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Chapter 21. A Basic Look at Portfolio Management and Capital Market Theory. Objectives. Understand the basic statistical techniques for measuring risk and return Explain how the portfolio effect works to reduce the risk of an individual security

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chapter 21

Chapter 21

A Basic Look at

Portfolio Management

and Capital Market


  • Understand the basic statistical techniques for measuring risk and return
  • Explain how the portfolio effect works to reduce the risk of an individual security
  • Discuss the concept of an efficient portfolio
objectives continued
Objectives continued
  • Explain the importance of the capital asset pricing model
  • Understand the concept of the beta coefficient
  • Discuss the required rate of return on an individual stock and how it relates to its beta
a basic look at portfolio management and capital market theory
A Basic Look at Portfolio Management and Capital Market Theory
  • Formal Measurement of Risk
  • Portfolio Effect
  • Developing and Efficient Portfolio
  • Capital Asset Pricing Model
  • Return on an Individual Security
  • Assumptions of the Capital Asset Pricing Model
a basic look at portfolio management and capital market theory continued
A Basic Look at Portfolio Management and Capital Market Theory continued
  • Appendix 21A: The Correlation Coefficient
  • Appendix 21B: Least Squares Regression Analysis
  • Appendix 21 C: Derivation of the Security Market Line (SML)
  • Appendix 21D: Arbitrage Pricing Theory
review from chapter 1 risk expected return
Review from Chapter 1Risk & Expected Return
  • Risk
    • uncertainty about future outcomes
    • The greater the dispersion of possible outcomes, the greater the risk
  • Most investors tend to be risk averse
    • all things being equal, investors prefer less risk to more risk
    • investors will increase risk-taking position only if premium for risk is involved
    • Each investor has different attitude toward risk
formal measurement of risk
Formal Measurement of Risk
  • Expected Value
  • Standard Deviation
formal measurement of risk1
Formal Measurement of Risk
  • How to measure risk?
  • Design probability distribution of anticipated future outcomes
  • Establish
    • Probability distribution
    • Determine expected value
    • Calculate dispersion around expected value

The greater the dispersion the greater the risk

formal measurement of risk2
Formal Measurement of Risk

Outcomes and associated probabilities are likely to be based on

  • Economic projections
  • Past experience
  • Subjective judgments
  • Many other variables
expected value
Expected Value




Probability of







standard deviation
Standard Deviation σ
  • The commonly used measure of dispersion is the standard deviation, which is a measure of the spread of the outcomes around the expected value

K = Possible outcomes   

P = Probability of that outcome based on the state of the economy

i = Investment i

For stocks,    

K = Price appreciation potential plus the dividend yield (total return)

= Expected Value


standard deviation2
Standard Deviation σ
  • Expected value of both investments is 10%
  • σi= 3.9%
  • σj= 5.1%
  • Compare investment i with j
  • j has a larger dispersion than i
  • j is riskier than i
  • Investment j is countercyclical
    • It does well during a recession
    • Poorly in a strong economy
portfolio effect expected value for a 2 asset portfolio
Portfolio Effect Expected Value for a 2-Asset Portfolio
  • Combine investment i andj into one portfolio
  • Weighted evenly (50-50)
  • New portfolio’s expected value = 10%
  • Kp = expected value of portfolio
  • X values represent weights assigned
portfolio effect for a 2 asset portfolio
Portfolio Effect - σ for a 2-Asset Portfolio

σ for combined portfolio (p )

using weighted average σof i & j

Portfolio σ would be 4.5%


  • Investor i appears to lose!
  • Expected value remains at 10%
  • σ increases from 3.9 to 4.5% WHY?

There is one fallacy in the analysis

portfolio effect for a 2 asset portfolio1
Portfolio Effect - σ for a 2-Asset Portfolio

Standard Deviation of a portfolio is not based on simple weighted average of individual standard deviations!

appropriate standard deviation two asset portfolio
Appropriate Standard Deviation Two-Asset Portfolio
  • σp =Standard deviation of portfolio
  • ri j = Correlation coefficient *
  • ri jmeasures joint movement of 2 variables
  • Value for ri jcan be from -1 to +1

*See Appendix 21A


Xi = 0.5

σi= 3.9

ri j= -0.70

See Appendix 21A

Xj = 0.5

σj = 5.1







Portfolio standard deviation is less than standard deviation of either investment


Combine 2 investments to reduce risk

  • Reduced risk (less dispersion)
  • Expected value constant at 10%
developing an efficient portfolio
Developing an Efficient Portfolio
  • Consider large number of portfolios based on
    • Expected value
    • Standard deviation
    • Correlations between the individual securities
  • A portfolio of 14 to 16 stocks is fully diversified
  • Portfolio theory developed by Professor Harry Markowitz (1950s)

Assume we have identified the following risk-return possibilities for eight different portfolios

Next slide shows graph

efficient frontier line
Efficient Frontier Line
  • 4 points out of 8 possibilities lie on the frontier
  • ACFH delineates the efficient set of portfolios
  • It is efficient because portfolios on this line dominate all other attainable portfolios

ACFH line: efficient frontier

because portfolios on it provide

best risk-return trade-off

developing an efficient portfolio1
Developing an Efficient Portfolio
  • Efficient frontier line gives
    • Maximum return for a given level of risk
    • Minimum risk for a given level of return
  • No portfolios exist above the efficient frontier
  • Portfolios below it are not acceptable alternatives compared to points on the line
risk return indifference curves
Risk-Return Indifference Curves
  • Investor’s trade-off between risk & return
  • Steeper slopes means more risk-averse
  • Investor B has a steeper slope than investor A
  • B requires more return (more risk premium) for each additional unit of risk
  • From point X to Y investor B requires approx. twice as much incremental return as A
optimum portfolio
Optimum Portfolio
  • Match indifference curve with

efficient frontier

  • Highest point is Con efficient frontier
  • Point of tangency of two curves
  • Same slope at point
  • Crepresents same risk-return characteristics


Relate risk-return indifference curves to

efficient frontier to determine that point

of tangency providing maximum benefits

capital asset pricing model capm
Capital Asset Pricing Model (CAPM)
  • Professors Sharpe et al advanced

efficient portfoliosto

capital asset pricing model

  • Assets value based on risk characteristics
  • CAPM takes off where efficient frontier stops
  • Introduce
    • New investment outlet
    • Risk-free asset (RF)
risk free rf asset
Risk-free (RF) Asset
  • Has no risk of default
  • Standard deviation of zero (-0-)
  • Lowest/safest return
    • U.S. Treasury bill
    • U.S. Treasury bond

Zero risk

CAPM combines risk-free

asset & efficient frontier

capital market line cml
Capital Market Line (CML)
  • RFMZ line capital market line (CML)
  • Formula for the capital market line

See next slide

Kp = Expected value of the portfolio

σP= Portfolio standard deviation

RF= Risk-free rate

KM = Market rate of return

σM= Market standard deviation

return on an individual security
Return on an Individual Security
  • Beta Coefficient
  • Systematic and Unsystematic Risk
  • Security Market Line
beta coefficient measures
Beta Coefficient Measures

The market

in general

A stock’s









Total return of stock i for 5 years

compared with the market return

return on an individual security1
Return on an Individual Security

Ki = Stock return, dependent variable, Y-axis

ai (alpha) = Line intersects vertical axis

bi (beta) = Slope of the line

KM = Market return, independent variable, X-axis

ei = Random error term

ai + biKM : Straight line

ei = Deviations, nonrecurring movements

  • Draw line of best fit - see Figure 21–11 or
  • Least squares regression analysis Appendix 21B

Market movement

Company specific

In a diversified portfolio

unsystematic risk approaches 0

security market line sml
Security Market Line (SML)
  • SML shows risk-return trade-off for a stock
  • CML shows risk-return trade-off for a portfolio

Ki= Expected return on stock i

RF = Risk-free rate of return

bi= Beta risk, systematic risk

KM= Market rate of return

assumptions of the capital asset pricing model
Assumptions of the Capital Asset Pricing Model

All investors

  • Can borrow/lend unlimited funds at risk-free rate
  • Have the same one-period time horizon
  • Maximize expected utility, evaluate investments by standard deviations of portfolio returns
assumptions of the capital asset pricing model continued
Assumptions of the Capital Asset Pricing Model continued

All investors

  • Have the same expectations
  • All assets are perfectly divisible
  • There are no taxes or transactions costs
  • The market is efficient and in equilibrium