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Interest Rates as Options
Published: 12/01/1995 | DOI: 10.1111/j.1540-6261.1995.tb05182.x
FISCHER BLACK
Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can be and has been negative, most recently (in the United States) during the Great Depression. The nominal short rate is the “shadow real interest rate” (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short rate is an option. Longer term interest rates are always positive, since the future short rate may be positive even when the current short rate is zero. We can easily build this option element into our interest rate trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative rate with zero.
Equilibrium Exchange Rate Hedging
Published: 07/01/1990 | DOI: 10.1111/j.1540-6261.1990.tb05111.x
FISCHER BLACK
We assume a world like the one that gives the capital asset pricing model, but with many goods and many countries. We assume that investors in a given country have homothetic utility functions with the same weights, and a currency that has a sure end‐of‐period value using a price index with those weights. Siegel's paradox (derived from Jensen's inequality) makes investors want a positive amount of exchange risk. When average risk tolerance is the same across countries, every investor will hold the same mix of market risk (through the world market portfolio of all assets) and exchange risk (in a diversified basket of foreign currencies). In fact, the ratio of exchange risk to market risk is equal to the average investor's risk tolerance. We can write the ratio of exchange risk to market risk (and the fraction of the market's exchange risk that investors hedge) as depending on an average of world market risk premia, an average of world market volatilities, and an average of exchange rate volatilities. The weights in these averages are the same as the weights of the different countries in the currency basket. Given these averages, the ratio (and the fraction hedged) will not depend directly on exchange rate means or covariances. In equilibrium, we can use the ratio of exchange risk to market risk to measure average risk tolerance: in this model, risk tolerance is observable.
INTRODUCTION
Published: 07/01/1985 | DOI: 10.1111/j.1540-6261.1985.tb04983.x
FISCHER BLACK
Noise
Published: 07/01/1986 | DOI: 10.1111/j.1540-6261.1986.tb04513.x
FISCHER BLACK
The effects of noise on the world, and on our views of the world, are profound. Noise in the sense of a large number of small events is often a causal factor much more powerful than a small number of large events can be. Noise makes trading in financial markets possible, and thus allows us to observe prices for financial assets. Noise causes markets to be somewhat inefficient, but often prevents us from taking advantage of inefficiencies. Noise in the form of uncertainty about future tastes and technology by sector causes business cycles, and makes them highly resistant to improvement through government intervention. Noise in the form of expectations that need not follow rational rules causes inflation to be what it is, at least in the absence of a gold standard or fixed exchange rates. Noise in the form of uncertainty about what relative prices would be with other exchange rates makes us think incorrectly that changes in exchange rates or inflation rates cause changes in trade or investment flows or economic activity. Most generally, noise makes it very difficult to test either practical or academic theories about the way that financial or economic markets work. We are forced to act largely in the dark.
TAXES AND THE PRICING OF OPTIONS
Published: 05/01/1976 | DOI: 10.1111/j.1540-6261.1976.tb01889.x
Fischer Black, Myron Scholes
Session Topic: Individual Investors and Mutual Funds
Published: 05/01/1974 | DOI: 10.1111/j.1540-6261.1974.tb03054.x
Jack L. Treynor, Fischer Black, Myron Scholes
Summary. The modern theory of finance suggests that most investors should put part or all of their money into a “market portfolio” mixed with borrowing or lending. Empirical evidence generally supports the theory, but there are some unanswered questions about the composition of the best market portfolio, about the apparent attractiveness of low risk stocks relative to high risk stocks, and about ways of minimizing transaction costs. Attempts to create a fund based on these principles and to make it available to a large number of investors have uncovered some important problems. Legal costs due to government regulation, the costs of managing a fund, and especially the costs of selling it are all much higher than one might expect. Despite these problems, efforts to create such funds seem destined for eventual success.