Personal Investment Management
ADMS 3531 - Fall 2011 – Professor Dale Domian
Lecture 1, Part 2 – Diversification and Asset Allocation – Sept 13
Chapter Two Outline
Expected return and variances.
Diversification and portfolio risk.
Correlation and diversification.
Markowitz efficient frontier.
Asset allocation and security selection decisions of portfolio formation.
 In fact, diversification has a profound effect on portfolio return and portfolio risk.
Diversification and Asset Allocation
 Our goal in this chapter is to examine the role of diversification and asset allocation
in investing.
 In the early 1950s, Professor Harry Markowitz was the first to examine the role and
impact of diversification.
 Based on his work, we will see how diversification works, and we can be sure that
we have ‘efficiently diversified portfolios’.
o An efficiently diversified portfolio is one that has the highest expected return,
given its risk.
o You must be aware of the difference between historic return and expected
Historical Returns
 Although it is important to be able to calculate historical returns, we really care
about expected returns, because we want to know how our portfolio will perform
from today forward.
Expected Returns
 Expected return is the ‘weighted average’ return on a risky asset, from today to
some future date.
 To calculate an expected return, you must first:
o Decide on the number of possible economic scenarios that might occur.
o Estimate how well the security will perform in each scenario, and
o Assign a probability to each scenario.
o (BTW, finance professors call these economic scenarios, ‘states’.)
 The next slide shows how the expected return formula is used when there are two
o Note that the ‘states’ are equally likely to occur in this example. BUT! They do
not have to be. They can have different probabilities of occurring.
Calculating the Variance of Expected Returns
 The variance of expected returns is calculated as the sum of the squared deviation of
each return from the expected return, multiplied by the probability of the state.
Standard Deviation
 The standard deviation is simply the square root of the variance.
 The following slide contains an example that shows how to use these formulas in a
 Portfolios are groups of assets, such as stocks and bonds that are held by an
 One convenient way to describe a portfolio is by listing the proportion of the total
value of the portfolio that is invested into each asset.
 These proportions are called portfolio weights.
o Portfolio weights are sometimes expressed in percentages.
o However, in calculations, make sure you use proportions.
Variance of Portfolio Expected Returns
 Note: unlike returns, portfolio variance is generally not a simple weighted average
of the variances of the assets in the portfolio.
Why Diversification Works, I
 Correlation: The tendency of the returns on two assets to move together. Imperfect
correlation is the key reason why diversification reduces portfolio risk as measured
by the portfolio standard deviation.
o Positive correlated assets tend to move up and down together.
o Negatively correlated assets tend to move in opposite directions.
 Imperfect correlation, positive or negative, is why diversification reduces portfolio
 The correlation coefficient measures correlation and ranges from:
o From -1 (perfect negative correlation).
o Through 0 (uncorrelated).
o To +1 (perfect positive correlation).
Correlation and Diversification
 The various combinations of risk and return available all fall on a smooth curve.
 This curve is called an investment opportunity set, because it shows the possible
combinations of risk and return available from portfolios of these two assets.
 A portfolio that offers the highest return for its level of risk is said to be an efficient
 The undesirable portfolios are said to be dominated or inefficient.
The Markowitz Efficient Frontier
 The Markowitz Efficient Frontier is the set of portfolios with the maximum return
for a given risk and the minimum risk given a return.
 For the plot, the upper left-hand boundary is the Markowitz efficient frontier.
Efficient Frontier
 All the other possible combinations are inefficient. That is, investors would not hold
these portfolios because they could get either.
o More return for a given level of risk, or
o Less risk for a given level of return.
Portfolio Formation Decisions
 Investors can form their using the following financial assets:
o Domestic stocks.
o Domestic bonds (government, municipal, provincial bonds, corporate bonds).
o Derivative instruments (options, futures, and swaps).
o Money market instruments (T-bills, certificate of deposits, repurchase
agreements, etc.).
o Foreign stocks and bonds.
Asset Allocation and Security Selection Decisions
 Investors face with two problems when they form portfolios of multiple securities
from different asset classes.
 These are as follows:
o Asset allocation problem.
o Security selection problem.
Asset Allocation Decision
 Asset allocation problem involves a decision of what percentage of investor’s
portfolio should be allocated among different asset classes (stocks, bonds,
derivatives, money market instruments, foreign securities).
Security Selection Decision
 Security selection is deciding which securities to pick in each class and what
percentage of funds to allocate to these securities (for example choosing different
stocks and their percentages within the asset class).