Is there a fundamental reason that some random elements can’t be cancelled out? Can’t you specifically hedge against the ultimate value of your first contract, thus nullifying any risk?
The phrasing incidentally is still a bit off. LH and LT are not indistinguishable contracts, since the contingencies in which they pay out is different. The things you should apply the law of one price to is the portfolio consisting of two units of “always pay 10,000” versus the portfolio consisting of one unit of LH and one unit of LT. Those two portfolios behave the same in all possible worlds, and therefore must have the same price.
Whether a risk can be hedged against or not is kindof the ultimate question of all financial markets—almost all interesting instruments (futures, options, CDSs, etc) are designed specifically to make hedging easier. Clearly some risk can’t be hedged—if Omega drops by and says “I’ll give you 10,000 iff my quantum coin comes up tails”, then that introduces some irreducible uncertainty into the system, and some speculator somewhere has to be compensated for taking it on. Of course, you can always buy insurance for the event that the coin does not come up tails, but then the person selling the insurance is taking on the risk and will want to be compensated according to their risk preferences.
On the other hand, suprisingly many risks can be hedged against. Figuring out how to hedge some risk which other people had not seen how to is the basis for all clever arbitrage trades.
A particularly interesting example of this is option pricing. A put option essentially is a tool for reducing variance (by eliminating cases where you lose much money because your stock decreases in value), so the price of the put option should be a direct indication of how much a risk-averse investor values the resulting decrease in variance. However, what Black and Scholes noticed was that, actually, provided the underlying stock price changes smoothly enough (follows log-normal Brownian motion), the same risk that the option allows you to eliminate can already be hedged away by just shorting the right amount of stock. So the risk is hedgable, writers of the option should not be compensated for taking it on, and option prices are exactly the same as if everyone was risk-neutral.
On the other hand, if the price of the underlying stock does not change smoothly—if it has random “chrashes” where it suddenly jumps a lot—then the risk mitigated by the option is not hedgable, and we can no longer price the option without knowing what the risk preferences of the investors are. Real-life option prices do not exactly follow the Black-Scholes model (they have so-called “volatility smiles”), which indicates that in the real world, for whatever reason, the corresponding risks are actually not completely hedgable.
Interesting. I’m sure the extra risk can still be hedged or reduced (as long as each contract has an “anti-contract” that pays out exactly the reverse), but it seems this is not exactly how the market operates in practice.
Think about a farmer who will get a good harvest of the sun shines. So he can sell a contract saying “pay 10,000 if the sun shines this summer”. Someone who buys that contract and want to hedge the risk needs to find someone who wants to sell an anti-contract: “pay 10,000 if it rains”. Maybe there is such a person on the market (mushroom pickers?), in which case the risk can be hedged. Or maybe everyone in the world is actually better off with sunshine (or at least, the total productivity in the economy will be higher), in which case the amount of sunshine is a systematic risk which cannot be hedged.
You’re right—weather (or other time dependent related events) cannot be risk reduced on the moment.
But they can be risk reduced over time, by aggregation. I would be willing to sell ten thousand contracts “pay 1 if it rains this year”, one for each of the next ten thousand years. I would do this if we assume the yearly rains are somewhat independent, and that I have a good estimate of their likelyhood, allowing me to price the events reasonably. This, in practice, is stupid because of the ten thousand year delay. Alternatively, I could sell these contracts in 10 000 different locations on the planet—but they would not longer be even approximately independent.
So there are three limitations to reducing risk through aggregation:
1) Reasonable time scale for aggregation.
2) Establishing a reasonable level of independence in the contracts.
3) Calculating the probabilites correctly.
What most people call “systematic risks”, seem to fail one or more of these three requirements, and so can’t be easily risk reduced through aggregation.
Good point. Adjusted the phrasing in the post.
Is there a fundamental reason that some random elements can’t be cancelled out? Can’t you specifically hedge against the ultimate value of your first contract, thus nullifying any risk?
The phrasing incidentally is still a bit off. LH and LT are not indistinguishable contracts, since the contingencies in which they pay out is different. The things you should apply the law of one price to is the portfolio consisting of two units of “always pay 10,000” versus the portfolio consisting of one unit of LH and one unit of LT. Those two portfolios behave the same in all possible worlds, and therefore must have the same price.
Whether a risk can be hedged against or not is kindof the ultimate question of all financial markets—almost all interesting instruments (futures, options, CDSs, etc) are designed specifically to make hedging easier. Clearly some risk can’t be hedged—if Omega drops by and says “I’ll give you 10,000 iff my quantum coin comes up tails”, then that introduces some irreducible uncertainty into the system, and some speculator somewhere has to be compensated for taking it on. Of course, you can always buy insurance for the event that the coin does not come up tails, but then the person selling the insurance is taking on the risk and will want to be compensated according to their risk preferences.
On the other hand, suprisingly many risks can be hedged against. Figuring out how to hedge some risk which other people had not seen how to is the basis for all clever arbitrage trades.
A particularly interesting example of this is option pricing. A put option essentially is a tool for reducing variance (by eliminating cases where you lose much money because your stock decreases in value), so the price of the put option should be a direct indication of how much a risk-averse investor values the resulting decrease in variance. However, what Black and Scholes noticed was that, actually, provided the underlying stock price changes smoothly enough (follows log-normal Brownian motion), the same risk that the option allows you to eliminate can already be hedged away by just shorting the right amount of stock. So the risk is hedgable, writers of the option should not be compensated for taking it on, and option prices are exactly the same as if everyone was risk-neutral.
On the other hand, if the price of the underlying stock does not change smoothly—if it has random “chrashes” where it suddenly jumps a lot—then the risk mitigated by the option is not hedgable, and we can no longer price the option without knowing what the risk preferences of the investors are. Real-life option prices do not exactly follow the Black-Scholes model (they have so-called “volatility smiles”), which indicates that in the real world, for whatever reason, the corresponding risks are actually not completely hedgable.
Interesting. I’m sure the extra risk can still be hedged or reduced (as long as each contract has an “anti-contract” that pays out exactly the reverse), but it seems this is not exactly how the market operates in practice.
Think about a farmer who will get a good harvest of the sun shines. So he can sell a contract saying “pay 10,000 if the sun shines this summer”. Someone who buys that contract and want to hedge the risk needs to find someone who wants to sell an anti-contract: “pay 10,000 if it rains”. Maybe there is such a person on the market (mushroom pickers?), in which case the risk can be hedged. Or maybe everyone in the world is actually better off with sunshine (or at least, the total productivity in the economy will be higher), in which case the amount of sunshine is a systematic risk which cannot be hedged.
You’re right—weather (or other time dependent related events) cannot be risk reduced on the moment.
But they can be risk reduced over time, by aggregation. I would be willing to sell ten thousand contracts “pay 1 if it rains this year”, one for each of the next ten thousand years. I would do this if we assume the yearly rains are somewhat independent, and that I have a good estimate of their likelyhood, allowing me to price the events reasonably. This, in practice, is stupid because of the ten thousand year delay. Alternatively, I could sell these contracts in 10 000 different locations on the planet—but they would not longer be even approximately independent.
So there are three limitations to reducing risk through aggregation:
1) Reasonable time scale for aggregation.
2) Establishing a reasonable level of independence in the contracts.
3) Calculating the probabilites correctly.
What most people call “systematic risks”, seem to fail one or more of these three requirements, and so can’t be easily risk reduced through aggregation.