# Taxation To Slow Down High-Frequency Speculation While Not Affecting Hedging Activity

But there’s the question of how tiny is tiny. Tobin himself said “let’s say 0.5%.” It wasn’t meant as a well-thought-out number, and it’s certainly far too high given typical bid-ask spreads. So what is a better number?

Trading happens for a number of reasons. Let’s focus on just two, hedging and speculation. Hedging is generally considered to be a good thing, as it is meant to reduce risk. Speculation can be good or bad. In my opinion it’s bad when it happens at such a high frequency that the relationship between the share price of a company and its value becomes irrelevant to making money. So let’s say we want a tax that’s big enough to hamper the shortest-term speculation, while small enough not to affect hedging.

The mathematics of hedging of derivatives in the presence of transaction costs goes back to Hayne Leland (1985) for simple calls and puts. Later this was extended to incorporate any derivatives by Hoggard, Whalley and yours truly. Out of this work comes a simple non-dimensional parameter related to costs, volatility and hedging frequency that tells you how much your hedging will affect you P&L. It’s all in *PWIQF2* if you want the details.

Supposing that you wanted to have less than 1% effect on profitability of a derivative (and that number is open to discussion but is easily well within the margins of model error), and supposing you hedge every day in a market with 20% volatility (again, two numbers that you are free to dispute or change), then the tax could be at most 0.008% of the value of each trade. Around one basis point.

Would this level affect good hedging? No. Would it affect speculation over medium and long term? No. Would it dampen short-term speculation? You bet.

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