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Portfolio Selection (chapter 8) Portfolio Selection (chapter 8)

Portfolio Selection (chapter 8) - PowerPoint Presentation

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Portfolio Selection (chapter 8) - PPT Presentation

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

portfolio risk efficient asset risk portfolio asset efficient allocation optimal systematic frontier classes markowitz unsystematic variance investor return assets

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Presentation Transcript

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;