A Simple Note on Taxation and Risk-Taking

Abstract

It has been shown that, under a variety of conditions, the imposition of an income tax with full loss offset leads to an increased demand for risky assets. The tax reduces potential gains, but it also reduces potential losses; and the latter seems to be enough to induce more risk-taking in many cases (see Mossin, 1968). However, there are cases in which the effect of taxation on risk-taking appears to be ambiguous. Stiglitz (1969, pp. 273-274) notes that the effect of taxation on risk-taking is ambiguous when a secure asset has a positive return and an investor's attitude towards risk implies a decreasing coefficient of relative risk aversion. Ahsan (1974, p. 322) notes ambiguity when an investor is permitted a lump-sum deduction from taxable income and his attitude towards risk implies an increasing coefficient of absolute risk aversion. The purpose of this note is to show that, by considering a different aspect of an investor's attitude towards risk, one can state conditions under which income taxation increases risk-taking even in these two apparently ambiguous cases. Specifically, the paper is concerned with the effect of an uncompensated increase in a marginal tax rate under a taxation formula that encompasses these two apparently ambiguous cases. It does not consider cases in which there is compensation of various kinds for an increase in the marginal tax rate or for other changes in a taxation formula. Hanson and Menezes (1968), Menezes and Hanson (1970) and Zeckhauser and Keeler (1970) have independently defined and interpreted a measure of risk aversion that Hanson and Menezes call the coefficient of partial risk aversion. An investor whose utility function reflects increasing partial risk aversion is one willing to pay an insurance premium that increases more than proportionately with an increase in a potential loss (Zeckhauser and Keeler, 1970, p. 662). It is shown in Section I that a result due to Stiglitz directly implies that, if an investor's utility function reflects increasing partial risk aversion, then increasing the marginal rate of income taxation increases the demand for a risky asset whether or not a secure asset has a positive return and whether or not an investor is allowed an exemption to taxable income. Section II employs some implications of increasing partial risk aversion to explain why income taxation's effect of reducing potential losses outweighs, in a sense, its effect of reducing potential gains when it leads to an increased demand for a risky asset.