Does this also mean if we can prove that markets are efficient then P = NP?
Markets are efficient if and only if P = NP (2010)
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Re: Markets are efficient if and only if P = NP (2010)
#32Interesting. It is well known in the high-frequency literature that at frequencies higher than 5-minute one obtains market microstructure noise. The observations you observe do not fully reflect the "true" price. I.e. you observe bid/ask quotes with a spread and the "true" price is somewhere in between. This is due to the bid-ask bounce and other latency factors. How can markets ever be efficient if we can not observe the true price of something?
Re: Markets are efficient if and only if P = NP (2010)
#33Does this also mean if we can prove that markets are efficient then P = NP?
Yes.
Re: Markets are efficient if and only if P = NP (2010)
#34Interesting. It is well known in the high-frequency literature that at frequencies higher than 5-minute one obtains market microstructure noise. The observations you observe do not fully reflect the "true" price. I.e. you observe bid/ask quotes with a spread and the "true" price is somewhere in between. This is due to the bid-ask bounce and other latency factors. How can markets ever be efficient if we can not observ…
There's a transaction cost in either direction.
If you buy a call option, the market-maker buys stock to hedge it. That moves the underlier, and raises the price of the call option he just sold. The reverse is true if you sell a call (or buy a put).
Not only that, but there is a cost for all the people and computers that your order touches as it gets executed.
Without price impact from transactions, markets can't be efficient, because new information has to get priced into the market somehow.
Re: Markets are efficient if and only if P = NP (2010)
#35Interesting. It is well known in the high-frequency literature that at frequencies higher than 5-minute one obtains market microstructure noise. The observations you observe do not fully reflect the "true" price. I.e. you observe bid/ask quotes with a spread and the "true" price is somewhere in between. This is due to the bid-ask bounce and other latency factors. How can markets ever be efficient if we can not observ…
I'm not familiar with high-frequency literature, but you can rarely measure something with 100% accuracy. Despite this, your house got built even if its measurements were taken with a +-0.5cm error. So if the noise is sufficiently small, you can know the true price with enough precision. I don't know if that is the case though.
Re: Markets are efficient if and only if P = NP (2010)
#36While this is a fun, the title is a little strong. There are three limitations (whuch apply to many papers about P=NP). 1. The market could still be efficient, because the situations which must arise to cause P vs NP problems are very complicated. In particular thry require very expensive indivisible things to buy, whereas in most situations we can treat things like shares as continuous with only a small error. 2. Ma…
While I technically agree with your points, you and the author use different definitions of "markets are efficient".
Re: Markets are efficient if and only if P = NP (2010)
#37I'm amazed that someone has written a paper that considers computational complexity that isn't written in LaTeX...
That reminds me of Scott Aaronson's post about the early signs a complexity paper is unlikely to be valid: https://www.scottaaronson.com/blog/?p=304 Not tex is the first point.
Re: Markets are efficient if and only if P = NP (2010)
#38[deleted]
Re: Markets are efficient if and only if P = NP (2010)
#39Somehow this seems to be a confusion of categories: markets are real-world mechanisms, while P and NP are mathematical abstractions. Does not compute. To the extent that it does, it's typical mathematical macroeconomic BS.
Re: Markets are efficient if and only if P = NP (2010)
#40Somehow this seems to be a confusion of categories: markets are real-world mechanisms, while P and NP are mathematical abstractions. Does not compute. To the extent that it does, it's typical mathematical macroeconomic BS.
I economics you sometimes define mathematical objects to model real world markets. It's these models that the paper talks about.