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Assuming I'm paying long term capital gains tax, what is the break even point where it is more worthwhile to switch from one fund to another?

For (a hypothetical) example, if I have a fund with an expected return of 3.5%, what would be the minimum expected return of another fund to make it worthwhile to pay the capital gains tax and switch to the other fund?

(I'm assuming the answer to this question is an equation involving investment horizon, capital gains tax rate, and my current taxable gains)

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First, some fairly specific partial answers can be given. As Bob Baerker notes, compounding ensures that getting into the higher-return fund is better if the time horizon is long enough. In practice, if you will remain invested for decades, you should switch even for a very small increase in return.

Moreover, regardless of horizon, one scenario in which you should be sure to switch is if the current return r, new return R, and tax rate m satisfy R > r/(1 - m). That is, you should switch if this is true (otherwise, you might or might not want to). For example, if you have a standard long-term tax rate m = 15%, you should switch from r = 3.5% in any case where R > 4.12%. To see this, note that at worst, if you have zero tax basis in the current fund, your capital shrinks by a factor (1 - m) when you sell and pay tax. If R > r/(1 - m), then you come out ahead right away (e.g., in the first year), as your dollar return immediately increases. And compounding will only, um, compound this effect over time.

The general switching criterion for horizon t, expressed in terms of simpler pretax quantities via an algebraic equivalence, is

P*e^(R*t) - m*G*(e^(R*t) - 1) > P*e^(r*t),

where P is the initial capital and G is the initial unrealized gain (i.e., the tax basis is P - G). This has a simple interpretation: The right-hand side (not switching) is the future value of P at return r. The left-hand side (switching) is the future value of P at return R, minus the cost of having to pay the tax m*G now instead of later.

Note: I am assuming that the tax rate is constant over time. Also, I am treating the "expected" returns as if they are guaranteed, and neglecting volatility and risk tolerance.

  • Consider me dazzled :->) – Bob Baerker Nov 28 '18 at 15:02
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Your assumption is correct. There are a number of variables required to construct an equation and simply providing a expected return of 3.5% in the current fund is insufficient information.

You'd need to provide more data:

  • How much is the capital gain?
  • What's the tax rate on it?
  • What's the time frame going forward? You can't have an open ended time period because the second fund with a higher return breaks even after a certain amount of time and then becomes profitable.
  • The tax rate can fluctuate between 0-20% based on income. I'm trying to understand the other two variables as, well, variables. I'm hazarding a guess it's possible to figure out the relationships without a concrete figure. – James Kraus Nov 28 '18 at 3:29

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