Simon Benninga

Optimal hedging in the futures market under price uncertainty

Abstract We show that there exists a simple optimal hedging rule in the futures markets, for all risk averse decision makers, given that (a) futures price today is an unbiased predictor of the futures price next period, (b) basis is independent of the spot price.

The equilibrium pricing of exchange rates and assets when trade takes time

Abstract When trade takes time, there are systematic deviations of the exchange rate from its Law of One Price value; these depend on the real interest rate in terms of the importable good. There is no systematic tendency for the spot rate to attain its LOP value in the long run. This means that agents in different countries price the same cash flows by using different risk premia, with agents in the ‘foreign’ country pricing the asset by adding a risk premium related to foreign exchange risk.

Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure

This paper examines the relation between nominal and real interest rates, and the nominal and real term structure under uncertainty. We show that two separate risk terms cause the Fisher theorem to fail. One risk term is related only to the variability of money prices, while the other is related to the purchasing power riskiness of the nominal bond. Monetary policy can affect the value of both these risk terms. We also show that the pure expectations hypothesis of the term structure fails for both real and nominal bonds because of risk premia. Even if the economy is neutral with respect to monetary policy, monetary policy can alter the nominal term structure.

Optimal international hedging in commodity and currency forward markets

Abstract This paper derives optimal hedging and production rules for an exporting firm which faces both commodity-price and foreign- exchange-rate uncertainty. The size of the commodity hedge is independent of the properties of the foreign-exchange market. However, the optimal foreign-exchange hedge depends on the commodity hedge and the properties of the commodity forward market. The firms production decision is independent of its objective function if both forward markets exist, but depends on the consumption beta of the unhedgeable risks in the absence of one or both of the markets.

Leverage, time preference and the ‘equity premium puzzle’☆

Abstract We re-examine the Mehra and Prescott (1985) model. A combination of the time preference factor greater than one and reasonable leverage ratios in the equity market resolve the ‘equity premium puzzle’. Such parameter values can be consistent with finite expected utility and a positive risk-free rate of interest rate. The model performs better for the MP target values than for economically reasonable variations around those values.

Shrinking the Covariance Matrix

The subject here is construction of the covariance matrix for portfolio optimization. In terms of the ex post standard deviation of the global minimum-variance portfolio, there is no statistically significant gain in using more sophisticated shrinkage estimators rather than simpler portfolios of estimators. This finding holds whether or not the investor imposes short sale constraints to prevent portfolio weights from being negative.

On the Use of Numeraires in Option Pricing

This article discusses the underlying theory of the numeraire technique, and illustrates it with five pricing problems: pricing savings plans that offer a choice of interest rates; pricing convertible bonds; pricing employee stock ownership plans; pricing options whose strike price is in a currency different from the stock price; and pricing options whose strike price is correlated with the short-term interest rate.

The Uncertainty Premium in an Ambiguous Economy

Theuncertainty premiumis the premium that is derived from not knowing the sure outcome (risk premium) and from not knowing the precise odds of outcomes (ambiguity premium). We generalize Pratts risk premium to uncertainty premium based on Klibanoffet al.s (2005) smooth model of ambiguity. We show that the uncertainty premium can decrease with an increase in decision makers risk aversion. This happens because increasing risk aversion always results in a lower ambiguity premium. The positive ambiguity premium may provide an additional explanation to the equity premium puzzle.

General equilibrium properties of the term structure of interest rates

Abstract The paper examines the allocation of consumption and investment in a three-date binomial model in order to determine the sign of the real term structure premium in general equilibrium. When production functions are concave, markets are complete, and future production possibilities are the same irrespective of which state of the world occurs, the term structure premium will be positive. In incomplete markets, constant or increasing absolute risk aversion is sufficient to guarantee a positive term structure premium, although in the (more likely) case of decreasing absolute risk aversion a negative premium cannot be ruled out.

Risk, returns, and values in the presence of differential taxation

Abstract We show that there exist separate security market lines (SMLs) for debt and equity securities in an equilibrium with differential taxation of debt and equity. We characterize the conditions under which these SMLs have the same price of risk (with different intercepts) and the conditions under which the tax effect of leverage is linear in debt value as in the adjusted present value method. We explore the implications of our results for cost of capital calculations: How to calculate the cost of capital for debt and equity and how to unlever betas correctly accounting for differential taxation.