Last Topics Study
• Markowitz Portfolio Theory
• Risk and Return Relationship
• Efficient Portfolio
Today’s Study Topics
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Borrowing & Lending
Efficient Frontier
Security Market Line
CAPM
Validity of CAPM
Testing the CAPM
Borrowing and Lending
• Lending and borrowing extend the range of
investment possibilities.
• If you invest in portfolio S and lend or borrow
at the risk-free interest rate, rf, you can
achieve any point along the straight line from
rf through S.
– This gives you a higher expected return for any
level of risk than if you just invest in common
stocks.
Efficient Frontier
•Lending or Borrowing at the risk free rate (rf) allows us to exist outside the
efficient frontier.
Expected Return (%)
T
rf
S
Standard Deviation
Efficient Portfolio
• If you can borrow money at the risk-free rate,
you can extend your possibilities beyond S.
• You can also see that regardless of the level of
risk you choose, you can get the highest
expected return by a mixture of portfolio S
and borrowing or lending.
– S is the best efficient portfolio. There is no reason
ever to hold, say, portfolio T.
Efficient Frontier
Example
Stocks
ABC Corp
Big Corp
s
28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
Efficient Frontier
Example
Stocks
ABC Corp
Big Corp
s
28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
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
Stocks
Portfolio
New Corp
s
28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
Efficient Frontier
Example
Stocks
Portfolio
New Corp
s
28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
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
Return
B
A
Risk
(measured
as s)
Efficient Frontier
Return
B
AB
A
Risk
Efficient Frontier
Return
B
AB
N
A
Risk
Efficient Frontier
Return
B
ABN
AB
N
A
Risk
Efficient Frontier
Goal is to move up
and left.
Return
WHY?
B
ABN
AB
N
A
Risk
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
Efficient Frontier
Return
B
ABN
AB
N
A
Risk
THE RELATIONSHIP BETWEEN RISK
AND RETURN
• The least risky investment was U.S. Treasury
bills.
• Since the return on Treasury bills is fixed, it is
unaffected by what happens to the market.
– In other words, Treasury bills have a beta of 0.
• We also considered a much riskier investment,
the market portfolio of common stocks.
– This has average market risk: Its beta is 1.0.
Continue
• Wise investors don’t take risks just for fun.
• Therefore, they require a higher return from
the market portfolio than from Treasury bills.
– The difference between the return on the market
and the interest rate is termed the market risk
premium.
Security Market Line
Return
.
r
Market Return = m
Efficient Portfolio
Risk Free
Return
=
rf
Risk
Continue
• What is the expected risk premium when beta is
not 0 or 1?
• In a competitive market, the expected risk
premium varies in direct proportion to beta.
• This means that all investments must plot along
the sloping line, known as the security market
line.
• The expected risk premium on an investment
with a beta of .5 is, therefore, half the expected
risk premium on the market;
Security Market Line
Return
.
r
Market Return = m
Efficient Portfolio
Risk Free
Return
=
rf
1.0
BETA
Security Market Line
Return
.
Risk Free
Return
Security Market Line (SML)
=
rf
BETA
Continue
• We can write this relationship as;
– Expected risk premium on stock =
beta x expected risk premium on market
r - rf = beta(rm - rf )
Security
Market
Line
Return
SML
rf
BETA
1.0
SML Equation = rf + B ( rm - rf )
Capital Asset Pricing Model
R = r f + B ( r m - rf )
CAPM
CAPM
• These estimates of the returns expected by
investors in July 2001 were based on the
capital asset pricing model.
• We assumed 3.5% for the interest rate rf and 8
percent for the expected risk premium rm - rf.
CAPM
• For example, suppose that you are analyzing a
proposal by Pfizer to expand its capacity.
– At what rate should you discount the forecast cash
flows?
• According to Table 2, investors are looking for
a return of 9.2% from businesses with the risk
of Pfizer.
• So the cost of capital for a further investment
in the same business is 9.2%.
Review of the Capital Asset Pricing
Model
• 1. Investors like high expected return and low
standard deviation. Common stock portfolios that
offer the highest expected return for a given
standard deviation are known as efficient
portfolios.
• 2. If the investor can lend or borrow at the riskfree rate of interest, one efficient portfolio is
better than all the others: the portfolio that offers
the highest ratio of risk premium to standard
deviation (that is, portfolio S).
Continue
• 3. The composition of this best efficient
portfolio depends on the investor’s
assessments of expected returns, standard
deviations, and correlations.
Validity of CAPM
• First, few people quarrel with the idea that
investors require some extra return for taking
on risk.
– That is why common stocks have given on average
a higher return than U.S. Treasury bills.
• Second, investors do appear to be concerned
principally with those risks that they cannot
eliminate by diversification.
Testing The CAPM
• The capital asset pricing model states that the
expected risk premium from any investment
should lie on the market line.
• The dots show the actual average risk premiums
from portfolios with different betas. The highbeta portfolios generated higher average returns,
just as predicted by the CAPM.
• But the high-beta portfolios plotted below the
market line.
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1931-65
SML
30
20
Investors
Market
Portfolio
10
0
1.0
Portfolio Beta
Continue
• The relationship between beta and actual
average return has been much weaker since
the mid-1960s.
• The CAPM predicts that the risk premium
should increase in proportion to beta, so that
the returns of each portfolio should lie on the
upward sloping security market line.
Continue
• The portfolios of investors 1 and 10 had very
different betas but both earned the same
average return over these 25 years.
– Of course, the line was correspondingly steeper
before 1966.
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1966-91
30
20
SML
Investors
10
Market
Portfolio
0
1.0
Portfolio Beta
Summary
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Borrowing & Lending
Efficient Frontier
Security Market Line
CAPM
Validity of CAPM
Testing the CAPM