Without knowledge of probabilities laws (the language of uncertainty) the risk reward balance can be a real challenge for intuition in investment decision making . To some extent there are aspects that are hidden, like the risk of a long run of losses. Computer simulations of 1000 bets for particular values of win% and av profit per bet can produce some suprising outcomes. One general point is that one should be prepared for a losing run that is more than twice the average losing run. Kelly maths is now used in stock markets as well as by betting syndicates. Its based upon proven probability laws. Whilst no maths can be used to calculate a staking plan to turn a loss making policy into a profitable one, it can assist in boosting profits of a profitable one. Most other discussed staking schemes fail the simulation 1000 bets test. VDW once proposed a staking method that produced disasterous results in the test. Later there was speculation that he was using dutching stakes, splitting a usual bet on one horse to cover several horses when the edge and strike rate of each horse warrants it; much better. Kelly maths showed that one should bet a proportion of the current bank. But full Kelly staking needs nerves of steel. I've used 0.5 x Kelly stakes that gives more stable stakes and bank. It gives slightly less profit but significantly reduces the risk of ruin. Thats for a single investment policy. If one has several policies with differing SR & Edge, its probably best to stake each as indicated by their separate stats.
Absolute "True" Kelly is a much misunderstood concept in A v
k type markets (multi-competitor sports such as horse racing), no matter what divisor you use, full, half, quarter etc, reason being that when John L. Kelly worked on that paper between 1956-58 he only used an A v
b type market scenario. It is a myth that serious big Kelly type bettors such as Benter, Woods, Zeljko/Walsh, Warren Buffett, Ed Thorpe, Charlie Munger, Bill Gross and probably the greatest of them all in any market type scenario - James Simons - bet only "overlays" determined by "perceived edge obtained". They also bet a proportion of slightly optimal "underlays" (usually ranked by "EV" in market order) based on their own personal risk/reward ratio. This retains "skin in the game", maximises "churn" in a turnover sense and negates some of the much maligned Risk Of Ruin (ROR) concept.
The original work that preceded much of Kelly's work at the Bell Labs industry in that time period was based on Claude Shannon's work on "information theory" and was based on a system that analysed information over networks. By far the biggest "driver" in the use of "True" Kelly type betting and it's related variations constructed over the years are a heavy reliance of the accuracy of the pre-outcome probabilities used in forecasting. Authors like Nick Mordin and others have over the years in print tried to simplify "Kelly" but have remained stuck to the single outcome scenario of the A v
b type market example used in Kelly's original paper hence causing some of the confusion.
So far it is the only known system of staking in any risk related venture to offer full mathematical proofing. For example, one major error still used in daily publications of stock exchange pricing such as Nasdaq, MorningStar etc is the use of this part of the formula - Kelly % = W – [(1 – W) / R], where W is the win probability and R is the ratio between profit and loss in the scenario. This is simply incorrect and does not account for "volatility" (which is the magnitude of potential profit/loss) but only their ratio to each other and only works in a market where bets are "binary". Changing that very small part of the formula to - Kelly % = W/A – (1 – W)/B, where W is the win probability, B is the profit in the event of a win, and A is the potential loss, minimizes the "downside scenario" of the formula. This is because in stock exchange pricing the downside-scenario probability must be set to the probability of a total capital loss, not the much larger probability of
some loss.
Any better
mick ?? - the 3 paragraphs are connected in a way.