Analysis of Risk and Return

1
Chapter 5

• Analysis of Risk and Return
• .This chapter develops the risk- return
  relationship for individual projects
  (investments) and a portfolio of projects.

2
Meaning of Risk

• Risk refers to the possibility that actual cash
  flows (returns) from an investment will be
  different from the forecasted cash flows
  (returns).

3
Outcomes and Probability

• Outcome
• Different possible return occurrences
• Probability
• The likelihood of of each outcome

We can use the return outcomes and their
probabilities to obtain statistical measures of
risk and returns.
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Expected Return

• Mean (average) value of possible return outcomes.
• The weighted average of the possible return
  outcomes, with the weight being the probability
  of each outcome.

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Expected Return

• r expected return
• rj return outcome j
• pj probability of the jth outcome
• n of possible outcomes
• Example Table 5-3

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Standard Deviation (SD)of Returns

• Measure of deviation of return outcomes about
  the expected return.
• Square root of the weighted average squared
  deviations of possible return outcomes from the
  expected return.
• Indicates the risk of an asset.
• An absolute measure of risk.

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Standard Deviation of Returns

• ? standard deviation
• rj return outcome j
• r expected return
• pj probability of the jth outcome
• n the number of possible outcomes
• Example Table 5-4

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Coefficient of Variation(CV)

• V coefficient of variation
• ? standard deviation
• expected return
• Provides a relative measure of risk
• Measures the risk per unit of expected return

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SD and CV

• The standard deviation is an appropriate measure
  of total risk when comparing two equal-sized
  investments.
• The coefficient of variation is an appropriate
  measure of total risk when comparing two
  investment projects of different size.

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Coefficient of Variation
STD Exp Ret CV Asset A 20 25 0.80 Asset
B 20 20 1.00 Asset C 15 20 0.75 Asset
D 18 26 0.69
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Risk-Return Relationship

• Required Rate of Return
• Risk-free return Risk Premium
• .
• Risk-Free Rate (Rf)
• Real Rate of Return Expected
• 
  Inflation premium
• Real Rate of Return
• Return in a world with no default risk and no
  expected inflation (2 to 4 percent)
• Inflation Premium
• Compensation for expected losses in purchasing
  power
• .

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Risk Premium

• Risk Premium
• Compensation for different risk elements such as
  
• Maturity risk premium
• Default risk premium
• Seniority risk premium
• Marketability risk premium
• Business risk
• Financial risk

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Maturity Risk

• Maturity Risk Premium
• Compensation for investing in longer-term
  securities.
• Yield Curve
• Yield curve indicates the maturity premium.
• Yield curve is the relationship between the time
  to maturity and the yields to maturity of
  securities that differ only in the length of time
  to maturity.
• Examine Figure 5-4

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Theories of the Yield Curve

• Expectations Theory
• Long-term interest rates are a function of
  expected short-term interest rates
• Upward Sloping Yield Curve Future short-term
  rates are expected to rise
• Down ward Sloping Yield Curve Future short term
  interest rates are expected to decline

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Theories of the Yield Curve

• Liquidity Preference Theory
• Lenders prefer to lend for shorter-maturities
  because of higher interest rate risk associated
  with longer-term bonds.
• Short-term securities have less price volatility
  than long-term bonds, when interest rates
  fluctuate.
• Short-term bonds can be converted into
  predictable amounts of cash.
• Yield curve must slope upward.

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Theories of the Yield Curve

• Market Segmentation Theory
• Securities markets are segmented by maturity.
• Demand and supply conditions in each market
  determine the interest rates in each segment.

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Default Risk

• Default Risk Premium
• Default risk is the likelihood that the company
  will default promised obligations (of interest
  and principal payments)
• Default Spread
• Corporate Bond Yield - Treasury Yield
• (for same maturity)
• See Table 5-5

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Seniority Marketability Risk

• Seniority Risk Premium
• Securities differ in their priority of claims on
  companys cash flows and assets in the event of
  default.
• Lower the priority, higher the seniority risk
  premium demanded by investors.
• Marketability Risk Premium
• Refers to the market liquidity of the security
  ability to sell quickly without a significant
  loss of value.
• Lower the liquidity, higher the premium.

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Business Financial Risk

• Business Risk
• Variability of the firms operating earnings
  (EBIT)
• Factors affecting business risk includes
• fluctuations in sales
• fluctuations in operating costs
• product diversification
• technology
• market power
• Financial Risk
• Additional variability of earnings due to the
  use of fixed-cost funds such as debt and
  preferred stock.

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Portfolio Return

• Investment Portfolio Collection of two or more
  assets in some proportion.
• Expected Return from a Portfolio

rp expected return of portfolio Wi proportion
of funds invested in asset i ri expected return
of asset i n number of assets in the portfolio
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Portfolio Return

• Example
• Expected Return
• Security A 10
• Security B 15
• Security C 20
• Portfolio return if wA0.5 wB0.5
• 0.5x10 0.5x15 12.5
• Portfolio return if wA0.5, wB0.3 wC0.2
• 0.5x10 0.3x15 0.2x20 13.5

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Portfolio Risk
Risk of a Two-Asset Portfolio A B
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CORRELATION

• Correlation measures the linear relationship
  between two variables (returns of two
  securities).
• Correlation Coefficients can vary from -1 to 1
• See Figure 5-7
• Example Figure 5-6
• Lesson Due to the negative correlation between
  aluminum industry and gold mining industry, a
  portfolio that combines both industries will have
  lower variability of returns.

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DIVERSIFICATION

• Generalization of the Lesson
• When correlation between returns of two
  securities is less than 1.0, a portfolio of the
  two securities will have lower variability.
• Diversification
• Reduction of risk that arises when securities
  which are less than perfectly positively
  correlated are combined to form a portfolio.
• Risk Systematic (Undiversifiable)
• Unsystematic
  (Diversifiable)

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Portfolio Risk

• Example
• Risk(?)
• Security A 10
• Security B 20
• WA0.75,WB0.25
• Calculate portfolio risk when correlation is 1.0,
  0.5, 0.0, -0.5, and -1.0

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Portfolio Risk
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Risk

• Total systematic riskUnsystematic risk risk
  (Nondiversifiable) (Diversifiable)

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Systematic and Unsystematic Risk

• Unsystematic risk caused by factors unique to
  the firm
• Diversifiable
• strikes
• government regulations
• managements capabilities

• Systematic risk caused by factors affecting the
  market as a whole
• Undiversifiable
• interest rate changes
• changes in purchasing power
• change in business outlook
• See Figure 5-12

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Relevant Risk Systematic Risk

• Relevant risk is the risk the asset contributes
  to the risk of the portfolio.
• A Security must be priced in proportion to the
  risk it contributes to the market portfolio.
• Relevant risk is the systematic risk
• Systematic risk is measured by beta (?)
• Beta measures the volatility of a securities
  return compared to the Market Portfolio.

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Efficient Portfolio

• Has the highest possible return for a given sd
• Has the lowest possible sd for a given expected
  return

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Systematic Risk is Measured by Beta ?

• A measure of the volatility of a securities
  return compared to the Market Portfolio

• A regression line of periodic rates of return for
  security j and the Market Portfolio

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SML shows the relationship between r and ß (SML
in terms of Beta)

SML

rf


ß

r
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Required rate of return

• The required return for any security j may be
  defined in terms of systematic risk, ßj , the
  expected market eturn,rm, and the expected risk
  free rate, rf

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The Capital Asset Pricing Model (CAPM)
The equilibrium relationship between required
rate of return and risk of securities. The
required rate of return of a security is a
function of the risk-free rate and a risk
premium, which varies according to the systematic
risk (beta) of the security. Security Market Line
(SML)
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Security Market Line (SML)
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CAPM Assumptions

• Investors hold well diversified portfolios
• Competitive markets
• Borrow and lend at the risk-free rate
• Investors are risk averse

• Investors are influenced by systematic risk
• Freely available information
• Investors have homogeneous expectations
• No taxes
• No brokerage charges

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Issues in the Application CAPM

• Estimating expected future market returns
• Determining an appropriate rf
• Determining the best estimate of ß
• Investors dont totally ignore unsystematic risk
• Betas are frequently unstable over time
• Required returns are determined by macroeconomic
  factors

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Example 1

• An investor currently has all his wealth in
  Treasury bills. He is considering investing
  one-third in Delta Airlines, whose beta is 1.3,
  with the remainder left in Treasury bills. The
  expected risk-free rate (Treasury bills) is 6
  percent and the market risk premium is 8.8
  percent. Determine the beta and the expected
  return on the proposed portfolio.

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Example 2

• Don has 3,000 invested in ATT with an expected
  return of 11.6 percent 10,000 in IBM with an
  expected return of 12.8 percent and 6,000 in GM
  with an expected return of 12.2 percent. What is
  Dons expected return on his portfolio?