Introduction

Two most important concepts in investing are risk and return. Much of the economic study of these concepts falls within the sphere of modern finance, which has three major building blocks: Modern Portfolio Theory, the Capital Asset Pricing Model (CAPM, pronounced “cap-em”), and the Black-Scholes formula. In 1952, Harry Markowitz pioneered the Modern Portfolio Theory. His seminal paper [7] established the framework for selecting investments to reduce risk. Extending Markowitz's theory,William Sharpe devised the CAPM, that describes the relationship between risk and expected return [8]. Fisher Black and Myron Scholes, assisted by Robert Merton, found an analytic formula for valuing option contracts and assessing risk [1]. Their model is considered the most important single breakthrough in the 1970s. Essentially, these intellectual giants addressed three fundamental questions: What is risk? What is an asset worth? What is risk worth? For their contributions to financial economics, Markowitz, Sharpe, and Merton Miller were awarded the Nobel Prize for Economic Sciences in 1990. Scholes and Merton received the Nobel in 1997. (Black had died in 1995.) This paper guides the reader through a series of problems to discover how undergraduate mathematics are used in financial modeling.