Chapter 06 Risk and Return

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Chapter 06Risk and Return
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Determinants of Intrinsic Value The Cost of
Equity
Net operating profit after taxes
Required investments in operating capital
-
Free cash flow (FCF)

FCF1
FCF2
FCF8
Value

...
(1 WACC)1
(1 WACC)8
(1 WACC)2
Weighted average cost of capital (WACC)
Market interest rates
Firms debt/equity mix
Cost of debt Cost of equity
Firms business risk
Market risk aversion
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Important Notes

1. Risk of financial asset is judged by the risk of
   its cash flow
2. Asset risk Stand Alone basis vs. Portfolio
   Context
3. Portfolio context Diversifiable Risk vs. Market
   Risk.
4. Investors in general are Risk Averse

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STAND ALONE RISK
Stand alone risk the risk an investor would face
if she or he held only one particular
asset. Investment risk pertains to the
probability of actually earning a low or negative
return. The greater the chance of low or negative
returns, the riskier the investment.
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Probability Distribution Expected Rate of Return

r expected rate of return.
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Probability Distribution Expected Rate of Return
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Stand Alone Risk Measurements

• Standard Deviation a measure of the tightness of
  the probability distribution. The tighter the
  probability distribution, the smaller the
  Standard Deviation and the less risky the asset.
• Coefficient of Variation Standard Deviation
  divided by return. It measures risk per unit of
  return, thus provides more standardized basis for
  risk profile comparison between assets with
  different return.

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Standard Deviation
Variance
Standard Deviation
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Standard Deviation
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Probability distribution
Basic Foods

• The larger the Standard Deviation
• the lower the probability that actual returns
  will be close to the expected return
• hence the larger the risk

Sale.com
Rate of return ()
90
15
-60
0
-15
45
Expected Rate of Return
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Historical Data to Measure Standard Deviation
Standard Deviation
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Coefficient of Variation (CV)
Standardized measure of dispersion about the
expected value
s
CV

r
Shows risk per unit of return.
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B
A
0
sA sB , but A is riskier because
larger probability of losses.
s
CVA gt CVB.

r
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Risk Return in Portfolio Context
Return

rp is a weighted average
n


rp S wiri.
i 1
Risk Correlation Coefficient to measure the
tendency of two variables moving together
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Portfolio Return
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Portfolio RiskStandard Deviation of
2-Asset-Portfolio
Variance
Covariance
Standard Deviation
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Portfolio RiskStandard Deviation of
2-Asset-Portfolio

• The standard deviation of a portfolio is
  generally not a weighted average of individual
  standard deviations (SD).
• The portfolio's SD is a weighted average only if
  all the securities in it are perfectly positively
  correlated. Risk is not reduced at all if the two
  stocks have r 1.0.
• Where the stocks in a portfolio are perfectly
  negatively correlated, we can create a portfolio
  with absolutely no risk, or Portfolios SD equal
  to 0. Two stocks can be combined to form a
  riskless portfolio if r -1.0.

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Portfolio RiskPerfectly Negative Correlation
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Returns Distribution for Two Perfectly Negatively
Correlated Stocks (? -1.0) and for Portfolio WM
Stock W
Stock M
Portfolio WM
.
.
.
40
40
40
.
.
.
.
.
.
.
15
15
15
0
0
0
.
.
.
.
-10
-10
-10
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Portfolio RiskPerfectly Positive Correlation
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Returns Distributions for Two Perfectly
Positively Correlated Stocks (? 1.0) and for
Portfolio MM
Stock M
Portfolio MM
Stock M
40
15
0
-10
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Portfolio RiskPartial Correlation
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Adding Stocks to a Portfolio

• What would happen to the risk of an average
  1-stock portfolio as more randomly selected
  stocks were added?
• sp would decrease because the added stocks would
  not be perfectly correlated, but the expected
  portfolio return would remain relatively constant.

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s1 stock 35sMany stocks 20
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Effects of Portfolio Size on Portfolio Risk
sp ()
Company Specific Risk
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Stand-Alone Risk, sp
sM
20 0
Market Risk
10 20 30 40 2,000
Stocks in Portfolio
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Market risk is that part of a securitys
stand-alone risk that cannot be eliminated by
diversification, and is measured by
beta. Firm-specific risk is that part of a
securitys stand-alone risk that can be
eliminated by proper diversification.
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Capital Asset Pricing Model The Concept of Beta

• Capital Asset Pricing Model (CAPM) relevant risk
  of individual stock is the amount of risk that
  the stock contributes to well-diversified stock
  portfolio, or the market portfolio.
• Market risk, which is relevant for stocks held in
  well-diversified portfolios, is defined as the
  contribution of a security to the overall
  riskiness of the portfolio. It is measured by a
  stocks beta coefficient.
• Beta measures a stocks market risk. It shows a
  stocks volatility relative to the market.
• Beta shows how risky a stock is if the stock is
  held in a well-diversified portfolio.
• Beta can be calculated by running a regression of
  past returns on Stock i versus returns on the
  market. The slope of the regression line is
  defined as the beta coefficient.
• If beta gt 1.0, stock is riskier than the market.
• If beta lt 1.0, stock less risky than the market.

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Using a Regression to Estimate Beta

• Run a regression with returns on the stock in
  question plotted on the Y axis and returns on the
  market portfolio plotted on the X axis.
• The slope of the regression line, which measures
  relative volatility, is defined as the stocks
  beta coefficient, or b.

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Beta - Illustration
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Calculating Beta in Practice

• Many analysts use the SP 500 to find the market
  return.
• Analysts typically use four or five years of
  monthly returns to establish the regression line.
  
• Some analysts use 52 weeks of weekly returns.

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Beta - Calculation
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How is beta interpreted?

• If b 1.0, stock has average risk.
• If b gt 1.0, stock is riskier than average.
• If b lt 1.0, stock is less risky than average.
• Most stocks have betas in the range of 0.5 to 1.5.

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Security Market Line (SML)
Relationship between required rate of return and
risk
ri rRF RPMbi .
ri rRF (rM rRF)bi .

• ri Required return on Stock i
• rRF Risk-free return
• (rM-rRF) Market risk premium
• bi Beta of Stock i

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Use the SML to calculate eachalternatives
required return.

• The Security Market Line (SML) is part of the
  Capital Asset Pricing Model (CAPM).
  
• SML ri rRF (RPM)bi .
• Assume rRF 8 rM rM 15.
• RPM (rM - rRF) 15 - 8 7.

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Impact of Inflation Change on SML
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Impact of Risk Aversion Change
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Portfolio Theory and Asset Pricing Models
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Efficient Portfolio2-asset case risk return

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Efficient Portfolio2-asset case risk
returnPositive Correlation

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Efficient Portfolio2-asset case risk
returnZero Correlation

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Efficient Portfolio2-asset case risk
returnNegative Correlation

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Efficient Set of Investments
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Optimal Portfolios
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Efficient Set of Investments Risk-Free Asset
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Optimal Portfolio with Risk-Free Asset
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Security Market Line (SML) Capital Market Line
(CML)
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Alternative Theories/Models

• Arbitrage Pricing Theory (APT)
• Include more factors to specify the equilibrium
  risk/return relationship
• Based on complex mathematical statistical
  theory
• Practical Usage has been limited
• Fama-French Three Factor Model
• Include 2 more factors to CAPM size of the
  company book-to-market ratio
• More use by academic researchers than corporate
  managers
• Necessary data generally not accessible by public
• Behavioral Finance
• Stocks may have short term momentum
• Blending psychology finance people dont
  always behave rationally including in
  investments