Statistik › Långsiktig avkastning › Kelly and over betting
Betting half as much again as Kelly takes your chance of ending below your stake from 7 per cent to 38
| Kelly fraction | Mean final wealth | Minimum final wealth | Chance of ending below the stake |
|---|---|---|---|
| 0.26 | 12,110 | 2,368 | 0% |
| 0.52 | 30,937 | 701 | 0.13% |
| 0.78 | 76,574 | -4,970 | 1.53% |
| 1.05, about full Kelly | 182,645 | -133,456 | 7.37% |
| 1.31 | 416,383 | -6,862,763 | 19.7% |
| 1.57 | 895,952 | -102,513,724 | 37.5% |
Forty annual decisions, 3,000 scenarios, 1,000 dollars initial wealth, investing in equities with a mean of 10.2 per cent and a standard deviation of 20.3 against bills at 3.9 per cent. The full Kelly position is 1.5288 times wealth, financed by borrowing 0.5228. The probabilities in the last column are arithmetic from the published scenario counts. No significance test of any kind is reported; this is a simulation study.
In a forty year simulation on equities against bills, the probability of finishing below the starting stake rises from 7.37 per cent at full Kelly to 37.5 at 1.57 times Kelly, while the arithmetic mean final wealth rises fivefold.
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