I completely fail to see the point of your first example. Obviously if the amount you bet is so insignificant that you're literally indifferent between winning the money or losing it, then the bet doesn't hedge anything. But who cares, and why have a table to work that out?
So I will comment on the one example that I can speak somewhat fluently on, which is Thought experiment #2.
In the modern economy, hedges are publicly traded as well as the stocks. It is impossible for one to rise in value without the other falling, simply because information is public. If the executive begins to buy huge hedges against his corporations stock, the value of the hedge will rise.
Even if no one knows who exactly is buying these hedges, the price is going up, and so people will either begin to buy hedges as well, thus reducing the gain on them, or they will sell the stock, lowering its price and reducing the gain on the hedge.
Also, buying hedges based on private information would also be insider trading....at least in the US.
**Thought experiment 1 – arbitrage opportunities in prediction market**
You’re Mitt Romney, biding your time before riding in on your white horse to win the US republican presidential preselection (bear with me, I’m Australian and don’t know US politics). Anyway, you’ve had your run and you’re not too fussed, but some of the old guard want you back in the fight.
Playing out like a XKCD comic strip ‘Okay’, you scheme. ‘Maybe I can trump Trump at his own game and make a bit of dosh on the election’.
A data-scientist you keep on retainer sometimes talks about LessWrong and other dry things. One day she mentions that decentralised prediction markets are being developed, one of which is Augur. She says one can bet on the outcome of events such as elections.
You’ve made a fair few bucks in your day. You read the odd Investopedia page and a couple of random forum blog posts. And there’s that financial institute you run. Arbitrage opportunity, you think.
You don’t fancy your chance of winning the election. 40% chance, you reckon. So, you bet against yourself. Win the election, lose the bet. Lose the bet, win the election. Losing the election doesn’t mean much to you, losing the bet doesn’t mean much to you, winning the election means a lot of to you and winning the bet doesn’t mean much to you. There ya go. Perhaps if you put
Let’s turn this into a probability weighted decision table (game theory):
Not participating in prediction market:
|
Election win (+2 value) |
Election lose (-1 value) |
|
40% |
60% |
Cumulative probability weighted value: (0.4*2) + (0.6*-1)=+0.2 value
participating in prediction market::
|
|
Election win +2 |
Election lose -1 |
|
Bet win (0) |
0 |
60% |
|
Bet lose (0) |
40% |
0 |
Cumulative probability weighted value: (0.4*2) + (0.6*-1)=+0.2 value
They’re the same outcome!
Looks like my intuitions were wrong. Unless you value winning more than losing, then placing an additional bet, even in a different form of capital (cash v.s. political capital for instance), then taking on additional risks isn’t an arbitrage opportunity.
For the record, Mitt Romney probably wouldn’t make this mistake, but what does post suggest I know about prediction?
**Thought experiment 2 – insider trading**
Say you’re a C level executive in a publicly listed enterprise. However, for this example you don’t need to be part of a publicly listed organisatiion, but it serves to illustrate my intuitions. Say you have just been briefed by your auditors of massive fraud by a mid level manager that will devastate your company. Ordinarily, you may not know how to safely dump your stocks on the stock exchange because of several reasons, one of which is insider trading.
Now, on a prediction market, the executive could retain their stocks, thus not signalling distrust of the company themselves (which itself is information the company may be legally obliged to disclose since it materially influences share price) but make a bet on a prediction market of impending stock losses, thus hedging (not arbitraging, as demonstrated above) their bets.
**Thought experiment 3 – market efficiency**
I’d expect that prediction opportunities will be most popular where individuals weighted by their capital believe they gave private, market relevant information. For instance, if a prediction opportunity is that Canada’s prime minister says ‘I’m silly’ on his next TV appearance, many people might believe they know him personally well enough that it’s a higher probability that the otherwise absurd sounding proposition sounds. They may give it a 0.2% chance rather than 0.1% chance. However, if you are the prime minister yourself, you may decide to bet on this opportunity and make a quick, easy profit…I’m not sure where I was going with this anymore. But it was something about incentives to misrepresent how much relevant market information one has, and the amount that competitor betters have (people who bet WITH you)