# Working Paper Abstracts – 1996

**01-96**

When the underlying process is one-dimensional diffusion, as well as in certain restricted stochastic volatility settings, a contingent claim’s delta is always bounded by the infimum and supremum of its delta at maturity. Further, if the claim’s payoff is convex (concave), then the claim’s price is a convex (concave) function of the underlying’s value. However when volatility is less specialized, or when the underlying price follows a discontinuous or non-Markovian process, then call prices can have properties very different from those of the Black-Scholes model: a call’s price can be a decreasing, concave function of the underlying price over some range; increasing with the passage of time; and decreasing in the level of interest rates.

**02-96**

We study a model of renegotiation between a borrower and lender in which there is the potential for moral hazard on each side of the relationship. The borrower may add risk to the project, while the lender may opportunistically hold-up the borrower by threatening to demand early payment. The result is a model in which banks play a unique role in monitoring borrowers’ activities, and in which risk is endogenous and state-dependent. The model also yields explicit predictions about renegotiation outcomes, and conditions under which bank loans add value to the firm.

**03-96**

The goal of this paper is to examine the impact of 1975 Congressional mandate to integrate the trading of NYSE-listed stocks. The conclusions are: Most of the time, the NYSE quote matches or determines the best displayed quote, and the NYSE is the most frequent initiator of quote changes. Non-NYSE markets attract a significant portion of their volume when they are posting inferior bids or offers, indicating they obtain order flow for other reasons, such as “payment for order flow.” Yet, when a non-NYSE market does post a better bid or offer, it does attract additional order flow.

**04-96**

This paper examines the optimal consumption and investment problem for a “large” investor, whose portfolio choices affect the instantaneous expected returns on the traded assets. Alternatively, our analysis can be interpreted in terms of an optimal growth problem with nonlinear technologies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities’ price process and the investor’s preferences. As an illustration of our characterization result, explicit solutions are provided for specific examples involving an agent with logarithmic utilities, and a generalized two-factor version of the CCAPM is derived. The analogy of the consumption problem examined in this paper to the consumption problem with constraints on the portfolio choices is emphasized.

**05-96**

This study explores multivariate methods for investment analysis based on a sample of return histories that differ in length across assets. The longer histories provide greater information about moments of returns, not only for the longer-history assets, but for the shorter-history assets as well. To account for the remaining parameter uncertainty, or “estimation risk,” portfolio opportunities are characterized by a Bayesian predictive distribution. Examples involving emerging markets demonstrate the value of using the combined sample of histories and accounting for estimation risk, as compared to truncating the sample to produce equal-length histories or ignoring estimation risk by using maximum-likelihood estimates.

**06-96**

It is often stated that bidders acquire poorly-run targets in order to improve firm performance. This inefficient management hypothesis is frequently tested by examining target stock returns in the years prior to an acquisition. While the hypothesis is commonly assumed in the literature to be true, previous papers generally do not show significantly negative returns for targets in the years prior to acquisition. Our paper re-examines this issue thoroughly with a number of methodological improvements and a large sample of acquisitions over the period from 1930 to 1987. We find that the abnormal returns are insignificant over the four years prior to the bid. But over the ten-year period before the bid, target firms experience a statistically significant abnormal return of -7% to -18%. Our results suggest that takeovers discipline managers, but with a delay that may protect them through much of their normal tenures. However, this delay is shorter during periods of lenient anti-trust enforcement, during merger waves, and for unregulated firms.

**07-96**

This paper formally incorporates parameter uncertainty and model error into the estimation of contingent claim models and the formulation of forecasts. This allows inference on functions of interest (option values, bias functions, hedge ratios) consistent with uncertainty in both parameters and models. We show how to recover the exact posterior distributions of the parameters or any function of the parameters. Exact posterior or predictive densities are crucial because a frequent updating setup results in small samples and requires the incorporation of specific prior information. Markov Chain Monte Carlo estimators are developed to solve this estimation problem. Within sample and predictive model specification tests are provided which can be used in dynamic testing (or trading systems) making use of cross-sectional and time series options data. Finally, we discuss several generalizations of the error structure.

These new techniques are applied to equity options using the Black-Scholes model. When model error is taken into account, the Black-Scholes appears very robust, in contrast with previous studies which at best only incorporated parameter uncertainty. We extend the Black-Scholes model by adding polynomial functions of its inputs. This allows for intuitive specification test. Although these simple extended models improve the in-sample error properties of the Black-Scholes, they do not result in major improvements in out of sample predictions. The differences between these models are important, however, because they produce different hedge ratios and posterior probabilities of mispricing.

**08-96**

This paper examines the use of seven mechanisms to control agency problems between managers and shareholders. These mechanisms are: shareholdings of insiders, institutions, and large blockholders; use of outside directors; debt policy; the managerial labor market; and the market for corporate control. We present direct empirical evidence of interdependence among these mechanisms in a large sample of firms. This finding suggests that cross-sectional OLS regressions of firm performance on single mechanisms may be misleading. Indeed, we find relations between firm performance and four of the mechanisms when each is included in a separate OLS regression. These are insider shareholdings, outside directors, debt, and corporate control activity. Importantly, the effect of insider shareholdings disappears when all of the mechanisms are included in a single OLS regression, and the effects of debt and corporate control activity also disappear when estimations are made in a simultaneous systems framework. Together, these findings are consistent with optimal use of each control mechanism except outside directors.

**09-96**

The threat of takeover acts to discipline managers, but it also makes shareholders’ assurances to managers less reliable and so interferes with contracting between them. These two effects have opposing implications about the level of executive compensation: the disciplinary effect implies a reduction in compensation; the contracting effect implies an increase. Which effect dominates is an empirical issue. We examine the relation between managerial compensation and the industry-wide threat of takeover to address this issue. Using compensation data for the CEOs of over 500 firms and after controlling for other determinants of executive compensation found in previous studies, we find this a positive effect of takeover, indicating that the contracting effect dominates. Moreover, effect occurs only in firms that do not provide CEOs with compensation assurance (such as a golden parachute). The size of the effect is economically significant. For CEOs without golden parachutes, the most popular compensation assurance provision, a 10% increase in the annual probability of takeover from 4.6% to 5.06% results in $11,200 more in the typical CEO’s salary and bonus and $15,000 more in total compensation. We also find a direct positive effect of compensation assurance provisions on CEO compensation. These results do not seem to be driven by industry effects and are robust to alternative specifications. Together, they provide evidence on an important way in which the market for corporate control affects internal contracting and add to the growing literature on the determinants of the level of executive compensation.

**10-96**

Most states (Vermont is the exception) have constitutional or statutory limitations restricting their ability to run deficits in the state’s general fund. Balanced budget limitations may be either prospective (beginning-of-the-year) requirements or retrospective (end-of-the-year) requirements. Importantly, the state limits apply only to the general fund, leaving other funds (capital, pensions, social insurance) as potential sources for deficits financing. Do these general fund balanced budget requirements limit deficit financing? If so, which balanced budget rules are most effective in constraining state deficit financing? Finally, how are state spending and taxation decisions affected by balanced budget rules? Using budget data from a panel of 47 U.S. states for the period 1970-1991, the analysis finds that state end-of-the-year (not prospective) balance requirements do have significant positive effects on a state’s general fund surplus. The surplus is accumulated through cuts in spending, not through tax increases. It is saved in a state “rainy day” fund in anticipation of possible future general fund deficits. We find little evidence here that the constraints “force” deficits into other fiscal accounts.

**11-96**

We provide a monotonic transformation of an initial diffusion with a level-dependent diffusion parameter that yields a second, deterministic diffusion parameter process. Altering the diffusion parameter while maintaining the original Brownian motion at the expense of the drift can be viewed as a counterpart to Girsanov’s Theorem. The transformed process provides a tractable basis for the analysis of the initial probability distribution, and hence provides insights into the value-at-risk (VAR), hedging and valuation of alternate investment strategies. Restrictions on the initial process imply theoretical bounds on VAR, position deltas and state prices, and an empirical bound on option deltas.

**12-96**

There are two distinct components to a specialist’s price schedule, prices and depths. This paper presents a model of a specialist’s problem of choosing prices and depths jointly in order to maximize profits. Closed form solutions are provided for both constrained and unconstrained versions of the model. The contribution of this work is twofold. First, the model demonstrates the strategic importance of depths for the specialist and highlights its effect on overall liquidity. Second, the joint responses of prices and depths to various concerns of the specialist may be useful in differentiating between competing microstructure effects. Comparative static results show how depths respond to changes in: (1) the amount of asymmetric information, (2) uncertainty about the terminal value, (3) the prior probability assessments of future prices and (4) the distribution of liquidity trades.

**13-96**

In recent years, the number of downgrades in corporate bond ratings has exceeded the number of upgrades. This fact has led some to conclude that the credit quality of US corporate debt has declined. However, declining credit quality is not the only possible explanation. An alternative explanation of this apparent decline in credit quality is that the rating agencies are now using more stringent standards in assigning ratings. An ordered probit analysis of a panel of firms from 1973 through 1992 suggests that rating standards have indeed become more stringent. The implication is that at least part of the downward trend in ratings is the result of changing standards and does not reflect a decline in credit quality.

**14-96**

The returns of assets that are traded on financial markets are more volatile than the returns offered by intermediaries such as banks and insurance companies. This suggests that individual investors are exposed to more risk in countries which rely heavily on financial markets. In the absence of a complete set of Arrow-Debreu securities, there may be a role for institutions that can smooth asset returns over time. In this paper, we consider one such mechanism. We present an example of an overlapping generations economy in which the incompleteness of financial markets leads to underinvestment in reserves. There exist allocations where by building up large reserves it is possible to smooth asset returns and eliminate nondiversifiable risk. This allows an ex ante Pareto improvement. We then argue that a long-lived intermediary may be able to implement this type of smoothing. However, the position of the intermediary is fragile; competition from financial markets can cause the intertemporal smoothing mechanism to unravel, in which case the intermediary will do no better than the market.

**15-96**

We solve an optimal managerial compensation contract’s wage, equity and options components, vesting dates, and control rights when firms are more complicated than standard principal-agent theory allows. Firms have asset-in-place, endure through time, and have many managers. A firm’s owner can transfer some control rights to a manager, thereby entrenching her. Managerial entrenchment makes deferred compensation credible but creates a hold-up problem. Deferring some, but not all, compensation reduces a manager’s incentive to free-ride on her replacement while simultaneously solving the hold-up problem. Under an optimal contract a senior manager will be entrenched, make no effort, and receive apparently performance-intensive compensation.