Optimal Selling Time of a Stock under Capital Gains Taxes

TL;DR

This paper models the optimal timing for selling a stock considering capital gains taxes, deriving a boundary strategy that guides the investor's decision based on stock price, taxes, and volatility.

Contribution

It introduces a boundary-based approach to determine optimal stock selling time under linear capital gains taxes and risk-neutral assumptions.

Findings

Derived a continuous, increasing boundary function over time.

Established the boundary decreases with higher stock volatility.

Provided a clear rule for optimal selling based on stock price crossing the boundary.

Abstract

We investigate the impact of capital gains taxes on optimal investment decisions in a quite simple model. Namely, we consider a risk neutral investor who owns one risky stock from which she assumes that it has a lower expected return than the riskless bank account and determine the optimal stopping time at which she sells the stock to invest the proceeds in the bank account up to the maturity date. In the case of linear taxes and a positive riskless interest rate, the problem is nontrivial because at the selling time the investor has to realize book profits which triggers tax payments. We derive a boundary that is continuous and increasing in time and decreasing in the volatility of the stock such that the investor sells the stock at the first time its price is smaller or equal to this boundary.