Risk and Return

1
Risk and Return

• Business 2039

1
1
K. Hartviksen
2
Finance

• Concerned with
• cash flow (financial integrity of the firm).
• securing outside capital for internal investment.
• making appropriate internal internal investment
  decisions to maximize the value of the firm.
• shareholder wealth maximization.

3
Capital Market Knowledge

• The financial manager must understand investors
  expectations and preferences in order to make
  appropriate decisions in the firm.
• Specifically
• how stock prices are established in the market
• what factors influence stock prices

4
The Capital Markets
5
The Capital Markets
6
Why is it important for the Financial Manager to
understand Capital Markets?

• New capital must be raised in the capital
  markets.
• The stock price is a good barometer for how the
  market views the health and management of the
  firm.
• When stock prices fall
• shareholders will start to ask questions at
  annual meetings
• the firm may become a takeover target
• When firms are taken over, under these
  circumstances, what often happens to senior
  management?

7
Wall Street Rule(sword of Damocles)

• Often institutional investors will choose not to
  get actively involved in trying to turn around a
  problematic investment.
• They instead, divest.
• If this is a widespread response to management
  performance, the stock price can be expected to
  fall a great deal.
• Such a firm is often taken over and reorganized.
  The poor managers are replaced and the firm is
  returned to operating and financial health.
• This is market discipline.

8
Wall Street Rule(implications)

• Even though the firm may not be actively seeking
  to raise new capital in the marketsmanagement
  ignores the discipline of the markets at its own
  peril.

9
Key Terms

• Expected return
• required return
• portfolio
• systematic risk
• unsystematic risk
• diversification
• beta coefficient
• security market line

• Market premium for risk
• capital asset pricing model
• cost of capital
• mean, variance, standard deviation
• correlation

2
2
K. Hartviksen
10
Risk and Return

• The tradeoff between risk and return is central
  to understanding the field of finance.
• CRITICAL UNDERLYING ASSUMPTION
• that the normal investor is a wealth-maximizing
  risk minimizer.
• That the normal investor is a diversified one.

3
11
Risk Averse Wealth Maximizer

• Such an investor, when confronted with a choice
  between two competing investment opportunities
  that offer the same return, but one is riskier
  than the otherwe assume that the investor will
  chose the safer alternative.
• It follows that some investment opportunities
  will dominate others.(next slide)

4
12
Investment Choices(Driven by our underlying
assumptions)
Return
A
B
10
D
C
5
Risk
To the risk-averse wealth maximizer, the choices
are clear, A dominates B, B dominates D, A
dominates C, C dominates D.
5
13
Capital Asset Pricing Model
Return
Required return Rf bs kM - Rf
km
Market Premium for risk
Security Market Line
Rf
Real Return
Premium for expected inflation
Beta Coefficient
BM1.0
6
14
CAPM

• This model is an equilibrium based model.
• It is called a single-factor model because the
  slope of the SML is caused by a single measure of
  risk the beta.
• Although this model is a simplification of
  realityit is robust (it explains much of what we
  see happening out there) and it enjoys widespread
  use in a great variety of applications.
• Although it is called a pricing model there are
  not prices on that graph.only risk and return.
• It is called a pricing model because it can be
  used to help us determine appropriate prices for
  securities in the market.

15
Risk

• Risk is the chance of harm or loss danger.
• We know that various asset classes have yielded
  very different returns in the past

16
Historical Returns and Standard Deviations1948 -
941

• Average Return Standard Deviation
• Canadian common stock 12.73 16.81
• U.S. common stock (Cdn ) 14.09 16.60
• Long term bonds 7.01 10.20
• Small cap stocks 15.67 24.40
• Inflation 4.52 3.54
• Treasury bills 6.15 4.17
• ___________________
• 1The Alexander Group

17
Risk and Return

• The foregoing data point out that those asset
  classes that have offered the highest rates of
  return, have also offered the highest risk levels
  as measured by the standard deviation of returns.
• The CAPM suggests that investors demand
  compensation for risks that they are exposed
  toand these returns are built into the
  decision-making process to invest or not.

18
Capital Asset Pricing Model
Return
Required return Rf bs kM - Rf
km
Market Premium for risk
Security Market Line
Rf
Real Return
Premium for expected inflation
Beta Coefficient
BM1.0
6
19
CAPM

• The foregoing graph shows that investors
• demand compensation for expected inflation
• demand a real rate of return over and above
  expected inflation
• demand compensation over and above the risk-free
  rate of return for any additional risk
  undertaken.
• We will make the case that investors dont need
  compensation for all of the risk of an investment
  because some of that risk can be diversified
  away.
• Investors require compensation for risk they
  cant diversify away!

20
Beta Coefficient

• The beta is a measure of systematic risk of an
  investment.
• Systematic risk is the only relevant risk to a
  diversified investor according to the CAPM since
  all other risk may be diversified away.
• Total risk of an investment is measured by the
  securities standard deviation of returns.
• According to the CAPM total risk may be broken
  into two partssystematic (non-diversifiable) and
  unsystematic (diversifiable)
• TOTAL RISK SYSTEMATIC RISK UNSYSTEMATIC RISK
• The beta can be determined by regressing the
  holding period returns (HPRs) of the security
  over 30 periods against the returns on the
  overall market.

7
21
Risk

• We cant measure risk until we first measure the
  returns of the investment.
• Since investors make investment decisions today,
  in the expectation of receiving future returns,
  past returns are relevant only to the extent that
  they can be used to predict future investment
  returns.

22
Measuring Returns

• We can use historical data (ex post data) (as
  long as we can reasonably assume nothing has
  fundamentally changed with the companyand so
  those historical returns can help us predict the
  future)
• Or we can use forecast (ex ante) data to estimate
  risk and return.

23
Measuring Historical Stock Returns

• The one-period returns realized on stock
  investments are measured through the
  Holding-period-return calculation

24
Measuring Historical Stock Returns
25
Measuring Historical Stock Returns

• The quarterly return on Bowater stock can be
  found by determining the market price that
  started and ended the quarter plus any dividends
  received during the quarter

26
Historical Returns

• To get a reasonable estimate of what has happened
  in the past we need to go back 30 quarters and
  measure the historical (realized) returns.
• The standard deviation of those historical
  returns will tell us how volatile they were over
  that past period.

27
Estimating the Beta using historical returns

• If we regress the realized returns on the stock
  with those realized on the market portfolio we
  will get an idea of the relative performance of
  the stock compared to the market.
• The beta coefficient is the slope of the
  regression (characteristic) line.

28
Historical Beta Estimation
29
Characteristic Line

• The characteristic line is a regression line that
  represents the relationship between the returns
  on the stock and the returns on the market over a
  period of time.
• The slope of the Characteristic Line is the Beta
  Coefficient
• The degree to which the characteristic line
  explains the variability in the dependent
  variable (returns on the stock) is measured by
  the coefficient of determination. (also known as
  the R2 (r-squared)).
• If the coefficient of determination equals 1.00,
  this would mean that all of the points of
  observation would lie on the line. This would
  mean that the characteristic line would explain
  100 of the variability of the dependent variable.

30
Forecasting Returns

• Sometimes a company changes its operating
  activities such that the past is no longer a good
  predictor of future performance.
• In this case the analyst can used subjective
  forecasts for returns on the stock and the market
  to estimate the beta coefficient.
• An example of forecast data follows

31
Predicting Stock Returns(ex ante returns)
Expected return is the weighted average of the
possible returns that have been predicted.
K. Hartviksen
32
Measuring Risk of the Individual Security

• Risk is the possibility that the actual return
  that will be realized, will turn out to be
  different than what we expect (or have forecast).
• This can be measured using standard statistical
  measures of dispersion for probability
  distributions. They include
• variance
• standard deviation
• coefficient of variation

33
Standard Deviation

• The formula for the standard deviation when
  analyzing population data (realized returns) is

34
Standard Deviation

• The formula for the standard deviation when
  analyzing forecast data (ex ante returns) is
• it is the square root of the sum of the squared
  deviations away from the expected value.

35
Forecasting Risk and Return for the Individual
Asset
K. Hartviksen
36
Using Forecasts to Estimate Beta

• The formula for the beta coefficient for a stock
  s is
• Obviously, the calculate a beta for a stock, you
  must first calculate the variance of the returns
  on the market portfolio as well as the covariance
  of the returns on the stock with the returns on
  the market.

37
Covariance

• The formula for the covariance between the
  returns on the stock and the returns on the
  market is
• Covariance is an absolute measure of the degree
  of co-movement of returns. The correlation
  coefficient is also a measure of the degree of
  co-movement of returnsbut it is a relative
  measurethis is why it is on a scale from 1 to
  -1.

38
Correlation Coefficient

• The formula for the correlation coefficient
  between the returns on the stock and the returns
  on the market is
• The correlation coefficient will always have a
  value in the range of 1 to -1.

39
Correlation

• The degree to which the returns of two stocks
  co-move is measured by the correlation
  coefficient.
• The correlation coefficient between the returns
  on two securities will lie in the range of 1
  through - 1.
• 1 is perfect positive correlation.
• -1 is perfect negative correlation.

10
40
Perfect Negatively Correlated Returns over Time
Returns
A two-asset portfolio made up of equal parts of
Stock A and B would be riskless. There would be
no variability of the portfolios returns over
time.
10
Returns on Stock A
Returns on Stock B
Returns on Portfolio
1994
1995
1996
Time
11
41
Portfolio ReturnsSimply the Weighted Average of
Expected Returns
14
5
K. Hartviksen
42
Grouping Individual Assets into Portfolios

• The riskiness of a portfolio that is made of
  different risky assets is a function of three
  different factors
• the riskiness of the individual assets that make
  up the portfolio
• the relative weights of the assets in the
  portfolio
• the degree of comovement of returns of the assets
  making up the portfolio
• The standard deviation of a two-asset portfolio
  may be measured using the Markowitz model

43
Diversification Potential

• The potential of an asset to diversify a
  portfolio is dependent upon the degree of
  comovement of returns of the asset with those
  other assets that make up the portfolio.
• In a simple, two-asset case, if the returns of
  the two assets are perfectly negatively
  correlated it is possible (depending on the
  relative weighting) to eliminate all portfolio
  risk.
• This is demonstrated through the following chart.

44
(No Transcript)
45
Diversification and Number of Assets in the
Portfolio

• Total risk of a portfolio with one asset in it is
  equal to the standard deviation of returns of the
  individual asset.
• As the portfolio is invested across more and more
  assets, the risk of the portfolio will
  declinebut it cannot be eliminated as
  demonstrated in the following graph

46
(No Transcript)
47
Systematic Risk

• The returns on most assets in our economy are
  influenced by the health of the system
• Some companies are more sensitive to systematic
  changes in the economy. For example durable
  goods manufacturers.
• Some companies do better when the economy is
  doing poorly (bill collection agencies).
• The beta coefficient measures the systematic risk
  that the security possesses.
• Since non-systematic risk can be diversified
  away, it is irrelevant to the diversified
  investor.

48
Systematic Risk

• We know that the economy goes through economic
  cycles of expansion and contraction as indicated
  in the following

49
Canadas Business cycles from
1873-1992 Trough to ExpansionPeak to
Contraction (months from trough to peak)(months
from peak to trough) Nov 1873 66 May
1879 38 July 1882 32 Mar 1885 23 Feb 1887 12 Feb
1888 29 July 1890 9 Mar 1891 23 Apr 1893 13 Mar
1894 17 Aug 1895 12 Aug 1896 44 Apr 1900 10 Feb
1901 22 Dec 1902 18 June 1904 30 Dec 1906 19 July
1908 20 Mar 1910 16 July 1911 16 Nov 1912 25 Jan
1915 36(WWI) Jan 1918 15 Apr 1919 14 June
1920 15 Sep 1921 21 June 1923 14 Aug 1924 56 Apr
1929 47 (Depression) Mar 1933 52 July 1937 15
(Depression) Oct 1938 80(WWII) June 1945 8 Feb
1946 33 Oct 1948 11 Sep 1949 44(Korean War) May
1953 14 July 1954 31 Feb 1957 12 Feb 1958 26 Apr
1960 10 Feb 1961 160 June 1974 10 Apr
1975 58 Feb 1980 6 July 1980 12 July 1981 6 Nov
1982 89 Apr 1990 22 Feb 1992
50
Companies and Industries

• Some industries (and by implication the companies
  that make up the industry) move in concert with
  the expansion and contraction of the economy.
• Some lead the overall economy. (stock market)
• Some lag the overall economy. (ie. automotive
  industry)

51
Amount of Systematic Risk

• Some industries may find that their fortunes are
  positively correlated with the ebb and flow of
  the overall economybut that this relationship is
  very insignificant.
• An example might be Imperial Tobacco. This firm
  does have a positive beta coefficient, but very
  little of the returns of this company can be
  explained by the beta. Instead, most of the
  variability of returns on this stock is from
  diversifiable sources.
• A Characteristic line for Imperial Tobacco would
  show a very wide dispersion of points around the
  line. The R2 would be very low (.05 5 or
  lower).

52
Characteristic Line for Imperial Tobacco
Characteristic Line for Imperial Tobacco
Returns on Imperial Tobacco
Returns on the Market (TSE 300)
53
High R2

• An R2 that approaches 1.00 (or 100) indicates
  that the characteristic (regression) line
  explains virtually all of the variability in the
  dependent variable.
• This means that virtually of the risk of the
  security is systematic.
• This also means that the regression model has a
  strong predictive ability. if you can predict
  what the market will dothen you can predict the
  returns on the stock itself with a great deal of
  accuracy.

54
Characteristic Line General Motors
Characteristic Line for GM (high R2)
Returns on General Motors
Returns on the Market (TSE 300)
55
Diversifiable Risk(non-systematic risk)

• Examples of this type of risk include
• a single company strike
• a spectacular innovation discovered through the
  companys RD program
• equipment failure for that one company
• management competence or management incompetence
  for that particular firm
• a jet carrying the senior management team of the
  firm crashes
• the patented formula for a new drug discovered by
  the firm.
• Obviously, diversifiable risk is that unique
  factor that influences only the one firm.

56
Partitioning Risk under the CAPM

• Remember that the CAPM assumes that total risk
  (variability of a securitys returns) can be
  separated into two distinct components
• Total risk systematic risk unsystematic risk
• 100 40 60 (GM)
• or
• 100 5 95 (Imperial Tobacco)
• Obviously, if you were to add Imperial Tobacco to
  your portfolio, you could diversify away much of
  the risk of your portfolio. (Not to mention the
  fact that Imperial has realized some very high
  rates of return in addition to possessing little
  systematic risk!)

57
Using the CAPM to Price Stock

• The CAPM is a fundamental analysts tool to
  estimate the intrinsic value of a stock.
• The analyst needs to measure the beta risk of the
  firm by using either historical or forecast risk
  and returns.
• The analyst will then need a forecast for the
  risk-free rate as well as the expected return on
  the market.
• These three estimates will allow the analyst to
  calculate the required return that rational
  investors should expect on such an investment
  given the other benchmark returns available in
  the economy.

58
Required Return

• The return that a rational investor should demand
  is therefore based on market rates and the beta
  risk of the investment.
• To find this, you solve for the required return
  in the CAPM
• This is a formula for the straight line that is
  the SML.

59
Security Market Line

• This line can easily be plotted.
• Draw Cartesian coordinates.
• Plot the yield on 91-day Government of Canada
  Treasury Bills as the risk-free rate of return on
  the vertical axis.
• On the horizontal axis set a scale that includes
  Beta1 (this is the beta of the market)
• Plot the point in risk-return space that
  represents your expected return on the market
  portfolio at beta 1
• Draw a straight line to connect the two points.
• Plot the required and expected returns for the
  stock at its beta.

60
Plot the Risk-Free Rate
Return
Rf
Beta Coefficient
1.0
61
Plot Expected Return on the Market Portfolio
Return
km 12
Rf 4
Beta Coefficient
1.0
62
Draw the Security Market Line
Return
SML
km 12
Rf 4
Beta Coefficient
1.0
63
Plot Required Return(Determined by the formula
Rf bskM - Rf
Return
SML
R(k) 13.6
km 12
R(k) 4 1.28 13.6
Rf 4
Beta Coefficient
1.0
1.2
64
Plot Expected ReturnE(k) weighted average of
possible returns
Return
SML
R(k) 13.6
R(k) 4 1.28 13.6
km 12
E(k)
Rf 4
Beta Coefficient
1.0
1.2
65
If Expected Required ReturnThe stock is
properly (fairly) priced in the market. It is in
EQUILIBRIUM.
Return
SML
R(k) 13.6
R(k) 4 1.28 13.6
km 12
E(k)
Rf 4
Beta Coefficient
1.0
1.2
66
If E(k) lt R(k)The stock is over-priced. The
analyst would issue a sell recommendation in
anticipation of the market becoming efficient
to this fact. Investors may short the stock to
take advantage of the anticipated price decline.
Return
SML
R(k) 13.6
R(k) 4 1.28 13.6
km 12
E(k)
E(k) 9
Rf 4
Beta Coefficient
1.0
1.2
67
Lets Look at the Pricing Implications

• In this example
• E(k) 9
• R(k) 13.6
• If the market expects the company to pay a
  dividend of 1.00 next year, and the stock is
  currently offering an expected return of 9, then
  it should be priced at
• But, given the other rates in the economy and our
  judgement about the riskiness of this investment
  we think that this stock should be worth

68
Practical Use of the CAPM

• Regulated utilities justify rate increases using
  the model to demonstrate that their shareholders
  require an appropriate return on their
  investment.
• Used to price initial public offerings (IPOs)
• Used to identify over and under value securities
• Used to measure the riskiness of
  securities/companies
• Used to measure the companys cost of capital.
  (The cost of capital is then used to evaluate
  capital expansion proposals).
• The model helps us understand the variables that
  can affect stock pricesand this guides
  managerial decisions.

69
Rf rises
SML2
Return
SML1
ks2
ks1
Rising interest rates will cause all required
rates of return to increase and this will force
down stock and bond prices.
Rf2
Rf1
Beta Coefficient
Bs1.2
70
The Slope of The SML rises(indicates growing
pessimism about the future of the economy)
SML2
Return
SML1
ks2
Growing pessimism will cause investors to demand
greater compensation for taking on riskthis will
mean prices on high beta stocks will fall more
than low beta stocks.
ks1
Rf1
Beta Coefficient
Bs1.2