Chapter 11 continued
Today’s Outline
• Announcements, Surprises, and Expected Returns
• Risk: Systematic and Unsystematic
• Diversification and Portfolio Risk
• Systematic Risk and Beta
• The Security Market Line
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I. Expected versus Unexpected Returns
• Stocks’ realized returns are generally not equal to expected
returns:
R = E(R) + U
• There is the expected component and the unexpected
(unanticipated) component
– At any point in time, the unexpected return can be
either positive or negative
– Over time, the average of the unexpected component is
zero
Announcements and News
• Announcements and news contain both an expected
component and a surprise component
Announcement = Expected part + Surprise
Expected part

E(R)
(influences)
- The market uses expected part of announcement to form
the expected return on a stock.
Surprise

U
- It is the surprise component that affects a stock’s price and
therefore its return.
• This is very obvious when we watch how stock prices move
when an unexpected announcement is made, or earnings are
different from anticipated.
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Efficient Markets
- a result of investors trading on the unexpected portion of
announcements
- involve random price changes because we cannot predict
surprises
Note: The easier it is to trade on surprises, the more efficient
markets should be
Systematic and Unsystematic Risk
Systematic Risk - risk factors that affect a large number of assets
• Also known as non-diversifiable risk or market risk
• Includes such things as changes in GDP, inflation, interest
rates, etc.
Unsystematic Risk - risk factors that affect a limited number of
assets
• Also known as unique risk and asset-specific risk
• Includes such things as labor strikes, part shortages, etc.
Returns
We know:
R = E(R) + U
But, U has 2 components:
- Unexpected return = systematic portion + unsystematic portion
Then,
R = E(R) + systematic portion + unsystematic portion
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II. Diversification
• Portfolio diversification- the investment in several different
asset classes or sectors
• Diversification is not just holding a lot of assets
• For example, if you own 50 Internet stocks, then you are not
diversified
• However, if you own 50 stocks that span 20 different
industries, then you are diversified
Table 11.7
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The Principle of Diversification
• Diversification can substantially reduce the variability of
returns without an equivalent reduction in expected returns
• This reduction in risk arises because worse-than-expected
returns from one asset are offset by better-than-expected
returns from another asset
• However, there is a minimum level of risk that cannot be
diversified away - that is the systematic portion
Figure 11.1
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Diversifiable Risk (unsystematic, unique, or asset-specific risk)
- The risk that can be eliminated by combining assets into a
portfolio
Note: If we hold only one asset, or assets in the same industry, then
we are exposing ourselves to risk that we could diversify away
Total Risk
• Total risk = systematic risk + unsystematic risk
• Measured by the standard deviation of returns (σ )
For well-diversified portfolios, unsystematic risk is very small
Consequently, the total risk for a diversified portfolio is essentially
equivalent to the systematic risk
Systematic Risk Principle
• There is a reward for bearing risk
• There is not a reward for bearing risk unnecessarily
• The expected return on a risky asset depends only on that
asset’s systematic risk since unsystematic risk can be
diversified away
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Measuring Systematic Risk
Beta (β) - used to measure systematic risk.
- Measures the systematic risk of an asset relative to the
average in the market.
For an asset:
If β =1  asset has the same systematic risk as the overall market
If β <1  asset has less systematic risk as the overall market
If β >1  asset has more systematic risk as the overall market
Table 11.8
Example: Yahoo! Finance provides beta, plus a lot of other
information under its profile link
• Click on the Web surfer to go to Yahoo! Finance
– Enter a ticker symbol and get a basic quote
– Click on key statistics
– Beta is reported under stock price history
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Total vs. Systematic Risk
• Consider the following information:
Standard Deviation
– Security C
20%
Beta
1.25
– Security K
0.95
30%
• Which security has more total risk?
• Which security has more systematic risk?
• Which security should have the higher expected return?
Portfolio Betas (βp)
βp = ∑ wi βi
Ex: Consider the following four securities
– Security
Weight
Beta
– DCLK
.133
4.03
– KO
.2
0.84
– INTC
.267
1.05
– KEI
.4
0.59
• What is the portfolio beta?
βp =
8
Ex 2: Suppose we invest in asset A with E(RA) = 20% and a riskfree asset. If 25% invested in ‘A’ and the rest in the risk-free asset
(rf = 8%).
E(RP) =
Note: a risk-free asset has no systematic risk => β= 0
Find the portfolio β: βP = ∑ Wi βi
βP = 0.25 x βA + 0.75 x 0
= 0.25 x 1.6
βP = 0.40
Note: we can invest more than 100% in investment A => borrow
at rf
But weights must sum to 1 => ∑ Wi = 1, for all assets in
portfolio.
Ex: You have $100 and borrow an extra $50 at rf and invest it all in
asset A => 150% investment in A. E(RP) = ∑Wi E(Ri)
Find E(RP): E(RP) = 1.50 x E(RA) + ( 1 - 1.50) x rf
= 1.5 x 0.20
+
-0.5
= 0.26 = 26%
Find βP: βP = 1.5 x βA + ( 1-1.5) x 0
x 0.08
βP = ∑ Wi βi
= 1.5 x 1.6 = 2.4
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The Security Market Line (Background)
Recall: Risk premium = E(R) – rf
Goal: define relationship between the risk premium and β so that we can
estimate the expected return.
It follows that: The higher the β → the greater the risk premium
Pt. rf => invest all $ in risk free asset => WA = 0; Wrf = (1-0) = 1.
Pt A => invest all $ in security A => Wa = 1; Wrf = (1-1) = 0
Pts between rf and A => 0 < Wa < 1
- Closer to rf => higher % of portfolio devoted to risk-free asset.
- Closer to A => higher % of portfolio devoted to asset A.
Pts w/ β > βA => more than 100% devoted to investment in asset A
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The Reward-to-Risk Ratio
We know slope =
Slope =
=
=
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Example: Portfolio Expected Returns and Betas
Given E(RA) =20% and Rf =8%
Percentage of
Portfolio in
Asset A
0%
25
50
75
100
125
150
Portfolio
Expected
Return
8%
11
14
17
20
23
26
Portfolio
Beta
.0
.4
.8
1.2
1.6
2.0
2.4
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In this example, Reward-to-risk ratio = (20 – 8) / 1.6 = 7.5
What if an asset has a reward-to-risk ratio of 8 (implying that the
asset plots above the line)?
What if an asset has a reward-to-risk ratio of 7 (implying that the
asset plots below the line)?
The Security Market Line and Market Equilibrium
• In equilibrium, all assets and portfolios have the same
reward-to-risk ratio, and each must equal the reward-to-risk
ratio for the market
E ( RA )  R f
A

E ( RM  R f )
M
The security market line (SML) is the representation of market
equilibrium
• slope of the SML is the reward-to-risk ratio:
(E(RM) – Rf) / M
• By definition, the  for the market is ALWAYS equal to 1.
• Slope = E(RM) – Rf = market risk premium
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Capital Asset Pricing Model (CAPM)
• CAPM defines the relationship between risk and return
Deriving CAPM:
For any asset “A” in the market, it must be true that:
E(RA) – Rf =
A
E(RM) – Rf
Rearranging terms:
E(RA) - Rf = A(E(RM) – Rf)
Then:
E(RA) = Rf + A(E(RM) – Rf)
Implications:
• If we know an asset’s systematic risk, we can use the CAPM
to determine its expected return
– This is true whether we are talking about financial
assets or physical assets
Factors Affecting E(RA) :
1. Pure time value of money – measured by Rf
2. Reward for bearing systematic risk – measured by (E(RM) – Rf)
3. Amount of systematic risk – measured by A
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Ex: CAPM
• Consider the betas for each of the assets given earlier. If the
risk-free rate is 3.15% and the market risk premium is 9.5%,
what is the expected return for each?
– Security
Beta
Expected Return
– DCLK
4.03
3.15 + 4.03(9.5) = 41.435%
– KO
0.84
3.15 + .84(9.5) = 11.13%
– INTC
1.05
3.15 + 1.05(9.5) = 13.125%
– KEI
0.59
3.15 + .59(9.5) = 8.755%
SML and Equilibrium
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