Risk and Value

1
Chapter 6

• Risk and Value

Shapiro and Balbirer Modern Corporate Finance
A Multidisciplinary Approach to Value
Creation Graphics by Peeradej Supmonchai
2
Learning Objectives

• Describe the pattern of historic returns in the
  capital markets.
• Understand how to measure risk and expected
  return for individual securities as well as for
  portfolios.
• Explain how diversification can reduce the risk
  of an investment portfolio.
• Identify the linkages between risk and expected
  return for securities, and use this relationship
  to calculate the required rate of return for a
  firms common stock.

3
Learning Objectives (Cont.)

• Explain how the capital asset pricing model
  (CAPM) and the arbitrage pricing theory (APT)
  measure risk and relate that risk to expected
  return.
• Indicate how the insights from capital market
  theory can be used to design corporate
  diversification strategies that can enhance
  shareholder value.
• Explain why globally diversifying a securities
  portfolio can reduce risk.

4

• Average Annual Security Returns
• 1926-1997
• (ALL FIGURES IN PERCENTS)
• Average Nominal Average
  Real Premium Over
• Security Type Rate of Return Rate of Return
  Treasury Bills
• Small-Firm 17.7
  14.5 13.9
• Common Stocks
• Large-Firm 13.0
  9.8 9.2
• Common Stocks
• Corporate Bonds 6.1
  2.9 2.3
• Treasury Bonds 5.6
  2.4 1.8
• Treasury Bills 3.8
  0.6 -0-

5
Risk-Return Characteristics of Different
Securities
6
Year-to-Year Stock Market Returns
7
Probability Distributions

• Investors cannot predict security returns with
  certainty.
• They can list the potential outcomes and have a
  sense for the likelihood that each of these
  outcomes will occur.
• Probabilities represent the relative likelihood
  each outcome will occur. The probabilities for
  the full range of outcomes must sum to one.
  Individual probabilities cannot be negative.

8
Expected Return of a Probability Distribution
Where Rj the jth investment outcome M the
number of possible investment outcomes pj the
likelihood that the jth outcome will occur
9
Standard Deviation of a Probability Distribution
10
Risk Premiums in a Portfolio Context

• Risk that can be diversified away does not
  command a risk premium.
• The market demands a return premium thats
  related to an assets contribution to the risk of
  a diversified portfolio.
• Diversification works because stock prices dont
  move in lock step.
• Portfolio risk depends on both the risk of the
  individual assets and how their returns relate to
  one another.

11
Systematic versus Unsystematic Risk

• Total Risk Market Risk Unique Risk
• Market Risk Systematic Risk
• Unique Risk Unsystematic, or Diversifiable Risk

12
Stock Price Movements and Economic Activity

• Cyclical Stocks
• Countercyclical Stocks
• Acyclical Stocks

13
Probability Distribution for GM

• State of the Probability or
  Forecasted Return
• Economy Likelihood (As a
  Percent)
• Economic Boom 0.50
  40
• Normal Year 0.30
  15
• Recession 0.20
  - 30

14
Calculating GMs Expected Return

• E (RGM) 0.50(40) 0.30(15) 0.20(-30)
• 18.5

15
Calculating GMs Standard Deviation of Returns

• sGM 0.5(40.0-18.5)20.3(15.0-18.5)20.2(-30-18
  .5)21/2
• 0.5(21.5)20.3(-3.5)20.2(-48.5)21/2
• 231.13.7470.51/2 26.6

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Building Portfolios - An Example

• PORTFOLIO PROBABILITY DISTRIBUTION
• 50 GENERAL MOTORS - 50 ECHLIN
• State of Probability
  GM-Return ECH-Return Portfolio
• Economy Return
• Economic Boom 0.50 40
  4 22.0
• Normal Year 0.30 15
  14 14.5
• Recession 0.20 -
  30 18 - 6.0
• Expected Return
  18.5 9.8 14.2
• Standard Deviation
  26.6 6.0 9.9

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Correlation Coefficient

• The correlation coefficient measures the extent
  to which security returns relate to one another.
• Positive correlation means that security returns
  move together, i.e. if one goes up, so does the
  other.
• Negative correlation means that security returns
  move in the opposite direction.
• Zero correlation means that security returns are
  unrelated to one another.

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Correlation and Portfolio Risk

• In general, the less positive the correlation
  among securities in a portfolio, the less the
  risk-reducing benefit of diversification will be.
  Conversely, a portfolio containing highly
  positive-correlated securities will do little to
  reduce risk.

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Portfolio Expected Returns

• Where
• E(RP) the expected return on the portfolio
• E(Ri) the expected return on asset I
• n the number of assets in the portfolio
• wi the fraction of the portfolio placed in
  the asset

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Portfolio Risk

• Where
• w1 the proportion of wealth placed in assets 1
• w2 the proportion of wealth placed in assets 2
• s1 the standard deviation of returns for
  securities 1
• s2 the standard deviation of returns for
  securities 2
• r12 the correlation coefficient

21
The Efficient Frontier
B is the maximum-risk-maximum- expected return
portfolio
22
Efficient Frontier

• Opportunity Set
• All possible combinations of risk and return
  that can be created with a given set of
  securities.
• Efficient Frontier or Efficient Set
• Portfolios that have the highest return for a
  given degree of risk, or
• Portfolios that have the lowest risk for a given
  return

23
The Efficient Frontier With a Risk-Free Asset
G
Capital market line
borrowing
M
lending
Expected return
E
F
C
D
Rf
Standard deviation
24
The Capital Market Line (CML)

• The Capital Market Line (CML) represents the
  markets trade-off between risk and return for
  efficient portfolios and are combinations of the
  risk-free asset and the market portfolio. The
  combination of risk-free asset and risky
  portfolio investors hold depends on their risk
  preferences.

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The Capital Market Line - Some Terminology

• Market Risk Premium (rM - rf) - Depends on the
  degree of risk aversion in the market as a whole
• Market Price of Risk (rM - rf)/sM- Slope of the
  CML represents a risk premium over-and-above the
  risk-free rate, per unit of risk.

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Concept of Beta

• The sensitivity of an assets return relative to
  the return on the market is called beta (b). Beta
  measures the systematic risk of a security.

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Systematic Risk and Beta
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Betas for Stocks in Different Industries

• Textile Companies Retailers
• Burlington Industries 0.70 Dayton Hudson
  1.05
• Cone Mills 0.70 Federated
  Stores 1.15
• Guilford Mills 0.60 JC Penney
  0.95
• Unifi 0.65
  Sears, Roebuck 1.10
• Westpoint Stevens 0.60 Wal-Mart
  0.95
• Foreign Electronics Firms Gold/Silver
  Mining Companies
• Hitachi 0.75
  Barrick Gold 0.70
• NEC Corporation 0.70 Coeur DAlene
  Mines 0.75
• Pioneer Electronics 0.80 Homestake
  0.65
• Sony Corporation 0.95 Newmont Mining
  0.70
• Philips Electronics 1.25 Placer Dome,
  Inc. 0.90

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The Characteristic Line

• The Characteristic Line is the relationship
  between the historic returns for an individual
  security and the market. It is obtained by
  collecting data on the individual security and
  using this information to compute total returns
  for a given year. Data on a broad-based
  portfolio, such as the SP 500, can also be
  collected to generate a set of returns for the
  market. Plotting this data on a graph and putting
  a line of best fit through the point using
  regression analysis gives us the characteristic
  line.

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The Characteristic Line for an Individual Stock
Characteristic line
Stock return
b
Market return
31
Analytical Representation of the Characteristic
Line

• Where
• Rit the return on an individual stock during
  time period t
• Rmt the return on the market in the same time
  period
• eit an error term representing the
  difference between an individual data point and
  the regression line
• a the Y-intercept of the regression line
• bi the volatility of an individual stocks
  returns with respect to the market

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Expected Return on a Risky Asset

• Expected Risk-Free Risk
• Return Return Premium

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Capital Asset Pricing Model (CAPM)

• Specifies the relationship between risk and
  return for individual security as

34
Estimating Required Returns Using the CAPM

• Suppose the CFO of IBM want to calculate the
  required rate of return on the firms common
  stock. The published beta for IBM is 1.00. With a
  Treasury bond rate of 5.25 and an estimated
  market risk premium of 6, the required rate of
  return on IBMs stock would be
• ri rf bi (rM - rf)
• 5.25 1.00(6) 11.25

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Basic Messages of CAPM

• If you want to earn higher returns, you must be
  prepared to bear higher risk.
• If you are not fully diversified, you are bearing
  risk without being compensated.

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Arbitrage Pricing Theory (APT)

• The APT offers an alternative to the CAPM by
  defining the relationship between risk and return
• Like the CAPM, APT assumes both perfectly
  competitive capital markets as well as
  homogeneous expectations on the part of
  investors.
• Unlike the CAPM that relies on a single risk
  factor, APT assumes that returns are related to
  multiple risk factor.
• The number and type of risk factors are not
  specified in advance they must be empirically
  determined.

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Arbitrage Pricing Theory (APT) - The Mathematics

• Where
• E(rf) the expected risk-free rate
• bij securitys systematic risk with
  respect to the jth risk factor
• lj the market price of risk for the
  jth risk factor
• n the number of common factors

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Arbitrage Pricing Theory- An Example

• APT Factor Sensitivities and Risk Premiums
• Factor Risk
• Factor Sensitivity Premium
• Individual Production 0.7 10
• Unanticipated Inflation 0.3 6
• Term Structure of Interest Rates 0.9 4
• Bond Risk Premiums 0.4 3

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Arbitrage Pricing Theory (APT) -An Example

• If the risk-free rate is 7.5 percent, the
  expected return is
• E(ri) E(rf) b1l1 b2 l2 b3 l3 b4 l4
• 7.5 0.7(10) 0.3(6) 0.9(4) 0.4(3)
• 21.1

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Capital Market Theory andCorporate
Diversification Strategies

• The CAPM indicates that the appropriate measure
  of risk for an individual security is beta- the
  securitys volatility with respect to the market.
  The investor can eliminate unsystematic risks
  through diversification. Therefore, corporate
  diversification that is undertaken for the sole
  purpose of risk reduction will not create
  shareholder wealth, since investors can eliminate
  unsystematic risk themselves through their own
  portfolio activities.

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Related versus Unrelated Diversification

• Related diversification involves entering lines
  of business which (1) serve similar markets or
  utilize similar channels of distribution, (2)
  employ similar production technologies, and (3)
  exploit science-based skills that are similar to
  existing lines of business. Related
  diversification has the potential to create
  synergies that can enhance shareholder value.
• In contrast, unrelated, or conglomerate
  diversification involves getting into lines of
  business that are different from those currently
  being pursued. Typically, few synergies arise
  from unrelated diversification.

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Global Diversification

• Expands the set of securities available to
  investors.
• If security returns are not perfectly
  synchronized, investors can achieve greater risk
  reduction through global diversification rather
  than limiting their choices in the domestic
  markets.
• Global diversification pushes out the efficient
  frontier.

43
The Global Efficient Set
Efficient frontier- US and foreign stocks
C
Efficient frontier- US stocks only
D
B
Expected return
A
Standard deviation
44
Risks of Holding Foreign Securities

• Dollar Return (Foreign Security Return)
  (Currency Gain or Loss)
• (1R) (1Rfx)(1g)
• R Rfx g

45
Risks of Holding Foreign Securities

• The standard deviation of dollar return (s) in
  holding a foreign security is
• 
  Where
• sf 2 variance of the foreign currency
  return
• sg2 variance of the change in exchange
  rate
• (corr)fg correlation between foreign
  currency return and changes in exchange
  rates

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Risk of Holding a Foreign Security - An Example

• Suppose the standard deviation of return on
  Matsushita (a Japanese firm) in terms of yen is
  23, and the standard deviation of change in the
  dollar/yen exchange rate is 17. Additionally,
  the correlation between the yen return on
  Matsushita, and the rate of change in exchange
  rates is 0.31.

47
Risk of Holding a Foreign Security - An Example

• The standard deviation of the dollar return for
  investing in Matsushita stock is
• s (0.23) 2 (0.17)2 2 (0.23) (0.17)
  (0.31) 1/2
• 0.3256 or 32.56