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chunkbot
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 9th, 2014, 3:43 pm

Aaron Brown, in The Poker Face of Wall Street, p. 196, discusses four approaches to deriving the same Black-Scholes-Merton option-pricing formula: QuoteEd Thorp, Myron Scholes, Robert Merton, and Fischer Black all had almost the same formula [for option-pricing], but each had a different reason for believing it was true. Ed showed that it was a way to make money, Scholes that it was required for market efficiency, Merton that it had to be true or there would be arbitrage, and Black that it was required for market equilibrium. Black's insight turned out to be the most important... What is the difference between "market efficiency", "no arbitrage", and "market equilibrium", and why would market equilibrium be considered the most important?
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Alan
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 9th, 2014, 4:31 pm

It's dangerous to try to read an authors mind, in this case Brown, but since he has been MIA from this forum for quite a while, I will give it a shot.If you read the orig. BS paper, you will find the BS formula derived in two different ways: (i) a delta-hedging argument, and (ii) a CAPM argumentThe CAPM model is a market equilibrium model -- why this would be considered the most important, I have no clue and probably would disagree.See wikipedia for more about CAPM.The delta-hedging argument constructed an instantaneously riskless position out of the stock and the option. The rate of return of that position was equated to a Tbill rate of return. Perhaps this could be labeled the market efficiency argument.Completely efficient markets presume (among other things) that all investments with the same payoffs in every state of the world should have the same price -- this is called the Law of One Price. Merton and others turned the delta-hedging argument around to show that, equivalently, a marketed option could be replicated by dynamic trading in the stock and bond.To avoid offering an arbitrage opportunity, the replicated option must cost the same as the marketed option.These are all fuzzy distinctions in the context of this model, however.For example, the delta-hedging argument is also a no-arbitrage argument.Market efficiency is really a concept distinct from the Law of One Price -- read `Efficient market hypothesis' at wikipedia.But the spirit of the quote -- that there are many routes to the BS formula -- is well-known and uncontested.Finally, markets can be efficient, offer no arbitrage opportunities, and follow an equilibrium model -- all with the BSM model being FALSE. Indeed, in the real world, securities markets are highly efficient and offer few arbitrage opportunities, and the BSM model is definitely false. HTH
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DavidJN
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 13th, 2014, 1:37 pm

The no-arbitrage paradigm is less ambitious than equilibrium models and that probably explains why the former has been much more successful than the latter.The no-arbitrage paradigm is a relative paradigm that explains a pricing relationship between two perfect substitutes. The obvious example is the Black Scholes model in which the price of an option must be equivalent to the price of a perfect delta-hedged replica comprised of the underlying and a riskless cash account. Note that the BS model does not try to explain the price of the underlying, it merely suggests that, given the underlying?s price and dynamics, the option must have a certain price or you?ve found a money machine. It is because the no-arbitrage paradigm doesn?t attempt to explain the price of the underlying that I say it is less ambitious than equilibrium theories like the CAPM, which tries to explain the prices of everything, whether perfect substitutes or not, relative to a market index.I?ve heard it said (and I can?t remember by whom, because it was so long ago) that it is possible for the no-arbitrage condition to hold while the market is not in equilibrium. But if the market is in equilibrium (whatever that means) then the no-arbitrage condition must also.The biggest challenge is constructing an equilibrium theory is aggregation. Economics has successfully created and defended powerful propositions about decision making under uncertainty at the individual level (e.g. risk aversion) but aggregation across all participants to the market level is problematic because aggregating utility across persons is intractable. So to get around the aggregation issue equilibrium theorists have tended to make a convenient but surely silly assumption of homogeneous expectations (all people are information clones). If all people have identical information sets it would seem to follow that equilibrium prices would be those at which no one would want to trade! Oldrich Vasicek claimed to have solved the aggregation problem some time ago. I never found out how because at the time I encountered his claim he wanted people to pay to look at his paper. I do not know or care if that has changed.
 
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acastaldo
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 13th, 2014, 2:43 pm

What R. C. Merton used to emphasize is that if the market is not in equilibrium that is sort of interesting to know but there may not be much that you or I can do about it, while if a no-arbitrage condition is violated there is clear profit opportunity that will attract limitless capital that will put pressure to restore the condition. He put great emphasis on the importance of no-arb for this reason.
 
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neuroguy
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 14th, 2014, 7:35 am

Nice question.My understanding is that no arbitrage is a concept that can apply to any set of assets: The idea being that you can always create a portfolio of those assets conditional on a given risk that dominates (has higher return than) all other portfolios having the same non-diversifyable risk. This is the no arbitrage portfolio.Another way of stating this is that for a given set of assets and a given available information set, there must be an optimal portfolio (or more correctly, an efficient frontier). And following from this, it is the optimal portfolio (frontier) precisely because it does not permit arbitrage. Implied is that the optimal portfolio incorporates the full information set (because it must have fully diversified out the diversifyable risk).The CAPM is what happens if you take the collection of assets as 'the market' and the information set as 'all publically available information'. Hence the CAPM can be regarded as a special case of the APT. In this framework an efficient market is simply one that returns the optimal return for given risk. Hence you cant 'beat the market' (if it is an efficient one).
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neuroguy
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 14th, 2014, 7:39 am

QuoteOriginally posted by: acastaldoWhat R. C. Merton used to emphasize is that if the market is not in equilibrium that is sort of interesting to know but there may not be much that you or I can do about it, while if a no-arbitrage condition is violated there is clear profit opportunity that will attract limitless capital that will put pressure to restore the condition. He put great emphasis on the importance of no-arb for this reason.Very interesting. However this implies that the market moves between some discrete set of states, but it seems more accurate to say that the market is in a state of, at best, neutral stability but that it occasionally has the odd violent lurch. Sure, easily arbitragable information decays very quickly. But that does not preclude the existence of some information from taking time to be adequately incorporated.Alternatively one can focus on the idea that the inclusion of information into the market requires computation. Given this consideration the strong efficient markets hypothesis cannot be correct. Such compuation cannot occur instantaneously. Furthermore one would expect that the latency of inclusion of information scales as the complexity of the computation that must occur in order for it to be incorporated (which really just means, time required to make it explicit). This is not just an issue of technology or communications, obviously these exert massive effects, but the point is that while this provides a multiplier, the fundamental factor influencing integration time is computational complexity.
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Paul
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 14th, 2014, 9:42 am

Surely the delta-hedging, no-arbitrage argument wins on the grounds of parsimony of assumptions? And those assumptions are relatively respectable. It's also self contained in that it's about one underlying, and doesn't require assumptions about the entire market, the behaviour of participants, etc. P
 
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neuroguy
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 14th, 2014, 11:55 am

QuoteOriginally posted by: PaulSurely the delta-hedging, no-arbitrage argument wins on the grounds of parsimony of assumptions? And those assumptions are relatively respectable. It's also self contained in that it's about one underlying, and doesn't require assumptions about the entire market, the behaviour of participants, etc. PAssumptions and parsimony are great. But in some ways people think of the market as 'normal' exactly when it conforms to those assumptions and 'abnormal' when it does not. And that is fine... but if one thinks that 'normal' somehow means 'default state' then it can mean that you are in exactly the wrong place when it gets 'abnormal', whereupon you are subsequently left wondering why principal X (all-be-it extremely intelligent) was violated... well it was violated because markets are socially and not physically defined.
 
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DominicConnor
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 14th, 2014, 2:15 pm

Market equilibrium is so important because it can be observed ?
 
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Traden4Alpha
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What is the difference between market efficiency, market equilibrium, and no-arbitrage?

November 14th, 2014, 6:33 pm

QuoteOriginally posted by: DominicConnorMarket equilibrium is so important because it can be observed ?Indeed! Worse that that, key players in the financial system have strong incentives to provoke disequilibrium. Churn and volatility create profits from transactions, advice, and data services.