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rajsodhi
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Joined: December 14th, 2007, 6:15 am

Can someone explain endowment economics?

August 18th, 2009, 5:23 am

Hello,I have been reading "A Survey of Behavioral Finance" by Barberis and Thaler, and everything was going fine until I got up to page 1076, when he describes an endowment economy. Could you guys help clarify this part? A copy of the paper may be found here:http://badger.som.yale.edu/faculty/ncb25/ch18_6.pdf"... consider the following an endowment economy, which we come back to a number of times in this section. There are an infinite number of identical investors, and two assets: a risk-free assets in zero net supply, with gross return Rf(t) between time t and t+1, and a risky asset - the stock market - in fixed positive supply, with gross return R(t+1) between time t and t+1. The stock market is a claim to a perishable stream of dividends {Dt}, whereD(t+1)/D(t) = exp(g_D + sigma_D*eps(t+1))(sorry about my poor equation transcription capabilities...)And where each period's dividend can be thought of as one component of a consumption endowment C(t),C(t+1)/C(t) = exp(g_C + sigma_C*eta(t+1))...Investors choose consumption Ct and an allocation St to the risky asset to maximizeEo * sum over all t ( rho^t * C(t)^(1-gam) / (1 - gam))"this is a result that shows up repeatedly, and is modified at various points in the paper. The problem is I can't even understand how they came up with the equation (6) in the first place. If you have any references on this that are more tutorial in nature, or if you think you could help explain it, I would be most appreciative. Thanks so much!YoursRaj
 
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QuantVader
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Joined: July 10th, 2008, 2:19 pm

Can someone explain endowment economics?

August 19th, 2009, 6:26 am

Equation 6 is a utility function (do you know what this is)? People get utility from consuming C_t. This equation is not derived from anywhere, but simply this happens to be the way the investor gets happiness from buying stuff.So the investor wishes to maximise the expected value of his life-time utility function (be as happy as possible). Rho is a discount factor (between 0 and 1) that basically means that people prefer consuming today than delaying consumption for later in life (what would you prefer, that I buy you a coffee now or one on February 10, 2056?)Gamma is a free parameter that represents risk aversion. While it has an economic meaning, it also makes the utility function to have the right "shape" so that the maximisation problem makes sense.
 
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hamster
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Joined: October 12th, 2008, 3:51 pm

Can someone explain endowment economics?

August 19th, 2009, 11:02 am

quantvader is right. you might look for relative risk aversion or arrows-pratt measure.
 
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rajsodhi
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Posts: 1
Joined: December 14th, 2007, 6:15 am

Can someone explain endowment economics?

August 20th, 2009, 2:26 pm

Thanks very much for your replies, 'QuantVader' and 'Hamster.'The variables explained by QuantVader are not shown in the text of the paper, so perhaps the authors assume that everyone has a background in utility functions.Would you say this is important to know?Here's what 'hamster' may have been referring to:http://en.wikipedia.org/wiki/Risk_aversionThanks again!Raj
 
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hamster
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Joined: October 12th, 2008, 3:51 pm

Can someone explain endowment economics?

August 23rd, 2009, 11:02 am

@rajsodhiit is not surprising that an article of an incollection exspect some preknowledge