MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
2e created Summer 11
Ch’s 11 & 12: Risk & Return In Capital Markets
Purpose of Ch’s 11 & 12: To understand financial risk and learn
how to measure the risk associated with securities
Learning Objectives:
Explain Systematic Risk and Unsystematic Risk
Describe the Causes of Systematic Risk and Unsystematic Risk
Explain How Standard Deviation Quantifies the Riskiness of a Security or
Portfolio
Explain Coefficient of Variation and Use It To Make An Investment
Decision
Describe Diversification and How It Reduces the Riskiness of a Portfolio
Describe the Concept of Correlation and How It Affects Diversification
Describe the Capital Asset Pricing Model (CAPM)
Explain What Beta Is
Compute the Required ROR of a Stock Using CAPM
Explain the Difference Between Rqd ROR of a Stock Computed with
CAPM and Rqd ROR Derived From the Average of Historical Returns
Explain the Concept of Risk Aversion and Its Effects on Security Valuation
and Return
Compute The Expected and Realized Returns of a Portfolio Using CAPM
Compute The Expected and Realized Returns of a Portfolio Using historical
Returns
1
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
2e v1.1 created Fall 13
Risk
Definitions:
 Webster’s: a hazard; a peril; exposure to loss or injury
 The chance that an outcome other than that which was
expected will occur
 The chance that an outcome other than that which was desired
(i.e. a negative return, negative future cash flows) will occur.
This is financial risk
Uncertainty: the lack of knowledge of what will happen in the
future
→uncertainty = risk
→the greater the uncertainty, the greater the risk
Average Annual Return (R): The arithmetic average of an
investment’s realized annual stock returns over a certain period
(usually 1 or 5 years)
R = 1/T(r1 + r2 + ……. + rT) (we learned how to compute r in Ch 7)
Example: The realized annual returns For Diamond Jim’s Inc. stock
for the last five years were: 8.6782% (2004), 7.4203% (2005),
8.2501% (2006), 6.5925% (2007) and 1.5943% (2008). What is the
average annual return for that period?
R = 1/5(8.6782% + 7.4203% + 8.2501% + 6.5925% + 1.5943%)
= 1/5(32.5354%)
= 6.5071%
Using the main principle of statistics (past performance is a predictor
of future performance) we estimate the expected return from the
realized return:
R = r (as discussed in Ch 7) Note: we will assume the individual realized annual
returns are independent, i.e. the data is “normally distributed”
2
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Quantifying the Risk of a Security – Standard Deviation
Two Basic Types of Risk:
Stand-alone Risk :
 The risk associated with an investment when it is held by itself
or in isolation, and not in combination with other assets
 The stand-alone-risk of a particular security can be compared
with that of other securities to assess relative riskiness
Portfolio Risk:
 The sum total risk of several securities held together in a
single “portfolio”. Must account for the correlation of the
securities to on another
Stand-alone Risk
Big question from statistics: How reliable is the estimate for
expected future return?
Standard Deviation answers this question
n
2
Variance = s = S
(ri - r)2Pi
i=1
Standard Deviation = s =
S
(ri - r)2Pi
i=1
Example: (continued) Compute the standard deviation of the realized
annual returns For Diamond Jim’s Inc. stock for the last five years.
n
ri
r
r - ri
(ri - r)2
Pi(= 1/n)
(ri - r)2Pi
8.6782%
6.5071%
2.1711%
0.0471%
0.20
0.009427%
7.4203%
6.5071%
0.9132%
0.0083%
0.20
0.001668%
8.2501%
6.5071%
1.7430%
0.0304%
0.20
0.006076%
6.5925%
6.5071%
0.0854%
0.0001%
0.20
0.000015%
1.5943%
6.5071%
-4.9128%
0.2414%
0.20
0.048271%
Variance = s2 =
0.065457%
Standard Deviation = s =
2.5585%
Note: since the probability (Pi) was the same for each stock return, it is computed simply
as 1/n where n = total number of data points, which is 5 in this case
3
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Stand-alone Risk (continued)
Standard Deviation Using Sample Data:
Since it is virtually impossible to find the true s for any population,
a sample of values is used:
n
Estimated Standard Deviation = S =
S (rt - rAVE)2
t=1
n-1
Probability Distribution: the possible values of outcomes associated
with the probability of their occurrence
Example: Probability distribution for the role of two 6-sided dice
Chart Format
Event Probability (P)
2
2.78%
3
5.56%
4
8.33%
5
11.11%
6
13.89%
7
16.67%
8
13.89%
9
11.11%
10
8.33%
11
5.56%
12
2.78%
Sum:
100.00%
Graph
18.00%
16.00%
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
2
3
4
5
6
7
8
9
10
11
12
Probability
If there are is a vary large number of discrete random events (data
points), the probability distribution looks more like this:
Event
4
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Stand-alone Risk (continued)
Normal Distribution:
Random Sampling:
→if n elements are selected from a population in such a way
that every set of n in a population has an equal probability of
being selected, the n elements are said to be a random sample.
(This is the definition of a simple random sample which is the
most common technique)
→The value of any element is not influenced by the value of
any other element; i.e. the data is independent
Normal Distribution: The results of Random Sampling
Historical returns of securities are not truly independent (i.e. the
closing price of a stock on any particular day may be influenced by
the closing stock price on previous days) but they are close enough to
being so that we usually treat them as being normally distributed
This means that the statistical methods for analyzing security
returns is relatively simple
Empirical Rule: For normally distributed data
68.26%
95.46%
99.74%
-3s
-2s
-1s
rs
5
+1s
+2s
+3s
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Stand-alone Risk (continued)
How Standard Deviation Quantifies Risk:
Standard deviation describes the degree of variation or the “range” of a
probability distribution
The higher the s, the greater the range of possible outcomes, the greater the
uncertainty concerning the next possible outcome, thus greater risk
A “tighter” or “narrower” probability distribution (as compared to other
probability distributions) means a lower relative s, which means less
uncertainty concerning the next possible outcome
The smaller the s, the more reliable the estimated expected return
Example: The probability distributions for two different stocks are shown
below. Both stocks have an expected return (rs) of 15%. Which stock is
Probability Density
riskier?
0.5 Diamond Jim’s Inc.
Note: the area under each
curve equals 1.00 (i.e.
100% probability)
Jihad Jim’s Military
Surplus LLC
15%
0%
Rate of Return (%)
Expected Rate of Return (rs)
Answer: Jihad Jim’s is riskier
Jihad Jim’s standard deviation is clearly much greater than that of Diamond
Jim’s
The possible range of values for next years stock return for Jihad Jim’s is
much greater than that for Diamond Jim’s
Jihad Jim’s expected stock return is much more uncertain
The estimate for expected return for Jihad Jim’s is much less reliable
Jihad Jim’s stock is much more risky than Diamond Jim’s stock
6
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets
(bdh2e)
Stand-alone Risk (continued)
Most Common Way to Determine Rs, rs and s
1) Find the monthly closing price of a stock for the last 61 months
2) Compute the ROR for each month (New-Old)/Old
3) Compute the average monthly ROR (use Excel function:
AVERAGE)
4) Convert the monthly average to an annual average. This is the
average annual return Rs for the five year period
5) As stated before: rs = Rs ≈ rs
5) Use the Excel function: STDEV to find s of monthly returns
6) Convert this to an annualized s, multiply by SQRT(12)
7
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Excel Example: Apple Inc. (AAPL) = (B4-B3)/B3
Date
1-Feb-02
1-Mar-02
1-Apr-02
1-May-02
3-Jun-02
1-Jul-02
1-Aug-02
3-Sep-02
1-Oct-02
1-Nov-02
2-Dec-02
2-Jan-03
3-Feb-03
3-Mar-03
1-Apr-03
1-May-03
2-Jun-03
1-Jul-03
1-Aug-03
2-Sep-03
1-Oct-03
3-Nov-03
1-Dec-03
2-Jan-04
2-Feb-04
1-Mar-04
1-Apr-04
3-May-04
1-Jun-04
1-Jul-04
2-Aug-04
1-Sep-04
1-Oct-04
1-Nov-04
1-Dec-04
3-Jan-05
1-Feb-05
1-Mar-05
1-Apr-05
2-May-05
1-Jun-05
1-Jul-05
1-Aug-05
1-Sep-05
3-Oct-05
1-Nov-05
1-Dec-05
3-Jan-06
1-Feb-06
1-Mar-06
3-Apr-06
1-May-06
1-Jun-06
3-Jul-06
1-Aug-06
1-Sep-06
2-Oct-06
1-Nov-06
1-Dec-06
3-Jan-07
1-Feb-07
Adjusted
Close
$10.85
$11.84
$12.14
$11.65
$8.86
$7.63
$7.38
$7.25
$8.03
$7.75
$7.16
$7.18
$7.51
$7.07
$7.11
$8.98
$9.53
$10.54
$11.31
$10.36
$11.44
$10.45
$10.69
$11.28
$11.96
$13.52
$12.89
$14.03
$16.27
$16.17
$17.25
$19.38
$26.20
$33.53
$32.20
$38.45
$44.86
$41.67
$36.06
$39.76
$36.81
$42.65
$46.89
$53.61
$57.59
$67.82
$71.89
$75.51
$68.49
$62.72
$70.39
$59.77
$57.27
$67.96
$67.85
$76.98
$81.08
$91.66
$84.84
$85.73
$84.74
Monthly
Returns
9.1244%
2.5338%
-4.0362%
-23.9485%
-13.8826%
-3.2765%
-1.7615%
10.7586%
-3.4869%
-7.6129%
0.2793%
4.5961%
-5.8589%
0.5658%
26.3010%
6.1247%
10.5981%
7.3055%
-8.3996%
10.4247%
-8.6538%
2.2967%
5.5192%
6.0284%
13.0435%
-4.6598%
8.8441%
15.9658%
-0.6146%
6.6790%
12.3478%
35.1909%
27.9771%
-3.9666%
19.4099%
16.6710%
-7.1110%
-13.4629%
10.2607%
-7.4195%
15.8653%
9.9414%
14.3314%
7.4240%
17.7635%
6.0012%
5.0355%
-9.2968%
-8.4246%
12.2290%
-15.0874%
-4.1827%
18.6660%
-0.1619%
13.4562%
5.3261%
13.0488%
-7.4405%
1.0490%
-1.1548%
Average
Monthly k
4.0847%
Average
Annual k
49.0165%
s (Monthly
Returns)
11.2596%
s (Annualized)
39.0043%
= 11.2596*SQRT(12)
= STDEV(C4:C63)
= 4.0847%*12 or D3*12
= AVERAGE(C4:C63)
R = 49.0165% per annum ≈ r
s = 39.043%
Note: monthly adjusted closing prices from Yahoo.com
8
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Risk Aversion: (Not covered in your text book)
Concept: Given two securities with equal expected returns but
different degrees of risk, the rational investor would choose the one
with lower risk
Most investors tend to choose less risky investments and accept
commensurately lower returns
Valuation Implications:
if two securities offer the same ROR, the riskier one is priced
lower if the seller of that security wants anybody to buy it (the
less riskier one is priced higher)
if two securities are priced the same, the riskier one must offer
higher expected returns if the seller of that security wants
anybody to buy it
the difference between these expected returns is a risk
premium
market forces (risk aversion influencing supply & demand)
force the above to occur
How much higher does the ROR have to be or how much lower
does the price have to be?
Answer:
ref. bonds (Ch 6): Consider 2 bonds with the same par value,
maturity & coupon rate but different rd (one bond is AAA rated with
rd of 4%, the other is B rated with rd of 6%). What’s the difference in
value between two ?
Example: FV=$1,000, rCPN = 5%, annual payment, 5-yr maturity
AAA Bond: N=5, I/YR=4%, PMT=50, FV=1000; PV= $1044.52
B Bond: N=5, I/YR=6%, PMT=50, FV=1000; PV= $957.88
ref. stocks (Ch 7): how does P0 change with different required
ROR’s?
9
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Coefficient of Variation (CV) (Not covered in your text book)
A way to quantify the relationship between risk and return
Given two securities with equal expected returns but different
degrees of risk, the rational investor would choose the one with lower
risk
The CV…..
 is defined as: CV = s / r ~ S / r ; smaller is better
 shows the risk per unit of return;
 it provides a standardized measure of risk; the basis of
comparison (per unit return) is the same
 provides a more meaningful basis for comparison when the
expected returns of two alternatives are not the same
Using CV to measure risk/return characteristics of two stocks is
like using miles per gallon (MPG) to measure fuel efficiency of two
cars
Example: Driver A travels 450 mi. in his ‘95 Geo Metro and
consumes 12 gal. of gas. Driver B travels 890 mi. in his ’71 LS5
(454+cu) Corvette, stopping 3 times to fuel up and consumes 65 gal.
of gas. What is the relative fuel efficiency of the two cars?
Geo: 450 mi./12 gal. = 37.5 mi. per gal
‘Vette: 890 mi./65 gal. = 13.7 mi. per gal.
The standardized measure is one gallon of gas
Example: An investor wants to compare the risk/reward characteristics
of two retail merchandising firms: Walmart and Target.
Probability
Walmart
Target
6.5% 9.3%
Expected Return (Average Return)
10
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Example (continued)
The average monthly returns for two firms over the last five years
are: Walmart, 6.5%; Target, 9.3%. Based on the same data, the
estimated standard of deviations (S) for the two firms are: Walmart,
10.3%; Target, 21.6%. Compute the coefficient of variation for the
two firms. Which has the best risk/return characterisitcs?
CVWalmart = s / r ~ S / r = 10.3% / 6.5% = 1.58
CVTarget = 21.6% / 9.3% = 2.32
The standardized measure is one unit of risk
Caution: CV doesn’t work if the expected returns are significantly
different
Example: Consider the probability distributions of two the two firms
shown below. CVKay-Mart is 1.93 while CVDiamond Jim’s is 3.76. CV
analysis indicates that Kay-Mart has superior risk/return
characteristics. However it would be more advantageous to invest in
Diamond Jim’s. Why?
Probability
Kay-Mart
Diamond Jim’s Inc.
3.5%
14.3%
Expected Return (Average Return)
11
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Portfolio Investing
Investing in a portfolio of securities is less risky than investing in
any single security. Why? Answer: the risks of the individual
securities comprising the portfolio are averaged. How?
Answer:
Diversification:
→the tendency for price movements of individual securities to
counteract each other
→This means that the price changes of the portfolio are usually
less than the price changes of the individual securities
→thus the price/return volatility (s) of the portfolio is less the
price/return volatility (s) of the individual securities
→Thus the risk of the portfolio is less than that of the securities
comprising the portfolio
As more securities are added to a portfolio, the overall risk (s) of
the portfolio decreases
The securities should not be very correlated
Securities (when combined in a portfolio) from companies in the
same industry are (usually) highly positively correlated thus not much
diversification effect
12
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
created Summer 09
Portfolio Returns
Portfolio Expected Returns (E[Rp] or rp): The weighted average of
the expected returns of the individual securities held in a portfolio
E[Rp] = w1E[R1] + w2E[R2] + …… wnE[Rn]
OR
rp = w1r1 + w2r2 + …… wnrn
Example: A portfolio consists of stocks from four companies and the
expected returns (rs) for each stock are given. Find rp.
400 x $43.67
$17,468 / $90,849.50
0.1923 x 5.65%
Stock
# of
Shares
Initial
Stock
Price
ATT&T
400
$43.67
$17,468.00
19.23%
5.65%
1.09%
GEE
450
$47.89
$21,550.50
23.72%
4.32%
1.02%
Microspongy
500
$34.23
$17,115.00
18.84%
4.87%
0.92%
Citigang
600
$57.86
$34,716.00
38.21%
3.87%
1.48%
Portfolio Value:
Initial Value
Weight
(by value)
Expected
Return (r)
$90,849.50
13
rP:
Weighted r
4.51%
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Portfolio Returns (continued)
Portfolio Realized Rate of Return (Rp):
The return that a portfolio actually earned
For a portfolio, realized ROR (Rp) is the weighted average of the
realized RORs of the individual securities held in a portfolio
Rp = w1R1 + w2R2 + …… wnRn
Example(continued): The portfolio is held for one year and the end of
period price for each stock is indicated below. Find rp and the value of
the portfolio at the end of the holding period.
($45.67 - $43.67) / $43.67
(New – Old) / Old
Stock
ATT&T
# of
Shares
400
Initial
Stock
Price
$43.67
Ending
Stock
Price
$45.67
Ending
Stock Value
$18,268.00
Weight
(by
value)
18.64%
Realized
Return
(r)
4.58%
Weighted
r
0.85%
GEE
450
$47.89
$51.89
$23,350.50
23.82%
8.35%
1.99%
Microspongy
500
$34.23
$39.56
$19,780.00
20.18%
15.57%
3.14%
Citigang
600
$57.86
$61.05
$36,630.00
37.37%
5.51%
2.06%
Portfolio Value:
$98,028.50
rP:
8.05%
Note:
1. The weights have changed
2. This example does not include dividend yield (Ch 9)
Another Way to Find rp:
Premise of statistics: past performance is an indicator of future
performance
rp for an upcoming period = rp for the previous period
14
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Diversification of a Portfolio
Correlation:
→the behavioral relationship between two or more variables
(stocks in a portfolio)
→a measure of the degree to which returns share common risk.
→it is calculated as the covariance of returns divided by the
standard deviation of each return
Various conditions (i.e. the economy, security market forces &
movements, financial performance of individual companies, political
developments, etc.) will cause the securities held in a portfolio to
change in value
The direction and magnitude of how the value of securities held in
a portfolio change with respect to each other can be described by
correlation
Positive Correlation: When external conditions cause the securities
in a portfolio to change value in the same direction (i.e. they all
increase in value or they all decrease in value)
Negative Correlation: When external conditions cause the securities
in a portfolio to change value in the opposite directions (one security
increases in value, another decreases in value)
No Correlation: The direction and magnitude of changes in value of
one security are totally unrelated to those of another security
15
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Diversification of a Portfolio (continued)
Correlation Coefficient (r):
A measure of the degree of correlation between variables (stock
securities, in this chapter)
Perfectly negative correlation; r = -1
Perfectly positive correlation; r = 1
No correlation; r = 0
How is correlation between two stocks determined?
The returns from stocks that are highly correlated tend to move
together
→they are affected by the same economic factors
→stocks in the same industry tend to be highly correlated
→they are exposed to similar risks
Academics have shown (after doing a whole lot of statistics) that:
The returns for two randomly selected stocks have an r of about 0.6
For most pairs of stock, r lies between 0.5 and 0.7
This means that that most stocks are partially positively correlated
and partially negatively correlated
This means that combining two stocks (in a portfolio) can reduce
overall risk
Portfolio Standard Deviation:
Unlike expected and realized portfolio returns, portfolio s is not a
weighted average of individual security s’s
Portfolio risk is usually smaller than the weighted average of
individual security s’s
Portfolio risk is entirely dependent on the correlation among the
securities held in the portfolio
Read pp 370-374 for a discussion on how to compute portfolio s
16
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Correlation & Diversification Effect on Portfolio Risk
Perfectly Positively Correlated Stocks (Note: sp = sM = sM’)
Portfolio GH
Stock H
Rate of Return (%)
Rate of Return (%)
Stock G
25
15
0
97
98
99
2000
25
15
0
97
98
99
2000
-10
-10
Perfectly Negatively Correlated Stocks (Note: sp = 0)
Stock L
Stock M
25
Rate of Return (%)
Rate of Return (%)
Portfolio LM
15
0
97
98
99
2000
-10
25
15
0
-10
17
97
98
99
2000
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Correlation & Diversification Effect on Portfolio Risk
Partially Correlated Stocks (Note: sp < sW & sY)
Portfolio Diversification
$55.00
Stock A
$50.00
Portfolio
$45.00
Stock C
Price
$40.00
$35.00
Stock B
$30.00
Stock D
$25.00
$20.00
J
F
M
A
M
J
J
A
S
O
N
D
Months
Diversification is important, especially for corporate investors; they
are very concerned about the liquidity of their investments
18
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Systematic Risk versus Unsystematic Risk
The total risk of any security is due to a combination of Systematic
Risk and Unsystematic Risk
Systematic Risk (Market Risk, Undiversifiable Risk or Beta Risk)
this is the volatility of the an entire securities market (NYSE,
NASDAQ, bond markets, etc)
this volatility is due to changes in macro-economic, broad
micro-economic conditions and geo-political events
it applies to most of the firm’s that trade in a specific market
(but not necessarily to the same extent)
Because most stocks are somewhat partially correlated, most
stocks do well when the economy is good and not so well when
the economy is not so good
there is no feasible way to eliminate the Systematic Risk of a
particular market
Unsystematic Risk (Diversifiable Risk, Firm Specific-Risk or
Unique Risk)
it is reflected in the volatility of the securities (stocks &
bonds) of a specific firm
it is that part of a security’s risk associated with factors
generated by events, or behaviors, specific to the firm or the
firm’s industry
it is the result of the firm’s inherent management decisions,
legal problems, product or service obsolescence, the firm’s
market viability, etc. and that of their competition
there is a way to reduce diversifiable (firm-specific) risk:
build a portfolio of securities from different industries or
industry sectors (stocks that are not well correlated with
each other)
this will produce the diversification effect
19
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
created Summer 09
Systematic Risk versus Unsystematic Risk (continued)
stotal
Portfolio Risk
Minimum Attainable Risk in a
Portfolio of Average Stocks
Total Portfolio Risk
Volatility (Risk)
Unsystematic (Firm-Specific,
Diversifiable) Risk
smarket
1
Systematic (Market or Beta) Risk)
10
20
30
40
1500+
Number of Stocks in the Portfolio
How Many Securities is Enough?
18 securities provide about 90% complete diversification
32 securities provide about 95% complete diversification
The law of diminishing returns is in effect here
 sp falls very slowly after about 40 stocks are included in the
portfolio.
By forming well-diversified portfolios, investors can eliminate
about half the riskiness of owning a single stock
Diversification does not reduce Firm-Specific Risk; it reduces the
effects of Firm-Specific Risk on a portfolio
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MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Measuring Systematic Risk
Portfolio standard deviation measures total risk
The book says only systematic risk is related to required return (i.e.
systematic risk is all that matters since unsystematic risk can be
diversified away)
→Prof. Jim has strong reservations concerning this statement
→it is true only if the stocks are truly randomly chosen and there
are at least 40 stocks (thus the portfolio is well diversified)
→it is not true if stocks in the portfolio are not randomly chosen
If systematic risk is the only one that matters, then we need a way
to quantify just the systematic risk
Market Portfolio & Market (Systematic) Risk:
A market portfolio is a portfolio of all risky investments, held in
proportion to their value
A market portfolio is a portfolio of all the stock in a particular
market (i.e. NYSE, NASDAQ, AMEX
the standard deviation of the market portfolio quantifies the
volatility of the entire system; it is the amount of systematic risk
that particular market has
Capital Asset Pricing Model (CAPM):
A theory that quantifies the market risk of an stock by comparing
the behavior of that stock to the behavior of the market portfolio
This behavioral relationship is expressed by a variable called Beta
(b)
Definition: b is a measure of the extent to which the returns of a
particular security move with respect to the returns of the securities
market as a whole
b measure a stock’s sensitivity to the market portfolio (the rest
of the market)
b quantifies a stock’s market risk
b tells us how risky a particular stock is compared to a market
portfolio (the rest of the market)
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MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Measuring Systematic Risk
Capital Asset Pricing Model (CAPM): (continued)
the market portfolio has b = 1 (by definition)
if a stock has b = 1, it’s returns will tend to move in the same
direction and magnitude as the market portfolio; the stock is just as
risky as the market
if a stock has b = 2, it’s returns will tend to move in the same
direction but twice the magnitude as the market portfolio; the stock is
twice as risky as the market
if a stock has b = -1, it’s returns will tend to move the same
magnitude but in the opposite direction as the market portfolio
if a stock has b = 0, the direction and magnitude of it’s returns
movements will be totally unrelated to the market portfolio
How to calculate b
plot the stock’s historical returns against historical returns of
the market portfolio
use regression (line fit techniques) to form a line
b is the slope of the fitted line
Analysts typically use five years’ of monthly returns to
establish the regression line. Some use 52 weeks of weekly
returns
Individual Stock Return
40
30
20
10
-40
-30
-20
-10
-10
-20
-30
22
-40
10
20
30
40
Market Portfolio Return
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Measuring Systematic Risk
Capital Asset Pricing Model (CAPM): (continued)
Individual Stock Return
b=2
40
b=1
30
b = 0.5
20
450
10
-40
-30
-20
-10
10
20
30
40
Market Portfolio Return
-10
-20
-30
b = -1
-40
You don’t have to calculate b’s on your own; you can find them
online (yahoo/finance; Hoover’s, WSJ, etc.)
Very few stocks have negative b’s
b quantifies a firm’s Market Risk; it doesn’t say anything about
Firm-Specific Risk
 CAPM assumes the stock in question is part of a well
diversified portfolio thus the Firm-Specific Risk of an
individual stock should have a negligible effect on portfolio
returns
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MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Measuring Systematic Risk
Capital Asset Pricing Model (CAPM): (continued)
More on Risk versus Return:
Recall the concept of risk premiums (DRP, LP, MRP)
30-day T-bills (which are considered riskless) compensate lenders
only for opportunity costs and inflation (i.e. rT-bill = r* + IP = rRF)
Individual stocks as well as entire stock markets must compensate
investors at least for opportunity costs, inflation and risk or nobody
would invest in them (r = r* + IP + RP from Ch 5)
Market Risk Premium:
We identified DRP, LP and MRP which we discussed in the
context of lending money
the same concepts behind the above premiums apply to stocks
but there are an unbelievably long and complex list of
additional factors that also apply to stocks which can’t easily be
broken down into individual components
therefore we lump them all together and just refer to the “risk
premium” (RP) for individual stocks and stock markets as a
whole
Any securities market has a required rate of return (rM)
rM for any market is simply the current average return for that
market (this assumes that market forces and risk aversion have
already been at work to “force” the required ROR to equal
average return)
The rM for any market is composed, in part, of some sort of
compensation for opportunity cost and inflation. This is the
nominal risk-free rate (rRF) (sound familiar?) The rest must be
compensation for risk.
Thus rM = rRF + Market Risk Premium(RPm)
Market Risk Premium: RPm = (rM - rRF) (by definition)
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MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Measuring Systematic Risk
Capital Asset Pricing Model (CAPM): (continued)
Example: If the NASDAQ has had an average ROR of 6.5% over the
last five years and 30-day T-bills have had an average return of 1.9%
for the last five years, what is the NASDAQ market risk premium?
Market Risk Premium: RPm = (rM - rRF)
= 6.5% - 1.9% = 4.6%
Individual Stock Risk Premium: RPs = (rM - rRF)bs = RPmbs
The risk of an individual stock as portrayed by its b is incorporated
in computing that stock’s risk premium
Finding Required ROR (rs) for an Individual Stock:
It should be apparent by now that rs for a stock should be related to
the riskiness of the firm that issues that stock. Thus:
rs = rRF + (rM - rRF)bs
= rRF + RPmbs
The above formula is call the “Capital Asset Pricing Model”
(CAPM) formula
Another way to look at the CAPM formula:
Mkt Risk Premium
(Cost of Risk)
Quantity of Risk
rs = rRF + (rM - rRF)bs
Compensation for Opp. Cost & Inflation
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Stock Risk Premium
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Measuring Systematic Risk
Finding Required ROR (rs) for an Individual Stock
Example: Jamaica Jim’s Caribbean Pirate Adventures Inc. stock trades
on the NASDAQ and has a b of 1.96. If the NASDAQ has had an
average ROR of 5.3% for the last 5 years and 30-day T-bills are
currently returning 1.4%, what is the required ROR for this stock?
rs = rRF + (rM - rRF)bs
= 1.4% + (5.3% - 1.4%)1.96
= 9.04%
Required ROR (rs) vs Expected ROR ( rs)
As discussed in Ch 9, rs for a rational investor is at least equal to rs
Thus rs > rs; for all practical purposes, rs = rs
Important Point Regarding Market Risk & Firm Specific
Risk:
rs produced by the CAPM formula and rs produced using statistical
averaging of historical returns (as discussed in Ch 10) won’t be equal
to each other. Why?
Answer:
The statistical rs incorporates both market risk and firm specific risk
The CAPM rs incorporates market risk only
 b is a measure of market risk only
 CAPM assumes all stocks under consideration will be part of a
well diversified portfolio, thus firm specific risk is negligible and
can be ignored
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MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Measuring Systematic Risk
Beta of a Portfolio:
bp is the weighted average of the b’s of the stocks that comprise the
portfolio
bp = w1b1 + w2b2 + w3b3 + …... wnbn
Example: A portfolio is comprised of the stocks indicated below.
Find the portfolio’s b.
Stock
ATT&T
GEE
Microspongy
Citigang
Pfazer
Northrap
b
0.87
0.75
1.67
1.30
0.14
0.87
Weight
20%
15%
15%
25%
10%
15%
bportf olio
Wt x b
0.174
0.1125
0.2505
0.325
0.014
0.1305
1.0065
Required ROR for a Portfolio (rp) using bp: This is the main
advantage of the CAPM
rp = rRF + (rM - rRF)bp
rp for a rational investor is at least equal to rp
Thus rp > rp; for all practical purposes, rp = rp
rp produced using CAPM (as shown above) and rp (as discussed
earlier) should be fairly close. Why?
Answer: Both methods incorporate diversification and thus minimize
firm specific risk. If the portfolio is well diversified, all that’s left is
market risk and it’s pretty much equal regardless of which method
you use to measure it
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MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
Security Market Line (SML):
The CAPM equation is also the algebraic equation for a line
rRF is the y-intercept
The slope of this line is rM - rRF (i.e. RPM)
This slope will change only when rM or rRF change
bj is the x-axis value
This line can be used to find k for any security, if you know b for
that security
SML : rj = rRF  (rM  rRF )b j
Required
ROR (%)
rhigh = 22
Relatively
Risky
Stock’s
Risk
Premium:
16%
rM = rA = 14
rLOW = 10
Safe Stock Risk
Premium: 4%
Market (Average
Stock) Risk Premium:
8%
rRF = 6
Risk-Free
Rate: 6%
0
0.5
1.0
Risk, (bj)
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1.5
2.0
MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)
What’s the point of all this stuff in Chapters 10 & 11?
Answer:
Security value & ROR are influenced by risk
If you know rs or rp….
 And if you know rs or rp……
 You should be able to determine if your investments are
performing as well as they should with respect to their theoretical
riskiness
Key Point: b is a tool to assess risk/reward potential of a security, it
is not (by itself) a predictor of how the security will perform in the
future
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