Systematic Volatility Research Articles

Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models

ABSTRACTWe propose using model‐free yield quadratic variation measures computed from intraday data as a tool for specification testing and selection of dynamic term structure models. We find that the yield curve fails to span realized yield volatility in the U.S. Treasury market, as the systematic volatility factors are largely unrelated to the cross‐section of yields. We conclude that a broad class of affine diffusive, quadratic Gaussian, and affine jump‐diffusive models cannot accommodate the observed yield volatility dynamics. Hence, the Treasury market per se is incomplete, as yield volatility risk cannot be hedged solely through Treasury securities.

Asymmetric pricing of implied systematic volatility in the cross-section of expected returns

Assuming a symmetric relation between returns and innovations in implied market volatility, Ang, A., Hodrick, R., Xing, Y., and Zhang, X. (2006) find that sensitivities to changes in implied market volatility have a cross-sectional effect on firm returns. Dennis, P., Mayhew, S., and Stivers, C. (2006), however, find an asymmetric relation between firm-level returns and implied market volatility innovations. We incorporate this asymmetry into the cross-sectional relation between sensitivity to volatility innovations and returns. Using both portfolio sorting and firm-level regressions, we find that sensitivity to VIX innovations is negatively related to returns when volatility is rising, but is unrelated when it is falling. The negative relation is robust to controls for other variables, suggesting only the increase in implied market volatility is a priced risk factor. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:34–54, 2011

Volatility risk and the value premium: Evidence from the French stock market

This paper documents that systematic volatility risk is an important factor that drives the value premium observed in the French stock market. Using returns on at-the-money straddles written on the CAC 40 index as a proxy for systematic volatility risk, I document significant differences between volatility factor loadings of value and growth stocks. Furthermore, when markets are classified into expected booms and recessions, volatility factor loadings are also time-varying. When expected market risk premium is above its average, i.e. during expected recessions, value stocks are seen riskier than their growth counterparts. This implies in bad times, investors shift their preferences away from value firms. Instead they use growth stocks as hedges against deteriorations in their wealth during those times. The findings are in line with the predictions of rational asset pricing theory and support a “flight-to-quality” explanation.

Keynes Meets Markowitz: The Tradeoff Between Familiarity and Diversification

We develop a model of portfolio choice to nest the views of Keynes---who advocates concentration in a few familiar assets---and Markowitz---who advocates diversification across assets. We rely on the concepts of ambiguity and ambiguity aversion to formalize the idea of investor's ``familiarity towards assets. The model shows that when investors are equally ambiguous about all assets, then the optimal portfolio corresponds to Markowitz's fully-diversified portfolio. In contrast, when investors exhibit different degrees of familiarity across assets, the optimal portfolio depends on (i)~the relative degree of ambiguity across assets and (ii)~the standard deviation of the estimate of expected return on each asset. If the standard deviation is low and the difference between the ambiguity about the familiar and unfamiliar assets is small, then the optimal portfolio is composed of a mix of both familiar and unfamiliar assets; moreover, an increase in correlation between assets causes investors to increase concentration in the assets with which they are familiar (flight to familiarity). Alternatively, if the standard deviation of the expected-return estimate is high and the difference between the ambiguity of familiar and unfamiliar assets is large, the optimal portfolio contains only the familiar asset(s) as Keynes would have advocated. In the extreme case in which the ambiguity about all assets and the standard deviation of the estimated mean are high, then no risky asset is held (non-participation). The model also has empirically testable implications for trading behavior: in response to a change in idiosyncratic risk the Keynesian portfolio always exhibits more trading than the Markowitz portfolio, while the opposite is true for a change in systematic volatility. In the equilibrium version of the model with heterogeneous agents who are familiar with different assets, we find that the risk premium of stocks depends on both systematic and idiosyncratic volatility, and that the equity risk premium is significantly higher than in the standard model without ambiguity.

Keynes Meets Markowitz: The Tradeoff between Familiarity and Diversification

We develop a model of portfolio choice to nest the views of Keynes - who advocates concentration in a few familiar assets - and Markowitz - who advocates diversification across assets. We rely on the concepts of ambiguity and ambiguity aversion to formalize the idea of an investor’s toward assets. The model shows that when an investor is equally ambiguous about all assets, then the optimal portfolio corresponds to Markowitz’s fully diversified portfolio. In contrast, when an investor exhibits different degrees of familiarity across assets, the optimal portfolio depends on (i) the relative degree of ambiguity across assets, and (ii) the standard deviation of the estimate of expected return on each asset. If the standard deviation of the expected return estimate and the difference between the ambiguity about familiar and unfamiliar assets are low, then the optimal portfolio is composed of a mix of both familiar and unfamiliar assets; moreover, an increase in correlation between assets causes an investor to increase concentration in the assets with which they are familiar (flight to familiarity). Alternatively, if the standard deviation of the expected return estimate and the difference between the ambiguity of familiar and unfamiliar assets are high, then the optimal portfolio contains only the familiar asset(s) as Keynes would have advocated. In the extreme case in which the ambiguity about all assets and the standard deviation of the estimated mean are high, then no risky asset is held (non-participation). The model also has empirically testable implications for trading behavior: in response to a change in idiosyncratic volatility, the Keynesian portfolio always exhibits more trading than the Markowitz portfolio, while the opposite is true for a change in systematic volatility. In the equilibrium version of the model with heterogeneous investors who are familiar with different assets, we find that the risk premium of stocks depends on both systematic and idiosyncratic volatility, and that the equity risk premium is significantly higher than in the standard model without ambiguity.

Precarious Politics and Return Volatility

We examine how local and global political risks affect industry return volatility. Our central premise is that some industries are more sensitive to political events than others. We find that industries that are more dependent on trade, contract enforcement, and labor exhibit greater return volatility when local political risks are higher. Political uncertainty in countries of trading partners of trade-dependent industries similarly results in greater volatility. Volatility decomposition results indicate that while systematic volatility is associated with domestic political uncertainty, global political risks translate into larger idiosyncratic volatility.

Time Varying Risk Premia in Corporate Bond Markets

We study the link between corporate bond risk premia and equity returns in a large panel of corporate bond transaction data. In contrast to previous work, we find that a significant part of the time variation in bond risk premia can be explained by equity implied bond risk premium estimates. We also document a large time variation in the expected loss component of bond spreads. This component is related to total asset volatility, whereas the risk premium is related to systematic volatility. In addition, we show by means of linear regressions that augmenting the set of variables predicted by typical structural models with equity-implied bond default risk premia significantly increases explanatory power.

Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models

We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most 'affine' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds (realized yield volatility) through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors are largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, Gaussian-quadratic and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. An important implication is that the bond markets per se are incomplete and yield volatility risk cannot be hedged by taking positions solely in the Treasury bond market. We also advocate using the empirical realized yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.

Investment, consumption, and hedging under incomplete markets

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investments. We extend the standard real options approach to an incomplete markets environment and analyze the joint decisions of business investments, consumption/savings, and portfolio selection. For a lump-sum investment payoff and an agent with a sufficiently strong precautionary savings motive, an increase in volatility can accelerate investment, contrary to the standard real options analysis. When the agent can trade the market portfolio to partially hedge against investment risk, the systematic volatility is compensated via the standard CAPM argument, and the idiosyncratic volatility generates a private equity premium. Finally, when the investment payoff is a series of flows, the agent's idiosyncratic risk exposure alters both the implied option value and the implied project value, causing a reversal of the results in the lump-sum payoff case.

Volatility in the U.S. Treasury Market - Application to the Institute for Quantitative Research in Finance (The Q Group) for Research Support

We investigate whether bonds can hedge volatility risk in the U.S. Treasury market, as predicted by most 'affine' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds ('realized yield volatility') through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors appear largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, quadratic diffusive and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. Hence, yield volatility risk per se cannot be hedged by taking positions in the Treasury bond market. We also advocate using these empirical yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.

Do Banks Affect the Level and Composition of Industrial Volatility?

ABSTRACTIn theory, better access to bank credit can reduce or increase output volatility depending on whether firms are more financially constrained during contractions or expansions. This paper finds that the volatility of industrial output is lower in countries with more bank credit. Most of the reduction in volatility is idiosyncratic, which follows from the ability of banks to pool and diversify shocks. Systematic volatility is reduced less strongly. Volatility dampening is achieved via countercyclical borrowing: At the firm level, short‐term borrowing is less (or more negatively) correlated with sales and inventories in countries with high levels of bank credit.

Stock Returns, Implied Volatility Innovations, and the Asymmetric Volatility Phenomenon

AbstractWe study the dynamic relation between daily stock returns and daily innovations in optionderived implied volatilities. By simultaneously analyzing innovations in index- and firmlevel implied volatilities, we distinguish between innovations in systematic and idiosyncratic volatility in an effort to better understand the asymmetric volatility phenomenon. Our results indicate that the relation between stock returns and innovations in systematic volatility (idiosyncratic volatility) is substantially negative (near zero). These results suggest that asymmetric volatility is primarily attributed to systematic market-wide factors rather than aggregated firm-level effects. We also present evidence that supports our assumption that innovations in implied volatility are good proxies for innovations in expected stock volatility.

CAPM over the long run: 1926–2001

Abstract A conditional one-factor model can account for the spread in the average returns of portfolios sorted by book-to-market ratios over the long run from 1926 to 2001. In contrast, earlier studies document strong evidence of a book-to-market effect using OLS regressions over post-1963 data. However, the betas of portfolios sorted by book-to-market ratios vary over time and in the presence of time-varying factor loadings, OLS inference produces inconsistent estimates of conditional alphas and betas. We show that under a conditional CAPM with time-varying betas, predictable market risk premia, and stochastic systematic volatility, there is little evidence that the conditional alpha for a book-to-market trading strategy is different from zero.

Financial Development, Financial Constraints, and the Volatility of Industrial Output

More financially developed countries show lower volatility of industrial output. Volatility is particularly reduced in industries that are more financially dependent. Most of the reduction is in idiosyncratic volatility. Systematic volatility is reduced less strongly, implying that industries are more closely correlated with GDP in more financially developed countries. At the firm level, short-term debt is negatively correlated with output as financial development increases, suggesting that debt is used in a countercyclical way to stabilize production. The results indicate that financial development relaxes financial constraints mainly to smooth negative cashflow shocks.

The Cross‐Section of Volatility and Expected Returns

ABSTRACTWe examine the pricing of aggregate volatility risk in the cross‐section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book‐to‐market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.

Stochastic Volatility Risk and the Size Anomaly

Investors’concerns about systematic volatility risk explain a large portion of the small …rm premia in the long run. This novel …nding supports the concept of market e¢ ciency and indicates a “‡ight to quality”during recessions: investors shift their preferences away from small …rms, which are considered as being relatively risky. Instead they use large, “quality”stocks, whose returns co-vary positively with innovations in volatility (a recession-and-distress proxy), and therefore

Investment, Consumption and Hedging under Incomplete Markets

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investments. Motivated by this observation, we extend the standard real options approach to investment to an incomplete markets environment and analyze the joint decisions of business investments, consumption-saving and portfolio selection. We show that precautionary saving motive affects the investment timing decision in an important way. When the investment payoffs are given in lump sum, risk aversion accelerates investment. For an agent with sufficiently strong precautionary motive, an increase in volatility may accelerate investment, opposite to the standard real options analysis. When the agent can trade the market portfolio to partially hedge against the investment risk, the systematic volatility is compensated via the standard CAPM argument, and the idiosyncratic volatility generates a private equity premium. Finally, for the flow payoff case, the agent's idiosyncratic risk exposure alters both the implied option value and the implied project value, causing the reversal of the results in the lump sum payoff case.

Information in the Idiosyncratic Volatility of Small Firms

Non-systematic volatilities of small firms are special as predictors of stock returns. They are positively related with future returns on all age and size portfolios. They dominate systematic volatility, big-firm volatility and other volatilities. And there is strong evidence that idiosyncratic risk is priced in small-firm returns. Small-firm volatility as a predictor of big-firm returns is in part a proxy for systematic volatility and consumption-wealth ratio. We rule out several hypotheses, including a liquidity premium, as potential explanations of our results, but not the idea that small-firm idiosyncratic volatility is correlated with the risk of the total investor portfolio, which includes non-equity assets.

Do Banks Affect the Level and Composition of Industrial Volatility and How?

In theory, better access to bank credit can increase or reduce output volatility depending on whether financially constrained firms face more cash-flow or investment opportunity shocks. This paper finds that countries with high levels of bank credit have low volatility of industrial output. Most of the reduction in volatility is idiosyncratic, which follows from the ability of banks to pool and diversify shocks. Systematic volatility is also reduced, but less strongly so. Volatility dampening is achieved via counter-cyclical borrowing: at the firm level, short-term borrowing is more negatively correlated with sales in countries with high levels of bank credit.

Errors in Implied Volatility Estimation

Estimating implied volatility by inverting the Black-Scholes formula is subject to considerable error when option characteristics are observed with plausible errors. Especially for options away from the money, large changes in volatility produce small changes in option prices. Conversely, small errors in option prices and other option characteristics produce large errors in implied volatilities. In the presence of small measurement errors, unobserved truncation of option prices that violate lower bounds for absence of arbitrage can also lead to systematic volatility smiles. The paper proposes feasible GLS estimators that reduce the noise and bias in implied volatility estimates.