post on -EV hedging

[Thremp]

HU 4 rollz pls.

[Ganchrow]

I'll invite all those interested in this topic to read my post as SBR Forum entitled Using Kelly to Determine Optimal Hedging Strategy.

[Korch]

nice

[trixtrix]

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Funny stuff.

In short...

Yes, you should constantly be optimizing your portfolio.

No, you do not take on unwarranted risk.

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so, if i may play devil's advocate:

someone offers you +150 on the flip of a fair coin. you know that you will have the opportunity to hedge the other side at +100 later. you would still risk the kelly recommended 25% on the first flip rather than more?

i know that arguing with you is pointless, but i would like to steer the readers away from your incorrect reasoning, lest they follow the stephen a. smith theory that being louder automatically makes you right about everything.

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You find a great opportunity and wish to invest 2% of your portfolio in XYZ Widget Corp at $1/share.

But then you start thinking... You know you can sell your shares later for at least $2 each because there's no possible way your analysis could ever be incorrect or unforeseen events might occur. The world is very predictable and you're smarter than everyone else.

So you take out three mortgages on your house, liquidate the kids' college funds, sell a kidney on the black market, rob the corner store, remove your wife's kidney and sell that, too. You take all these funds and sink them right into XYZ Widget because it's a lock to appreciate. You can just sell them for a profit whenever you feel like remodeling the vacation castle or buying a second yacht for your butler to water-ski behind.

That's sound money management.

That's also why I make a living at this and you sell picks for $10 a week to mouth-breathers and think a 5% edge at +100 is the same thing as a 5% edge at +250.

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you just got a new admirer

your utter contempt >> my utter contempt

[lotus guardian]

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and think a 5% edge at +100 is the same thing as a 5% edge at +250.

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This is true crockpot. You seem to be experienced, why do u size your bets according to your edge and don't consider your odds of winning?

[Hoya]

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and think a 5% edge at +100 is the same thing as a 5% edge at +250.

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This is true crockpot. You seem to be experienced, why do u size your bets according to your edge and don't consider your odds of winning?

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Does that matter when you are placing multiple bets a day over an entire season? I'm far from an expert but it seems to me that it wouldn't.

[lotus guardian]

Yes it matters, that's what optimal bet sizing is for. Your bankroll will grow faster if you bet the optimal amounts.

[Hoya]

So you should bet less on riskier events, even with the same edge? I guess this would be to reduce variance/risk of ruin?

[lotus guardian]

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So you should bet less on riskier events, even with the same edge? I guess this would be to reduce variance/risk of ruin?

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That's correct. Here's a link about that:

http://en.wikipedia.org/wiki/Kelly_criterion

[Ganchrow]

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someone offers you +150 on the flip of a fair coin. you know that you will have the opportunity to hedge the other side at +100 later. you would still risk the kelly recommended 25% on the first flip rather than more?

[/ QUOTE ]Given odds of +150 on a coinflip, while the edge on the bet would indeed be 25%, the Kelly stake would actually be 16 2/3%.

If you knew with 100% certainty that you'd later be able to hedge your position at +100, then assuming zero opportunity cost, the Kelly stake would be 50% of bankroll on the +150 bet and 50% on the +100 hedge. See my Kelly Calculator.

However, just as Ben has (perhaps harshly) indicated, it's probably not realistic to assume that a bettor will later have a 100% probability of hedging at fair value. Within the confines of Kelly one simple way of handling this might be to assume that the bettor will have some probability, call it p, of being able to eventually hedge.

So given the original problem, expected utility (as a function of x and h, where x corresponds to the percentage of bankroll wagered at +150, and h corresponds to the percentage of bankroll (potentially) hedged at +100) maximization problem would look like:

Maximize E(U(x,h))
= 50% * [ p * ln(1 + 1.5x - h) + (1-p) * ln(1 + 1.5x) ] +
50% * [ p * ln(1 - x + h) + (1-p) * ln(1 - x) ]

s.t. x >=0, h >= 0, x + h <= 1

I'll spare you the messy algebra, but what we find is that the budget constraint binds for p >= 2/3. What this means is that for p < 2/3, the bettor will select x such that he'll be able to hedge out all risk if given the opportunity, while for p > 2/3, x will be selected such that the bettor will always retain some risk after hedging.

Here are a few examples of optimal solutions for selected values of p:
p x h
0% 16.67% -
5% 17.54% 21.93%
25% 22.13% 27.66%
50% 32.18% 40.22%
66.67% 44.44% 55.56%
75% 46.01% 53.99%
90% 48.51% 51.49%
100% 50% 50%

Anyway, this is obviously a very simple example, but I think it nicely illustrates the methodology involved in using Kelly to size bets in the face of a potential hedge at a later date. In general, the greater the probability of eventually being able to hedge, the higher the true Kelly stake will be. Realize, however, that this isn't some exception to Kelly, but rather this is is just the solution when the Kelly problem is properly specified.