Model setting

The baseline model of this paper is largely developed from Fishman and Parker (2015). There are two types of projects: good projects and bad projects. Good projects generate a return of 𝑅𝑅𝑔𝑔 _{and bad projects generates a return of 𝑅𝑅}𝑏𝑏_{. All projects require investment of 1 to originate.}

The alternative cost of this investment would be the gross interest rate 𝑅𝑅. We assume the bad projects are not profitable to invest and the good projects are. i.e. 𝑅𝑅𝑏𝑏⁄ < 1 < 𝑅𝑅𝑅𝑅 𝑔𝑔⁄ . It is a 𝑅𝑅 common knowledge that projects have a probability of 𝜆𝜆 being good in the market. There is a

175 unit mass of risk neutral sellers in the market, either holding good projects or bad projects and unaware of their project qualities ex ante.

There are 2 types of investors in the market: sophisticated investors and unsophisticated investors. Both types of investors are risk neutral. Sophisticated investors have access to limited valuation capacity and can use them at a cost of c per unit. The number of sophisticated investors is finite denoted as 𝑁𝑁. Those sophisticated investors have an aggregate valuation capacity of 𝐻𝐻�. Each sophisticated investor 𝑖𝑖 chooses to use ℎ_𝑛𝑛 unit of valuation capacity. For simplicity, we assume these sophisticated investors are homogenous. Sophisticated investors could correctly identify good projects3 and only buy good ones right after the valuation4.

Key assumption: Assume valuation capacity 𝐻𝐻� is not enough to value all projects5.

This assumption is particularly important for those markets the underlying projects are too many to value (e.g. small business loan/consumer loans market) or relatively new industries where only a limited amount of human capitals/skills are available to assess the projects (e.g. start-up financing industry like venture capital).

A central piece where this paper departs from previous literature is that we explore the mechanism where information can be shared by sophisticated investors. When valuation is neither verifiable nor simultaneous, after a bad project holder gets rejected by a sophisticated investor, he/she still can approach another investor (either sophisticated or unsophisticated) for

3 _{This assumption could be relaxed later in section 5.1 and the main result sustains.}

4 _{It is possible sophisticated investors buying unvalued assets when the expected return exceeds their origination}

cost. However, in that particular scenario, sophisticated investors are indifferent with unsophisticated investors. One may think of a case that sophisticated investors have two division operating differently with regard to their buying strategy. And we treat that one does value and buy as sophisticated investor and the other one as unsophisticated investor.

5 _{Glode and Lowery (2016) emphasise the scarcity of financial experts’ labour supply in their study of financial}

experts’ compensations. This limited valuation capacity is also an important part of Fishman and Parker (2015)’s discussion. Nevertheless, this is not a crucial assumption for our result. In fact, this paper relaxed the valuation capacity assumption used in Fishman and Parker (2015). Even when sophisticated investors have valuation capacity to value all projects once, they could not value and buy all the good assets due to the dilution activities.

176 a sale. Sophisticated investor 𝑖𝑖 has a common belief he/she can identify 𝜆𝜆_𝑛𝑛∗ unit of good projects using one unit of valuation capacity. The information acquired by the sophisticated investor is the quality of the projects. Since good projects are purchased right away after the valuation, sharing such information will not change any decisions of market participant and therefore is trivial. On the other side, information sharing about valued bad projects is important for both sellers and buyers. The remaining part of paper, information sharing refers to the information about valued bad projects.

The key mechanism we will look at is closely associated with the bad projects’ holders’ incentive. The existence of unsophisticated investor market creates incentive for bad projects sellers to dilute sophisticated investors’ valuation capacity. By doing so, fewer good projects are valued and purchased by sophisticated investors aggregately. A portion of good projects are thus crowded out to pooling markets where the prices are set based on average quality. Consequently, the aggregate quality of the pooling market improves, and bad projects could be sold at a higher value. Due to the non-verifiable nature of valuation, sophisticated investors are unable to identify and punish this predatory behaviour. The only way to mitigate this predatory behaviour is through information sharing.

Unsophisticated investors are in a perfect competitive market. Therefore, the market is cleared in a break-even price 𝑃𝑃𝑈𝑈 for unsophisticated investors.

[1] 𝑃𝑃𝑈𝑈 = 𝑤𝑤_𝑈𝑈𝑔𝑔∗ (𝑅𝑅𝑔𝑔⁄𝑅𝑅) + 𝑤𝑤_𝑈𝑈𝑏𝑏∗ (𝑅𝑅𝑏𝑏⁄ 𝑅𝑅)

The weights of good projects and bad projects (𝑤𝑤_𝑈𝑈𝑔𝑔 ,𝑤𝑤_𝑈𝑈𝑏𝑏) in the pooling market depend on the valuation costs, prior quality and level of information sharing among sophisticated investors. On the other hand, sophisticated investors have all bargaining power against good projects sellers and will offer a price marginally higher than the alternative price offered by

177 unsophisticated investors or the origination cost. 𝑃𝑃𝑆𝑆 = max {1, 𝑃𝑃𝑈𝑈 + 𝜖𝜖} . The expected profits for the sophisticated investor 𝑖𝑖 can be written as 𝐸𝐸_𝑛𝑛(𝜋𝜋𝑆𝑆) = max {0, ℎ_𝑛𝑛[ 𝜆𝜆_𝑛𝑛∗(𝑅𝑅𝑔𝑔⁄ 𝑃𝑃𝑅𝑅- 𝑆𝑆) − 𝑐𝑐]}.

Timing

The timing of the events happens as the following. First, project holders approach sophisticated investors to get valued. The approaching process takes long enough so that those valued bad projects have sufficient time to go to all sophisticated investors. In the meantime, sophisticated investors decide the level of valuation capacity to use given certain level of information sharing (either exogenously decided by the regulator or endogenously chosen by sophisticated investor). Given the valuation capacity used, all participants have sufficient knowledge to form their beliefs of projects quality. Thus, prices are determined. Finally, market clears for both types of investors. Sophisticated investors will buy good projects if valuation occurs. Unsophisticated investors will buy the pooling projects if the return is attractive i.e. 𝑃𝑃𝑈𝑈 _{≥ 1.}