Reading Asset Pricing by John Cochrane (2005), in his second chapter he defines the risk free rate as:

Rf = 1 / sum [pc(s)]

Where pc(s) are state contingent claims, where s is the state of nature realised from a possible set S.

This is quite an elementary question I'm sure, but I just cannot grasp why this is the case. If anyone could enlighten me intuitively that would be most appreciated!


1 Answer 1


By buying all the state contingent claims you ensure that you will receive 1 USD in the next period (since one of the states will occur), and that is the definition of a risk free security: something that is guaranteed to pay off 1. The price at which it sells today is lower than 1, and that discounting defines the Risk Free rate. If the risk free basket of claims sells for 0.9 then the interest rate is 1/0.9 = 1.11 or 11% in net terms.

  • $\begingroup$ For example I could buy a sc claim that pays 1 if the Republican candidate is elected president, a similar claim for the Democratic candidate and an sc claim that pays 1 for any Third Party candidate. This basket of claims is a risk free security, whose pricing today depends only on the interest rate (and in a sense defines what we mean by the interest rate). $\endgroup$
    – nbbo2
    Commented Apr 29, 2016 at 13:24

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