STOCHASTIC

case to a case of one riskless and one risky asset. It is then easily shown that
a proportional income tax leads to increased demand for the risky assets.
When there are two risky assets and no riskless asset, it is shown that an increase
in taxation will (essentially) lead risk averters to increase their demand for
the risky asset with higher mean.
It is apparent from the Stiglitz and Naslund papers that the effects of
taxation on risk-taking will depend on the investor's formulation of the
portfolio problem (e.g., expected utility versus safety first), on his attitudes
toward risk (e.g., decreasing absolute risk aversion), and on the nature of the
tax itself (e.g., offset provisions). As an extension to the Stiglitz paper, the
reader is invited in Exercise ME-19 to ponder the effects of a progressive
(convex) income tax on the portfolio allocation of an expected utility maximizer.
For additional material regarding taxation effects, the Lepper (1967)
article is recommended. This article examines effects on portfolios of various
loss-offset provisions, progressive rate structures, and capital gains provisions
through the numerical solution of representative problems. See also Russell
and Smith (1970) for a stochastic dominance approach to the taxation problem.
214 PART III STATIC PORTFOLIO SELECTION MODELS