In financial theory, the stocks, corporate bonds, and options issued by a single company are inherently linked. A shock to the firm should ripple through all its issued securities. Expanding this concept to the broader economy suggests that aggregate risks should drive returns simultaneously across the stock, bond, and options markets.
Researchers recently published an NBER working paper investigating whether a shared structure of risk actually connects these three distinct financial arenas. The authors identified strong common risk factors that pervade all three markets. They then used these factors to measure how disconnected the markets remain from one another.
Organizing Unbalanced Data
The research team included Zhongtian Chen of the University of Wisconsin Madison, Nikolai Roussanov of the University of Pennsylvania, Xiaoliang Wang of the Hong Kong University of Science and Technology, and Dongchen Zou of Indiana University. The authors noted that identifying cross-market commonality has historically presented severe empirical challenges.
Datasets covering corporate bonds and options contain thousands of individual securities, but many of these assets have very short trading histories. Options, for example, frequently expire in a matter of weeks. Traditional statistical methods require long, balanced data histories to effectively isolate common risk patterns across a large group of assets.
To bypass these limitations, the researchers employed a multi-step statistical approach designed to handle unbalanced data. First, they sorted the individual securities into organized portfolios based on specific asset characteristics, such as momentum, illiquidity, and firm leverage. By creating these characteristic-based portfolios every month, they transformed a chaotic, shifting pool of individual assets into a stable dataset.
The team then applied a statistical technique called principal component analysis to these managed portfolios. This mathematical process allowed them to isolate the underlying, latent risk factors driving returns across the board.
Macroeconomic Links and Mispricing
The analysis relied on monthly return data from July 2004 to December 2021, covering over 8,000 firms. The data revealed ten common risk factors that significantly influence asset prices across all three markets. These factors are not tied to any single asset class, but instead capture systematic risks spanning the entire corporate financial system.
The researchers linked these newly identified common factors to established economic indicators. The dominant factors exhibited strong correlations with macroeconomic variables like consumption growth, inflation, and industrial production. They also tracked closely with financial conditions such as credit spreads, the VIX volatility index, and economic policy uncertainty.
The first common factor proved to be highly cyclical, dropping sharply during major market stress events like the 2008 global financial crisis and the 2020 pandemic. A second common factor showed high sensitivity to monetary policy changes and the federal funds rate. The authors interpret these common factors as forward-looking reflections of the underlying aggregate economy.
Even though the ten common factors explained a large portion of the return variation across markets, they did not account for everything. The data revealed persistent pricing errors. Certain asset characteristics continued to predict returns beyond what the common risk exposures would suggest.
The authors found that these pricing discrepancies were especially pronounced in the options market. Motivated by these anomalies, the researchers simulated a pure-alpha trading strategy to see if the mispricing could be exploited. This hypothetical portfolio was designed to capitalize on the predictive power of asset characteristics while maintaining zero exposure to the ten common risk factors.
The strategy generated substantial out-of-sample returns, achieving high return-to-risk ratios regardless of how many common factors were hedged out. A breakdown of the results showed that the high performance was driven primarily by mispricing in the options market. Equities contributed a modest amount to the strategy, while corporate bonds contributed very little.
Cross-Market Hedging and Segmentation
Building on their common factor model, the team constructed a joint mean-variance efficient portfolio across stocks, corporate bonds, and options. This type of portfolio is mathematically designed to maximize expected returns for a given level of volatility. The joint portfolio across all three markets achieved a significantly higher return-to-risk ratio than similar portfolios restricted to just one asset class.
The authors trace this outperformance to cross-market hedging. Because the joint portfolio operates across three different asset classes, it can take offsetting positions on the exact same underlying risk factor. For example, the portfolio might take a long position on a specific common factor in the options market while shorting that same factor in the corporate bond market.
This mutual hedging neutralized much of the portfolio’s overall volatility while capturing the high average returns. The presence of this hedging opportunity led the researchers to question the degree of integration among the three markets. In a perfectly integrated financial system, investors should theoretically receive the same compensation for bearing a specific risk regardless of where they take on that risk.
The researchers measured market distance by calculating the difference in the risk premium assigned to the same common factors across different markets. If the same risk exposure earns different prices in different markets, those markets are considered segmented.
The statistical tests revealed a significant degree of segmentation between all pairs of the three markets. The pricing of common risks in the options market was largely disconnected from both the stock and corporate bond markets. Stocks and corporate bonds were slightly more integrated with one another, but the differences in risk pricing remained statistically significant.
The authors interpret this mispricing of common factors as the primary driver of the hedging opportunities observed in their joint portfolio model. Because the identical risk is priced differently depending on the asset class, investors can theoretically allocate capital to the market offering the higher premium while shorting the market offering the lower premium. These persistent price dispersions point to limits to arbitrage that prevent investors from forcing the markets into perfect alignment.
