# The Effect of Taxation and Uncertain Inflation on the Equilibrium Pricing of Risky Assets

#### Abstract

The purpose of this study is the derivation of an extended capital asset pricing model that incorporates the effect of both taxation and uncertain inflation. The technique utilized is based on the assumption that an investor's utility function can be completely described by the expected value and variance of his end of period wealth. By maximizing the investor's utility with respect to his holdings of the various securities available in the market and applying the equilibrium requirement of market clearance, an expression for the equilibrium expected return on any risky security results. The extended model developed in this manner is stated as: ${\rm \bar R\sb{j} = R\sb{f} + L1Cov(\tilde R\sb{j},\tilde R\sb{m})} -$L2Cov${\rm (\tilde R\sb{j},\tilde R\sb{a})}$ + L3$(\varepsilon\sb{\rm j} - {\rm R\sb{f}),}$ Where: ${\rm \bar R\sb{j}}$ = the expected end of period return on risky security j; ${\rm R\sb{f}}$ = the risk free rate; L1 = the after tax market variability coefficient; ${\rm Cov(\tilde R\sb{j},\tilde R\sb{m})}$ = the covariance between the returns on the risky security and the market portfolio of all risky securities; L2 = the coefficient that weights inflation risk based on total tax adjusted investable wealth and tax adjusted investor risk return tradeoffs; ${\rm Cov(\tilde R\sb{j},\tilde R\sb{a})}$ = the covariance of returns on the risky security with uncertain inflation; L3 = the coefficient that weights the penalty on payment of dividends based on the differential between the ordinary income tax rate and the effective capital gains tax rate; $\varepsilon\sb{\rm j}$ = the certain dividend yield on risky security j.

The conclusion of this study is that the traditional capital asset pricing model that excludes the effects of taxation and inflation may not adequately describe real world equilibrium pricing of risky assets. While the extended model developed in this study does not purport to remove all the deficiencies of the traditional model, it does address some of the criticisms of the traditional model and also offers theoretical support to some previous empirical findings not adequately explained by the traditional model.