### Optimal Position Sizing

Vince suggests that every position has an optimal f, where the investor maximizes return over a long time frame. He essentially generalizes the Kelly criterion to the typical situation that a trader faces. The Kelly criterion, developed by engineers at Bell Labs in the late 1940s, in order to resolve the problem of data transmission over long-distance lines, can be reapplied in the context of geometric growth, and how it applies to money-management, as both problems “are the product of an environment of favorable uncertainty”. With some basic back testing, a trader gets a sense of what may happen to a position and whether it is worth putting one on. The values generated during back testing can then be used as inputs into Vince’s formulas. Vince uses an empirical approach based on statistical distributions to calculate the optimal f for a particular position. If trader uses of value below optimal f, he will be generating less returns than he could be, assuming a particular investment is modeled as a time series, generating P&L of a certain mean and standard deviation, i.e. a statistical distribution of returns. If the trader is above his optimal f, he runs the risk of complete wipeout, due to his position sizing. This means that a few losses in a row can completely take him out of the market. This modeling of a particular position as a random walk provides a framework for calculating its optimal size.

With this approach, Vince is essentially talking about the amount of leverage being put on a position. While leverage increases the total amount of return, it can also increase total losses. Assuming a particular position continues to follow a random walk according to certain patterns, patterns which can then be described mathematically, it becomes possible to optimize returns via the size of the position. Because the approach is largely empirical, it is rather simple to also include the effect of transaction and financing costs, and their implications for the position size.

Key takeaways:

1. traders should strive to maximize geometric, but not arithmetic growth, in positions
2. the actual approach to position sizing depends on the total value of your portfolio
3. classical folio construction, Markowitz, can be superseded by newer models, which take into account the properties of the new asset classes, including derivatives

While in theory, he is right, in practice, I think he is avoiding a few important issues. Position sizing based on historical performance implies that all of future performance will follow the same distribution. This is not necessarily the case, and can be hazardous to your health. Also, you cannot assume that you’re operating environment will always be the same, particularly when trading in a bull market. For example, just because it is easy to enter into and exit transactions in a bull market, when sentiments go south, you can be stuck with positions in which you know will continue to lose money for you, but that you cannot sell; therefore, more conservative position sizing is in order.

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