Diversification is key to risk management Asset allocation most important single decision Using Markowitz Principles Step 1 Identify optimal riskreturn combinations using the Markowitz analysis ID: 656902
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Slide1
Portfolio Selection
(chapter 8)Slide2
Diversification is key to risk managementAsset allocation most important single decision
Using Markowitz PrinciplesStep 1: Identify optimal risk-return combinations using the Markowitz analysis Inputs: Expected returns, variances, covariancesStep 2: Choose the final portfolio based on your preferences for return relative to risk
8-
2
Building a PortfolioSlide3
100% bonds
100% stocks
Example: NOT on the EXAMSlide4
The Efficient Frontier
Efficient Frontier – represents the set of all mean/variance efficient (optimal) portfoliosOptimal portfolio has maximum return for a given level of risk or minimum risk for a given level of returnPortfolios on the efficient frontier dominate all other portfoliosNo portfolio on the efficient frontier dominates another portfolio on the frontierSlide5
Efficient Portfolios
Efficient frontier or Efficient set (curved line from A to B)Global minimum variance portfolio (represented by point A)Portfolios on AB dominate those on AC
x
B
A
C
y
Risk =
E(R)Slide6
Portfolio weights are the output from Markowitz analysisAssume investors are risk averse
Indifference curves (ICs) help select individual’s optimal portfolioIC, description of preferences for risk and returnIC reflects portfolio combinations that are equally desirableICs match investor preferences with portfolio possibilities
8-
6
Selecting an Optimal Portfolio
of Risky AssetsSlide7
The Optimal Portfolio
Efficient Frontier
Investor 2 indifference/utility curves
Investor 1 indifference curves
•
•
Goal is to achieve highest (most NW) attainable curve)Slide8
Markowitz portfolio selection modelAssumes investors use only risk and return to decideGenerates a set of equally “good” portfolios
Does not address the issues of borrowed money or risk-free assetsCumbersome to apply
8-
8
Selecting an Optimal Portfolio
of Risky AssetsSlide9
Another way to use Markowitz model is with asset classesAllocation of portfolio to asset typesAsset class rather than individual security is most important for investorsCan be used when investing internationally
Different asset classes offer various returns and levels of riskCorrelation coefficients may be quite low
8-
9
Selecting Optimal Asset ClassesSlide10
Includes two dimensionsDiversifying between asset classes
Diversifying within asset classesAsset classes include:Equities – foreign and domesticBondsTreasury Inflation-Protected Securities (TIPS)Alternative assets – real estate, commodities, private equity, hedge funds, etc.
8-
10
Asset AllocationSlide11
Correlation among asset classes must be considered
Correlations change over timeFor investors, allocation depends onTime horizonRisk toleranceDiversified asset allocation does not guarantee against loss
Asset AllocationSlide12
Index Mutual Funds and ETFsCover various asset classes: domestic and foreign stocks (all investment styles), alternative assets (e.g. real estate, commodities), bonds of all types
Life Cycle AnalysisVaries asset allocation based on investor age Life-cycle funds (target-date funds) vary allocation as investor agesNo one “correct” approach to allocation
Asset AllocationSlide13
Systematic & Unsystematic Risk
Total = Systematic + Unsystematic Risk Risk Risk p2 = Systematic + Unsystematic Variance Variance The variance (risk) of a portfolio, or a single security, consists of both systematic risk and unsystematic riskSlide14
Systematic & Unsystematic Risk
Systematic risk is not diversifiableSystematic risk - risk of an overall movement in the marketnondiversifiable systematic marketUnsystematic risk is diversifiableUnsystematic risk - risk of an event that is unique to the asset or a small group of assets diversifiable unsystematic
uniqueSlide15
s
p
%
35
20
0
Number of securities in portfolio
10 20 30 40 ...... 100+
Diversifiable (nonsystematic) risk
Nondiversifiable (systematic) risk
Portfolio Risk and Diversification
Total riskSlide16
Learning objectives
Know the concept of optimal risk-return combinations
Know the concepts of efficient frontier, global minimum variance, efficient set, indifference curves, and selecting optimal portfolio
International diversification
Important conclusions about Markowitz modelAsset Allocation decision and major asset classesAsset allocation using stocks and bondsSystematic and nonsystematic riskEnd of chapter questions 8.1 to 8.7;