Ch 10 and Ch 11
Risk and Return
1
Ch 10 and 11


Dollar return and Percentage Return
Measuring Return and Risk




Capital market history
Understanding Risk



Systematic risk vs. Unsystematic risk
Diversification
Capital Asset pricing Model (CAPM)



Historical returns and risk
Expected returns and risk
Security Market Line (SML)
Beta
Stock Market Efficiency
2
3
Dollars
Return: Capital Market History
$6,640.79
$10,000
$2,845.63
$1,000
Small-company
stocks
$100
$40.22
Large-company
stocks
Long-term
government bonds
$10
$15.64
$9.39
Inflation
$1
Treasury bills
$0.1
1925
1935
1945
1955
1965
1975
Year-end
1985
1995
1999
4
Risk: The Great Bull Market of 1982 –
1999, “Bumps Along the Way”
Period
% Decline in S&P 500
Oct. 10, 1983 – July 24, 1984
-14.4%
Aug. 25, 1987 – Oct. 19, 1987
-33.2%
Oct. 21, 1987 – Oct. 26, 1987
-11.9%
Nov. 2, 1987 – Dec. 4, 1987
-12.4%
Oct. 9, 1989 – Jan. 30, 1990
-10.2%
July 16, 1990 – Oct. 11, 1990
-19.9%
Feb. 18, 1997 – Apr. 11, 1997
-9.6%
July 19, 1999 – Oct. 18, 1999
-12.1%
6
7
Calculating returns


Dollar return
= dividend income + capital gain (or loss)
Percentage return
= dividend yield + capital gains yield


where,
dividend yield
= dividend income / beginning price
capital gains yield
= (ending price – beginning price) / beginning price.
Example: $ Return, % Return
$14
$1
$13
-$10
8
Measuring Return and Risk
Historical return and risk
 Expected return and risk

9
10
Historical returns
Example: Find the average returns and standard
deviation of the stock for given four years data.
Assume that at Year 0, the price was $100.
Year Actual Return
1
15%
2
9%
3
-6%
4
12%
Price
$115.00
$125.35
$117.83
$131.97
Historical return and risk

Historical average return
¯r = ri / N
= (15 + 9 + (-6) + 12 ) / 4
= 30 / 4
= 7.5%
11
What is investment risk?
Typically, investment returns are not
known with certainty.
 Investment risk pertains to the
probability of earning a return less than
that expected.
 The greater the chance of a return far
below the expected return, the greater
the risk.
 Risk = volatility of returns = standard
deviation of returns

12
Standard Deviation: “Rolling a Dice”

Suppose Michelle, Jennifer, and Christine
play at the Rolling Dice Contest. Each
contestant rolls a dice four times.




Michelle: 1, 6, 6, 1
Jennifer: 3, 4, 4, 3
Christine: 2, 5, 5, 2
Which contestant’s outcomes shows the
highest standard deviation?
13
Picturing Risk: Frequency distribution of
returns on common stocks
13
12
4
1973
1966
1
1 1974 1957
1936 1937 1930 1941
2
0
-50
-40
-30
-20
11
1990
1981
1977
1969
1962
1953
1946
1940
1939
1934
1932
1929
-10
1994
1993
1992
1987
1984
1978
1970
1960
1956
1948
1947
0
13
1988
1986
1979
1972
1971
1968
1965
1964
1959
1952
1949
1944
1926
10
12
1999
1998
1996
1983
1982
1976
1967
1963
1961
1951
1943
1942
20
1997
1995
1991
1989
1985
1980
1975
1955
1950
1945 3
2
1938 1956
1936 1935 1954
1927 1928 1933
30
40
50
60
Return (%)
70
80
90
Risk can be pictured by constructing frequency distribution.
The flatter the distribution is, the greater the risk.
14
Picturing Risk: Normal Distribution
15
Suppose average return on large common stocks is
13.3%, and standard deviation of returns is 20.1%
Probability
Low Risk
68%
High Risk
95%
>99%
-3 -2
-1
0
+1 +2 +3
-47.0% -26.9% -6.8% 13.3% 33.4% 53.5% 73.6%
Return on
large
common
stocks
Normal Distribution



Of all observed values, 68.3 percent will
occur within plus/minus one standard
deviation of the mean
Of all observed values, 95.7 percent will
occur within plus/minus one standard
deviation of the mean
Of all observed values, 99.7 percent will
occur within plus/minus one standard
deviation of the mean
16
Historical return and risk

Historical risk
We measure risk by calculating
standard deviation of returns.
 The greater the standard deviation,
the greater the risk.
 Standard deviation = risk = volatility

17
Measuring Risk
Variance - Average value of squared
deviations from mean. A measure of
volatility. We square them to give equal
weights to negative returns.
Standard Deviation – Standardized
average value of squared deviations
from mean. A measure of volatility.
Historical return and risk
r r


Variance,  
2
2
i
N 1
(.15  .075) 2  (.09  .075) 2  (.06  .075) 2 .......

4 1
.0261

3
 .0087
SD,    2
 .0087
 .0933 or 9.33%
19
20
Historical returns and risks of various
instruments
Series
Large-company
stocks
Small-company
stocks
Average Standard
Return Deviation
13.3%
20.1%
*
17.6
33.6
5.9
8.7
5.5
9.3
5.4
5.8
U.S. Treasury
bills
3.8
3.2
Inflation
3.2
4.5
Long-term
corporate bonds
Long-term
government
Intermediate-term
government
Distribution
-90%
0%
90%
Lesson from capital market history
There is a reward for bearing risk
 The greater the potential reward, the
greater the risk
 This is called the risk-return trade-off

21
Risk Premium



Definition: The “extra” return earned for
taking on risk
The return on Treasury bills are
considered to be risk-free rate
The risk premium is the return over and
above the risk-free rate
22
Historical Risk Premiums




23
Large stocks: 13.3 – 3.8 = 9.5%
Small stocks: 17.6 – 3.8 = 13.8%
Long-term corporate bonds: 5.9 – 3.8 =2.1%
Long-term government bonds: 5.5 – 3.8 = 1.7%
Expected returns: Using forecasted
returns with probability

24
A stock analyst projects the future
performance of a company XYZ’s stock.
A today’s price is $100.00
State of
Rate of
Economy Probability Return Price
Recession
30%
-13% $87.00
Boom
70%
15% $115.00
25
Calculating the Expected Rate of
Return
^
r = expected rate of return.

r =
n
 rP .
i
i
i=1
^
r = -13% (0.3) + 15% (0.7)
= 6.6%
26
Calculating Standard Deviation
using Probability Distribution
  Standard deviation
 
Variance


2
 2


   ri  r  Pi

i 1 
n
 (.13  .066) 2 .3  (.15  .066) 2 .7
 .0165
 .128 or 12.8%
Calculating return and risk of portfolio



A portfolio is a collection of assets
An asset’s risk and return is important in how
it affects 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
27
Calculating return and risk of portfolio

Example: Suppose you had $1 million to invest
on stocks. You bought stock A for $500,000,
stock B for $250,000, and stock C for $250,000,
respectively. Your brokerage firm sent the
following projections on these stocks. What are
the portfolio’s expected returns and standard
deviations?
Returns
State of
Economy Probability Stock A
Boom
0.4
10%
Bust
0.6
8%
Stock B
15%
4%
Stock C
20%
0%
28
Calculating returns and risk of
portfolio

Step One: Calculate the weighted average of
returns for each of given economy status



Expected Return of portfolio for “Boom” Economy
= (500K/1,000K)10% + (250K/1,000K)15% + (250K/1,000K)20%
= 13.75%
Expected Return of portfolio for “Bust” Economy
= 5%
Step Two: Compute the expected return of
portfolio as we did for the single stock
29
Calculating Return and Risk: Portfolio
Case
State of
Economy
Boom
Bust
Probability
0.4
0.6
1
Rate of
Return
13.75%
5.00%
30
Return Deviation
Expected from Expected Squared
Product Return
Return
Deviation Product
0.055
8.50%
0.0525
0.002756 0.001103
0.03
8.50%
-0.035
0.001225 0.000735
8.50%
0.001838
4.29%
Diversification

Portfolio diversification is the investment in
several different asset classes or sectors
Diversification can substantially reduce the variability of
returns
 This reduction in risk arises because worse than
expected returns from one asset are offset by better
than expected returns from another


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

31
32
Correlation

Returns Distributions for Two Perfectly
Positively Correlated Stocks (correlation
= +1.0) and for Portfolio MM’
Stock M’
Stock M
Portfolio MM’
25
25
25
15
15
15
0
0
0
-10
-10
-10
33
Correlation

Returns Distribution for Two Perfectly
Negatively Correlated Stocks (Correlation =
-1.0) and for Portfolio WM
Stock W
.
25 .
.
0
.
.
.
25
15
-10
Stock M
.
25
.
15
15
0
0
-10
Portfolio WM
.
.
-10
. . . . .
Correlation
34
Total Risk

Total risk can be decomposed into
Unsystematic Risk
 Systematic Risk

36
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.
37
Unsystematic Risk



Risk factors that affect a limited number
of assets
Also known as unique risk, assetspecific risk, diversifiable risk, and
company-specific risk
Includes such things as labor strikes,
part shortages, etc.
38
Pop Quiz:
Systematic Risk or Unsystematic Risk?




The government announces that inflation
unexpectedly jumped by 2 percent last month.
Systematic Risk
One of Big Widget’s major suppliers goes
bankruptcy.
Unsystematic Risk
The head of accounting department of Big Widget
announces that the company’s current ratio has
been severely deteriorating.
Unsystematic Risk
Congress approves changes to the tax code that
will increase the top marginal corporate tax rate.
Systematic Risk
39
40
Risk Reduction
(3)
Ratio of Portfolio
Standard Deviation to
Standard Deviation
of a Single Stock
(1)
Number of Stocks
in Portfolio
(2)
Average Standard
Deviation of Annual
Portfolio Returns
1
49.24 %
2
37.36
.76
4
29.69
.60
6
26.64
.54
8
24.98
.51
10
23.93
.49
20
21.68
.44
30
20.87
.42
40
20.46
.42
50
20.20
.41
100
19.69
.40
200
19.42
.39
300
19.34
.39
400
19.29
.39
500
19.27
.39
1,000
19.21
.39
1.00
41
Average annual
standard deviation (%)
49.2
Risk Reduction
Diversifiable risk
23.9
19.2
Nondiversifiable
risk
1
10
20
30
40
Number of stocks
1,000 in portfolio
The Principle of Diversification
Diversification can substantially reduce the variability
of 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

42
Diversifiable Risk



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
Diversifiable Risk = Unsystematic Risk
43
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.
Conclusion: The reward for bearing risk depends
only on the systematic risk of an investment.
44
So, the important question is how to
measure systematic risk of a stock (or
portfolio)?
 The
answer is a beta.
 This is where Capital Asset Pricing
Model and Security Market Line
come in.
45
What is a beta? (the Greek Symbol )
A
beta coefficient (or a beta shortly): the
amount of systematic risk present in a
particular risky asset relative to that in an
average risky asset.
46
What does a beta tell us?



A beta of 1 implies the asset has the same
systematic risk as the overall market portfolio (or
average asset)
A beta < 1 implies the asset has less systematic risk
than the overall market portfolio
A beta > 1 implies the asset has more systematic
risk than the overall market portfolio
Note: A beta of the market portfolio (or average portfolio) is 1.
Typically, we use S&P 500 Index as a proxy portfolio to
represent the market portfolio.
47
48
Company
Beta Coefficient
McDonalds
.85
Gillette
.90
IBM
1.00
General Motors
1.05
Microsoft
1.10
Harley-Davidson
1.20
Dell Computer
1.35
America Online
1.75
(I)
Beta and the Risk Premium

Remember



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
return and beta (or risk)?

YES! Capital Pricing Asset Model (CAPM)
49
Capital Asset Pricing Model (CAPM)





Created by William F. Sharpe and others
A Nobel Prize winner idea
Widely used by Wall Street professionals
Describes the relationship between return
and risk (i.e., systematic risk)
A beta (the Greek symbol, β) measures
systematic risk of a stock or portfolio.
50
Capital Asset Pricing Model (CAPM)

E(Ri) = Rf + (E(Rm) – Rf)i
Rf = Risk-free rate, or Treasury bill return
 E(Rm) = Expected return on the market
portfolio, often S & P 500 index return is
used as a proxy.
 i = Beta

51
52
Security Market Line (SML)
30%
Expected Return
25%
E(RA)
(E(RA) – Rf)/ A
20%
15%
10%
Rf
5%
0%
0
0.5
1

1.5 A
Beta
E(Ri) = Rf + (E(Rm) – Rf)i
2
2.5
3
Example - CAPM

Consider the betas for each of the assets given
earlier. If the risk-free rate is 6.15% and the market
risk premium is 9.5%, what is the expected return for
each?




Security
DCLK
KO
INTC
KEI
Beta
4.03
0.84
1.05
0.59
Expected Return
6.15 + 4.03(9.5) = 44.435%
6.15 + .84(9.5) = 14.13%
6.15 + 1.05(9.5) = 16.125%
6.15 + .59(9.5) = 11.755%
53
Example: Portfolio Betas
“What if we want to invest on many
stocks, instead of single stock? “

Suppose you have $1 million to invest. You allocated
your money as follows:
What
Stocks
Allocations
Beta
CIN
$300,000
0.47
MOT
$500,000
1.69
CAG
$200,000
0.62
is the portfolio beta?
=(0.3)(0.47)+(0.5)(1.69)+(0.2)(0.62) = 1.11
54
What’s the Efficient Market
Hypothesis (EMH)?
 Stock
prices reflect new events efficiently.
 Therefore, securities are normally in
equilibrium and are “fairly priced.”
 Stock prices follows “random” process.
 Therefore, one cannot “beat the market”
except through good luck or inside
information.

If this is true, then you should not be able to
earn “abnormal” or “excess” returns
consistently.
55
Common Misconceptions about
EMH
markets DO NOT imply that you can’t
make money from stock market
 They do imply that, on average, you will earn
a return that is appropriate for the risk
undertaken
 Efficient

There is not a bias in prices that can be exploited
to earn excess returns
56
What Makes Markets Efficient?
 There
are many investors out there doing
research
100,000 or so trained analysts--MBAs, CFAs, and
PhDs--work for firms like Fidelity, Merrill, Morgan,
and Prudential.
 These analysts have similar access to data and
megabucks to invest.
 Thus, news is reflected in stock price (P0) almost
instantaneously.
 Therefore, prices should reflect all available public
information

57
58
59
60
61
An Example of Diversification

If you invest
individually,

If you invest collectively,
i.e., investing on 50-50
portfolio,
Avg R of Starcents = 10%
SD of Starcents = 20%
Avg R of 50-50 P = 25%
Avg R of jPhone = 40%
SD of jPhone = 60%
However, it is possible that
SD of 50-50 P can be smaller
than the avg of two SDs (40%)
or even smaller than the
smaller of two SDs (20%) !!!
62