Chapter 1 An Overview of Managerial Finance

1

Chapter 4Risk and Rates of Return
2
Defining and Measuring Risk

• Risk is the chance that an unexpected outcome
  will occur
• A probability distribution is a listing of all
  possible outcomes with a probability assigned to
  each
• must sum to 1.0 (100).

3
Expected Rate of Return

• Rate of return expected to be realized from an
  investment during its life
• Mean value of the probability distribution of
  possible returns
• Weighted average of the outcomes, where the
  weights are the probabilities

4
Expected Rate of Return
State of the economy Prob. Martin Product RETURNS Martin Product RETURNS US Electric RETURNS US Electric RETURNS
(1) (2) (3) (4) (2 x 3) (5) (6) (2 x 5)
Boom 0.2 110 20
Normal 0.5 22 16
Recession 0.3 -60 10
E(K)
5
Expected Rate of Return
6
Continuous versus Discrete Probability
Distributions

• Continuous Probability Distributionnumber of
  possible outcomes is unlimited, or infinite.

7
Measuring Risk The Standard DeviationMartin
Product
K E(K) K E(K) K E(K)2 Pr. K E(K)2 x Pr
(1) (2) (3) (1 2) (4) (5) (6) (4 x 5)
110 0.2
22 0.5
-60 0.3

8
Measuring Risk The Standard Deviation
9
Measuring Risk Coefficient of Variation

• Standardized measure of risk per unit of return
• Calculated as the standard deviation divided by
  the expected return
• Useful where investments differ in risk and
  expected returns

10
Risk Aversion and Required Returns

• Risk Premium (RP)
• The portion of the expected return that can be
  attributed to an investments risk beyond a
  riskless investment
• The difference between the expected rate of
  return on a given risky asset and that on a less
  risky asset

11
Portfolio Risk and theCapital Asset Pricing Model

• CAPM
• A model based on the proposition that any stocks
  required rate of return is equal to the risk-free
  rate of return plus a risk premium, where risk is
  based on diversification.
• Portfolio
• A collection of investment securities

12
Portfolio Risk and Return

• The goal of finance manager is to create
• AN EFFICIENT PORTFOLIO Maximizes return
• for a given level of risk or minimizes risk for a
• given level of return.

13
Portfolio Returns

• Expected return on a portfolio,

• The weighted average expected return on the
  stocks held in the portfolio

14
Portfolio Returns

• Realized rate of return, k
• The return that is actually earned
• Actual return usually different from expected
  return

15
Portfolio Risk

• Correlation Coefficient, r
• Measures the degree of relationship between two
  variables.
• Perfectly correlated stocks have rates of return
  that move in the same direction.
• Negatively correlated stocks have rates of return
  that move in opposite directions.

16
Portfolio size and risk

• Inc size of a portfolio ? risk dec
• Risk dec to a certain point .. (Co. risk 0)
• If we take all sec in the stock mkt as one
  portfolio (max size) ? still some risk exist
  (Market Risk) relevant risk the contribution
  of a secs risk to a portfolio.

17
Portfolio Risk

• Risk Reduction
• Combining stocks that are not perfectly
  correlated will reduce the portfolio risk through
  diversification.
• The riskiness of a portfolio is reduced as the
  number of stocks in the portfolio increases.
• The smaller the positive correlation, the lower
  the risk.

18
Firm-Specific Risk versus Market Risk

• Firm-Specific Risk
• That part of a securitys risk associated with
  random outcomes generated by events, or
  behaviors, specific to the firm.
• Firm-specific risk can be eliminated through
  proper diversification.

19
Firm-Specific Risk versus Market Risk

• Market Risk
• That part of a securitys risk that cannot be
  eliminated through diversification because it is
  associated with economic, or market factors that
  systematically affect all firms.

20
Firm-Specific Risk versus Market Risk

• Relevant Risk
• The risk of a security that cannot be diversified
  away, or its market risk.
• This reflects a securitys contribution to a
  portfolios total risk.

21
NO GOOD

• .. of thinking how risky a security is if helf in
  isolation you need to measure its market risk
  measure how sensitive it is to market this
  sensitivity is called BETA

22
The Concept of Beta

• Beta Coefficient, b
• A measure of the extent to which the returns on a
  given stock move with the stock market.
• b 0.5 Stock is only half as volatile, or
  risky, as the average stock.
• b 1.0 Stock has the same risk as the average
  risk.
• b 2.0 Stock is twice as risky as the average
  stock.

23
Steps in deriving Beta

• Plot mkt ret (X) and asset ret (Y) at various
  point in time.
• Regression the slope beta
• The higher the beta the higher the risk
• Beta for the market 1, all other betas are
  viewed in relation to this value.
• Beta may be ve or v, ve is the norm
• Majority of betas fall between .5 and 2.

24
Portfolio Beta Coefficients

• The beta of any set of securities is the weighted
  average of the individual securities betas
• IF mkt ret inc by 10, a port with a beta of .75
  will experience a 7.5 inc in its return (.75 x
  10)

25
The Relationship Between Risk and Rates of Return
26
Market Risk Premium

• RPM is the additional return over the risk-free
  rate needed to compensate investors for assuming
  an average amount of risk.
• Assuming
• Treasury bonds yield 6,
• Average stock required return 14,
• Then the market risk premium is 8 percent
• RPM kM - kRF 14 - 6 8.

27
The Required Rate of Return for a Stock

• Security Market Line (SML)
• The line that shows the relationship between risk
  as measured by beta and the required rate of
  return for individual securities.

28
Security Market Line - CAPM
29
The Impact of Inflation

• kRF is the price of money to a riskless borrower.
• The nominal rate consists of
• a real (inflation-free) rate of return, and
• an inflation premium (IP).
• An increase in expected inflation would increase
  the risk-free rate.

30
Changes in Risk Aversion

• The slope of the SML reflects the extent to which
  investors are averse to risk.
• An increase in risk aversion increases the risk
  premium and increases the slope.

31
Changes in a Stocks Beta Coefficient

• The Beta risk of a stock is affected by
• composition of its assets,
• use of debt financing,
• increased competition, and
• expiration of patents.
• Any change in the required return (from change in
  beta or in expected inflation) affects the stock
  price.

32
Stock Market Equilibrium

• The condition under which the expected return on
  a security is just equal to its required return
• Actual market price equals its intrinsic value as
  estimated by the marginal investor, leading to
  price stability

33
Changes in Equilibrium Stock Prices

• Stock prices are not constant due to changes in
• Risk-free rate, kRF,
• Market risk premium, kM kRF,
• Stock Xs beta coefficient, bx,
• Stock Xs expected growth rate, gX, and
• Changes in expected dividends, D0.