Knowledge that Transforms

Horse racing data permit interesting tests of attitudes toward risk. The present paper studies a new sample of racetrack results from Atlantic City, New Jersey. The questions examined are: (1) Are the market odds the best data for predicting the order of finish? (2) Do horses go off at odds that reflect their true probability of winning? (3) Is there any evidence that late bettors have better information than early bettors? It is found that market odds predict the order of finish well, but that ‘favorites’ are good bets and ‘long shots’ are poor ones. The data suggest that there does exist an ‘informed’ class of bettors and that bettors are on the whole neither risk neutral nor risk averse.

This paper examines the pricing performance of the valuation equation for American call options on stocks with known dividends and compares it with two suggested approximation methods. The approximation obtained by substituting the stock price net of the present value of the escrowed dividends into the Black-Scholes model is shown to induce spurious correlation between prediction error and (1) the standard deviation of stock return, (2) the degree to which the option is in-the-money or out-of-the-money, (3) the probability of early exercise, (4) the time to expiration of the option, and (5) the dividend yield of the stock. A new method of examining option market efficiency is developed and tested.

A variety of financial models are cast as nonlinear parameter restrictions on multivariate regression models, and the framework seems well suited for empirical purposes. Aside from eliminating the errors-in-the-variables problem which has plagued a number of past studies, the suggested methodology increases the precision of estimated risk premiums by as much as 76%. In addition, the approach leads naturally to a likelihood ratio test of the parameter restrictions as a test for a financial model. This testing framework has considerable power over past test statistics. With no additional variable beyond β, the substantive content of the CAPM is rejected for the period 1926–1975 with a significance level less than 0.001.

This paper examines a large, randomly chosen, sample of bond indentures focusing on the constraints they set on dividend payments that have the potential to transfer wealth from the bondholders (i.e., payments which are financed by a new debt issue or reduced investment). The nature of these restrictions support the hypothesis that bond convenants are structured to control the conflict of interest between stockholders and bondholders. Further, the empirical evidence suggests that these constraints are not binding — i.e., stockholders do not pay themselves as much dividends as they are allowed to. Explanations of this puzzling empirical regularity are suggested.

This paper examines the effect of alternative bond indenture provisions on the allocation of risk among the firm's claimants. The approach taken here differs from that of earlier studies in that risk allocation is examined while the firm's leverage (in market value terms) is held constant. In this context, four indenture provisions are examined: (1) the time to maturity, (2) the promised payment schedule, (3) financing restrictions and (4) priority rules. It is concluded that risk is transferred from stockholders to bondholders as the time to maturity and promised payment increase appropriately. Furthermore substitution of longer-term debt for an equal amount of shorter-term debt also increases the risk to bondholders while decreasing the risk to stockholders. The analysis shows that a coupon bond can be represented by a unique discount bond with the same risk and value. This permits the characterization of the effective maturity of a risky debt issue, a concept analogous to the stochastic duration of a default-free coupon bond. These results are shown to be independent of the means used to finance the debt issue. Finally, it is concluded that the relative risk associated with different bonds issued by the same firm cannot be determined by the structure of priority rules alone. It is also necessary to consider the timing of the promised payments compared to that of the other debt issues in the firm's capital structure.

This paper examines the pricing of intermediate-term line commitments, often called revolving credit agreements. Their characteristics, covenant, and compensating balance features are discussed. The fixed portion of the line is described as a dual phased option; it behaves as a put or a call depending on whether bank borrowing is undertaken. Two valuation models, based on the use of the borrowing, are derived for infinitely-lived line commitments. The pattern of borrowing by the firm is shown to principally depend on the relative size of the fixed and variable costs of the line.

In most instances, investors are not indifferent to risk. Their attitudes toward it influence their decisions. Temporal risk aversion, the dynamic analogue of the usual concept of risk aversion, has a marked effect on investors' decisions but is usually ignored in the literature. This paper investigates the liquidity preference of temporally risk-averse investors. The analysis shows that, all other things being equal, temporal risk aversion reduces the liquidity premium investors must receive to hold an asset that is not perfectly reversible. Thus, the optimal investment policy is closer to what one would expect had a frictionless exchange market existed for the irreversible asset. As far as an individual's investment behavior is concerned, temporal risk aversion counters the effects of an asset's irreversibility and tends to compensate for the absence of frictionless exchange.

We show how a given probability distribution can be approximated by an arbitrary distribution in terms of a series expansion involving second and higher moments. This theoretical development is specialized to the problem of option valuation where the underlying security distribution, if not lognormal, can be approximated by a lognormally distributed random variable. The resulting option price is expressed as the sum of a Black-Scholes price plus adjustment terms which depend on the second and higher moments of the underlying security stochastic process. This approach permits the impact on the option price of skewness and kurtosis of the underlying stock's distribution to be evaluated.

This paper presents an alternative approach to derive the Breeden-Litzenberger valuation formula, which expresses the price of an arbitrary derivative security in terms of call options' prices. This valuation formula follows from the observation that a continuous derivative security can be replicated by a portfolio including a bond and call options with all possible exercise prices. Discrete terms are added to the original Breeden-Litzenberger formula to reflect possible discontinuities of the call option price's derivative with respect to the exercise price. These discontinuities are subsequently shown to correspond to mass points of the probability distribution of the stock price. Several applications of the Breeden-Litzenberger valuation formula are demonstrated.

A technique is presented for deriving equilibrium models of asset risk premia in continuous time models which does not require the complete solution of a consumer's continuous time stochastic control problem. The technique is used to show that even if traders have heterogeneous information about asset returns and/or there are non-traded assets, then the risk premium of a traded asset is determined by the covariance between the asset's return and the rate of change in per capita consumption. We only require the assumption that traders' consumptions and traded asset values form an Ito process.