Equilibrium exchange rate hedging

Article Abstract:

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. (Reprinted by permission of the publisher.)

Research, Prices and rates, Hedging (Finance), Foreign exchange, Foreign exchange rates, Foreign exchange market

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Interest rates as options

Article Abstract:

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. (Reprinted by permission of the publisher.)

Analysis, Options (Finance), Interest rates

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Presidential address: noise

Article Abstract:

In modeling financial markets and trading thereon, 'noise' may be defined as several small events that combine to obscure information. Noise in this sense is any event or reaction to an event that makes market observations imperfect or incorrect. Noise, then, is not necessarily audible. Having defined noise in this manner, the president of the American Finance Association, in an address before that group, discusses the effects of noise on financial markets and market traders. Noise is seen as: (1) helping to create trading, (2) adding to market inefficiencies, (3) preventing traders from taking advantage of market inefficiencies, (4) causing, at least in part, the existence of business cycles and their resistance to government intervention, (5) attributing to and being affected by inflation, and (6) complicating research tests of economic and financial theories in practical environments.

Models, Conferences, meetings and seminars, Marketing, Marketing models, American Finance Association, transcript, Financial research

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