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I understand that in complete market, ex post consumption growth is equal for all investors. Why is that perfect risk sharing? The book also states that

only aggregate shocks should matter for risk prices. Any idiosyncratic risk will be equally shared.

Why is this case in complete market? What does it have to do with financial innovation?

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  • $\begingroup$ What is "The book" you are quoting from? $\endgroup$
    – Giskard
    Commented May 15, 2016 at 8:00
  • $\begingroup$ @denesp it is from section 3.4 of Cochrane's Asset Pricing. $\endgroup$
    – user1559897
    Commented May 15, 2016 at 13:14

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Idiosyncratic shocks are those for which each individual face a different shock – while there is no uncertainty in the aggregate. Aggregate shocks are those which affect all individuals within an economy. When you have complete markets –– those on which there are securities for each possible combinations of the idiosyncratic shocks –– individuals will trade to insure optimal levels of consumption across all possible states. So, to get the value of risky options one only need to look on aggregate shocks –– as ultimately these are the ones which will determine prices.

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  • $\begingroup$ I am not quite sure what risk sharing means. Does it mean idiosyncratic risk is gone from the market? If i recall correctly, idiosyncratic risk is the risk uncorrelated with utility. I do not see any usage of correlation/co-variance in the math derivation. Please explain. I am reading Cochrane's Asset Pricing by the way. $\endgroup$
    – user1559897
    Commented May 15, 2016 at 13:25
  • $\begingroup$ Risk sharing means that agents can insure against all possible states if needed. No, idiosyncratic risk can be correlated or uncorrelated with utility. Idiosincratic risk just entails risk that is exclusive to one individual which does not affect the rest of the individuals and which in the aggregate disappears. $\endgroup$
    – MathUser
    Commented May 16, 2016 at 7:51
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Idiosyncratic shock affect to only a part of the population, so it won't transmit to prices and only the affected part will suffer the effect of the risk taken. On the other hand Aggregate shocks, will affect everyone in a proportional manner.

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