The Equivalence between State Contingent Tax Policy and Options and Forwards: An Application to Investing the Social Security Trust Fund in Equities

Abstract

ABSTRACT Government guarantees are often priced by appealing to an analogy with option pricing techniques pioneered by Black and Scholes (1973) and Merton (1973). Of course, in reality, the government does not purchase options in the open market. Instead, barring a Ponzi game opportunity, the government must adjust tax revenue or spending in response to shocks in the value of the asset being insured for the government to maintain its intertemporal budget constraint. Nonetheless, this article derives an exact mathematical relationship between fiscal policy and option pricing. Explicitly deriving the option pricing equivalence from first principles proves that the analogy is, in fact, correct and suitable for use by public finance economists and government officials to estimate the cost of government guarantees. Starting from first principles also has the benefit of showing that an additional mathematical term, which multiplies the option price, is necessary to capture the pay-as-you-go nature of most perpetual governme nt guarantees-- a term that is missing in the previous work. The author develops the analysis in the context of a highly relevant example: investing the Social Security trust fund in equities. Advocates of this policy have argued that the higher expected returns would help prefund future benefits and, therefore, would require less of a tax increase on future workers. Several government agencies have scored hypothetical legislation and have concluded likewise. The results herein show just the opposite. By focusing on expected returns, trust fund investment creates an instant windfall for current workers and is mathematically equivalent to a tax increase on all future workers, relative to a baseline policy of maintaining the current payroll tax rate. National saving is reduced. The author computes President Clinton's proposal to invest in equities to be equivalent to increasing the future payroll tax by 0.8 percent in perpetuity. A policy recommendation to invest about 40 percent of the trust fund in stocks analyzed recently by the Social Security Administration is equ ivalent to a 21 percent increase in the future payroll tax. INTRODUCTION As Robert Merton noted in his Nobel address, the use of option pricing technology has extended well beyond financial operations and has been used in numerous valuation problems, including government guarantees. The list is extensive and includes deposit insurance, student loan guarantees, loans to business, the government right to change quotas, and many other guarantees. [1] Of course, in reality, the government does not purchase options for the purpose of hedging. Instead, barring a Ponzi game opportunity, the government must adjust tax revenue or spending in response to shocks in the value of the asset being insured for the government to maintain its intertemporal budget constraint. Government policy then becomes state contingent and the government's intertemporal budget constraint must be taken explicitly into account. Although most analyses of guarantees rationalize using options pricing based on an analogy, this article starts with fiscal policy instruments and proves that the analogy is, in fact, true--with a modification. The author derives an exact mathematical equivalence between state-contingent fiscal policies and option pricing. Deriving implicit option prices from the government's intertemporal budget constraint not only brings an even greater sense of reality to the case for using arbitrage pricing technology to value government guarantees, but it is also important because many government guarantees are not prefunded. The option pricing formulae must be augmented with a multiplicative term that recognizes the pay-as-you-go nature of most perpetual guarantees. As a relevant example, this article considers the proposal to alter the Social Security trust fund's portfolio from exclusively holding government debt to holding equity as well. …