Table of Contents

Copula: A Primer for Fund Managers

Wing Cheung, Nomura

Required Rates of Return and Financial Contracting for Entrepreneurial Ventures

Richard L. Smith, University of California, Riverside - Anderson Graduate School of Management

A Snakes and Ladders Representation of Stock Prices and Returns

Philip C. Gager, University of Cumbria
Mark B. Shackleton, Lancaster University - Department of Accounting and Finance

FINANCE EDUCATOR: COURSES, CASES & TEACHING ABSTRACTS

"Copula: A Primer for Fund Managers" Free Download

WING CHEUNG, Nomura
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Traditional equity risk models focus on estimating stock return variance-covariance matrix. Ignoring high-order moments, they implicitly assumes normal return distributions. The recent credit crisis has reminded us again that the normality assumption is insufficient in risk management. Moving away from normality requires a tractable technique to allow investigation of alternative distributions. Copula is a good choice since it helps modulise our job and enriches our distribution selection menu.

This paper aims to demystify copulas for equity portfolio managers by addressing the following questions:1) What is copula and what does it represent 2) With correlation as a commonly used dependence measure, why is copula worth the extra complexity 3) What is 'tail dependence' 4) What are Gaussian, t-, Clayton, Gumbel and Frank copulas; how do they look and behave; and how to simulate 5) How to model equity markets with copulas where the dimensions are high 6) How can copula-based market model be applied to equity PM process.

"Required Rates of Return and Financial Contracting for Entrepreneurial Ventures" Free Download

RICHARD L. SMITH, University of California, Riverside - Anderson Graduate School of Management
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Investments in new venture involve financial contracts between an entrepreneur and one or more outside investors. Outside investors (such as venture capital firms) generally represent well-diversified investors. Even private investors generally commit small fractions of total wealth to any given venture. The entrepreneur, in contrast, usually must commit a substantial fraction of human and financial capital to the venture. In this paper, we assume that the Capital Asset Pricing Model is a reasonable approximation of the asset pricing model used by well-diversified investors, and that the entrepreneur faces the risk-return tradeoff of the CAPM as the opportunity cost of holding an under-diversified portfolio that includes investment in the venture. The result is that the entrepreneur's required rate of return depends on total risk of the investment, in the context of other assets in the entrepreneur's portfolio. We model the required rate of return of the entrepreneur, assuming that investment in the venture is one of two assets in the portfolio and that the other is the market portfolio. Since the required rate of return for the entrepreneur is always higher than that of a diversified investor, opportunities arise for value-enhancing financial contracts to be devised based on allocation of risk. In the paper, we explore opportunities for value creation when the parties to a financial contract have different costs of bearing risk, and where adverse selection and moral hazard are both concerns. The analysis yields a number of testable implications for the structures of new venture financial contracts.

"A Snakes and Ladders Representation of Stock Prices and Returns" Free Download

PHILIP C. GAGER, University of Cumbria
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MARK B. SHACKLETON, Lancaster University - Department of Accounting and Finance
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Snakes and ladders is an ancient Indian game of chance that offers amusement as well as a metaphor for life's many ups and downs. Games offer useful and fun ways of conveying ideas as well as solution techniques and this game has considerable mathematical tractability. This note shows how snakes and ladders can be used to represent the ups and downs of share ownership and solve for fair values of a multistage project that pays fixed dividends at uncertain completion times and has random returns.

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