post on -EV hedging

[crockpot]

for those of you who don't read my blog (and there's hardly an excuse for that [img]/images/graemlins/grin.gif[/img]), i wrote a long-winded post on hedging and when it is correct to do so at the cost of EV.

borderline spam? maybe, but i spent an hour writing it, so the hell with the rules.

[jelly]

Good read.

It touches a field I have been thinking about lately - futures bet sizing. I am convinced that you should overbet Kelly and the main reason is an opportunity to take -EV hedge later, when your equity raises. If this sounds heretic to you, just imagine you bet Kelly and your 100-1 dog reaches the finals. Hedging seems obvious here. So if you are going to hedge anyway (betting less to avoid hedging makes no sense), you might as well bet more preseason.
I am going to dig into the math as the hockey season approaches, so I would like to hear anyone's thoughts before I do.

[calmB4storm]

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betting less to avoid hedging makes no sense

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Can you explain why? It seems like that makes perfect sense.

[jelly]

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betting less to avoid hedging makes no sense

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Can you explain why? It seems like that makes perfect sense.

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Because if you never had an opportunity to hedge (say you went to trip to Mars during the entire season), you would still correctly bet what Kelly told you to bet.
The fact that hedging before the final game is correct does not imply that original wager was too large.

[Performify]

Thanks for posting, Crockpot. Good stuff...

-P

[Thremp]

All,

You shouldn't use Kelly when betting futures as they aren't independent events. If you bet only WS winners, one winner precludes all others from winning ergo each bet provides a hedge against another, this allows larger than Kelly units in and of themselves before you even get into overbetting teams to hedge etc.

[NeedATimeMachine]

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Thanks for posting, Crockpot. Good stuff...



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[jelly]

Let me give you an example. I know that evenly matched final is not likely, but it is easier to follow. It proves the point anyway, you can run your numbers, if you want to.

Your bankroll is $10,000 (BR=10000) and you get +10000 (Future_odds or F=100) on a team that you handicap as 50-1 shot and you bet 1% of you BR as Kelly recommends (Bet=100). You get hibernated and wake up before the final, where your team meets equally skilled opposition. So you can hedge at -110 if you want to (Hedge_odds or H=10/11)

1) What is your EV if you let it ride?
0.5*$20100+0.5*$9900=$15000

2) What is your net worth at the moment?
It is your BR if you hedge completely, giving up some EV.
Say you bet Hedge

BR(future wins)=BR(future loses)
BR + Bet*F - Hedge = BR - Bet + Hedge*H
Bet * (1+F) = Hedge * (1+H)
Hedge = Bet * (1+F)/(1+H)

Hedge = $100 * (1+100)/(1+ 10/11)
Hedge = $5290

So BR(full hedge) = BR + Bet*F - Hedge = $14710

3) Can you let it ride?

Letting it ride equals to betting $4810 to win $5390

$4810 = $14710-$9900
$5390 = $20100-$14710


If you let it ride, you bet a coinflip at +112.
With $14710 bankroll, correct Kelly size for such bet is $788. Letting it ride bets more than six times as much so you should clearly hedge.

[crockpot]

- your EV is 14950, not that it's really important for this discussion.

- by letting it ride you are essentially betting at +110, since you are refusing to take -110 on the other side.

- i'm not sure that this calculation can be used to find the optimal hedge amount for every example, but it should work here. you want to maximize the geometric mean of your bankrolls after each possible outcome. since you're dealing with a coin flip, you want to maximize BR(win)*BR(loss), which should be done by reducing your risk amount in the championship game to the kelly recommended bet size.

- that said, the idea behind the hedge is that you can risk a higher fraction of your bankroll than you would otherwise. this is especially true for high-ROI longshots. so your example should probably involve the hero betting $200 or so on the team.

[ImStillBen]

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So if you are going to hedge anyway (betting less to avoid hedging makes no sense), you might as well bet more preseason.

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No.