lecture 8 risk and return managerial finance fina 6335 ronald f. singer
TRANSCRIPT
Lecture 8Lecture 8Risk and ReturnRisk and Return
Managerial Finance
FINA 6335
Ronald F. Singer
8-2
Topics CoveredTopics Covered
Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives
8-3
Markowitz Portfolio TheoryMarkowitz 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.
8-4
Markowitz Portfolio TheoryMarkowitz Portfolio Theory
Price changes vs. Normal distribution
Microsoft - Daily % change 1986-1997
0
100
200
300
400
500
600
-10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
# of
Day
s (f
requ
ency
)
Daily % Change
8-5
Markowitz Portfolio TheoryMarkowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment C
0
2
4
6
8
10
12
14
16
18
20
-50 0 50
%
prob
abili
ty
% return
8-6
Markowitz Portfolio TheoryMarkowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment D
0
2
4
6
8
10
12
14
16
18
20
-50 0 50
%
prob
abili
ty
% return
8-7
Markowitz Portfolio TheoryMarkowitz Portfolio Theory
Bristol-Myers Squibb
McDonald’s
Standard Deviation
Expected Return (%)
45% McDonald’s
Expected Returns and Standard Deviations vary given different weighted combinations of the stocks.
8-8
Efficient FrontierEfficient 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.
8-9
Efficient FrontierEfficient 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 FrontierEfficient Frontier
Correlation Coefficient = 0.4Stocks % of Portfolio Avg.
ReturnABC 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 FrontierEfficient Frontier
Correlation Coefficient = .3
Stocks % of Portfolio Avg. Return
Portfolio 28.1 50% 17.4%
New CorpNew Corp 3030 50%50% 19% 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 FrontierEfficient Frontier
Return
Risk (measured as )
A
B
AB
Efficient FrontierEfficient Frontier
A
BN
Return
Risk
AB
Efficient FrontierEfficient Frontier
A
BN
Return
Risk
ABABN
Efficient FrontierEfficient Frontier
A
BN
Return
Risk
AB
Goal is to move up and left.
WHY?
ABN
Efficient FrontierEfficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
Efficient FrontierEfficient Frontier
Return
Risk
A
BNABABN
Security Market LineSecurity Market Line
Return
Risk
.
rf
Efficient PortfolioRisk Free
Return =
Security Market LineSecurity Market Line
Return
Risk
.
rf
Risk Free
Return =
Market Return = rm
Efficient Portfolio
Security Market LineSecurity Market Line
Return
Risk
.
rf
Risk Free
Return =
Market Return = rm
Efficient Portfolio
Security Market LineSecurity Market Line
Return
BETA
.
rf
Risk Free
Return =
Market Return = rm
Efficient Portfolio
1.0
Security Market LineSecurity Market Line
Return
BETA
rf
Risk Free
Return =
Market Return = rm
1.0
Security Market Line (SML)
Security Market LineSecurity Market Line
Return
BETA
rf
1.0
SML
SML Equation = rf + B ( rm - rf )
Capital Asset Pricing ModelCapital Asset Pricing Model
R = rf + B ( rm - rf )
CAPM
Testing the CAPMTesting 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 CAPMTesting 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 CAPMTesting the CAPM
0
5
10
15
20
25
Average Return (%)
Company size
Smallest Largest
Company Size vs. Average Return
Testing the CAPMTesting the CAPM
0
5
10
15
20
25
Average Return (%)
Book-Market Ratio
Highest Lowest
Book-Market vs. Average ReturnBook-Market vs. Average Return
8-29
Consumption Betas Vs. Market BetasConsumption 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 TheoryArbitrage 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 TheoryArbitrage 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
6.36Mrket
.83-Inflation
.49GNP Real
.59-rate Exchange
.61-rateInterest
5.10%spread Yield)(r
ium Risk PremEstimatedFactor
factor fr