gsb-711-lecture-note-05-risk-return-and-capm
DESCRIPTION
This is the fifth presentation for the University of New England Graduate School of Business course GSB711 Managerial Finance, offered by Dr Subba Reddy Yarram. This presentation examines risk, return and the Capital Asset Pricing Model (CAPM).TRANSCRIPT
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GSB711 Managerial Finance – Topic 05 Page No. 1 GSB711 Managerial Finance – Topic 05 Page No. 1
Risk, Return and Capital Asset Pricing Model
Topic 05GSB711 – Managerial Finance
Readings: Chapter: Introduction to Risk, Return and the Opportunity Cost of Capital (Pages
220 – 246) Questions: 1, 3, 6, 7 and Problems: 9, 13, 16, 20, 21 and 23.
Chapter: Risk, Return and Capital Budgeting (Pages 248 – 273)Questions: 1, 2, 4 and Problems: 6, 7, 9, 10, 13, 16, 17, 21, 25 and 29.
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Topics Covered
• Rates of Return: A Review• A Century of Capital Market History• Measuring Risk• Risk & Diversification• Measuring Market Risk
– Beta• Risk and Return
– CAPM• Capital Budgeting and Project Risk
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Rates of Return
26.1%or .261=
75.06
37.123.18 =Return Percentage
P e rc e n ta g e R e tu rn = C a p i ta l G a in + D iv id e n d In i t ia l S h a re P r ic e
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Rates of Return
D iv id e n d Y ie ld = D iv id e n d In i t ia l S h a re P r ic e
C a p i t a l G a in Y ie ld = C a p i t a l G a inIn i t i a l S h a r e P r i c e
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Rates of Return
%1.8or 018.75.06
1.37= Yield Dividend
%24.3or 243.75.06
18.23= YieldGain Capital
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Rates of ReturnNominal vs. Real
1+ real ror = 1 + nominal ror1 + inflation rate
%1.21ror real
211.1=ror real+1 .041 + 1.261 + 1
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Market Indexes
Dow Jones Industrial Average (The Dow)Value of a portfolio holding one share in each of 30 large industrial firms.
Standard & Poor’s Composite Index (The S&P 500)Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues.
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The Value of an Investment of $1 in 1900
Source: Ibbotson Associates
1
10
100
1000
10000
100000
Common StocksLong T-BondsT-Bills
Inde
x
Year Start
$22,745
$192
$69
2008
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Rates of Return
-60.00%
-40.00%
-20.00%
0.00%
20.00%
40.00%
60.00%R
etu
rn (
%)
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Common Stocks (1900-2007)
2007
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Expected Return
7.6+2.2=9.8% (2008)
7.6+14=21.6% (1981)
premium
risk normal+
billsTreasury
on rateinterest =
return
market Expected
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What is Risk?• Risk, in traditional terms, is viewed as a ‘negative’.
Webster’s dictionary, for instance, defines risk as “exposing to danger or hazard”. The Chinese symbols for risk, reproduced below, give a much better description of risk
• The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity.
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Country Risk Premia (%)
0
2
4
6
8
10
12Italy
Japan
France
Germany
Australia
S Africa
Sweden
USA
Average
Netherlands
UK
Norway
Canada
Ireland
Spain
Switzerland
Belgium
Denmark
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Measuring Risk
Variance - Average value of squared deviations from mean. A measure of volatility.
Standard Deviation - Average value of squared deviations from mean. A measure of volatility.
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Expected Returns
• Expected returns are based on the probabilities of possible outcomes
• In this context, “expected” means average if the process is repeated many times
• The “expected” return does not even have to be a possible return
n
iiiRpRE
1
)(
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Example: Expected Returns
• Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?– State Probability C T– Boom 0.3 15 25– Normal 0.5 10 20– Recession ??? 2 1
• RC = .3(15) + .5(10) + .2(2) = 9.99%• RT = .3(25) + .5(20) + .2(1) = 17.7%
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Variance and Standard Deviation
• Variance and standard deviation still measure the volatility of returns
• Using unequal probabilities for the entire range of possibilities
• Weighted average of squared deviations
n
iii RERp
1
22 ))((σ
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Example: Variance and Standard Deviation
• Consider the previous example. What are the variance and standard deviation for each stock?
• Stock C– 2 = .3(15-9.9)2 + .5(10-9.9)2 + .2(2-9.9)2 =
20.29– = 4.5
• Stock T– 2 = .3(25-17.7)2 + .5(20-17.7)2 + .2(1-
17.7)2 = 74.41– = 8.63
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Portfolios
• A portfolio is a collection of assets• An asset’s risk and return are important in how
they affect the risk and return of the portfolio• The risk-return trade-off for a portfolio is
measured by the portfolio expected return and standard deviation, just as with individual assets
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Example: Portfolio Weights
• Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security?– $2000 of DCLK– $3000 of KO– $4000 of INTC– $6000 of KEI
• DCLK: 2/15 = .133• KO: 3/15 = .2• INTC: 4/15 = .267• KEI: 6/15 = .4
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Portfolio Expected Returns
• The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio
• You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities
m
jjjP REwRE
1
)()(
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Example: Expected Portfolio Returns
• Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?– DCLK: 19.69%– KO: 5.25%– INTC: 16.65%– KEI: 18.24%
• E(RP) = .133(19.69) + .2(5.25) + .167(16.65) + .4(18.24) = 13.75%
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Portfolio Variance
• Compute the portfolio return for each state:RP = w1R1 + w2R2 + … + wmRm
• Compute the expected portfolio return using the same formula as for an individual asset
• Compute the portfolio variance and standard deviation using the same formulas as for an individual asset
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Measuring RiskCoin Toss Game-calculating variance and
standard deviation(1) (2) (3)
Percent Rate of Return Deviation from Mean Squared Deviation
+ 40 + 30 900
+ 10 0 0
+ 10 0 0
- 20 - 30 900
Variance = average of squared deviations = 1800 / 4 = 450
Standard deviation = square of root variance = 450 = 21.2%
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Histogram of Returns
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 5502468
1012
Common Stocks
Return, percent
Nu
mb
er
of Y
ea
rs
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 550
10
20
30
40
50
Treasury Bonds
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 550
20
40
60
80
Treasury Bills
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Risk and Diversification
Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.
Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”
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Risk and Diversification
Deviations from SquaredYear Rate of Return, % Average Return, % Deviations
2002 -20.9 -29.4 864.362003 31.6 23.1 533.612004 12.5 4.0 16.002005 6.4 -2.1 4.412006 15.8 7.3 53.292007 5.6 -2.9 8.41
Total 51.0 1,480.08
Average return = 51.0/6 = 8.50%246.6815.71%
Variance = average of squared deviations = 1,480.08/6 = Standard deviation = square root of variance =
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Risk and Diversification
Portfolio rate
of return=
fraction of portfolio
in first assetx
rate of return
on first asset
+fraction of portfolio
in second assetx
rate of return
on second asset
((
((
))
))
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Diversification
• Portfolio diversification is 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, you
are not diversified• However, if you own 50 stocks that span 20
different industries, then you are diversified
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29
Portfolio diversification with additional stocks in a portfolio
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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
• However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion
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Portfolio diversification and numbers of stocks in a portfolio
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Diversifiable Risk
• The risk that can be eliminated by combining assets into a portfolio
• Often considered the same as unsystematic, unique or asset-specific risk
• If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away
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Total Risk
• Total risk = systematic risk + unsystematic risk• The standard deviation of returns is a measure of
total risk• For well-diversified portfolios, unsystematic risk is
very small• Consequently, the total risk for a diversified
portfolio is essentially equivalent to the systematic risk
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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
• How do we measure systematic risk?• We use the beta coefficient to measure
systematic risk• What does beta tell us?
– A beta of 1 implies the asset has the same systematic risk as the overall market
– A beta < 1 implies the asset has less systematic risk than the overall market
– A beta > 1 implies the asset has more systematic risk than the overall market
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Total versus Systematic Risk
• Consider the following information: Standard Deviation Beta– Security C 20% 1.25– Security K 30% 0.95
• Which security has more total risk?• Which security has more systematic risk?• Which security should have the higher expected
return?
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Beta and the Risk Premium
• Remember that the risk premium = expected return – risk-free rate
• The higher the beta, the greater the risk premium should be
• Can we define the relationship between the risk premium and beta so that we can estimate the expected return?– YES!
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Stock Market Volatility 1900-2007
0
10
20
30
40
50
60
1900
1905
1910
1915
1920
1925
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Std
Dev
200
7
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GSB711 Managerial Finance – Topic 05 Page No. 39 GSB711 Managerial Finance – Topic 05 Page No. 39
The Value of Investments
Aug-0
4
Nov 0
4
Feb 0
5
May
05
Aug 0
5
Nov 0
5
Feb 0
6
May
06
Aug 0
6
Nov 0
6
Feb 0
7
May
07
Aug 0
7
Nov 0
70
20
40
60
80
100
120
140
160
Network Mining
Ford
Portfolio
Val
ue (
Aug
ust
2004
= 1
00)
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Risk and Diversification
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
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05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
Risk and Diversification
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Measuring Market Risk
Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index is used to represent the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio.
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Measuring Market Risk
Example - Turbo Charged Seafood has the following % returns on its stock, relative to the listed changes in the % return on the market portfolio. The beta of Turbo Charged Seafood can be derived from this information.
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GSB711 Managerial Finance – Topic 05 Page No. 44 GSB711 Managerial Finance – Topic 05 Page No. 44
Measuring Market Risk
Month Market Return % Turbo Return %
1 + 1 + 0.8
2 + 1 + 1.8
3 + 1 - 0.2
4 - 1 - 1.8
5 - 1 + 0.2
6 - 1 - 0.8
Example - continued
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GSB711 Managerial Finance – Topic 05 Page No. 45 GSB711 Managerial Finance – Topic 05 Page No. 45
Measuring Market Risk
B = = 0.81.62
• When the market was up 1%, Turbo average % change was +0.8%
• When the market was down 1%, Turbo average % change was -0.8%
• The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8.
Example - continued
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GSB711 Managerial Finance – Topic 05 Page No. 46 GSB711 Managerial Finance – Topic 05 Page No. 46
Measuring Market RiskExample - continued
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Market Return %
Turbo return %
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GSB711 Managerial Finance – Topic 05 Page No. 47 GSB711 Managerial Finance – Topic 05 Page No. 47
Portfolio Betas
• Diversification decreases variability from unique risk, but not from market risk.
• The beta of your portfolio will be an average of the betas of the securities in the portfolio.
• If you owned all of the S&P Composite Index stocks, you would have an average beta of 1.0
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GSB711 Managerial Finance – Topic 05 Page No. 48 GSB711 Managerial Finance – Topic 05 Page No. 48
Stock Betas
BBetas calculated with price data from January 2003 thru December 2007
Stock BetaAmazon.com 2.39Ford 2.46Newmont Mining 0.84Intel 1.59Microsoft 1.04Dell Computer 1.27Boeing 1.23McDonalds 1.44Pfizer 0.67Dupont 1.24Disney 1.00ExxonMobil 0.81IBM 1.13Wal-Mart 0.24Campbell Suop 0.46GE 0.76Heinz 0.59
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GSB711 Managerial Finance – Topic 05 Page No. 49 GSB711 Managerial Finance – Topic 05 Page No. 49
Risk and Return
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Market Return (%)
Va
ngu
ard
Exp
lore
r R
etu
rn (
%)
Vanguard Explorer Fund return
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GSB711 Managerial Finance – Topic 05 Page No. 50 GSB711 Managerial Finance – Topic 05 Page No. 50
Risk and ReturnVanguard Index 500 return
-10 -8 -6 -4 -2 0 2 4 6 8 10
-10
-8
-6
-4
-2
0
2
4
6
8
10
Market Return (%)
Va
ngu
ard
Re
turn
(%
)
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GSB711 Managerial Finance – Topic 05 Page No. 51 GSB711 Managerial Finance – Topic 05 Page No. 51
Measuring Market RiskMarket Risk Premium - Risk premium of
market portfolio. Difference between market return and return on risk-free Treasury bills.
0
2
4
6
8
10
12
14
0 0.2 0.4 0.6 0.8 1
Beta
Exp
ecte
d R
etu
rn (
%)
. Market Portfolio
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GSB711 Managerial Finance – Topic 05 Page No. 52 GSB711 Managerial Finance – Topic 05 Page No. 52
Measuring Market RiskCAPM - Theory of the relationship
between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.
Market risk premium = r - r
Risk premium on any asset = r - r
Expected Return = r + B(r - r )
m f
f
f m f
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GSB711 Managerial Finance – Topic 05 Page No. 53 GSB711 Managerial Finance – Topic 05 Page No. 53
Measuring Market RiskSecurity Market Line - The graphic
representation of the CAPM.
Beta
Exp
ecte
d R
etu
rn (
%)
.
Rf
Rm
Security Market Line
1.0
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GSB711 Managerial Finance – Topic 05 Page No. 54 GSB711 Managerial Finance – Topic 05 Page No. 54
Capital Asset Pricing Model
R = rf + B ( rm - rf )
CAPM
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GSB711 Managerial Finance – Topic 05 Page No. 55 GSB711 Managerial Finance – Topic 05 Page No. 55
Testing the CAPM
Avg Risk Premium 1931-2005
Portfolio Beta1.0
SML30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
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GSB711 Managerial Finance – Topic 05 Page No. 56 GSB711 Managerial Finance – Topic 05 Page No. 56
Testing the CAPM
0.1
1
10
10019
26
1936
1946
1956
1966
1976
1986
1996
2006
High-minus low book-to-market
Return vs. Book-to-MarketDollars(log scale)
Small minus big
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
200
7
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GSB711 Managerial Finance – Topic 05 Page No. 57 GSB711 Managerial Finance – Topic 05 Page No. 57
Stock Expected Returns
)(rE
Stock Expected returnAmazon.com 19.8Ford 20.2Newmont Mining 8.9Intel 14.1Microsoft 10.3Dell Computer 11.9Boeing 11.6McDonalds 13.1Pfizer 7.7Dupont 11.7Disney 10.0ExxonMobil 8.7IBM 10.9Wal-Mart 4.7Campbell Suop 6.2GE 8.3Heinz 7.1
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GSB711 Managerial Finance – Topic 05 Page No. 58 GSB711 Managerial Finance – Topic 05 Page No. 58
Capital Budgeting & Project Risk
• We discuss more on capital budgeting in a later topic
• The project cost of capital depends on the use to which the capital is being put. Therefore, it depends on the risk of the project and not the risk of the company.
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GSB711 Managerial Finance – Topic 05 Page No. 59 GSB711 Managerial Finance – Topic 05 Page No. 59
Capital Budgeting & Project
Example - Based on the CAPM, ABC Company has a cost of capital of 17%. [4 + 1.3(10)]. A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used?
1/3 Nuclear Parts Mfr. B=2.01/3 Computer Hard Drive Mfr. B=1.31/3 Dog Food Production B=0.6
AVG. B of assets = 1.3
Risk
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GSB711 Managerial Finance – Topic 05 Page No. 60 GSB711 Managerial Finance – Topic 05 Page No. 60
Capital Budgeting & Project Risk
Example - Based on the CAPM, ABC Company has a cost of capital of 17%. (4 + 1.3(10)). A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used?
R = 4 + 0.6 (14 - 4 ) = 10%
10% reflects the opportunity cost of capital on an investment given the unique risk of the project.
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GSB711 Managerial Finance – Topic 05 Page No. 61 GSB711 Managerial Finance – Topic 05 Page No. 61
Alternative Models
• CAPM emphasizes market as the major determinant of expected return
• Major criticism from Fama and French in early 1990s
• Other models take into account other aspects– Arbitrage pricing theory and Multi factor
models• Is beta dead?• Long-live beta