Would You Take This Bet?
I thought I’d introduce a little analytical thinking to the list today. A while back I wrote a post on binary options and efficient pricing models. Much of what we discussed was based on the fundamentals of statistics. For example we said a 50:50 bet with a 100% downside would be efficiently matched by a 100% upside. I want to start a discussion of the practical application of expected values and efficient payoffs.
Let’s use a coin flip example where there is a 50:50 chance of a 50% loss or a 50% gain, a seemingly efficient payout. Consider playing this game 10 consecutive times. For simplicity assume that we get 5 heads and 5 tails. Our payout would be:
Dollar Amount * (1.5)^5 * (.5)^5 = 23.7% of our original investment
This seems counterintuitive to the idea that efficient payouts should have an expected value equal to the original investment. In reality the theory holds that investments of equal size will have an equal payout.
The point here, is be careful on the interpretation of statistics, normal curves and expected values. Even if you find alpha, if you don’t employ the correct strategy you will introduce unnecessary risk. What if you discovered an options spread that pays out 75% gain, 50% of the time and 50% loss 50% of the time? How would you capture the value in this investment. Letting your capital role will result in a decreased value. Assume 10 trials again with 5 heads, 5 tails.
Dollar Amount * (1.75)^5 * (.5)^5 = 51.3% of our original investment
How would you capture this alpha?
No, were not doing your statistics homework.
ALPHA BROOOOOOO
op clearly read that one quant book lol
what about the sequencing of the gains/losses? once you lose 50% of your capital you're not going to recover by making similar bets.
doesnt matter. Example A, lose 50% then gain 50% = you have 75% of what you started with. Example B, gain 50% then lose 50% = you have 75% of what you started with.
I'll bet on anything...I even bet on WWE
you enjoy donkeys
Reminds me of one of my favorite scenes from the movie Dirty Work:
Dr. Farthing: I know there's really nobody to blame for this but myself, well, I don't know, maybe the Buffalo Bills, the Boston Red Sox, or Mr. T or, or the Jets... Mitch: Wait a minute, Mr T.? Are you telling me that you bet on the fight in Rocky III, and that you bet against Rocky? Dr. Farthing: Hindsight is twenty-twenty, my friend
Artie Lange was class in that movie
What if the payout ratios don't stay constant over the 10 trials as is more realistic? Letting the capital roll will lock you into your initial probabilities which may become more favorable than your overall outcome and payout possibilities by the nth trial.
short the fucking thing and hedge the gamma
you're overcomplicating this
threw together a quick iteration (n=10,000) and got north of 200% for E(R). have a look and feel free to modify. there's a chance i missed something.
http://bit.ly/My2pOt
[quote=speedmerchant]threw together a quick iteration (n=10,000) and got north of 200% for E(R). have a look and feel free to modify. there's a chance i missed something.
http://bit.ly/My2pOt[/quote]
Couple of things:
1.) After pressing "Run" that spreadsheet caused my Excel to hang. Thanks bro 2.) That spreadsheet leaks your name and employer in the metadata. I would take this thing down or scrub it if I were you.
whats up with this question though. maybe i just dont understand. youve already fixed the outcome to be 5 heads 5 tails and established that the expected value doesnt care about the combination of gains and losses... where is the strategy? what do you mean by capture alpha? after each round do you have the option to go long or short the next one, or withdraw/deposit notional capital? in that case youd look at the combination of results and exclude the ones that already happened and get a new expected value after each round. but that wouldnt happen in reality because (assuming?) both parties have the same information there would be no market
I am trying to simplify this. The point is even if something has a positive expected value, letting notional principal ride, will always end in a loss eventually. Additional point, sequence doesn't matter.
point #1: yes that is true unless you start with a negative dollar amount or have negative % payouts or let the number of trials go to negative infinity. point #2: yes right again because what really happens is each possible outcome does occur in decoherent universes. quantum ftw
these are really the exact same point. look at the schrodinger eqn. it has a wave in it. you square the wave to get probabilities. the wave has i. when you square those guys you get -1. quantum mech is (only) a generalization of probability theory that says a) everything that can happen does a la point #2 b) your probabilities can have minus signs, a la point #1, and do away with the unintuitiveness of probability theory. which is what you were initially drawing our attention to.
look up "convexity"
right. so as trials approach positive infinity, e(r) approaches -100%. i think this is the only point the op was trying to make. just because you found an opportunity that is seemingly profitable doesn't mean that it will be profitable. you have to implement it appropriately.
if you allow the player to select the number of trials, they could "Win" by stopping the game after they achieve an absolute gain. see below. outcomes are the same but include a win test if the player achieves a gain at any point before trial 10, and decides to stop playing. in this scenario, win probability is ~75%.
.
Here's a special case of what OP was talking about: http://epchan.com/downloads/compound_return.pdf
First of all, you would never find a trade like that. If you did, your best bet would be to diversify the position and play 100 hands, bets, or trades simultaneously (or take your pick of the desired number). If these trades are uncorrelated, you would win virtually all the time. Roughly (.5 x 1.75) + (.5 x .5) = .875 + .25 - 1 = .125 payoff for every dollar invested. Of course, this opportunity doesn't exist
This reminds me a little of the guy who asks this question: You see a guy on the street who has flipped 20 heads in a row. What are the odds that he gets heads on the next flip?
Statistics student: 50% Street smarts guy: virtually zero percent, the coin is obviously weighted
and both answers are FUCKING WRONG
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