Chapter 5
Modern Portfolio
Concepts
Required computations (10-12)
• Various return concepts (HPR, IRR, realized return, expected
return)
• Compute the average return and standard deviation on a
time series using excel.
• Compute the mean/expected return and standard deviation
given scenarios with probabilities.
• Compute the mean return, beta of a portfolio of multiple
assets
• Compute the standard deviation of a two-asset portfolio
• Apply CAPM to compute required rate of return, return
sensitivity to market moves, and market risk premium.
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-2
What is a Portfolio?
• Portfolio is a collection of investments
assembled to meet one or more investment
goals.
• Efficient portfolio
– A portfolio that provides the highest return for a
given level of risk
– Requires search for investment alternatives to
get the best combinations of risk and return
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-3
Portfolio Return and Risk Measures
• The return on a portfolio is simply the
weighted average of the individual assets’
returns in the portfolio
• The standard deviation of a portfolio’s
returns is more complicated, and is a
function of the portfolio’s individual assets’
weights, standard deviations, and
correlations with all other assets
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-4
Return on Portfolio
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-5
Correlation:
Why Diversification Works!
• Correlation is a statistical measure of the
relationship between two series of numbers
representing data
• Positively Correlated items tend to move in the
same direction
• Negatively Correlated items tend to move in
opposite directions
• Correlation Coefficient is a measure of the
degree of correlation between two series of
numbers representing data
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-6
Correlation Coefficients
• Perfectly Positively Correlated describes two
positively correlated series having a
correlation coefficient of +1
• Perfectly Negatively Correlated describes
two negatively correlated series having a
correlation coefficient of -1
• Uncorrelated describes two series that lack
any relationship and have a correlation
coefficient of nearly zero
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-7
Figure 5.1 The Correlation Between
Series M, N, and P
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-8
Correlation:
Why Diversification Works!
• Assets that are less than perfectly positively
correlated tend to offset each others
movements, thus reducing the overall risk
in a portfolio
• The lower the correlation the more the
overall risk in a portfolio is reduced
– Assets with +1 correlation eliminate no risk
– Assets with less than +1 correlation eliminate some risk
– Assets with less than 0 correlation eliminate more risk
– Assets with -1 correlation eliminate all risk
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-9
Figure 5.2 Combining Negatively
Correlated Assets to Diversify Risk
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-10
Figure 5.3 Portfolios of IBM and
Celgene
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-11
Figure 5.4 Risk and Return for Combinations of
Two Assets with Various Correlation Coefficients
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-12
Why Use International
Diversification?
• Offers more diverse investment alternatives than
U.S.-only based investing
• Foreign economic cycles may move independently
from U.S. economic cycle
• Foreign markets may not be as “efficient” as U.S.
markets, allowing true gains from superior
research
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-13
International Diversification
• Advantages of International Diversification
– Broader investment choices
– Potentially greater returns than in U.S.
– Reduction of overall portfolio risk
• Disadvantages of International
Diversification
–
–
–
–
Currency exchange risk
Less convenient to invest than U.S. stocks
More expensive to invest
Riskier than investing in U.S.
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-14
Methods of
International Diversification
• Foreign company stocks listed on U.S. stock
exchanges
–
–
–
–
Yankee Bonds
American Depository Shares (ADS’s)
Mutual funds investing in foreign stocks
U.S. multinational companies (typically not
considered a true international investment for
diversification purposes)
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-15
Components of Risk
• Diversifiable (Unsystematic) Risk
– Results from uncontrollable or random events
that are firm-specific
– Can be eliminated through diversification
– Examples: labor strikes, lawsuits
• Nondiversifiable (Systematic) Risk
– Attributable to forces that affect all similar
investments
– Cannot be eliminated through diversification
– Examples: war, inflation, political events
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-16
Components of Risk
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-17
Beta: A Popular Measure of Risk
• A measure of undiversifiable risk
• Indicates how the price of a security responds to market
forces
• Compares historical return of an investment to the market
return (the S&P 500 Index)
• The beta for the market is 1.0
• Stocks may have positive or negative betas. Nearly all are
positive.
• Stocks with betas greater than 1.0 are more risky than the
overall market.
• Stocks with betas less than 1.0 are less risky than the overall
market.
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-18
Beta as a Measure of Risk
Table 5.4 Selected Betas and Associated
Interpretations
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-20
Interpreting Beta
• Higher stock betas should result in higher expected
returns due to greater risk
• If the market is expected to increase 10%, a stock
with a beta of 1.50 is expected to increase 15%
• If the market went down 8%, then a stock with a
beta of 0.50 should only decrease by about 4%
• Beta values for specific stocks can be obtained
from Value Line reports or websites such as
yahoo.com
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-21
Interpreting Beta
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-22
Capital Asset Pricing Model (CAPM)
• Model that links the notions of risk and
return
• Helps investors define the required return
on an investment
• As beta increases, the required return for a
given investment increases
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-23
Capital Asset
Pricing Model (CAPM) (cont’d)
• Uses beta, the risk-free rate and the
market return to define the required return
on an investment
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-24
Capital Asset
Pricing Model (CAPM) (cont’d)
• CAPM can also be shown as a graph
• Security Market Line (SML) is the “picture”
of the CAPM
• Find the SML by calculating the required
return for a number of betas, then plotting
them on a graph
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-25
Figure 5.6 The Security Market Line
(SML)
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-26
Two Approaches to Constructing
Portfolios
Traditional Approach
versus
Modern Portfolio Theory
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-27
Traditional Approach
• Emphasizes “balancing” the portfolio using
a wide variety of stocks and/or bonds
• Uses a broad range of industries to diversify
the portfolio
• Tends to focus on well-known companies
– Perceived as less risky
– Stocks are more liquid and available
– Familiarity provides higher “comfort” levels for
investors
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-28
Modern Portfolio Theory (MPT)
• Emphasizes statistical measures to develop
a portfolio plan
• Focus is on:
– Expected returns
– Standard deviation of returns
– Correlation between returns
• Combines securities that have negative (or
low-positive) correlations between each
other’s rates of return
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-29
Key Aspects of MPT:
Efficient Frontier
• Efficient Frontier
– The leftmost boundary of the feasible set of
portfolios that include all efficient portfolios:
those providing the best attainable tradeoff
between risk and return
– Portfolios that fall to the right of the efficient
frontier are not desirable because their risk
return tradeoffs are inferior
– Portfolios that fall to the left of the efficient
frontier are not available for investments
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-30
Figure 5.7 The Feasible or Attainable
Set and the Efficient Frontier
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-31
Key Aspects of MPT:
Portfolio Betas
• Portfolio Beta
– The beta of a portfolio; calculated as the
weighted average of the betas of the individual
assets the portfolio includes
– To earn more return, one must bear more risk
– Only nondiversifiable risk (relevant risk)
provides a positive risk-return relationship
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-32
Figure 5.8 Portfolio Risk and
Diversification
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-33
Key Aspects of MPT: Portfolio Betas
Table 5.6 Austin Fund’s Portfolios V and W
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-34
Interpreting Portfolio Betas
• Portfolio betas are interpreted exactly the same
way as individual stock betas.
– Portfolio beta of 1.00 will experience a 10% increase when
the market increase is 10%
– Portfolio beta of 0.75 will experience a 7.5% increase
when the market increase is 10%
– Portfolio beta of 1.25 will experience a 12.5% increase
when the market increase is 10%
• Low-beta portfolios are less responsive and less
risky than high-beta portfolios.
• A portfolio containing low-beta assets will have a
low beta, and vice versa.
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-35
Interpreting Portfolio Betas
Table 5.7 Portfolio Betas and Associated Changes in Returns
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-36
Reconciling the Traditional
Approach and MPT
• Recommended portfolio management policy uses
aspects of both approaches:
– Determine how much risk you are willing to bear
– Seek diversification between different types of securities
and industry lines
– Pay attention to correlation of return between securities
– Use beta to keep portfolio at acceptable level of risk
– Evaluate alternative portfolios to select highest return for
the given level of acceptable risk
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-37
Figure 5.9 The Portfolio Risk-Return
Tradeoff
Copyright ©2014 Pearson Education, Inc. All rights reserved.
5-38