The turnover ratio is one of those metrics that, in aggregate, probably does more good than harm for the industry, but on the fringes can be entirely misunderstood.

Higher turnover generally implies higher commissions, higher trading costs, and that the strategy is more likely to generate short-term capital gains instead of the preferable long-term capital gains. The short-term capital gains are only half the story on the tax side, however: we should also consider the *forced* realization of gains and thus the forced taxation. A purely passive strategy has the opportunity to compound returns on unrealized gains without being taxed on them until the point of sale. As Albert Einstein said, "compound interest is the eighth wonder of the world."

So high turnover must be a bad thing, right? Like all statistics, the turnover ratio is just a number. In broad strokes, lower turnover may be preferable, but it is not necessarily true. In fact, it is easy to construct cases where an extremely high turnover ratio coincides with a tax efficient strategy.

Consider the following table (and suspend any issues regarding drift for the moment):

Summing month-to-month purchases and sales gives us a turnover figure of 110%. But does 110% tell the whole story? Sure, we made a total number of purchases and sales that *in aggregate *was in excess of our portfolio size, but on the other hand, 90% of the assets in the portfolio never actually moved. 90% of the portfolio was completely static. Take this to the extreme with daily trading and we could create 2520% turnover (assuming 252 trading days in a year) and still have 90% of the assets be completely static.

That's a bit of a conundrum.

For measuring tax efficiency, what we really want to identify is what percent of dollars actually turnover in a year. Beyond marking and tracking each dollar in the strategy, we can simplify by using a system of debits and credits for each asset. We start by assuming the balance for each asset is 0. As allocations decrease, we mark a debit; as allocations increase, we mark a credit. This allows us to track the movement of dollars from one asset into another, assuming a LIFO methodology (in other words, the last share I bought is the first share I sell). So in the above scenario, we get the following cumulative credits and debits table:

What we see, in this table, is that it is really the same 10% sloshing back and forth between Asset A and B. To create a summary statistic from this table, we take the min value from each column and take the sum of absolute values. This methodology gives us the number we are looking for: 10%. Very different from the 110% we originally calculated. A short-cut to this methodology is to simply take the difference between the starting allocation for each asset and its minimum allocation over the period and sum those values.

Unfortunately our number can now never exceed 100%. From a tax efficiency perspective, this is fine: we don't actually care if dollar turnover exceeds 100% – every dollar is getting taxed at the short-term capital gains rate. So to run this methodology over multiple years, we have to do it on a rolling basis. We can then take an average to find the expected dollar turnover within any 12-month period.

We call this summary statistic the *taxable turnover ratio.*

Using the traditional method of turnover calculation on one of Newfound's tactical strategies, we get an annualized turnover ratio of nearly 161% over the entire backtest. Using our new method, we get a taxable turnover ratio of 65% over the backtest. These numbers tell a different story, but together provide a great overview: there is likely to be a considerable amount of trading within the strategy, but only about 2/3rds of the portfolio's dollars are really active in the trading; the other 1/3rd is static.

Of course, no statistic tells the entire story. These averages don't tell us how *clustered* the turnover was over time. For example, did the strategy go years without trading and then have 700% turnover in a year or was it consistent throughout the period? Did the trading occur during periods where we would *expect* the strategy to be tactical, or was it consistent and needless? While the traditional method of measuring turnover can answer a lot of questions about *trading* costs, it leaves plenty of stones unturned relative to measuring the tax efficiency of a strategy.

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