Chapter 8 Risk and Return. Topics Covered Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives.

Chapter 8

Risk and Return

Topics Covered

Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives

Markowitz Portfolio Theory

Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation.

Correlation coefficients make this possible. The various weighted combinations of stocks

that create this standard deviations constitute the set of efficient portfoliosefficient portfolios.

Markowitz Portfolio Theory

Price changes vs. Normal distribution

Microsoft - Daily % change 1990-2001

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

Pro

port

ion

of D

ays

Daily % Change

Markowitz Portfolio Theory

Standard Deviation VS. Expected Return

Investment A

0

2

4

6

8

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12

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18

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-50 0 50

%

prob

abili

ty

% return

Markowitz Portfolio Theory

Standard Deviation VS. Expected Return

Investment B

0

2

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-50 0 50

%

prob

abili

ty

% return

Markowitz Portfolio Theory

Standard Deviation VS. Expected Return

Investment C

0

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-50 0 50

%

prob

abili

ty

% return

Markowitz Portfolio Theory

Standard Deviation VS. Expected Return

Investment D

0

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prob

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% return

Markowitz Portfolio Theory

Coca Cola

Reebok

Standard Deviation

Expected Return (%)

35% in Reebok

Expected Returns and Standard Deviations vary given different weighted combinations of the stocks

Efficient Frontier

Standard Deviation

Expected Return (%)

•Each half egg shell represents the possible weighted combinations for two stocks.

•The composite of all stock sets constitutes the efficient frontier

Efficient Frontier

Standard Deviation

Expected Return (%)

•Lending or Borrowing at the risk free rate (rf) allows us to exist outside the

efficient frontier.

rf

Lending

BorrowingT

S

Efficient Frontier

Example Correlation Coefficient = .4

Stocks % of Portfolio Avg Return

ABC Corp 28 60% 15%

Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6

Standard Deviation = Portfolio = 28.1

Return = weighted avg = Portfolio = 17.4%

Efficient Frontier

Example Correlation Coefficient = .4

Stocks % of Portfolio Avg Return

ABC Corp 28 60% 15%

Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6

Standard Deviation = Portfolio = 28.1

Return = weighted avg = Portfolio = 17.4%

Let’s Add stock New Corp to the portfolio

Efficient Frontier

Example Correlation Coefficient = .3

Stocks % of Portfolio Avg Return

Portfolio 28.1 50% 17.4%

New CorpNew Corp3030 50%50% 19% 19%

NEW Standard Deviation = weighted avg = 31.80

NEW Standard Deviation = Portfolio = 23.43

NEW Return = weighted avg = Portfolio = 18.20%

Efficient Frontier

Example Correlation Coefficient = .3

Stocks % of Portfolio Avg Return

Portfolio 28.1 50% 17.4%

New Corp 30 50% 19%

NEW Standard Deviation = weighted avg = 31.80

NEW Standard Deviation = Portfolio = 23.43

NEW Return = weighted avg = Portfolio = 18.20%

NOTE: Higher return & Lower risk

How did we do that? DIVERSIFICATION

Efficient Frontier

A

B

Return

Risk (measured as )

Efficient Frontier

A

B

Return

Risk

AB

Efficient Frontier

A

BN

Return

Risk

AB

Efficient Frontier

A

BN

Return

Risk

ABABN

Efficient Frontier

A

BN

Return

Risk

AB

Goal is to move up and left.

WHY?

ABN

Efficient Frontier

Return

Risk

Low Risk

High Return

High Risk

High Return

Low Risk

Low Return

High Risk

Low Return

Efficient Frontier

Return

Risk

Low Risk

High Return

High Risk

High Return

Low Risk

Low Return

High Risk

Low Return

Efficient Frontier

Return

Risk

A

BNABABN

Security Market Line

Return

Risk

.

rf

Risk Free

Return =

Efficient Portfolio

Market Return = rm

Security Market Line

Return

.

rf

Risk Free

Return =

Efficient Portfolio

Market Return = rm

BETA1.0

Security Market Line

Return

.

rf

Risk Free

Return =

BETA

Security Market Line (SML)

Security Market LineReturn

BETA

rf

1.0

SML

SML Equation = rf + B ( rm - rf )

Capital Asset Pricing Model

R = rf + B ( rm - rf )

CAPM

Testing the CAPM

Avg Risk Premium 1931-65

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

Testing the CAPM

Avg Risk Premium 1966-91

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

Testing the CAPM

0

5

10

15

20

2519

28

1933

1938

1943

1948

1953

1958

1963

1968

1973

1978

1983

1988

1993

1998

High-minus low book-to-market

Return vs. Book-to-MarketDollars

Low minus big

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

Consumption Betas vs Market Betas

Stocks (and other risky assets)

Wealth = marketportfolio

Market risk makes wealth

uncertain.

Stocks (and other risky assets)

Consumption

Wealth

Wealth is uncertain

Consumption is uncertain

Standard

CAPM

Consumption

CAPM

Arbitrage Pricing Theory

Alternative to CAPMAlternative to CAPM

Expected Risk

Premium = r - rf

= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …

Return = a + bfactor1(rfactor1) + bf2(rf2) + …

Arbitrage Pricing Theory

Estimated risk premiums for taking on risk factors

(1978-1990)

6.36Mrket

.83-Inflation

.49GNP Real

.59-rate Exchange

.61-rateInterest

5.10%spread Yield)(r

ium Risk PremEstimatedFactor

factor fr