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Product No. 99784 Supplementary Print Price: FREE with membership
 

An Introduction to Portfolio Theory (UMAP)

Paul R. Thie


Application Areas:
Finance, Mathematical probability, Optimization
Prerequisites:
Background in mathematical probability, including covariance matrix for a set of random variables; familiarity with the method of Lagrange multipliers, with matrix formulation of objective function and constraints.

| ©2002 by COMAP, Inc. | UMAP/ILAP Modules 2001-02 | 74 pages |


Portfolio theory concerns balancing return and risk in the selection of an investment portfolio. We present an introduction to portfolio theory through an example investment problem and models for optimal portfolios.

Table of Contents:

INTRODUCTION

RETURN AND RISK

PORTFOLIO VARIANCE

THE PORTFOLIO SELECTION MODEL

LAGRANGE MULTIPLIERS
P(m) Implies L(m)
One Active Investment
L(m) Implies P(m)
Summary

RESOLUTION OF P(m) WITH THE RISK-FREE INVESTMENT

RESOLUTION OF P(m) WITHOUT THE RISK-FREE INVESTMENT

THE EFFICIENT FRONTIER

LEVERAGING
Resolution of P(m) when v1 = umax
Resolution of P(m) when v1 < umax
The Efficient Frontier with Leveraging

AN EXAMPLE WITH MUTUAL FUNDS

SOLUTIONS TO SELECTED EXERCISES

APPENDIX: GEOMETRY AND THE LAGRANGE/KKT CONDITIONS

REFERENCES

ABOUT THE AUTHOR