ON THE RATIONALITY OF COMMON STOCK RETURN VOLATILITY

This paper derives the relationship between the population unconditional variance of common stock returns and the variance of expected returns conditional on a well-specified information set. As a consequence, a lower bound is obtained for the variance of common stock returns. The sample counterpart of this bound is then empirically tested against the sample variance of returns. The paper's main conclusion can be stated as follows: the observed volatility of real (inflation-adjusted) common stock returns is not “irrationally” large. The paper admits of this conclusion because the point estimate of the lower-bound variance derived in this model is actually larger than the point estimate of common stock return volatility. However, since these point estimates are found to have a statistically insignificant difference, equality of the two variances cannot be ruled out. Hence, “rationality” of common stock returns—as implied by a utility-based valuation conditional on a specified information set—cannot be rejected.     

Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model

We consider an optimal time-consistent reinsurance-investment strategy selection problem for an insurer whose surplus is governed by a compound Poisson risk model. In our model, the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a simplified financial market consisting of a risk-free asset and a risky stock. The dynamics of the risky stock is governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset’s price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategies and the corresponding value functions are obtained in both the compound Poisson risk model and its diffusion approximation. Numerical examples are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.     

Optimal hedging of variance derivatives

We examine the optimal hedging of derivatives written on realised variance, focussing principally on variance swaps (VS) (but, en route, also considering skewness swaps), when the underlying stock price has discontinuous sample paths, i.e. jumps. In general, with jumps in the underlying, the market is incomplete and perfect hedging is not possible. We derive easily implementable formulae which give optimal (or nearly optimal) hedges for VS under very general dynamics for the underlying stock which allow for multiple jump processes and stochastic volatility. We illustrate how, for parameters which are realistic for options on the S&P 500 and Nikkei-225 stock indices, our methodology gives significantly better hedges than the standard log-contract replication approach of Neuberger and Dupire which assumes continuous sample paths. Our analysis seeks to emphasise practical implications for financial institutions trading variance derivatives.     

THE SPEED OF ADJUSTMENT OF PRICES TO PRIVATE INFORMATION: EMPIRICAL TESTS

We estimate speeds of adjustment of individual stock prices to private information using daily data. We use a model in which private information gives rise to return variance and private information decays linearly over time. We find that, on average, about 85 percent to 88 percent of private information is incorporated into prices within one trading day, with variation depending upon the stock's trading volume and whether the stock is listed on an exchange. The findings support strong form market efficiency.     

The Risk‐Return Relation in International Stock Markets

We investigate the risk‐return relation in international stock markets using realized variance constructed from MSCI (Morgan Stanley Capital International) daily stock price indices. In contrast with the capital asset pricing model, realized variance by itself provides negligible information about future excess stock market returns; however, we uncover a positive and significant risk‐return tradeoff in many countries after controlling for the (U.S.) consumption‐wealth ratio. U.S. realized variance is also significantly related to future international stock market returns; more importantly, it always subsumes the information content of its local counterparts. Our results indicate that stock market variance is an important determinant of the equity premium.     

The Danish stock and bond markets: comovement,return predictability and variance decomposition

VAR models of the kind developed by Shiller and Beltratti [J. Monetary Econ. 30 (1992) 25] and Campbell and Ammer [J. Finance 48 (1993) 3] are used to analyze the Danish stock and bond markets and their comovement. In contrast to these papers, however, VAR parameter estimates are bias-adjusted and VAR generated statistics, including their standard errors and confidence intervals, are computed using bootstrap simulation. In addition, we modify the Campbell–Ammer variance decomposition such that it can handle returns from a long-term coupon bond. Some parts of the results for the Danish stock and bond markets are quite similar to the US results reported by Shiller and Beltratti and Campbell and Ammer, but other parts stand in sharp contrast to the results for the US. The most important differences between the US and Denmark are that in Denmark news about higher future inflation lead to an increase in expected future stock returns, and that excess stock return news and excess bond return news are negatively correlated.     

Insiders' hedging in a jump diffusion model

In this paper, we formulate the optimal hedging problem when the underlying stock price has jumps, especially for insiders who have more information than the general public. The jumps in the underlying price process depend on another diffusion process, which models a sequence of firm-specific information. This diffusion process is observed only by insiders. Nevertheless, the market is incomplete to insiders as well as to the general public. We use the local risk minimization method to find an optimal hedging strategy for insiders. We also numerically compare the value of the insider's hedging portfolio with the value of an honest trader's hedging portfolio for a simulated sample path of a stock price.     

Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects

This paper provides empirical support for the notion that Autoregressive Conditional Heteroskedasticity (ARCH) in daily stock return data reflects time dependence in the process generating information flow to the market. Daily trading volume, used as a proxy for information arrival time, is shown to have significant explanatory power regarding the variance of daily returns, which is an implication of the assumption that daily returns are subordinated to intraday equilibrium returns. Furthermore, ARCH effects tend to disappear when volume is included in the variance equation.     

Risk management,firm reputation,and the impact of successful cyberattacks on target firms

We develop a model where a firm has an optimal exposure to cyber risk. With rational, fully informed agents and with no hysteresis, a successful cyberattack should have no impact on a financially unconstrained target's reputation and post-attack policies. In contrast, when a successful attack involves the loss of personal financial information, there is a significant shareholder wealth loss, which is much larger than the attack's out-of-pocket costs. This excess loss is higher when the attack decreases sales growth more and lower when the board pays more attention to risk management before the attack. Further, an attack decreases a firm's risk appetite, as it beefs up its risk management and information technology and decreases the risk-taking incentives of management. Finally, successful cyberattacks adversely affect the stock price of firms in the target's industry. These results imply that successful attacks with personal financial information loss provide adverse information about cyber risk to target firms, their stakeholders, and their competitors.     

Asymmetric Price and Volatility Adjustments in Emerging Asian Stock Markets

This paper tests the hypothesis that stock returns in emerging stock markets adjust asymmetrically to past information. The evidence suggests that both the conditional mean and the conditional variance respond asymmetrically to past information. In agreement with studies dealing with developed stock markets, the conditional variance is an asymmetrical function of past innovations, rising proportionately more during market declines. More importantly, the conditional mean is also an asymmetrical function of past returns. Specifically, positive past returns are more persistent than negative past returns of an equal magnitude. This behaviour is consistent with an asymmetric partial adjustment price model where news suggesting overpricing (negative returns) are incorporated faster into current prices than news suggesting underpricing (positive returns). Furthermore, the asymmetric adjustment of prices to past information could be partially responsible for the asymmetries in the conditional variance if the degree of adjustment and the level of volatility are positively related.     

A Likelihood Ratio Test of Price Volatilities: Comparing Stock Index Spot and Futures

This paper uses three methods to estimate the price volatility of two stock market indexes and their corresponding futures contracts. The classic variance measure of volatility is supplemented with two newer measures, derived from the Garman-Klass and Ball-Torous estimators. A likelihood ratio test is used to compare the classic variance measure of price volatilities of two stock market indexes and their corresponding futures contracts during the bull market of the 1980s. The stock market volatilities of the Standard & Poor's 500 (S&P 500) and New York Stock Exchange (NYSE) indexes were found to be significantly lower than their respective futures price volatilities. Since information may flow faster in the futures markets than in the corresponding stock market, our results support Ross's information-volatility hypothesis. It was also noted that the NYSE spot volatility was lower than the S&P 500 spot volatility. If the rate of information flow and firm size are positively related, then the lower NYSE spot volatility is explained by the size effect. The futures price volatilities for the two indexes were insignificantly different from each other. With stock index spot-futures price correlations approaching unity, one implication of our results for index futures activity is that smaller positions in futures contracts may suffice to achieve hedging or arbitrage goals.     

Bias-correcting the realized range-based variance in the presence of market microstructure noise

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. This has led to widespread use of constructing the realized variance, a sum of squared intraday returns, from sparsely sampled data, for example 5- or 15-minute returns. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias correction to the range-statistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise. We can select an optimal partition of the high-frequency data in order to minimize its asymptotic conditional variance. The finite sample properties of our estimator are studied with Monte Carlo simulations and we implement it using Microsoft high-frequency data from TAQ. We find that a bias-corrected range-statistic often leads to much smaller confidence intervals for the integrated variance, relative to the realized variance. We should like to thank an anonymous referee and the associate editor for insightful comments on an earlier draft. Parts of this paper were written while Kim Christensen was at the University of California, San Diego, whose hospitality is gratefully acknowledged. Mark Podolskij received financial support from CREATES funded by the Danish National Research Foundation, and Mathias Vetter was supported by the Deutsche Forschungsgemeinschaft grant SFB 475 “Reduction of Complexity in Multivariate Data Structures.” The code for this paper was written in the Ox programming language, due to Doornik (2002). All views expressed here are those of the authors and do not necessarily represent the views of Nordea.     

Overstatement of Implied Variance in the Dollar/Yen Currency Option Market

This paper investigates the predictive power of implied variancesextracted from the dollar/yen option prices. Implied variances areestimated from transaction prices of currency options traded on PHLXusing the option pricing model of Garman and Kohlhagen (1983). Incontrast to recent findings on stock and stock index options, theout-of-sample tests indicate that the implied variance is an upwardbiased estimator of future variance; and that the variance forecastsfrom GARCH and historical models do not contain significantincremental information in predicting future variance. Tradingstrategies are also developed to exploit the observed overstatementof variance in the dollar/yen option market. Traders that can executethe delta-neutral trading strategies at the observed markettransaction prices could lock in a significant profits during theperiod examined. However, for investors that facing highertransaction costs, the magnitude of the profits is generally notlarge enough to allow for abnormal risk-adjusted profits.     

A frequency-domain alternative to long-horizon regressions with application to return predictability

This paper aims at improved accuracy in testing for long-run predictability in noisy series, such as stock market returns. Long-horizon regressions have previously been the dominant approach in this area. We suggest an alternative method that yields more accurate results. We find evidence of predictability in S&P 500 returns even when the confidence intervals are constructed using model-free methods based on subsampling.     

The Impact of Capital Structure Change on Firm Value: Some Estimates

This study develops a model based on current corporate finance theories which explains stock returns associated with the announcement of issuer exchange offers. The major independent variables are changes in leverage multiplied by senior security claims outstanding and changes in debt tax shields. Parameter estimates are statistically significant and consistent in sign and relative magnitude with model predictions. Overall, 55 percent of the variance in stock announcement period returns is explained. The evidence is consistent with tax-based theories of optimal capital structure, a positive debt level information effect, and leverage-induced wealth transfers across security classes.     

Capital Structure and the Market for Corporate Control: The Defensive Role of Debt Financing

A capital structure theory based on corporate control considerations is presented. The optimal debt level balances a decrease in the probability of acquisition against a higher share of the synergy for the target's shareholders. This leads to the following implications: (i) the probability of firms becoming acquisition targets decreases with their leverage, (ii) acquirers' share of the total equity gain increases with targets' leverage, (iii) when acquisitions are initiated, targets' stock price, targets' debt value, and acquirers' firm value increase, and (iv) during the acquisition, target firms' stock price changes further; the expected change is zero and the variance decreases with targets' debt level.     

Confidence intervals of the premiums of optimal bonus malus systems

In view of the economic importance of motor third-party liability insurance in developed countries the construction of optimal BMS has been given considerable interest. However, a major drawback in the construction of optimal BMS is that they fail to account for the variability on premium calculations which are treated as point estimates. The present study addresses this issue. Specifically, nonparametric mixtures of Poisson laws are used to construct an optimal BMS with a finite number of classes. The mixing distribution is estimated by nonparametric maximum likelihood (NPML). The main contribution of this paper is the use of the NPML estimator for the construction of confidence intervals for the premium rates derived by updating the posterior mean claim frequency. Furthermore, we advance one step further by improving the performance of the confidence intervals based on a bootstrap procedure where the estimated mixture is used for resampling. The construction of confidence intervals for the individual premiums based on the asymptotic maximum likelihood theory is beneficial for the insurance company as it can result in accurate and effective adjustments to the premium rating policies from a practical point of view.     

A Utility-Based Model of Common Stock Price Movements

This paper develops and tests a nonlinear utility-based econometric model of the temporal behavior of aggregate stock price movements based on a constant relative risk aversion utility function and an observable information set consisting of aggregate consumption, aggregate dividends, and past stock prices. The stochastic process derived from time-series analyses of consumption and dividends measured over annual intervals is used to derive and empirically test a closed-form solution for stock-price movements. The endogenization of discount rate changes in the utility-based model is shown to be more consistent with aggregate stock price movements over a twenty-year holdout period than constant discount rate models. The model is also used to estimate the representative investor's relative risk aversion. The estimate of 4.22 is consistent with that used by Grossman and Shiller in their perfect foresight model and is significantly higher than the relative risk aversion of 1.0 implied by logarithmic utility.     

Investor sentiment and the mean–variance relation

This study shows the influence of investor sentiment on the market's mean–variance tradeoff. We find that the stock market's expected excess return is positively related to the market's conditional variance in low-sentiment periods but unrelated to variance in high-sentiment periods. These findings are consistent with sentiment traders who, during the high-sentiment periods, undermine an otherwise positive mean–variance tradeoff. We also find that the negative correlation between returns and contemporaneous volatility innovations is much stronger in the low-sentiment periods. The latter result is consistent with the stronger positive ex ante relation during such periods.     

Jackknife Empirical Likelihood Intervals for Spearman’s Rho

Abstract

In connection with copulas, rank correlation such as Kendall’s tau and Spearman’s rho has been employed in risk management for summarizing dependence between two variables and estimating parameters in bivariate copulas and elliptical models. In this paper a jackknife empirical likelihood method is proposed to construct confidence intervals for Spearman’s rho without estimating the asymptotic variance. A simulation study confirms the advantages of the proposed method.