A final look at the Strong Draw results for 2011, specifically a look at how Kelly would have fared as a staking system.
While Kelly would have indeed have increased the ROI to 63.9% (versus 19.5% at level stakes), the volatility of Kelly makes this a rather meaningless comparison. Had the final selection of the season been a loss rather than a win, the ROI would have been just 6.6%, a reflection of the huge 3.85 that was available on this game.
Working with a starting bank of £1,000, the biggest draw-down would have been £110.82, and the average stake would have been £98.91, with a high of £175.11 and a minimum of £40.16.
Half-Kelly would have resulted in an ROI of 49.75%, with a draw-down of £39.80, an average stake of £48.37, with a high of £85.96 and a minimum of £19.82.
These numbers are for illustrative purposes only since, in practice, some games are played simultaneously and I have also made no adjustments for commission charges.
At the risk of being stupid, I'm not clear how a Kelly fractional makes a difference to the ROI.
ReplyDeleteFor example, if I employ 1/10th Kelly, all my stakes are 1/10th of the size, as are all my wins and losses - but my ROI remains the same? Instead of +250 +250 +250 -100 -100 -100 -100 -100 -100 from 900 staked in total for example, I have +25 +25 +25 -10 -10 -10 -10 -10 -10 from 90 staked if I use 1/10th Kelly? ROI the same in both cases?
Also if the highest stake was 175.11, surely the biggest draw-down is more than 110.82?
But the stakes are a percentage of the bank, and won't be half in money terms (after the first bet). A 5% loss followed by a 5% gain doesn't result in half the bank of a 10% loss followed by a 10% gain.
ReplyDeleteAs for the draw-down using full Kelly, the lowest the mythical 1000 point bank went down to was 889.18, a draw-down of 110.92 after a sequence 20 losers in 28 bets.