# Optimal asset allocation for passive investing with capital loss harvesting

Daniel N. Ostrov, Thomas Wong

Research output: Contribution to journalArticle

### Abstract

This article examines how to quantify and optimally utilize the beneficial effect that capital loss harvesting generates in a taxable portfolio. We explicitly determine the optimal initial asset allocation for an investor who follows the continuous time dynamic trading strategy of Constantinides (1983). This strategy sells and re-buys all stocks with losses, but is otherwise passive. Our model allows the use of the stock position's full purchase history for computing the cost basis. The method can also be used to rebalance at later times. For portfolios with one stock position and cash, the probability density function for the portfolio's state corresponds to the solution of a 3-space+1-time dimensional partial differential equation (PDE) with an oblique reflecting boundary condition. Extensions of this PDE, including to the case of multiple correlated stocks, are also presented. We detail a numerical algorithm for the PDE in the single stock case. The algorithm shows the significant effect capital loss harvesting can have on the optimal stock allocation, and it also allows us to compute the expected additional return that capital loss harvesting generates. Our PDE-based algorithm, compared with Monte Carlo methods, is shown to generate much more precise results in a fraction of the time. Finally, we employ Monte Carlo methods to approximate the impact of many of our model's assumptions.

Original language English (US) 291-329 39 Applied Mathematical Finance 18 4 https://doi.org/10.1080/1350486X.2010.513499 Published - Sep 1 2011 Yes

### Fingerprint

Asset Allocation
Harvesting
Optimal Allocation
Partial differential equations
Partial differential equation
Monte Carlo methods
Monte Carlo method
Probability density function
History
Boundary conditions
Oblique
Numerical Algorithms
Investing
Optimal asset allocation
Continuous Time
Quantify
Costs
Computing
Model

### All Science Journal Classification (ASJC) codes

• Finance
• Applied Mathematics

### Cite this

In: Applied Mathematical Finance, Vol. 18, No. 4, 01.09.2011, p. 291-329.

Research output: Contribution to journalArticle

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