Binary options traded outside the U. They offer a viable alternative when speculating or hedging, but only if the trader fully understands the two potential and opposing outcomes. These types of options are typically found on internet-based trading platforms, not all of which comply with U.

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Thorp then took his theory to Las Vegas and ended up making a fortune playing blackjack for years there. He ended up publishing a book on his strategy called Beat the Dealer. Source: Amazon. Thorp eventually stopped betting in casinos and decided to take on Wall St. He co-founded a hedge fund called Princeton Newport Partners. The RHS post described how it turned out:. The results were perhaps the greatest risk-adjusted returns any hedge fund had ever delivered before or since.

Between and Princeton Newport had a compound annualized return of The modified Kelly Criterion for stock market return was as follows:. With the risk free rate being that of short term government bonds and volatility being the standard deviation of returns during the period examined. Using the starting point of when the first ETF was traded in , the authors took a look at the data set of returns. This was assumed to be normally distributed and 9.

Source: RHS Financial. However the RHS authors offered an alternative: invest instead in a lower volatility portfolio. This portfolio returned 9. The Kelly Criterion for this low volatility portfolio would be Take a look at the plotted returns over the period examined below.

Source: CNBC. The author cautions that these are not realistic portfolios due to practical matters such as the rates that brokers charge for margin and limits on leverage etc. However this is limited thinking. As I pointed out in my last post , leverage can also come from real estate, especially if you are renting your properties to cover part or all of the costs.

At this time, you can re-lever up through re-financing. A portfolio like half Kelly is often described as investing at half the allocation of the peak. However, Kelly is usually presented as the presence or absence of leverage cash. Doing so makes makes this problem go away.

So we start there and then return to the unlevered problem. From a scale perspective they are interchangeable, and I will flip it in the next chart. It is a smooth curve. Half Kelly is often explained this way, so people think of it as investing with half the recommend position, or investing at half the recommended volatility. The problem is, these metrics are not what Kelly is about. They are secondary. Kelly is about the slope of the geometric frontier. The slope of the curve.

At a full Kelly peak, the trade off ceases to exist. The slope is flat. Full Kelly is a portfolio section criteria which says to invest with more and more risk until additional risk provides no further benefit to the geometric return. Remember, when using leverage the geometric frontier is a smooth parabola.

Its starting slope equals the Sharpe ratio and moves downward to a final slope of zero at full Kelly. Therefore a half Kelly portfolio invests at a slope along the curve equivalent to half the Sharpe ratio. This is a very powerful concept. One that can be applied to all different geometric frontier shapes, not just smooth ones. Take the geometric frontier, and invest at the point where the initial slope has been cut in half and:.

Much of the time, a half Kelly portfolio will pick a spot shortly after the tangency portfolio example 1. This is because the curve bends the most when cash falls out and the curve begins to move along the Markowitz frontier. Therefore the slope is most likely to cross the threshold right above the tangency portfolio.

This risk return trade off warrants taking on more risk. To the point that when the investing world is tame volatility is low , half Kelly can even pick the portfolio on the the far right end of the geometric frontier example 3. The risk return trade off at the end of the curve is still worth taking. Maybe you think half Kelly is too conservative. Sometimes the tangency point is extremely conservative example 2.

At other times the tangency portfolio is still very volatile and risky example 4.

In probability theory, the Kelly criterion, is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The Kelly Criterion is a mathematical formula that helps investors and gamblers calculate what percentage of their money they should allocate to each. The Kelly criterion is currently used by gamblers and investors for risk and money management purposes, to determine what percentage of their bankroll/capital.