standard factors1 and also with the orthogonal principal components of those. The HETIC betas significantly outperform a number of rival betas, including two option-implied methodologies, historical rolling window estimation from daily returns and parametric DCC-MIDAS betas. The only betas that HETIC cannot beat in all the cases are the high-frequency rolling window betas; we count as our additional contribution that we show how utilizing high-frequency data for correlations and volatilities estimation makes the beta predictors more precise compared to daily data.
For the market betas our method significantly decreases the prediction error of the one-month realized betas for the S&P500 stocks to 0.12 in terms of mean squared error (MSE) from 0.15 in the case of the standard rolling historical daily betas and the parametric DCC-MIDAS betas. For the six-month betas the MSE goes down from 0.11 to 0.07 for the same set of betas. Moreover, we observe a considerable boost in predictability precision for all factors: the MSE decreases for one-month betas on average by 30%, compared to the MSE of daily betas.
As a result of enhanced predictability, investors can benefit from using HETIC factor betas in practical applications. For instance, in the popular pairs trading strategy a hedge fund goes long one stock and short the other from a pair of cointegrated stocks to earn some money from their relative mispricing. Market movements can deteriorate the profitability of the strategy, and one typically makes the portfolio market-neutral. We compare the realized market betas of the market-neutral pairs’ portfolios for different beta methods. HETIC market betas statistically and economically outperform all other betas in terms of MSE for relevant holding periods of 5, 10, and 21 trading days. For a more general application of the HETIC factor betas, we perform an extension of the pairs trading to multiple stocks and factors. We immunize an arbitrary portfolio with respect to the selected factors, i.e., we get expected factor exposures of zero and show that our option-implied betas again outperform the other methods in terms of the error in the realized portfolio factor betas.
Contents
1 Introduction
2 Factor Betas
2.1 Stock Market and Factor Betas Definition
2.2 Volatility and Correlation Risk Premium Assumptions
2.3 Defining HETIC and Competing Factor Betas
- 2.3.1 Implied Betas
2.3.2 Non-parametric Betas
2.3.3 Parametric DCC-MIDAS Betas
2.4 Implied Betas and Change of Measure: HETIC vs. Alternatives
3 Data Description and Preparations
3.1 Stock and Option Data
3.2 Realized Covariances (under the P-measure)
3.3 Implied Volatility, Variance and Skewness (under the Q-Measure)
4 Factor Betas Horse Race: Empirical Investigation
4.1 Factor Beta Estimation
4.2 Realized Beta Predictability
- 4.2.1 Market Factor
4.2.2 Other Factors
4.3 Applications
- 4.3.1 Pairs Trading
4.3.2 Portfolio Immunization
4.4 Risk-Return Relationship Revisited
5 Robustness Tests
6 Conclusion
A Proofs
B Construction of Risk-Neutral Moments
C Factor Mimicking Portfolios
Figures
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