Knowledge that Transforms

The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.1) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation. This property is then used to derive a partial differential equation for bond prices. The solution to that equation is given in the form of a stochastic integral representation. An interpretation of the bond pricing formula is provided. The model is illustrated on a specific case.

In practice, there are substantial deviations from the doctrine of ‘absolute priority’, which governs the rights of the firm's claimholders in the event of bankruptcy. To determine whether or not the possibility of such deviations is reflected in the prices of the firm's securities, this study examines the risk and return characteristics of financial claims against firms in court-supervised bankruptcy proceedings. Debt claims against bankrupt firms are indeed ‘risky’, exhibiting levels of systematic risk similar to that of common stocks in general. While some of the findings are anomalous, the data are generally consistent with the view that the capital market ‘properly’ prices risky debt claims to reflect both their risk characteristics and the possibility of departures from the doctrine of absolute priority.

This paper develops a Monte Carlo simulation method for solving option valuation problems. The method simulates the process generating the returns on the underlying asset and invokes the risk neutrality assumption to derive the value of the option. Techniques for improving the efficiency of the method are introduced. Some numerical examples are given to illustrate the procedure and additional applications are suggested.

This paper analyzes the optimal portfolio choice problem when security returns have a joint multivariate normal distribution with unknown parameters. For the case of limited, but sufficient (sample plus prior) information, we show that for a general family of conjugate priors, the optimal portfolio choice is obtained by the use of a mean-variance analysis that differs from traditional mean-variance analysis due to estimation risk. We also consider two illustrative cases of insufficient sample information and minimal prior information and show that in these cases it is asymptotically optimal for an investor to limit diversification to a subset of the securities. These theoretical results corroborate observed investor behavior in capital markets.

Testing the two-parameter asset pricing theory is difficult (and currently infeasible). Due to a mathematical equivalence between the individual return/‘beta’ linearity relation and the market portfolio's mean-variance efficiency, any valid test presupposes complete knowledge of the true market portfolio's composition. This implies, inter alia, that every individual asset must be included in a correct test. Errors of inference inducible by incomplete tests are discussed and some ambiguities in published tests are explained.

In this paper large block stock transactions are examined in the context of a trading rule devised by Grier and Albin. The study makes use of the actual intra-day history of stock transactions. Considerable effort is taken to correctly incorporate the effects of transaction costs on trading rule profits and evidence is presented on the sensitivity of such profits to variations in these costs. The use of intra-day prices yields results consistent with the weak form of the efficient markets hypothesis and provides important evidence on the speed of price adjustment.

Many corporate assets, particularly growth opportunities, can be viewed as call options. The value of such ‘real options’ depends on discretionary future investment by the firm. Issuing risky debt reduces the present market value of a firm holding real options by inducing a suboptimal investment strategy or by forcing the firm and its creditors to bear the costs of avoiding the suboptimal strategy. The paper predicts that corporate borrowing is inversely related to the proportion of market value accounted for by real options. It also rationalizes other aspects of corporate borrowing behavior, for example the practice of matching maturities of assets and debt liabilities.

This paper develops a new distribution theory for common stock returns. The model is composed of a calendar time diffusion process and a jump process where the magnitudes of the jumps may be autocorrelated. Empirical tests are performed on a month of transactions returns for twenty New York Stock Exchange securities. The data analysis supports the validity of the proposed theory.