Asset Returns, Portfolio Choice, and Proportional Wealth Taxation

Abstract

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: (i) the coefficient of variation of wealth is invariant to the tax rate; (ii) optimal portfolio weights are independent of the tax rate; (iii) the wealth tax is orthogonal to portfolio choice, inducing a homothetic contraction of the opportunity set that preserves the Sharpe ratio of every portfolio; (iv) taxed and untaxed investors price assets identically. Results are derived under geometric Brownian motion and generalised to the location-scale family. A Modigliani-Miller analysis confirms pricing neutrality and identifies an inconsistency in the literature regarding the discount rate for after-tax cash flows. Under CAPM with CRRA preferences, after-tax betas equal pre-tax betas and the security market line contracts by the tax factor; general-equilibrium prices are unchanged. This resolves an error in Fama (2021). The neutrality results depend on three conditions commonly violated in practice: universal taxation at market value, frictionless markets, and dividend consumption. We formalise three channels through which relaxing these conditions breaks neutrality: book-value taxation, liquidity frictions, and dividend extraction, and show they have opposing effects on asset prices.

Figures (4)

• Figure 1: The proportional-dilution mechanism. At each period end, a fraction $\tau_w$ of the investor's shares is transferred to the government as tax. The share price process $P_t$ is unaffected. After $n$ periods, the number of shares has decayed by the deterministic factor $(1-\tau_w)^n$, while the return per share remains $P_n/P_0$---identical for taxed and untaxed investors.
• Figure 2: Orthogonality in continuous time. The wealth tax translates the entire opportunity set vertically by $-\tau_w$: the efficient frontier, the risk-free rate, and the capital allocation line all shift down by the same amount. The tangency portfolio $T$ moves to $T'$ at the same volatility $\sigma^*$---the tax is orthogonal to portfolio choice.
• Figure 3: Orthogonality in discrete time. In the $(\sigma, \, 1{+}\mu)$ plane, the wealth tax induces a homothetic contraction of the opportunity set toward the origin by the factor $(1-\tau_w)$. Every point moves radially inward: the efficient frontier, the risk-free gross return, and the tangency portfolio $T$ all contract along their respective rays from the origin. The slope of the capital allocation line---and hence the Sharpe ratio---is preserved.
• Figure 4: The security market line under a proportional wealth tax. The pre-tax SML (solid blue) connects the risk-free gross return $1{+}r_f$ to the market portfolio $M$. The correct after-tax SML (dashed red) is a uniform vertical contraction by $(1{-}\tau_w)$: both the intercept and the slope are scaled down, preserving the Sharpe ratio and all betas. Fama2021's (Fama2021) implicit SML (dotted grey) shifts upward by $\tau_w$, adding the wealth tax to the cost of capital while keeping the risk-free rate unchanged; this overstates the required return because it does not account for the wealth tax on the discount rate itself. Parameters: $r_f = 0.04$, $\text{MRP} = 0.06$, $\tau_w = 0.15$ (exaggerated for visibility).

Theorems & Definitions (36)

• Proposition 1: CV Invariance, GBM
• Remark : Risk sharing
• Proposition 2: Portfolio Invariance, GBM
• Proposition 3: Orthogonality, GBM
• Proposition 4: Pricing Neutrality, GBM
• Remark
• Proposition 5: Generalised CV Invariance
• proof
• Remark
• Proposition 6: Generalised Portfolio Invariance