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## Sharpe Ratios and Wealth

Returning to the old school, the two main branches found different kinds of market opportunities, distinguished by Sharpe ratio. We're going to get a bit mathematical again, but you don't need the numbers to follow the argument. The Sharpe ratio of a strategy is defined as the return of the strategy minus what you could make investing the same capital in risk-free instruments, divided by the standard deviation of the return. It is a measure of risk-adjusted return. A strategy with an annualized Sharpe ratio of 1 will make more than the risk-free rate about five years out of six. A strategy with an annualized Sharpe ratio of 2 will make more than the risk-free rate about 39 years out of 40. However, it's hard to find Sharpe ratios near or above 1 in high-capacity, liquid strategies that are inexpensive to run.

You don't need a Sharpe ratio near or at 1 to get rich. For a Kelly investor, the long-term growth of capital above the risk-free rate is approximately equal to the Sharpe ratio squared (it's actually always higher than this, substantially so for high Sharpe ratios, but that doesn't affect the points I want to make). A Sharpe ratio of 1 means growing at 100 percent per year—that is, doubling your capital. A Sharpe ratio of 2 means growing at 400 percent per year. (For the purists, the actual figures are 173 percent and 5,360 percent.) Clearly both of those strategies will have to hit some kind of short-term limit. In fact, Sharpe ratios above one are ...

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