Asset Returns, Portfolio Choice, and Proportional Wealth Taxation

Anders G Fr{\o}seth

arxiv: 2603.05264 · v2 · submitted 2026-03-05 · ⚛️ physics.soc-ph · econ.GN· q-fin.EC· q-fin.PM

Asset Returns, Portfolio Choice, and Proportional Wealth Taxation

Anders G Fr{\o}seth This is my paper

Pith reviewed 2026-05-15 15:20 UTC · model grok-4.3

classification ⚛️ physics.soc-ph econ.GNq-fin.ECq-fin.PM

keywords wealth taxportfolio choiceasset pricingtax neutralityCAPMgeometric Brownian motionlocation-scale familySharpe ratio

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The pith

Proportional wealth tax leaves asset prices and optimal portfolios unchanged

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

A proportional wealth tax levied each year on the market value of holdings acts like the government taking a proportional stake in every investor's portfolio. This scales expected wealth and risk down by exactly the same factor, so the return earned per share of any asset stays the same. Because the scaling is uniform, the best mix of risky assets remains the same no matter the tax rate, and both taxed and untaxed investors assign identical prices to every security. The result first appears under geometric Brownian motion returns and then extends to any return distribution in the location-scale family. Under the CAPM it also implies that after-tax betas equal pre-tax betas and that equilibrium prices are unaffected when investors have constant relative risk aversion.

Core claim

The tax is economically equivalent to government risk-sharing that multiplies both mean wealth and volatility by the same constant (1-τ_w). This multiplicative separability leaves the distribution of returns per share untouched, so optimal portfolio weights—including the tangency portfolio—are independent of τ_w. The opportunity set contracts homothetically in mean-standard-deviation space, preserving every portfolio's Sharpe ratio. Consequently both taxed and untaxed investors pay the same price per share for any asset, after-tax betas equal pre-tax betas, and general-equilibrium returns and prices remain unchanged under CRRA preferences.

What carries the argument

Multiplicative separability created by the wealth tax acting as a proportional government stake that reduces expected wealth and risk by the same factor

If this is right

The coefficient of variation of wealth is invariant to the tax rate.
Optimal portfolio weights and the tangency portfolio remain independent of the tax rate.
The wealth tax contracts the mean-standard-deviation opportunity set homothetically while preserving Sharpe ratios.
After-tax betas equal pre-tax betas and the security market line scales uniformly by (1-τ_w).
General-equilibrium asset returns and prices are unchanged under CRRA preferences.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Neutrality would break if taxation shifted to book value, introducing a wedge between market and tax basis.
Liquidity frictions or constraints on dividend extraction could allow the tax to alter effective returns and therefore prices.
The result suggests that a uniform market-value wealth tax could raise revenue while leaving capital allocation unchanged, provided the stated conditions hold.

Load-bearing premise

The tax must be levied uniformly on current market value for every investor with no trading frictions or dividend-extraction opportunities.

What would settle it

Observe whether investors change their portfolio weights or asset prices differ between taxed and untaxed investors after a uniform market-value wealth tax is introduced.

read the original 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. 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Proportional wealth taxes leave portfolio weights and per-share prices unchanged under market-value taxation and frictionless markets, by mapping the tax to a government stake that scales mean and risk equally.

read the letter

The main thing here is that a flat wealth tax on market value acts like the government buying a proportional slice of every investor's holdings each period. Because both expected wealth and its standard deviation get scaled by the same factor (1 minus the tax rate), the coefficient of variation stays fixed, Sharpe ratios are untouched, and optimal weights—including the tangency portfolio—do not move with the tax. The same scaling leaves the price per share the same for taxed and untaxed investors once markets clear. That is the core result, first shown for geometric Brownian motion and then extended to any location-scale return distribution. The Modigliani-Miller check also straightens out the discount-rate inconsistency in Fama (2021), so after-tax betas equal pre-tax betas and the security market line simply shrinks uniformly. The paper states the boundary conditions plainly and lists the three channels (book-value taxation, liquidity costs, dividend extraction) that break neutrality when those conditions fail. The derivations are direct, rest on standard homogeneity arguments rather than fitted parameters, and avoid circular citations. The only real limitation is that everything is theoretical; there are no Monte Carlo checks or empirical illustrations of how often real markets satisfy the universal market-value assumption. That keeps the practical reach modest but does not undermine the internal logic. Readers working on tax effects in asset pricing or public-finance models of portfolio choice will find the invariance conditions useful and the Fama correction worth noting. The work is coherent on its own terms and deserves a serious referee.

Referee Report

0 major / 2 minor

Summary. The paper analyzes the effects of a proportional wealth tax levied annually on the market value of all holdings. It shows that the tax is equivalent to the government acquiring a proportional stake in each investor's portfolio, which scales expected wealth and risk by the same factor (1-τ_w) while leaving returns per share unchanged. This leads to four main results: invariance of the coefficient of variation of wealth, independence of optimal portfolio weights (including the tangency portfolio) from the tax rate, preservation of Sharpe ratios under a homothetic contraction of the opportunity set, and identical willingness of taxed and untaxed investors to pay the same price per share. Results are first derived under geometric Brownian motion, then generalized to the location-scale family of returns. A complementary Modigliani-Miller analysis confirms pricing neutrality, identifies an inconsistency in Fama (2021) on discount rates for after-tax cash flows, and shows that under CAPM after-tax betas equal pre-tax betas with the security market line contracting uniformly by (1-τ_w). Neutrality holds only under universal market-value taxation and frictionless markets; three violation channels (book-value taxation, liquidity frictions, dividend extraction) are formalized.

Significance. If the derivations hold, the paper provides a clean theoretical demonstration that a uniform wealth tax acts as proportional risk-sharing without distorting portfolio choice or equilibrium prices, with explicit boundary conditions and falsifiable channels for breakdown. The correction to Fama (2021) and the invariance results under standard stochastic assumptions (GBM and location-scale) add value for asset-pricing and public-finance models.

minor comments (2)

The generalization from GBM to the full location-scale family would benefit from an explicit statement of the required moment conditions or a short appendix lemma showing that all relevant ratios remain invariant.
In the Modigliani-Miller section, the identification of the pre-tax discount rate could be cross-referenced to the earlier GBM derivation to make the link between the two approaches more transparent.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the thorough and accurate summary of the paper, the positive assessment of its contributions, and the recommendation to accept. The referee's description correctly captures the core equivalence result, the invariance properties, the generalization to the location-scale family, the Modigliani-Miller analysis, and the conditions under which neutrality holds.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's core neutrality results follow directly from first-principles scaling arguments under geometric Brownian motion and the location-scale family: the wealth tax is mapped to a proportional government stake that multiplies both expected wealth and risk by the same factor (1-τ_w), leaving Sharpe ratios and optimal weights invariant. These steps rely on standard stochastic assumptions and explicit boundary conditions (universal market-value taxation, frictionless markets) rather than fitted parameters, self-citations, or imported uniqueness theorems. The Fama (2021) reference serves only to flag an inconsistency in discount-rate usage, not to justify the new claims. The derivation is self-contained against external benchmarks and does not reduce any prediction to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model rests on standard continuous-time finance assumptions plus the location-scale property for returns; no new entities are postulated and the tax rate enters only as an exogenous policy parameter.

free parameters (1)

wealth tax rate tau_w
Policy parameter that scales wealth and risk proportionally; not fitted to data.

axioms (2)

domain assumption Asset returns follow geometric Brownian motion or belong to the location-scale family
Used to establish multiplicative separability of the tax effect.
domain assumption Markets are frictionless and taxation is universal at market value
Required for the neutrality results to hold.

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discussion (0)

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