Knowledge that Transforms

The downside risk in a leveraged stock position can be eliminated by using stop-loss orders. The upside potential of such a position can be captured using contingent buy orders. The terminal payoff to this stop-loss start-gain strategy is identical to that of a call option, but the strategy costs less initially. This article resolves this paradox by showing that the strategy is not self-financing for continuous stock-price processes of unbounded variation. The resolution of the paradox leads to a new decomposition of an option’s price into its intrinsic and time value. When the stock price follows geometric Brownian motion, this decomposition is proven to be mathematically equivalent to the Black–Scholes (1973) formula.

Examination of 41 closed-end fund intial public offerings (IPOs) during the period from January 1986 to June 1987 reveals that the mean intial day's return is not significantly different from zero in contrast to previous findings for nonfund IPOs. New funds also show significant negative after- market returns unlike other new issues. Despite the disparity between our findings and previous results, our results are consistent with existing models. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

This article is a reexamination of the clearing and settlement process in financial markets (particularly the futures market) and its performance during the 1987 stock market crash. It provides both some institutional background and some conceptual perspective on the problems faced by the system during the week of October 19. Much of the discussion is based on the useful analogies that can be drawn between the clearinghouse and other financial intermediaries, such as banks and insurance companies. A major conclusion is that the Federal Reserve played a vital role in protecting the integrity of the clearing and settlements system during the crash.

This article generalizes the Cox, Ross, and Rubinstein (1979) binomial option-pricing model, and establishes a convergence from discrete-time multivariate multinomial models to continuous-time multidimensional diffusion models for contingent claims prices. The key to the approach is to approximate the N-dimensional diffusion price process by a sequence of N-variate, (N+1)-nomial processes. It is shown that contingent claims prices and dynamic replicating portfolio strategies derived from the discrete time models converge to their corresponding continuous-time limits.

In a model of takeovers under asymmetric information, we identify a separating equilibrium in which the value of the bidder firm is revealed by the mix of cash and securities used as payment for the target. The model predicts that the revealed bidder value is monotonically increasing and convex in the fraction of the total offer that consists of cash. We examine the model restrictions using data from Canada, where mixed offers are both relatively frequent and free of the confounding tax-related options characterizing mixed offers in the United States. We find that the average announcement-month bidder abnormal return in mixed offers is large and significant. However, maximum likelihood estimates of parameters in both linear and nonlinear cross-sectional regressions fail to support the model predictions.

The role of the medium of exchange in competition among bidders and its effect on returns to stockholders in corporate takeovers are investigated. Consistent with recent empirical evidence, our model shows that stockholders of both acquiring and target firms obtain higher returns when a takeover is financed with cash rather than equity, and that returns to target shareholders increase with competition. The model predicts that the fraction of synergy captured by the target decreases with the level of synergy. Finally, it is shown that, as competition increases, the cash component of the offer as well as the proportion of cash offered increases.

I am pleased to offer a comment on this very interesting article by an author who is always in the forefront of the research on empirical financial models. This article presents data analysis that estabishes the stylized facts about stock market volatility around market crashes. He concludes that volatility is high during periods of stock market decline and that it gradually returns to more normal levels. In the case of 1987, the peak was higher than usual and the decline was more rapid. The article uses 28,000 daily observations but does not really estimate a usable model; instead, it explores the data by estimating highly overparameterized models that reveal important features of the data. I suggest that this be considered an exploratory investigation and that in the face of more parsimonious models, rather interesting and somewhat different conclusions are revealed. The basic model estimated by Schwert is a 22-order autoregression of daily returns with a heteroskedastic error standard deviation which is itself assumed to be a 22-order autoregression in the absolute errors. Even with 28,000 observations, there is apparently a lot of noise in the coefficients. To allow for a risk premium, the mean is related to the variance, and in this case it is therefore related to 22 lagged absolute residuals. This part of the model uses 66 parameters. An alternative model is a first-order generalized autoregressive conditionally heteroskedastic model with variance influencing the mean [GARCH (l, l)-m], with a first-order moving average to correct for non-synchronous trading as used in Engle, Lilien, and Robins (1987), French, Schwert, and Stambaugh (1987), or Chou (1988), following the earlier work of Engle (1982). This requires only four coefficients! In the context of the parsimonious model, the parameter regulating the risk-return trade-off can be interpreted as the median agent’s taste for risk or his coefficient of relative-risk aversion. One naturally asks whether this parameter is constant over time, and we then recognize that the Schwert parameterization cannot answer the question.

The short-run interdependence of prices and price volatility across three major international stock markets is studied. Daily opening and closing prices of major stock indexes for the Tokyo, London, and New York stock markets are examined. The analysis utilizes the autoregressive conditionally heteroskedastic (ARCH) family of statistical models to explore these pricing relationships. Evidence of price volatility spillovers from New York to Tokyo, London to Tokyo, and New York to London is observed, but no price volatility spillover effects in other directions are found for the pre-October 1987 period.

We find that conditional means and variances of consumption growth vary through time, and this variation appears to be associated with the business cycle. A pricing model with fluctuating means and variances of consumption growth provides implications about conditional moments of returns for both short and long investment horizons, and these implications are explored empirically. The U-shaped pattern of first-order autocorrelations of returns, as well as business cycle patterns in the price of risk, appears to be consistent with the model, but our exploration suggests that other implications about conditional return moments are at odds with the data.