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# Venture Capital

## Armin Höll-Steiner

This book contains three studies. The first study investigates the relationship between private equity investors and fund managers and how intermediaries can mitigate their agency problems. The incentive structure of three intermediary types and their behavior in signaling fund qualities to investors are studied theoretically. A recommendation which intermediary to consult is given. The second study presents a new statistical method to predict the performance distribution of venture capital direct investments. The accuracy of this method is investigated and compared to existing approaches. The third study is about the European venture capital market’s historic development before and after the internet bubble and reasons for the bad development especially after the bubble.

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# Appendices

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for Chapter 2 1 Proof of Lemma 1 Proof. The average reputation after certifying a PEF has to be positive for the certiﬁer to remain in business, i. e. the reputation change from investors x ·RI,g − y ·RI,b has to be geater or equal to 0. In the long run, the certiﬁer wants to keep his reputation for any x and y. In consequence x ·RI,g − y ·RI,b ≥ 0 x ·RI,g ≥ y ·RI,b With RI,b ≥ RI,g and x > 0 the inequality returns 1 ≥ RI,g RI,b ≥ y x x ≥ y . For x = 0 we get −y · RI,b ≥ 0, so y would have to be 0. In this case the certiﬁer would not issue any certiﬁcates. 2 Proof of Lemma 2 Proof. If a certiﬁer blindly certiﬁes with z > 0 funds his reputation gain will be z · γ · RI,g − z · (1 − γ) · RI,b which has to be at least 0 to keep his reputation level. Rewritten it follows RI,g RI,b ≥ 1− γ γ . 238 Appendices for Chapter 2 Due to Equation (2.2) the reputation ratio is less than 1. This is only true for γ ≥ 0.5 which is excluded by assumption (2.1). 3 Proof of Theorem 3 Proof. To proof the condition p ≥ 1 − γ, I consider the contrary case p 0 p ≥ (1− p) · 1− γ γ RI,b RI,g p · (1 + 1− γ γ RI,b RI,g ) ≥ 1− γ γ RI,b RI,g p ≥ 1−γ γ RI,b...

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