Suppose I have 200$ and I want to track Microsoft's stock (MSFT). For the sake of simplicity suppose I don't pay any commissions and there is no bid/ask spread and no counterparty risk. I have two options:

  1. Buy the stock.
  2. Buy swaps to emulate track the stock (like synthetic funds do).

Now, suppose a 100$ dividend is distributed (of course my stock drops 100$ accordingly).

  1. In option 1, I receive this dividend and pay taxes, say 30$. I reinvest the remaining 70$, so now I have 100$ + 70$ = 170$ worth of stock.
  2. In option 2, I hold no physical stock, so no actual dividend is distributed, and no taxable event occurs. My swap is still worth 200$, since dividends are priced in.

I've been told that the above calculation is incorrect, because taxation is priced into derivatives (e.g. swaps) as well. However, I don't see how that's possible, seeing as different entities are subject to different dividend tax rates (depends on income tax rate for US persons, tax treaties for non-resident aliens, corporations may have different rates altogether, etc.).

Also, the following article seems to support my understanding: http://canadiancouchpotato.com/2012/01/26/tax-efficient-investing-with-etfs/

  • Tax laws differ from country to country. I'm guessing you're from Canada based on the links, so I put a location tag on your question – littleadv Dec 6 '13 at 16:40
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    I'm actually from Israel. We don't have good resources for investment but Canada is similar in some ways (non-US, small economy, etc) so Canadian advice, especially as good as the couch potato, is very helpful. At any rate, specific tax laws are irrelevant. My point is that tax rates can change depending on the shareholder so I don't understand how they can be priced in the derivative. – t0x1n Dec 6 '13 at 20:20
  • It would be nice if downvoters actually commented with the reason. This is a real life question that I need to understand before purchasing synthetic ETFs. – t0x1n Dec 7 '13 at 13:19

No. Black Scholes includes a number of variables to calculate the value of the derivative but taxation isn't one of them. Whether you are trading options or futures, the dividend itelf may be part of the equation, but not the tax on said dividend.

  • Suppose we have two funds, one physical and one synthetic, with the same expense ratio. According to what you say, assuming a negligible tracking error, the synthetic fund will always outperform, will it not ? – t0x1n Dec 6 '13 at 20:54
  • Perhaps, but upon sale, the tax would be due and the advantage would collapse, if I understand your comment. – JTP - Apologise to Monica Dec 6 '13 at 21:02
  • It won't collapse completely, since you'll be deferring the tax, allowing your net investment to compound in the meantime... – t0x1n Dec 6 '13 at 23:52
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    Perhaps, but typical synthetics are pretty time limited, and in the US, Futures are marked to market at year end, so one must pony up each year. If this phenomenon benefits you, by all means take advantage of it. – JTP - Apologise to Monica Dec 7 '13 at 2:02
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    In the US, taxes are due each year on the dividend and cap gain distribution for funds not inside a tax sheltered account. Again, it depends on the investment and the nature of the derivative. – JTP - Apologise to Monica Dec 7 '13 at 14:02

While derivative pricing models are better modeling reality as academia invests more into the subject, none sufficiently do.

If, for example, one assumes that stock returns are lognormal for the purposes of pricing options like Black Scholes does, the only true dependent variable becomes log-standard deviation otherwise known as "volatility", producing the infamous "volatility smile" which disappears in the cases of models with more factors accounting for other mathematical moments such as mean, skew, and kurtosis, etc. Still, these more advanced models are flawed, and suffer the same extreme time mispricing as Black Scholes. In other words, one can model anything however one wants, but the worse the model, the stranger the results since volatility for a given expiration should be constant across all strikes and is with better models.

In the case of pricing dividends, these can be adjusted for the many complexities of taxation, but the model becomes ever more complex and extremely computationally expensive for each eventuality. Furthermore, with more complexity in any model, the likelihood of discovering a closed form in the short run is less.

For equities in a low interest rate, not high dividend yield, not low volatility, low dividend tax environment, the standard swap pricing models will not provide results much different from one where a single low tax rate on dividends is assumed.

If one is pricing a swap on equity outside of the bounds above, the dividend tax rate could have more of an effect, but for computational efficiency, applying a single assumed dividend tax rate would be optimal with D*(1-x), instead of D in a formula, where D is the dividend paid and x is the tax rate.

In short, a closed form model is only as good as its assumptions, so if anomalies appear between the actual prices of swaps in the market and a swap model then that model is less correct than the one with smaller anomalies of the same type. In other words, if pricing equity swaps without a dividend tax rate factored more closely matches the actual prices than pricing with dividend taxes factored then it could be assumed that pricing without a dividend tax factored is superior. This all depends upon the data, and there doesn't seem to be much in academia to assist with a conclusion.

If equity swaps do truly provide a tax advantage and both parties to a swap transaction are aware of this fact then it seems unlikely swap sellers wouldn't demand some of the tax advantage back in the form of a higher price. A model is no defense since volatility curves persist despite what Black Scholes says they should be.

  • Thanks for the detailed (if theoretical) response! If I read you correctly, you're saying factoring in dividend taxation is very complicated, but due to market efficiency it makes sense it will be factored in somehow. – t0x1n Dec 7 '13 at 13:39

It is true that the standard Black-Scholes assumptions do not take into account tax rates. But you can include non-zero tax rates, and will still end up with the Black-Scholes formula, with a different drift, as you are then not in the risk-neutral world anymore, but in the tax world.

There is an old paper from Myron Scholes himself, which explains all the details: Taxes and the Pricing of Options (1976)

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