Money Markets and Finance
Lecture 7
Diversification: Portfolio Theory
1. Lecture Overview
During this lecture, we will discuss the concepts of
portfolio
theory
and
diversification
.
Diversification allows an
individual to reduce the risk of their investment without
sacrificing any expected return simply by spreading their
wealth over a portfolio comprising a number of assets in an
appropriate way.
During the course of the lecture we will
discuss:
–
What diversification is;
–
How including multiple assets in a portfolio can achieve
diversification;
–
Which assets to include in order to achieve the greatest level
of diversification; and,
–
How to construct a diversified portfolio in practice.
2. Review of Statistics
Before we start discussing portfolio theory and the
concept of diversification, we will briefly review the
statistical terms discussed last lecture.
These terms
are important to understand as they are central to
portfolio theory.
More specifically, we will revisit
the definitions of:
–
Random variables;
–
Expected values; and,
–
Standard deviation and variance.
2. Review of Statistics
Random Variables:
A random variable is one that can take on any number of
different values.
Each value has an associated probability of
occurring. The uncertainty associated with the outcome of a
random variable is described by a probability distribution,
with the most commonly used distribution being the
normal
distribution
, see below:
75
65
55
45
35
25
15
5
5
15
25
35
45
55
65
75
0.020
0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
Probability density
Stock market return
2. Review of Statistics
Expected Values:
The value we expect a random variable (
X
) to take is known as its
expected value
or mean.
Standard Deviation:
Standard deviation,
σ
, is a measure of spread. It is based on how
far each value of
X
varies from the mean. A small standard
deviation means that the data doesn’t vary a lot from the mean. A
large standard deviation means that the data is more spread out.
Variance:
The variance,
σ
2
, is simply the standard deviation squared.
3. Diversification
Recall from last week the assumption that
investors are risk averse and therefore prefer
less risk to more.
Diversification provides a
means of reducing risk faced by investors
without sacrificing expected return by combining
assets that don’t move perfectly together in a
portfolio. Note that the ideas we are about to
discuss can be extended to consider more than
2 assets.
You will consider these extensions in
FINM3001 Investments.
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3.1 Measuring How Assets Move
Together
Correlation and Covariance:
The covariance between variables
X
and
Y
,
σ
XY
, is a
measure of association between the two variables. For
example, we may be interested in whether there is an
association between the return on a company’s stock
and the return on the stock market in general:
–
If the market always went up at the same time company’s
stock went up, the covariance would be positive;
–
If the return on the stock and the return on the market were
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 Standard Deviation, Variance, Review of Statistics

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