32 research outputs found

    The Arbitrage Pricing Model: A Pedagogic Derivation and a Spreadsheet-Based Illustration

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    This paper derives, from a pedagogic perspective, the Arbitrage Pricing Model, which is an important asset pricing model in modern finance. The derivation is based on the idea that, if a self-financed investment has no risk exposures, the payoff from the investment can only be zero. Microsoft Excel plays an important pedagogic role in this paper. The Excel illustration not only helps students recognize more fully the various nuances in the model derivation, but also serves as a good starting point for students to explore on their own the relevance of the noise issue in the model derivation

    Geometric Brownian Motion, Option Pricing, and Simulation: Some Spreadsheet-Based Exercises in Financial Modeling

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    This paper presents some Excel-based simulation exercises that are suitable for use in financial modeling courses. Such exercises are based on a stochastic process of stock price movements, called geometric Brownian motion, that underlies the derivation of the Black-Scholes option pricing model. Guidance is provided in assigning appropriate values of the drift parameter in the stochastic process for such exercises. Some further simulation exercises are also suggested. As the analytical underpinning of the materials involved is provided, this paper is expected to be of interest also to instructors and students of investment courses

    Connecting Binomial and Black-Scholes Option Pricing Models: A Spreadsheet-Based Illustration

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    The Black-Scholes option pricing model is part of the modern financial curriculum, even at the introductory level. However, as the derivation of the model, which requires advanced mathematical tools, is well beyond the scope of standard finance textbooks, the model has remained a great, but mysterious, recipe for many students. This paper illustrates, from a pedagogic perspective, how a simple binomial model, which converges to the Black-Scholes formula, can capture the economic insight in the original derivation. Microsoft ExcelTM plays an important pedagogic role in connecting the two models. The interactivity as provided by scroll bars, in conjunction with Excel's graphical features, will allow students to visualize the impacts of individual input parameters on option pricing

    The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration

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    This study considers, from a pedagogic perspective, a crucial requirement for the covariance matrix of security returns in mean-variance portfolio analysis. Although the requirement that the covariance matrix be positive definite is fundamental in modern finance, it has not received any attention in standard investment textbooks. Being unaware of the requirement could cause confusion for students over some strange portfolio results that are based on seemingly reasonable input parameters. This study considers the requirement both informally and analytically. Electronic spreadsheet tools for constrained optimization and basic matrix operations are utilized to illustrate the various concepts involved

    Estimation Error in the Correlation of Two Random Variables: A Spreadsheet-Based Exposition

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    Although the statistical term correlation is well-known across many academic disciplines, estimation error in the correlation has traditionally been considered to be a topic too difficult for students outside statistical fields. This pedagogic study presents an approach for the estimation that does not require any advanced statistical concepts. By using familiar spreadsheet functions to facilitate the required computations, it intends to make the analytical material involved accessible to more students

    Bond Duration: A Pedagogic Illustration

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    In view of the importance of reliable duration measures for bond immunization strategies, this paper considers, from a pedagogic perspective, the duration concept. Both a basic bond model and a more realistic bond model, which accounts for the accrued interest, are considered. The use of graphical features and scroll bars in Microsoft ExcelTM allows the duration concept to be delivered via an interactive approach. This paper also addresses an unresolved issue on bond duration. Specically, it explains why a saw-toothed time pattern of traditionally-defined duration exists and provides a corrective measure, which is easy to implement on Excel. Analytical materials pertaining to bond duration, as well as illustrative examples based on actual bond quotation data, are provided