Ch

1
2e created Summer 11

• Chs 11 12 Risk Return In Capital Markets
• Purpose of Chs 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

2
2e v1.1 created Fall 13

• Risk
• Definitions
• Websters 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 investments 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
  Jims 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

3

• 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
• Example (continued) Compute the standard
  deviation of the realized annual returns For
  Diamond Jims Inc. stock for the last five years.

n
S (ri - r)2Pi
Variance s2
i 1
n
S (ri - r)2Pi
Standard Deviation s
i 1
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 Variance s2 0.065457
Standard Deviation s 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
4
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

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
Graph
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
If there are is a vary large number of discrete
random events (data points), the probability
distribution looks more like this
Probability
Event
5
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
6
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 riskier?
Probability Density
0.5 -
Diamond Jims Inc.
Note the area under each curve equals 1.00
(i.e. 100 probability)
Jihad Jims Military Surplus LLC
Rate of Return ()
15
0
Expected Rate of Return (rs)

• Answer Jihad Jims is riskier
• Jihad Jims standard deviation is clearly much
  greater than that of Diamond Jims
• The possible range of values for next years stock
  return for Jihad Jims is much greater than that
  for Diamond Jims
• Jihad Jims expected stock return is much more
  uncertain
• The estimate for expected return for Jihad Jims
  is much less reliable
• Jihad Jims stock is much more risky than Diamond
  Jims stock

7

• 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)

8
Excel Example Apple Inc. (AAPL)
(B4-B3)/B3
Adjusted Monthly Average Average s (Monthly
Date Close Returns Monthly k Annual k Returns) s (Annualized)
1-Feb-02 10.85 4.0847 49.0165 11.2596 39.0043
1-Mar-02 11.84 9.1244
1-Apr-02 12.14 2.5338
1-May-02 11.65 -4.0362
3-Jun-02 8.86 -23.9485
1-Jul-02 7.63 -13.8826
1-Aug-02 7.38 -3.2765
3-Sep-02 7.25 -1.7615
1-Oct-02 8.03 10.7586
1-Nov-02 7.75 -3.4869
2-Dec-02 7.16 -7.6129
2-Jan-03 7.18 0.2793
3-Feb-03 7.51 4.5961
3-Mar-03 7.07 -5.8589
1-Apr-03 7.11 0.5658
1-May-03 8.98 26.3010
2-Jun-03 9.53 6.1247
1-Jul-03 10.54 10.5981
1-Aug-03 11.31 7.3055
2-Sep-03 10.36 -8.3996
1-Oct-03 11.44 10.4247
3-Nov-03 10.45 -8.6538
1-Dec-03 10.69 2.2967
2-Jan-04 11.28 5.5192
2-Feb-04 11.96 6.0284
1-Mar-04 13.52 13.0435
1-Apr-04 12.89 -4.6598
3-May-04 14.03 8.8441
1-Jun-04 16.27 15.9658
1-Jul-04 16.17 -0.6146
2-Aug-04 17.25 6.6790
1-Sep-04 19.38 12.3478
1-Oct-04 26.20 35.1909
1-Nov-04 33.53 27.9771
1-Dec-04 32.20 -3.9666
3-Jan-05 38.45 19.4099
1-Feb-05 44.86 16.6710
1-Mar-05 41.67 -7.1110
1-Apr-05 36.06 -13.4629
2-May-05 39.76 10.2607
1-Jun-05 36.81 -7.4195
1-Jul-05 42.65 15.8653
1-Aug-05 46.89 9.9414
1-Sep-05 53.61 14.3314
3-Oct-05 57.59 7.4240
1-Nov-05 67.82 17.7635
1-Dec-05 71.89 6.0012
3-Jan-06 75.51 5.0355
1-Feb-06 68.49 -9.2968
1-Mar-06 62.72 -8.4246
3-Apr-06 70.39 12.2290
1-May-06 59.77 -15.0874
1-Jun-06 57.27 -4.1827
3-Jul-06 67.96 18.6660
1-Aug-06 67.85 -0.1619
1-Sep-06 76.98 13.4562
2-Oct-06 81.08 5.3261
1-Nov-06 91.66 13.0488
1-Dec-06 84.84 -7.4405
3-Jan-07 85.73 1.0490
1-Feb-07 84.74 -1.1548
11.2596SQRT(12)
STDEV(C4C63)
4.084712 or D312
AVERAGE(C4C63)
Note monthly adjusted closing prices from
Yahoo.com
9

• 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). Whats the
  difference in value between two ?
• Example FV1,000, rCPN 5, annual payment,
  5-yr maturity
• AAA Bond N5, I/YR4, PMT50, FV1000 PV
  1044.52
• B Bond N5, I/YR6, PMT50, FV1000 PV
  957.88
• ref. stocks (Ch 7) how does P0 change with
  different required RORs?

10

• 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 (454cu) 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.
11
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 doesnt 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 Jims is 3.76. CV analysis
  indicates that Kay-Mart has superior risk/return
  characteristics. However it would be more
  advantageous to invest in Diamond Jims. Why?

Probability
Kay-Mart
Diamond Jims Inc.
3.5
14.3
Expected Return (Average Return)
12

• 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

13
created Summer 09

• Portfolio Returns
• Portfolio Expected Returns (ERp or rp) The
  weighted average of the expected returns of the
  individual securities held in a portfolio
• ERp w1ER1 w2ER2 wnERn
• rp w1r1 w2r2 wnrn

OR
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 Initial Value Weight (by value) Expected Return (r) Weighted r
ATTT 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 Portfolio Value 90,849.50 rP rP 4.51
14

• 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 of Shares Initial Stock Price Ending Stock Price Ending Stock Value Weight (by value) Realized Return (r) Weighted r
ATTT 400 43.67 45.67 18,268.00 18.64 4.58 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 Portfolio Value 98,028.50 rP 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

15

• 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

16

• 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

17
Correlation Diversification Effect on Portfolio
Risk
Perfectly Positively Correlated Stocks (Note sp
sM sM)
Stock G
Portfolio GH
Stock H
25
25
15
15
Rate of Return ()
Rate of Return ()
0
0
-10
-10
Perfectly Negatively Correlated Stocks (Note sp
0)
Rate of Return ()
18
Correlation Diversification Effect on Portfolio
Risk
Partially Correlated Stocks (Note sp lt sW sY)
Diversification is important, especially for
corporate investors they are very concerned
about the liquidity of their investments
19

• 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 firms 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 securitys risk associated
  with factors generated by events, or behaviors,
  specific to the firm or the firms industry
• it is the result of the firms inherent
  management decisions, legal problems, product or
  service obsolescence, the firms 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

20
created Summer 09
Systematic Risk versus Unsystematic Risk
(continued)
stotal
Portfolio Risk
Unsystematic (Firm-Specific, Diversifiable) Risk
Minimum Attainable Risk in a Portfolio of Average
Stocks
smarket
Volatility (Risk)
Total Portfolio Risk
Systematic (Market or Beta) Risk)
1
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
• ?p 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

21
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 stocks sensitivity to the market
  portfolio (the rest of the market)
• b quantifies a stocks market risk
• b tells us how risky a particular stock is
  compared to a market portfolio (the rest of the
  market)

22

• Measuring Systematic Risk
• Capital Asset Pricing Model (CAPM) (continued)
• the market portfolio has b 1 (by definition)
• if a stock has b 1, its 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, its 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, its 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 its returns movements will be totally
  unrelated to the market portfolio
• How to calculate b
• plot the stocks 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

23
Measuring Systematic Risk Capital Asset Pricing
Model (CAPM) (continued)
Individual Stock Return
40
b 2
b 1
30
b 0.5
20
450
10
-10
40
-20
-30
-40
10
20
30
Market Portfolio Return
-10
-20
-30
b -1
-40

• You dont have to calculate bs on your own you
  can find them online (yahoo/finance Hoovers,
  WSJ, etc.)
• Very few stocks have negative bs
• b quantifies a firms Market Risk it doesnt 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

24

• 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 cant 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)

25

• 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 stocks
  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

Mkt Risk Premium Quantity
of Risk (Cost of Risk) rs rRF
(rM - rRF)bs Compensation for Opp. Cost
Inflation Stock Risk Premium
26

• Measuring Systematic Risk
• Finding Required ROR (rs) for an Individual Stock
• Example Jamaica Jims 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 gt 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) wont be equal to each
  other. Why?
• Answer
• The statistical rs incorporates both market risk
  and firm specific risk

27

• Measuring Systematic Risk
• Beta of a Portfolio
• bp is the weighted average of the bs of the
  stocks that comprise the portfolio
• bp w1b1 w2b2 w3b3 ... wnbn
• Example A portfolio is comprised of the stocks
  indicated below. Find the portfolios b.

• 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 gt 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 thats left is
  market risk and its pretty much equal regardless
  of which method you use to measure it

28

• 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

Required ROR ()
rhigh 22 rM rA 14 rRF 6
Relatively Risky Stocks Risk Premium 16
Market (Average Stock) Risk Premium 8
rLOW 10
Safe Stock Risk Premium 4
Risk-Free Rate 6
0 0.5 1.0
1.5 2.0
Risk, (bj)
29

• Whats 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