(inefficiently low volume of asset reallocations). This exercise applies the logic of corporate...

(inefficiently low volume of asset reallocations). This exercise applies the logic of corporate risk management developed in Chapter 5 to show that, even with frictionless resale markets, there will be an inefficiently low volume of transactions in the secondary market. There are three dates, t = 0, 1, 2, and at least two firms i = 1, 2. Firm 1, the firm of interest, is managed by a riskneutral entrepreneur, who owns initial wealth A at date 0 and is protected by limited liability. This firm invests at a variable investment level I ∈ [0, ∞). The per-unit profitability of investment is random and learned at date 1. The investment yields RI with probability p + τ and 0 with probability 1 − (p + τ). The random variable τ is drawn from a continuous distribution. The variable p is equal to pH if the entrepreneur behaves (no private benefit) and pL if the entrepreneur misbehaves (private benefit BI). Let

denote the random continuation per-unit NPV and pledgeable income when the entrepreneur behaves and the realization of profitability is τ. The distribution on τ induces a cumulative distribution function F(ρ0) on [ρ _{0}, ρ_{0}]. At date 1, the firm may either continue or resell assets I to firm 2 (or to a competitive market). Firm 2 has a known level ρˆ0 of per-unit pledgeable income per unit of investment (its NPV per unit of investment is in general larger than this). Firms 1 and 2 do not contract with each other at date 0. Rather, investors in firm 1 make a take-itor-leave-it offer to firm 2 at date 1 if firm 1’s initial contract specifies that assets ought to be reallocated. Assume for simplicity that the contract between firm 1’s investors and the entrepreneur can be contingent on the realization of ρ0. Show that at the optimal contract assets are resold whenever ρ_{0} ∗ 0 , where

and so the volume of asset reallocations is ineffi- ciently low