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Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
TOPICS COVERED
Over a Century of Capital Market History
Measuring Portfolio Risk
Calculating Portfolio Risk
How Individual Securities Affect Portfolio Risk
Diversification & Value ‘Additivity’
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
$1
$10
$100
$1,000
$10,000
$100,000
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Start of Year
Dol
lars
(log
sca
le)
Common Stock
US Govt Bonds
T-Bills
14,276
24171
2008
THE VALUE OF AN INVESTMENT OF $1 IN 1900
$1
$10
$100
$1,000
1900
1909
1919
1929
1939
1949
1959
1969
1979
1989
1999
Start of Year
Dol
lars
(log
sca
le)
Equities
Bonds
Bills
581
9.85
2.87
2008
Real Returns
The Value of an Investment of $1 in 1900
Investment of Rs.100 over the period 1978 – 2011
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
AVERAGE MARKET RISK PREMIA (BY COUNTRY)
4.29 4.69 5.05 5.43 5.5 5.61 5.67 6.04 6.29 6.94 7.137.94 8.34 8.4 8.74 9.1 9.61 10.21
0123456789
1011
Den
mar
k
Bel
giu
m
Sw
itze
rlan
d
Irel
and
Sp
ain
Nor
way
Can
ada
U.K
.
Net
her
lan
ds
Ave
rage
U.S
.
Sw
eden
Au
stra
lia
Sou
th A
fric
a
Ger
man
y
Fra
nce
Jap
an
Ital
y
Risk premium, %
Country
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MARKET RISK PREMIUM IN INDIA
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DIVIDEND YIELD
Dividend yields in the U.S.A. 1900–2008
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DIVIDEND YIELD ON SENSEX
Rates of Return 1900-2008
Source: Ibbotson Associates Year
Per
cent
age
Ret
urn
Stock Market Index Returns
Rates of Return for Sensex: 1980 - 2011
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MEASURING RISK
1 24
11 11
21
17
24
13
32
0
4
8
12
16
20
24
-50
to -
40
-40
to -
30
-30
to -
20
-20
to -
10
-10
to 0
0 to
10
10 t
o 20
20 t
o 30
30 t
o 40
40 t
o 50
50 t
o 60
Return %
# of Years
Histogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns
(1900-2008)(1900-2008)
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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.
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
MEASURING RISK
Coin Toss Game-calculating variance and standard deviation
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MEASURING RISK
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EQUITY MARKET RISK (BY COUNTRY)
17.02 18.45 19.22 20.16 21.83 22.05 22.99 23.23 23.42 23.51 23.98 24.09 25.2828.32 29.57
33.93 34.3
0
5
10
15
20
25
30
35
40
Can
ada
Au
stra
lia
Sw
itze
rlan
d
U.S
.
U.K
.
Den
mar
k
Sp
ain
Net
her
lan
ds
Sou
th A
fric
a
Irel
and
Sw
eden
Bel
giu
m
Fra
nce
Nor
way
Jap
an
Ital
y
Ger
man
y
Sta
ndar
d D
evia
tion
of A
nnua
l Ret
urns
, %
Average Risk (1900-2008)
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DOW JONES RISK
Annualized Standard Deviation of the DJIA over the preceding 52 weeks
(1900 – 2008)
Years
Sta
ndar
d D
evia
tion
(%
)
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SENSEX RISK
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MEASURING RISK
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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COMPARING RETURNS
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MEASURING RISK
05 10 15
Number of Securities
Po
rtf
oli
o s
tan
dard
devia
tio
n
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MEASURING RISK
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
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PORTFOLIO RISK
22
22
211221
1221
211221
122121
21
σxσσρxx
σxx2Stock
σσρxx
σxxσx1Stock
2Stock 1Stock
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PORTFOLIO RISK
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PORTFOLIO RISK Example
Suppose you invest 62% of your portfolio in Bharti Airtel and 38% in Tata Motors. The expected dollar return on your Bharti Airtel stock is 14% and on Tata Motors is 17%. The standard deviation of their annualized daily returns are 33.5% and 54.8%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.
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PORTFOLIO RISK
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PORTFOLIO RISK
%12)1540(.)1060(. ReturnExpected
Another Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is:
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PORTFOLIO RISK
2222
22
211221
2112212221
21
)3.27()40(.σx3.272.181
60.40.σσρxxCola-Coca
3.272.181
60.40.σσρxx)2.18()60(.σxMobil-Exxon
Cola-CocaMobil-Exxon
Another Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.
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PORTFOLIO RISKAnother Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.
% 21.8 0.477 DeviationStandard
0.47718.2x27.3)2(.40x.60x
]x(27.3)[(.40)
]x(18.2)[(.60) Variance Portfolio22
22
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PORTFOLIO RISK
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
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PORTFOLIO RISK
Example
Stocks % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Correlation Coefficient = .4
Standard Deviation = weighted avg. = 33.6
Standard Deviation = Portfolio = 28.1
Real Standard Deviation: = (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4) = 28.1 CORRECT
Return : r = (15%)(.60) + (21%)(.4) = 17.4%
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PORTFOLIO RISK
Example Correlation Coefficient = .4
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
Stocks σ % of Portfolio
Average Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
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PORTFOLIO RISK
Example Correlation Coefficient = .3
NEW Standard Deviation = weighted average = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted average = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION
Stocks σ % of Portfolio
Average Return
Portfolio 28.1 50% 17.4%
New Corp 30 50% 19%
The shaded boxes contain variance terms; the remainder contain covariance terms.
1
2
3
4
5
6
N
1 2 3 4 5 6 N
STOCK
STOCK
To calculate portfolio variance add up the boxes
Variance
Covariance
It is the average covariance that constitutes the bedrock of risk remaining after diversification has done its work. The risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio.
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PORTFOLIO RISK
Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the Sensex, is used to represent the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio.
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PORTFOLIO RISK
The return on Tata Steel stock changes on average by 1.77% for each additional 1% change in the market return. Beta is therefore 1.77.
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PORTFOLIO RISK
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PORTFOLIO RISK
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PORTFOLIO RISK
Covariance with the market
Variance of the market
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BETA
(1) (2) (3) (4) (5) (6) (7)Product of
Deviation Squared deviationsDeviation from average deviation from average
Market Anchovy Q from average Anchovy Q from average returnsMonth return return market return return market return (cols 4 x 5)
1 -8% -11% -10% -13% 100 1302 4 8 2 6 4 123 12 19 10 17 100 1704 -6 -13 -8 -15 64 1205 2 3 0 1 0 06 8 6 6 4 36 24
Average 2 2 Total 304 456
Variance = σm2 = 304/6 = 50.67
Covariance = σim = 736/6 = 76
Beta (β) = σim/σm2 = 76/50.67 = 1.5
Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of
the variance to the covariance (i.e., β = σim/σm2)
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ANNOUNCEMENTS, SURPRISES,AND EXPECTED RETURNS
41
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ANNOUNCEMENTS AND NEWS
42
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SYSTEMATIC AND UNSYSTEMATIC RISK
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THE PRINCIPLE OF DIVERSIFICATION The process of spreading an investment across assets (and thereby forming a portfolio) is called diversification.
The principle of diversification tells us that spreading an investment across many assets will eliminate some of the risk.
45
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DIVERSIFICATION
Unsystematic risk
Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets has almost no unsystematic risk.
Also called diversifiable risk, unique risk, or asset-specific risk.
Systematic risk
systematic risk affects almost all assets to some degree, so no matter how many assets we put into a portfolio, the systematic risk doesn’t go away.
The terms systematic risk and non-diversifiable risk are hence used interchangeably.
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SYSTEMATIC RISK AND BETA
THE SYSTEMATIC RISK PRINCIPLE
The systematic risk principle states that the reward for bearing risk depends only on the systematic risk of an investment.
Because unsystematic risk can be eliminated by diversifying, there is no reward for bearing it, the market does not reward risks that are borne unnecessarily.
The expected return on an asset depends only on that asset’s systematic risk.
No matter how much total risk an asset has, only the systematic portion is relevant in determining the expected return (and the risk premium) on that asset.
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SYSTEMATIC RISK AND BETA
MEASURING SYSTEMATIC RISK
The amount of systematic risk present in a particular risky asset relative to that in an average risky asset.
An average asset has a beta of 1.0 relative to itself. An asset with a beta of .50, therefore, has half as much systematic risk as an average asset; an asset with a beta of 2.0 has twice as much.
Assets with larger betas have greater systematic risks, they will have greater expected returns.
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SYSTEMATIC RISK AND BETA
PORTFOLIO BETAS
A portfolio beta, can be calculated, just like a portfolio expected return.
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SYSTEMATIC RISK AND BETA
50
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THE SECURITY MARKET LINE
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THE SECURITY MARKET LINE
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THE SECURITY MARKET LINE
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THE SECURITY MARKET LINE OF B
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SECURITY MARKET LINES
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investors would be attracted to Asset A and away from Asset B. As a result, Asset A’s price would rise and Asset B’s price would fall.The reward-to-risk ratio must be the same for all the assets in the market.
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SECURITY MARKET LINE
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THE CAPITAL ASSET PRICING MODEL
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