Portfolio Theory: Understanding Diversification, Measuring Risk, and Efficient Frontier, Slides of Financial Theory

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STRATEGIC FINANCIAL

MANAGEMENT

Portfolio Theory

Introduction

• Diversification is a strategic device for dealing with risk

• “Don’t put all your eggs in one basket”

• A portfolio is a combination of assets (e.g. shares,

securities, projects, investments)

• A well-diversified portfolio may lower an investor’s

exposure to risk

• Diversification can be undertaken by companies as well as

by investors

• It is advisable to hold assets or invest in projects which

react differently to changing economic conditions

• Covariance, covAB:
  • (^) Is a measure of the interrelationship between the returns

on the two assets;

• (^) Shows a measure of how the returns move together; and
• (^) Correlation coefficient, rAB:
• (^) =
• (^) NB: -1 ≤ r ≤ 1
• (^) The minimum risk portfolio with two assets is:
• (^) Where *A is invested in asset A; and
• *A =

Portfolio Analysis Where Risk and Return Differ Asset Expected Return Standard Deviation Z 15% 20% Y 35% 40% rZY = -0.25 covZY = -0.25 x 20 x 40 = - Portfolio Z weighting Y weighting 100% 0% 15% 20% 75% 25% 20% 16% 50% 50% 25% 20% 25% 75% 30% 29% 0% 100% 35% 40%

Different Degrees of Correlation

• (^) Two investments, A & B, where A has a higher expected return

and carries a higher risk

• (^) The portfolio effect will depend on the level of correlation, rAB:
  • (^) rAB = +1 is perfect positive correlation
    • (^) No portfolio effect possible, combinations lie on AB, lowest risk is holding asset B alone
  • rAB = -1 is perfect negative correlation
    • (^) Combinations lie along AXB. Risk can be eliminated (X) by holding the right combination of assets
  • (^) Intermediate levels will achieve a portfolio effect which will be greater for lower levels of rAB
  • (^) See following graph

Efficient frontiers with changing correlations ERP 0 σP

A

B

X

Perfect positive Perfect negative Reducing correlation

Portfolio Theory and CIA

• Portfolio theory can be applied to projects and sectors for

companies but has the following problems:

• (^) Projects may not be purely divisible;
• (^) Constant returns to scale are unlikely;
• (^) Subjective probability measures;
• (^) Risk-return preference of shareholders (?);
• (^) Project risk analysis is unduly management-oriented, but attitudes to risk of managers and shareholders need not be the same.

• Portfolio theory provides the infrastructure for the Capital

Asset Pricing Model (CAPM)