Comm 371 Lecture Notes 6

Investment
Theory
Alexandre
Corhay
Overview
Return on a
Portfolio
Expected
Return and
Variance
Benefits of
Diversification
M-V Opt. and the
Portfolio
Frontier

Investment Theory
Portfolio Theory

Alexandre Corhay
Sauder School of Business
University of British Columbia

P-F with
Risky
Assets Only
Limits of
Diversification
P-F with a
Riskless
Asset
Tangent
Portfolio
Property

Copyright c 2012 J. Bena, H. Kung, A. Pavlova and D. Vayanos

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Overview of the Lecture
Investment
Theory
Alexandre
Corhay

Big question: How to choose a stock portfolio?
Overview

1
Return on a
Portfolio
Expected
Return and
Variance
Benefits of
Diversification

Return on a Portfolio

2

Expected Return and Variance of a Portfolio

3

Benefits of Diversification

4

Mean-Variance Optimization and the Portfolio Frontier
Portfolio Frontier with Risky Assets Only

5

• Two Assets
• Short Sales
• More than Two Assets

M-V Opt. and the
Portfolio
Frontier
P-F with
Risky
Assets Only
Limits of
Diversification

6

Limits of Diversification: Systematic vs. Idiosyncratic risk

7

Portfolio Frontier with a Riskless Asset

8

An Important Property of the Tangent Portfolio

P-F with a
Riskless
Asset
Tangent
Portfolio
Property

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Return on a Portfolio
Investment
Theory
Alexandre
Corhay
Overview
Return on a
Portfolio
Expected
Return and
Variance

Determine the return on a stock portfolio given the returns on the individual stocks. • Consider a portfolio consisting of X1 dollars in Disney and X2 dollars in

IBM.
• The value of the portfolio at date 0 is X = X1 + X2 .
• The value of the portfolio at date 1 is

Benefits of
Diversification
M-V Opt. and the
Portfolio
Frontier
P-F with
Risky
Assets Only
Limits of
Diversification
P-F with a
Riskless
Asset
Tangent
Portfolio
Property

X1 (1 + R1 ) + X2 (1 + R2 ), where R1 is the return on Disney and R2 the return on IBM