Asset Returns, Portfolio Choice, and Proportional Wealth Taxation

We analyse the effect of a proportional wealth tax on asset returns, portfolio choice, and asset pricing. The tax is levied annually on the market value of all holdings at a uniform rate. We show that such a tax is economically equivalent to the government acquiring a proportional stake in the investor's portfolio each period -- a form of risk sharing in which expected wealth and risk are reduced by the same factor, while the return per share is unaffected. This multiplicative separability drives four main results. First, the coefficient of variation of wealth is invariant to the tax rate. Second, the optimal portfolio weights -- and in particular the tangency portfolio -- are independent of the tax rate. Third, the wealth tax is orthogonal to portfolio choice: it induces a homothetic contraction of the opportunity set in the mean-standard deviation plane that preserves the Sharpe ratio of every portfolio. Fourth, both taxed and untaxed investors are willing to pay the same price per share for any asset. The results are derived first under geometric Brownian motion and then generalised to any return distribution in the location-scale family. A complementary Modigliani-Miller analysis confirms pricing neutrality and identifies an inconsistency in the existing literature regarding the discount rate used for after-tax cash flows. Imposing the CAPM as a special case confirms that after-tax betas equal pre-tax betas and the security market line contracts uniformly by $(1-\tau_w)$; under CRRA preferences, general-equilibrium returns and prices are unchanged. This resolves an error in Fama (2021). The neutrality results depend on universal taxation at market value and frictionless markets. We formalise three channels -- book-value taxation, liquidity frictions, and dividend extraction -- through which these conditions break neutrality.