Sep 19, 2017

(INVESTOR RISK AVERSION AND RISK PREMIA). ONE OF THE KEY DEVELOPMENTS IN THE THEORY OF MARKET…

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(investor risk aversion and risk premia). One of the key developments in the theory of market finance has been to find methods to price claims held by investors. Market finance emphasizes state-contingent pricing, the fact that 1 unit of income does not have a uniform value across states of nature. This book assumes that investors are risk neutral, and so it does not matter how the pledgeable income is spread across states of nature. This assumption is made only for the sake of computational simplicity, and can easily be relaxed. Consider a two-date model of market finance with a representative consumer/investor. This consumer has utility of consumption u(c0) at date 0, the date at which he lends to the firm, and utility of consumption u(c(ω)) at date 1, date at which he receives the return from investment. There is macroeconomic uncertainty in that the representative consumer’s date-1 consumption depends on the state of nature ω. The state of nature describes both what happens in this particular firm and in the rest of the economy (even though aggregate consumption is independent of the outcome in this particular firm to the extent that the firm is atomistic, which we will assume). Suppose that the entrepreneur works. Let S denote the event “the project succeeds” and F the event “the project fails.” Let

The firm’s activity is said to covary positively with the economy (be “procyclical”) if qS

(i) Interpret this assumption.

(ii) In the fixed-investment model of Section 3.2 (and still assuming that the entrepreneur is risk neutral), derive the necessary and sufficient condition for the project to receive financing.

(iii) What is the optimal contract between the investors and the entrepreneur? Does it involve maximum punishment (Rb = 0) in the case of failure? How would your answer change if the entrepreneur were risk averse? (For simplicity, assume that her only claim is in the firm. She does not hold any of the market portfolio.)


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