Terry A. Marsh

Dividend Behavior for the Aggregate Stock Market

We develop and estimate a model of the dynamic behavior of aggregate corporate dividends as a function of the change in permanent earnings of firms. Although structured along the lines of the Lintner-Brittain-FamaBabiak models of individual-firm dividend behavior, the model uses changes in stock prices instead of accounting earnings to measure permanent earnings changes. The performance of the model is compared with both the accounting earnings-based models and the trend-autoregressive model associated with Shiller (1981a).

Variations in economic uncertainty and risk premiums on capital assets

We study the movements in equity prices caused by variation over time in uncertainty about corporate dividends. The framework for our analysis is a general equilibrium model which we fit to NYSE index returns using a method of simulated moments (MSM). Using the model and the MSM estimates, we find that: in general, equity risk premiums are not proportional to return volatility, but are reasonably linear in return variance; equity return volatility is about twice as high as dividend volatility, even though equity prices in our model are rationally determined; dividend-price ratios ‘predict’ subsequent equity returns with about the same precision as found in practice; long-run market returns are negatively autocorrelated; and, consistent with empirical evidence, risk premiums on levered equity are a monotonically increasing function of junk bond yield spreads.

Measuring tail thickness under GARCH and an application to extreme exchange rate changes

Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including GARCH and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias strongly relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail-thickness due to small sample bias. As a consequence, high quantile estimation may lead to a substantial underestimation of tail risk.

Surprise volume and heteroskedasticity in equity market returns

Heteroskedasticity in returns may be explainable by trading volume. We use different volume variables, including surprise volume—i.e. unexpected above-average trading activity—which is derived from uncorrelated volume innovations. Assuming weakly exogenous volume, we extend the Lamoureux and Lastrapes (1990) model by an asymmetric GARCH in-mean specification following Golsten et al. (1993). Model estimation for the US as well as six large equity markets shows that surprise volume provides superior model fit and helps to explain volatility persistence as well as excess kurtosis. Surprise volume reveals a significant positive market risk premium, asymmetry and a surprise volume effect in conditional variance. The findings suggest that e.g. a surprise volume shock (breakdown)—i.e. large (small) contemporaneous and small (large) lagged surprise volume—relates to increased (decreased) conditional market variance and return.

Tail index estimation in small smaples Simulation results for independent and ARCH-type financial return models

Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator’s performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.

On Adaptive Tail Index Estimation for Financial Return Models

Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimators performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.

Why Doesn't the Black--Scholes Model Fit Japanese Warrants and Convertible Bonds?

In this paper, we investigate the systematic departures of traded prices of Japanese equity warrants and convertible bonds from their theoretical Black-Scholes values. We briefly consider transactions costs and the dilution adjustment as potential explanations of the discrepancy between price and value, showing that they can, in principle, explain some of the discrepancy. However, our major focus is on shifts in volatility of the prices of the underlying stocks as a function of the stock price changes; such shifts are not taken into account in the Black-Scholes values. We assume that the pseudo-probability distributions of prices of stocks of cross-sections of companies which are roughly similar in size are identical. This simple assumption (which can be generalized) enables us to infer the implied probability distribution and binomial tree for stock price changes using the Derman and Kani (1994), Dupire (1994), Rubinstein (1994), and Shimko (1993) approach. The cross-section of warrant prices implies an inverse volatility smile and a positively skewed probability density for stock prices. Rubinsteins identifying assumptions generate an implied binomial tree in which the relative size of up-steps and down-steps, and thus volatility, changes systematically as stock prices change. We briefly consider potential explanations for the implied behavior, and for the difference in the smile pattern between index options and the warrants and convertibles.

Flight to Quality and Asset Allocation in a Financial Crisis

With respect to the recent financial crisis, the authors argue that the appropriate adjustments to portfolio allocations in response to the market dislocation are determined by equilibrium considerations (supply must equal demand) and depend on individual investors’ characteristics relative to societal averages. Using a simple model that captures the magnitude of the recent crisis, the authors show that the optimal tactical adjustments for most portfolios require a turnover of less than 10%. In the recent financial crisis, investors suffered losses on their portfolios on the order of 20%–30%. In addition, they faced a market in which the volatility of most asset classes and the correlations among those asset classes surged, all of which served to greatly increase the risk of their portfolio positions. The challenging issue facing investors was the appropriate tactical adjustment they should make to their portfolio allocations in response to this market dislocation. In this article, the authors argue that the appropriate adjustment for any given investor is determined by equilibrium considerations (supply must equal demand) and depends on that investor’s characteristics relative to societal averages. Although this point should be obvious, it seems to have been ignored by many investors and their advisers. In a simple model calibrated to capture the magnitude of the 2007–09 crisis, the authors show that the optimal tactical portfolio adjustments for most investors are not large, requiring turnover of less than 10%, and that this finding is quite robust to changes in their assumptions.

Chapter 9 Term structure of interest rates and the pricing of fixed income claims and bonds

Publisher Summary This chapter discusses how the intertemporal and risk neutral pricing techniques can be applied in the fixed income area. The exposition follows essentially the reverse of the chronological order in which the applications took place. It begins with an explanation of how the risk-neutral approach has been adapted from the options pricing literature. It then turns to the equilibrium bond pricing models that were the focus of research in the late 1970s and early 1980s. Both the risk-neutral and equilibrium approaches are presented under the assumption that term structure movements depend upon only a single factor –the short rate of interest. This factor, and thus movements in bond prices, can then be represented in the tree diagram which is now routinely used in explaining contingent claim pricing methods. Once the arbitrage-free and equilibrium approaches to modeling the term structure have been introduced, questions such as how many factors are needed in practice to adequately describe term structure movements, and the extent to which the equilibrium and risk-neutral approaches incorporate the information in the current term structure, are discussed in the chapter. Some of the issues that arise in fitting the fixed-income models and applying them in the valuation of interest-rate derivatives are addressed.

Alpha Signals, Smart Betas, and Factor Model Alignment

The authors consider the case for augmenting risk models to be used in portfolio construction to reflect information embedded in the portfolio manager’s alphas. They consider both smart beta models and cases in which alpha signals are partly factor driven but incorrectly perceived to be stock specific. In smart beta cases, the authors argue that mechanically augmenting the risk model can cause losses by distorting an otherwise-correct factor structure. The authors show that for cases in which asset-specific alpha signals might unexpectedly be related to hidden systematic factors, errors of omission—missing these hidden factors—generally result in larger expected losses in portfolio efficiency than do errors of commission—unintentionally including nonexistent “phantom” factors. When the alpha signals are very noisy, the practice of mechanically augmenting the risk model with a custom risk factor to offset that noise can improve portfolio efficiency. However, in those cases, the custom risk factor has nothing to do with underlying sources of true risk that all investors face, but instead serves as a penalty that in a back-door way tends to adjust for weak quality of the manager’s alphas.