Chapter 8
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Based on annual returns from 1926-2004
Avg. Return
Std Dev.
Small Stocks
17.5%
33.1%
Large Co. Stocks
12.4%
20.3%
L-T Corp Bonds
6.2%
8.6%
L-T Govt. Bonds
5.8%
9.3%
U.S. T-Bills
3.8%
3.1%
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Risk: The Big Picture
Expected Return
Stand Alone Risk
Portfolio Return and
Risk
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Risk Diversification
Market Risk

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Beta
CAPM/Security Market
Line Equation (SML)
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Risk is an uncertain outcome or chance of an
adverse outcome.
Concerned with the riskiness of cash flows
from financial assets.
Stand Alone Risk: Single Asset

relevant risk measure is the total risk of expected
cash flows measured by standard deviation .
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Portfolio Context: A group of assets. Total
risk consists of:

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Diversifiable Risk (company-specific,
unsystematic)
Market Risk (non-diversifiable, systematic)
Small group of assets with Diversifiable Risk
remaining: interested in portfolio standard
deviation.

correlation ( or r) between asset returns which
affects portfolio standard deviation
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Well-diversified Portfolio
Large Portfolio (10-15 assets) eliminates
diversifiable risk for the most part.
Interested in Market Risk which is the risk
that cannot be diversified away.
The relevant risk measure is Beta which
measures the riskiness of an individual asset
in relation to the market portfolio.
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HPR = (End of Period Price - Beginning Price
+ Dividends)/Beginning Price
HPR = Capital Gains Yield + Dividend Yield
HPR = (P1-P0)/P0 + D/P0
Example: Bought at $50, Receive $3 in
dividends, current price is $54
HPR = (54-50+3)/50 = .14 or 14%
CGY = 4/50 = 8%, DY = 3/50 = 6%
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Expected Rate of Return given a probability
distribution of possible returns(ri): E(r)
n
E(r) = Pi ri
i=1
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Realized or Average Return on Historical
Data:
-
n
r = 1/n  ri
i=1
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Relevant Risk Measure for single asset
Variance = 2 =  ( ri - E(r))2 Pi
Standard Deviation = Square Root of Variance
Historical Variance = 2 = 1/n(ri – rAVG )2
Sample Variance = s2 = 1/(n-1) (ri – rAVG )2
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State of
Contrary
Economy Probability MAD Inc. Co. (CON)
Boom
0.25
80%
-6%
Normal
0.60
30%
10%
Recession
0.15
-30%
20%
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Most investors are Risk Averse, meaning
they don’t like risk and demand a higher
return for bearing more risk.
The Coefficient of Variation (CV) scales risk
per unit of expected return.
CV = /E(r)
CV is a measure of relative risk, where
standard deviation measures absolute risk.
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MAD Inc.
E(r) = 33.5%
 = 34.0%
 CV = 34%/33.5%
 CV = 1.015
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Contrary Co.
E(r) = 7.5%
 = 8.5%
 CV = 8.5%/7.5%
 CV = 1.133
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E(rp) = wiE(ri) = weighted average of the
expected return of each asset in the portfolio
In our example, MAD E(r) = 33.5% and CON
E(r) = 7.5%
What is the expected return of a portfolio
consisting of 60% MAD and 40% CON?
E(rp) = wiE(ri) = .6(33.5%) + .4(7.5%) = 23.1%
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Looking at a 2-asset portfolio for simplicity,
the riskiness of a portfolio is determined by
the relationship between the returns of each
asset over different states of nature or over
time.
This relationship is measured by the
correlation coefficient( r ): -1<= r < =+1
All else constant: Lower r = less portfolio risk
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State of
Economy
Boom
Normal
Recession
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Probability MAD Inc.
0.25
80%
0.60
30%
0.15
-30%
Contrary MAD-CON
Co. (CON) Portfolio
-6%
45.6%
10%
22.0%
20%
-10.0%
Each MAD-CON ri = .6(MAD)+.4(CON);
E(Rp) = 23.1%
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Portfolio standard deviation
Diversifiable
risk
Market risk
0
5
10
15
Number of Securities
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As more and more assets are added to a
portfolio, risk measured by  decreases.
However, we could put every conceivable
asset in the world into our portfolio and still
have risk remaining. (See Fig. 8-8, pg. 265)
This remaining risk is called Market Risk and
is measured by Beta.
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Beta(b) measures how the return of an individual asset (or
even a portfolio) varies with the market.
b = 1.0 : same risk as the market
b < 1.0 : less risky than the market
b > 1.0 : more risky than the market
Beta is the slope of the regression line (y = a + bx) between a
stock’s return(y) and the market return(x) over time, b from
simple linear regression.
Sources for stock betas: ValueLine Investment Survey (at
BEL), Yahoo Finance, MSN Money, Standard & Poors
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The story is the same as Chapter 6: a stock’s
required rate of return = nominal risk-free
rate + the stock’s risk premium.
The main assumption is investors hold well
diversified portfolios = only concerned with
market risk.
A stock’s risk premium = measure of market
risk X market risk premium.
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RPM = market risk premium = rM - rRF
RPi = stock risk premium = (RPM)bi
ri = rRF + (rM - rRF )bi
= rRF + (RPM)bi
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What is Intel’s required return if its B = 1.2
(from ValueLine Investment Survey), the
current 3-mo. T-bill rate is 5%, and the
historical US market risk premium of 8.6% is
expected?
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The beta of a portfolio of stocks is equal to the
weighted average of their individual betas: bp =
wibi
Example: What is the portfolio beta for a portfolio
consisting of 25% Home Depot with b = 1.0, 40%
Hewlett-Packard with b = 1.35, and 35% Disney with b
= 1.25. What is this portfolio’s required (expected)
return if the risk-free rate is 5% and the market
expected return is 14%?
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AT&T currently sells for $36.50. Should we
add AT&T with an expected price and
dividend in a year of $39.54 & $1.42 and a b =
1.2 to our portfolio?
To make our decision find AT&T’s expected
return using the holding period return
formula and compare to AT&T’s SML return.
Recall that rRF = 5% and rM = 14%
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A graphical representation of the CAPM/SML
equation.
Gives required (expected) returns for investments
with different betas.
Y axis = expected return, X axis = beta
Intercept = risk-free rate = 3-month T-bill rate (B = 0)
Slope of SML = market risk premium
For the following SML graph, let’s use a 3-month Tbill rate of 5% and assume investors require a
market return of 14%.
Graph r = 5% + B(14%-5%)
Market risk premium = 14% - 5% = 9%
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25.00%
Return
20.00%
15.00%
12.20%
10.00%
5.00%
0.00%
0
0.5
1
Beta
1.5
2
2.5
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What happens if inflation increases?
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What happens if investors become more risk
averse about the stock market?
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Check out the following graphs with our base
SML = 5% + (14%-5%)b
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35.00%
30.00%
Return
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
0
0.5
1
1.5
Beta
2
2.5
3
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35.00%
30.00%
Return
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
0
0.5
1
1.5
Beta
2
2.5
3
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There are two functions in Excel that will find
the X coefficient (beta).
The functions are LINEST and SLOPE.
The format is =LINEST(y range,x range)
The above format is the same for SLOPE.
Remember the stock’s returns is the y range,
and the market’s returns is the x range.
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