Fischer Black

The Pricing of Options and Corporate Liabilities

If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.

The pricing of commodity contracts

Abstract The contract price on a forward contract stays fixed for the life of the contract, while a futures contract is rewritten every day. The value of a futures contract is zero at the start of each day. The expected change in the futures price satisfies a formula like the capital asset pricing model. If changes in the futures price are independent of the return on the market, the futures price is the expected spot price. The futures market is not unique in its ability to shift risk, since corporations can do that too. The futures market is unique in the guidance it provides for producers, distributors, and users of commodities. Using assumptions like those used in deriving the original option formula, we find formulas for the values of forward contracts and commodity options in terms of the futures price and other variables.

The effects of dividend yield and dividend policy on common stock prices and returns

Abstract This paper suggests that it is not possible to demonstrate, using the best available empirical methods, that the expected returns on high yield common stocks differ from the expected returns on low yield common stocks either before or after taxes. A taxable investor who concentrates his portfolio in low yield securities cannot tell from the data whether he is increasing or decreasing his expected after-tax return by so doing. A tax exempt investor who concentrates his portfolio in high yield securities cannot tell from the data whether he is increasing or decreasing his expected return. We argue that the best method for testing the effects of dividend policy on stock prices is to test the effects of dividend yield on stock returns. Thus the fact that we cannot tell, using the best available methods, what effects dividend yield has on stock returns implies that we cannot tell what effect, if any, a change in dividend policy will have on a corporations stock price.

International capital market equilibrium with investment barriers

Abstract This paper outlines models of capital market equilibrium when there are explicit barriers to international investment in the form of a tax on holdings of assets in one country by residents of another country. There is a corresponding subsidy on short positions in foreign assets. Asset prices deviate from the predictions of the world capital asset pricing model. Investors do not hold a mixture of national market portfolios, but the mix of risky assets is the same for every investor in a country. Optimal portfolios tend to be heavy in domestic assets, and light in foreign assets. Tax free investors, however, tend to hold assets anywhere in the world that are taxed heavily. Estimates of the magnitude of the average tax (or the magnitude of effective barriers to international investment) can be made by comparing the average return on the minimum variance zero β portfolio, z , with the average across countries and time of the short-term interest rate. When barriers are ineffective, the expected return on portfolio z will be the average short-term interest rate, and the world capital asset pricing model will hold.

Theory of Constant Proportion Portfolio Insurance

Abstract We study constant proportion portfolio insurance (CPPI), a dynamic strategy that maintains the portfolios risk exposure a constant multiple of the excess of wealth over a floor, up to a borrowing limit. We use this simple rule to investigate how transaction costs and borrowing constraints affect portfolio insurance-type strategies. Absent transaction costs, CPPI is equivalent to investing in perpetual American call options, and is optimal for a piecewise-HARA utility function with a minimum consumption constraint. As the multiple increases, the payoffs under CPPI approach those of a stop-loss strategy. The expected holding-period return is not monotonic in the multiple, and a higher expected return can be obtained under CPPI than with a stop-loss strategy.

Bank funds management in an efficient market

Abstract This paper discusses general principles for choosing bank assets and liabilities, for deciding on when to make a loan and what interest rate to charge, for pricing funds transfer services such as the handling of checks, for establishing compensating balance requirements, and for dealing with government regulation. The discussion assumes markets are efficient and deals first with an unregulated environment and then with policies in the face of regulatory constraints. Most of the policies which would be optimal in an unregulated environment will be optimal in the regulated environment such as in the U.S. today, because it is relatively easy to get around most of the regulations that are applied to banks by the use of non-deposit liabilities, compensating balances and negative checking accounts.

[U.S. Commercial Banking: Trends, Cycles, and Policy]: Comment

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The Rhetoric of Economics.

McCloskey’s “Rhetoric of Economics” states the importance of rhetoric and analyzes the poverty of rhetoric in mainstream economics. Particularly interesting is the criticism of the “modernist methodology” and of the existence of a prescriptive methodology in itself. Analysis of the rhetoric is according McCluskey the way to recover a sound scientific research in economics. The debate raised by Deirdre N. McCluskey’s book is in part reported at the end of this work.