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Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
In this case, expected return is a measure of the relative balance of win or loss weighted by their chances of occurring. For example, if a fair die is thrown and numbers 1 and 2 win $1, but 3-6 lose $0.5, then the expected gain per throw is
Some traders love to focus on a high win rate. The problem is that a few losses (or even just one loss) can fully wipe out the gains made in weeks or months from winning trades, causing huge ...
An example of this effect was seen during economic crises such as the 2008 financial crash, when panic induced sell-offs heavily impacted market stability. The period prior to the Great Recession had a "decade-long expansion in US housing market activity peaked in 2006 [4]," which came to a halt in 2007. As the trends prior to 2008 hinted at ...
More simply, the Pythagorean formula with exponent 2 follows immediately from two assumptions: that baseball teams win in proportion to their "quality", and that their "quality" is measured by the ratio of their runs scored to their runs allowed. For example, if Team A has scored 50 runs and allowed 40, its quality measure would be 50/40 or 1.25.
A loss of $0.05 is perceived as having a greater utility loss than the utility increase of a comparable gain. In cognitive science and behavioral economics, loss aversion refers to a cognitive bias in which the same situation is perceived as worse if it is framed as a loss, rather than a gain.
For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% probability).
Therefore, the replacement effect should be considered when introducing a new model, which will lead to economic leakage and injection. Thus introducing new models requires caution. For example, if the number of new airlines departing from and arriving at the airport is the same, the economic contribution to the host city may be a zero-sum game.