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My essays on Advanced Topics delve into some of the more nuanced subjects in Sports Betting, from how to free yourself from 'results-oriented' thinking to understanding how Bayesian Probability calls into question the claims of other touts.

I also explore some basic financial concepts that underlie Sports Investing, as well as how to weigh your options when you have multiple long-term positive expectations on opportunities, from multiple bets to growth in other markets.

## Section 6: The Sharpe Ratio

Portfolio Theory describes an 'optimal curve' of expected return vs. risk, which encompasses all efficient portfolios. The easiest way to define 'risk' is to use the standard deviation of past returns, which tells us how volatile a particular investment has been over its lifespan. Given the choice between two investments of equal expected return, an investor would obviously opt for the less risky choice, and would consider a more volatile option only if there were greater expected returns associated with it.

A simple way to measure risk adjusted return is by using the Sharpe Ratio, which describes the ratio of the difference between the expected return (R) and minus the risk free return (Rf) to the standard deviation (o) of the investment:

The risk free rate varies from year, but consider an example where it is about 3.5%. The long-term return of the S&P 500 is about 10%, with a standard deviation of 16%. This gives the S&P 500 a Sharpe Ratio of (10%-3.5% / 16%) of 0.406.

If we examine the returns of my Combined Football & Basketball picks over the last 10 years, I have an average return of 72.98% (even without factoring in my 55% Strong Opinions) with a standard deviation of 97.08%. We can then use this data to realize that my investment has a Sharpe Ratio of (72.98%-3.5% / 97.08%) 0.715. Thus, not only does investing in my picks have an expected return about seven times higher than the S&P 500, but it also has a more attractive Sharpe Ratio.

An investor can reduce risk of their overall portfolio by holding investments which are not positively correlated with other investments. As the economic crash in 2008 demonstrated, even an investor who has dutifully diversified themselves between different kinds of stocks and real estate found themselves completely exposed when the market tanked in almost all areas. The advantage of sports betting is that it is completely removed from any other market. It's the very definition of zero correlation, and is a fantastic way to diversify any portfolio.

Factoring sports betting into portfolio optimization is a fairly complex task because one must factor in other opportunities and then adjust for risk tolerance. However, given that both the annual return and risk adjusted return (Sharpe Ratio) of my investments are well above those of the S&P 500, it's safe to say that my picks would be a valuable investment for you. I would recommend allocating between 5% and 15% of your annual investing budget to sports betting

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