Tax-loss harvesting: Decomposing sources of tax benefits with an interactive tool, Part II

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In this next installment of our series on tax-loss harvesting, we explore three sources of tax-loss harvesting benefits in greater detail, following up from the previous post, Part I1:

  1. Pre-tax compounding: Tax Loss Harvesting(TLH) strategies generally do not realize gains. By holding on to unrealized gains, the investment returns compound at a pre-tax return level.
  2. Time value of deferral: Investors save taxes by utilizing the tax losses to offset gains in other investments, making the investor’s overall asset allocation more tax efficient. The tax savings today would be reinvested to high-yielding investment opportunities while paying the taxes later when you unwind the investment.
  3. Long-term vs short-term tax rate differential: When a TLH strategy generates a short-term capital loss (STCL), it offsets any short-term capital gains (STCG) you have, saving you a larger amount of taxes since the short-term capital gains tax rate is higher than the long-term capital gains tax rate.  And if you then invest the proceeds from the tax savings holding for a longer-term horizon, you may end up paying taxes at the long-term rate.

Interactive calculator for tax-loss harvesting benefits2

Quantinno presents a simple interactive tool so that our readers use their own assumptions and gauge the impact on the value of tax-loss harvesting.

Let’s define variables under the Assumptions section:

  • STCG (short-term capital gains) tax rate = \(t_{st}\)
  • LTCG (long-term capital gains) tax rate = \(t_{lt}\)
  • Beginning wealth (the initial dollars invested) = \(W_{0}\)
  • Pre-tax investment return (enter your expected return for your portfolio aside from any tax considerations) = \(r\)
  • Holding period (number of years portfolio will be held) = \(N\)
  • Tax-loss harvesting applied at the beginning (enter the amount of the beginning wealth that is subject to tax-loss harvesting, in dollars) = \(TL\)
  • Post-tax investment return (investment returns compounded, if need to pay taxes along the way assuming long-term tax rates) = \(r \cdot (1-t_{lt})\)

To decompose the sources of tax-loss harvesting benefits, let’s define 4 distinct scenarios, A, B, C and D.

  • (A) Base – pay taxes at the long-term capital gains tax rate each year as the investment earns returns (post-tax compounding).
  • (B) Compounding – while the investment earns returns, there are no taxable gains realized/distributed. As a result, the investment compounds at the pre-tax rate and then pays the long-term capital gains tax rate at the liquidation.
  • (C) TLH w/ LT – utilize tax losses at the beginning (offsetting current long-term capital gains elsewhere) and reinvest the tax savings, compound at the pre-tax rate, and pay the long-term rate at liquidation.
  • (D) TLH w/ ST – utilize tax losses at the beginning (offsetting current short-term capital gains or ordinary income elsewhere) and reinvest the tax savings, compound at the pre-tax rate, and pay the long-term rate at liquidation.

Let’s go through what each line item means.

  1. Start with $1,000 beginning wealth, \(W_0\)
  2. How much tax savings from the tax losses = \(TL \cdot t_{lt}\) or \(TL \cdot t_{st}\)
  3. Reinvest the TLH tax savings into your investment portfolio.
  4. The portfolio compounds over the holding period (e.g., 20 years) at the assumed reinvestment rate (e.g., 5%). For base case A, it needs to pay taxes along the way at the LT rate and compounds at the post-tax rate, which is 3.81% = 5% * (1 – LTCG tax rate 23.8%). For the rest of the scenarios, it utilizes a tax-efficient TLH strategy to compound the investment at a pre-tax rate, which is 5%.
  5. Liquidate at the end of the horizon and pay LT taxes (including TLH used at the beginning), except for the base case.
  6. After-tax wealth, which is (4) – (5).
  7. Decomposition: pre-tax compounding = \(W_N^B - W_N^A\)
  8. Decomposition: time value of deferral = \(W_N^C - W_N^B\)
  9. Decomposition: LT vs ST rate differential = \(W_N^D - W_N^C\)

The after-tax wealth at the end of the holding period for each scenario is defined as follows:

  • \(W_N^A = W_0 (1+r(1 - t_{lt}))^N\)
  • \(W_N^B = W_0 (1+r)^N - (W_0 ((1+r)^N - 1)) \cdot t_{lt}\)
  • \(W_N^C = (W_0 + TL \cdot t_{lt}) \cdot (1+r)^N - ((W_0 + TL \cdot t_{lt}) \cdot ((1+r)^N - 1) + TL) \cdot t_{lt} \)
  • \(W_N^D = (W_0 + TL \cdot t_{st}) \cdot (1+r)^N - ((W_0 + TL \cdot t_{st}) \cdot ((1+r)^N - 1) + TL) \cdot t_{lt} \)

The benefit of tax-loss harvesting is substantial over time and all three components add significant value.

So, when TLH is not adding value? Let’s change numbers on the interactive tool above. Set the reinvestment rate to zero (this is the nominal rate, which means the real return of investment after inflation is negative for a very long time), and then set the ST rate the same as the LT rate, say 40.8% for both. Now, you see the tax benefit of TLH is zero.  Outside the extreme scenario where the United States would have to experience a prolonged period of negative real rates, TLH can improve investor’s after-tax wealth in a significant way.

1. The information provided herein is presented as a summary of potential benefits of tax-loss harvesting and does not purport to be a full description of the strategy and the investment considerations related thereto. The information contained herein is based on Quantinno’s market research and views and actual results may vary materially. There is no guarantee that any investor will achieve the results described herein. Prospective investors are urged to consult with their advisors prior to making an investment in any tax-loss harvesting instrument, including a Quantinno-sponsored vehicle.

2. These examples are purely hypothetical and are included only to illustrate the potential benefits of tax-loss harvesting. They should not be construed as an indication of performance or the effectiveness of tax-loss harvesting in actual market conditions. The information in this example is based on many assumptions that are not expected to reflect actual events that will occur. 


This post is not intended or presented as investment advice, and any discussion of a particular investment should not be construed as a recommendation of such investment. Readers should consult their own tax, legal, accounting or financial advisors before engaging in any investment transaction.

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