To hedgers: Adding insult to injury

[limit refugee]

Some people are possibly a little crazy...everyone made a risk/reward decision, everybody profited...can't we all get along.

[bgoalie35]

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I think pzhon is my favorite 2+2 poster.

The poster who just called OP pompous is ridiculous. He is pointing out an interesting hedging observation, one that many posters here probably missed. No where is he telling you exactly what to bet, as he notes that is dependent upon your risk tolerance level (3rd paragraph of OP).

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OP made an interesting and informative post on the EV of hedging this promotion. Unfortunately, instead of posting this a week ago when he could have helped the 2+2 comunity, he chose to wait until several hours AFTER the game to enlighten everyone on the value of hedging.

If he posts this a week ago, I thank him for his contribution to the forum. If he posts it when he did, I have to agree he's just being a pompous ass, bragging about what he knew all along.

Disclaimer: If he did post this a week ago, and the hedgers just ignored him and shouted him down, then its your own damn fault.

[thing85]

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OP

you can't figure out what's optimal for others without considering their attitude towards risk

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I believe this to be the correct answer in the thread. I haven't read all responses, so others may have made similarly correct remarks. While maximizing EV is certainly one perspective and certainly a valid one, it is not the only valid one. Like econ_tim has pointed out, the "optimal decision" depends on both EV and attitude towards risk. If I have a 0% risk tolerance, I am hedging 100%, and that is the correct move for me.

I am not a stock trader nor do I think stock trading is gambling per se, but I like to use it as a comparative example. Startup company A's stock will often have an EV higher than that of an established company. Risk, however, is much higher. Which is the correct investment? The answer is, it depends. If I'm creating a short-term portfolio to fund my child's upcoming college education, I may choose the risk-averse, lower EV option.

Similarly, if I know that I need $500 for rent this month and I don't know if I will be able to make that money otherwise, I'm going to take the lower EV, 100% hedged bet to guarantee my rent will be paid on time.

Realize that this example isn't without its flaws, but it illustrates the importance of risk tolerance. EV can't be viewed inside a vacuum.

[JPT III]

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The first half of the full hedge gives you 3/4 of the value, while the last half gives you 1/4 of the value. So, in some sense, the last half is 3 times as expensive as the first half.

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This thread is kind of intriguing to me, although I hate seeing my 2+2 brethren argue over this kind of thing. OP, could you elaborate on the above quote from your original post? I understand the concept of your post (i.e., that a risk aversion that requires a hedge does usually not call for a full hedge) and I agree (or did I misunderstand?). I'm not sure exactly what you mean by the above quote however. How did you arrive at the 1/4 and 3/4 figures? (or where you choosing convenient figures to get a point across?)

Also, in the above quote, when you speak of "1/4 of the value" -- don't you mean "1/4 of the utility"? (as in "benefit"?). After all, I think we agree that one gains no actual "value" by hedging, but rather derives "utility" from reducing one's risk through a hedge. If additional action on the Pitt game added value, it wouldn't be a hedge, it would be arbitrage.

Anyways, I don't mean to be annoyingly technical with your word choice but rather inquire for my own edification. And I'd love to hear from you on how you arrived at the 1/4 and 3/4 figures referenced above.

[grando]

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lol I love how people who let it ride when the line was at -5/-4.5 talk about how the hedgers gave up EV

when the line moved to even hedging when it was -5/-4.5 was much much more +EV than letting it ride at -5/-4.5 was

nice suckout fish

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Ummmm, if I am Pitt -5, how does hedging with Miami +1 do me any good? I had planned on hedging, but I didn't expect the line change so quickly. To say we were stupid not to hedge once the line changed only shows how ignorant you are.

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no, the reason people hedged was to avoid situations like this - I didn't say people were stupid anywhere - learn to read please

hedging at -5/-4.5 was a choice people made - I have NO CLUE why the people that didn't hedge are getting so mad and rubbing it in the hedger's faces, especially since people getting it at -5/-4.5 lucked out hardcore

everyone won money who cares, seriously

[flight2q]

pzhon, you are one of the few thinking about it the right way! But your numbers are a bit off.

advantage of reduced hedge is 0.05
standard deviation of reduced is 1.05
full hedge is 523.8 to win 476.2
(assume -110 and perfect hedge; e.g. -4.5 and +4.5 or -1 and +1.5)

neutral bankroll if only full or no hedge possible
is 5775 (full Kelly)
neutral bankroll if only full or no hedge possible
is 23100 (if believe in 1/4 Kelly)

(bankroll includes both the 1100 and the 476.2)

correct amount to hedge (full Kelly, 476.2 is full hedge)
BR hedge
1600 404
2500 363
4000 295
7000 159
10k 23
10.5k 0

If someone has a bonus at a book, then if it is not used for the hedge, then it can only be gotten by making other wagers (hence, more risk). But this is a tiny factor, assuming the bonus could be cleared by making a flock of tiny wagers.

The other possibility is if someone with quite limited funds needs to deposit for a bonus before the 476 will be realized. But people in that situation are the ones who will be wanting to hedge near the full amount anyway, so they should just deposit what they have and hedge with it.

[pzhon]

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you can't figure out what's optimal for others without considering their attitude towards risk

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In fact, econ_tim, the type of analysis I performed is standard in economics, and it is easy to show that people are acting suboptimally without determining what is optimal. Recall the notion of Pareto efficiency in a related (but not identical) context.

I mentioned that for some people, a 0% hedge was appropriate, for some 20%, and for some 80%. For almost no one was a 100% hedge appropriate. I'm not telling you how much the optimal hedge was for you. I'm telling you that hedging 100% was almost certainly wrong, even if it was better for you than hedging 0%.

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While maximizing EV is certainly one perspective and certainly a valid one, it is not the only valid one.

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It looks like you completely missed the point, and are attacking a straw man argument. I'm not saying hedging is never right, and I stated that I considered hedging here. The V of my EV didn't stand for money, but for utility. I'm saying that many people hedged the wrong amount after making a common error.

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If I have a 0% risk tolerance, I am hedging 100%, and that is the correct move for me.

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No advantage gambler has 0 risk tolerance.

For an advantage gambler, hedging 100% is an inconsistent choice. I don't have to determine the right choice to point out that an inconsistent choice is wrong.

If you recognize that hedging 100% was wrong, but decided it was too much effort to do better, that's ok. Not noticing that hedging 100% was wrong indicates a conceptual error that is likely to be repeated. Being unable to admit that hedging 100% was wrong after it is pointed out and explained by a mathematician is just being dense.

[pzhon]

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The first half of the full hedge gives you 3/4 of the value, while the last half gives you 1/4 of the value. So, in some sense, the last half is 3 times as expensive as the first half.

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OP, could you elaborate on the above quote from your original post?


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In an expected utility context, there is something fundamentally quadratic about risk. Except in contrived situations, the cost of making a wager that is 2 times as large is about 4 times as great, at least for small wagers. Betting $100 on a fair coinflip is like making 10,000 $1 wagers.

More technicaly, let your utility function be V, normalize you initial bankroll to be 0, V'(0)=1 and V(0)=0, and consider the certainty equivalent of a fair coin-toss. For sufficiently small fair coin-tosses for $x, the expected value (utility) of the gamble is about
-x^2 V"(0)/2
~ V(- 1/2 x^2 V"(0)).

So, the certainty equivalent of wagering $x on a fair coinflip is about $-1/2 x^2 V"(0). That's the damage to our utility by wagering $x, expressed in $. The certainty equivalent of wagering $2x is about 4 times worse, $-2 x^2 V"(0). You should be willing to pay up to about $3/2 x^2 V"(0) to reduce the $2x bet to $x, but only about $1/2 x^2 V"(0) to reduce the $x bet to 0.

The first half of the hedge bet costs just as much as the second half of the hedge bet, but it gives you 3 times as much of an improvement in your certainty equivalent. The first 1/10 of the hedge bet gives you 19 times as much of an improvement as the last 1/10.

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I understand the concept of your post (i.e., that a risk aversion that requires a hedge does usually not call for a full hedge) and I agree (or did I misunderstand?).


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That's it.

Also, people may see a +EV option relative to some base point, and choose it without considering whether this is the best option.

[Mark L]

phzon,

you are wrong. the hedgers not only lowered their variance but also increased their EV quite significantly (over $200) through bonuses.

[Blowup Doll]

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phzon,

you are wrong. the hedgers not only lowered their variance but also increased their EV quite significantly (over $200) through bonuses.

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Non-hedgers could get the same bonuses.