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Question - Suppose that asset returns satisfy this Euler equation:
1/Ct = Et0.94(1+rt+1)1/Ct+1
where rt+1 denotes the return from period t to period t + 1 and C is real consumption in the US. For simplicity suppose there is no inflation. Suppose that in any period C can take on two values, 1.00 and 1.02, each with probability 0.5. There is no autocorrelation in consumption.
(a) Call ht the price of a one-period bond that pays 1 in all states of the world in period t + 1. Find the interest rate on this bond first when Ct = 1 and second when Ct = 1.02.
(b) Call hjt the price of a one-period bond (issued by a sovereign government in an emerging economy) that pays 1 in period t+ 1 with probability 1 - λ and pays 0.8 with probability λ. The event of this partial default is uncorrelated with the value of consumption in period t + 1. Solve for the expected return on this bond first when Ct = 1 and second when Ct = 1.02.
(c) How could an analyst estimate the value of the default probability λ?
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