An Introduction to Portfolio Theory (UMAP)

Portfolio theory concerns balancing return and risk inthe selection of an investment portfolio. We presentan introduction to portfolio theory through an exampleinvestment 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