Abstract

Does a Liquidity Trap Exist from the Point of View of Portfolio Theory?

In macroeconomics, liquidity traps are assumed to exist without microfoundations, and the Japanese crisis has made liquidity traps a subject for discussion again. For this reason, this article discusses for two types of assets (money and securities) the issue of whether liquidity traps exist from the point of view of portfolio theory within the framework of a classical mean-variance approach. A stochastically inflationary investment environment and an investment behaviour without money illusion is assumed. The result is negative insofar as liquidity traps can be precluded as long as the expected difference between the rates of return on the two asset types is positive in favour of securities. Liquidity traps can also be precluded as long as the risk pertaining to the rate-of-return differential plays a negative role, i. e. as long as the risk is above zero while risk aversion holds. For a liquidity trap to exist, it is necessary that there either is no risk at all (standard deviation of zero of the rate-of-return differential) or that investors show no risk aversion. A non-positive (i. e. a negative or a zero) nominal rate of return on fixedinterest securities would be necessary and sufficient to permit the existence of a liquidity trap in an environment of risk aversion, of a secure rate-of-return differential as well as of a secure zero nominal rate of interest on the money asset. Against the background of a zero expected capital-value change, customary in macroeconomics, this means that a liquidity trap is only possible where the nominal rate of interest is either zero or negative.

The constellation referred to as liquidity trap in the macroeconomic literature (flat curve of the money demand function and a positive nominal interest rate above zero) implies from a portfolio theory point of view that there is no liquidity trap, but a security trap.

If the literature on macroeconomic theory continues to maintain the notion that a liquidity trap may occur when interest rates are positive, it will be necessary to admit capital-value changes and to abandon the assumption that interest rates represent opportunity costs of money holding at the same time. The very moment capital value changes are admitted, it is logically unavoidable to abandon such an assumption. From a portfolio-theory point of view, macroeconomic theory is therefore confronted with the need either to undergo change or to continue to contradict itself as well as to remain in opposition to portfolio theory.