Essentials of Managerial Finance

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Chapter 4 Risk and Rates of Return
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Expected Rate of Return

• The weighted average of various possible
  outcomes it is based on the probability that
  each outcome will occur where the outcomes
  probabilities as weights are used. It is the most
  likely return on a asset.

ki the result of outcome i Pri the
probability that outcome i will occur
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Expected Rate of Return - Example
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Probability Distributions
Discrete Probability Distributions A limited or
finite number of outcomes
Continuous Probability Distributions Unlimited
or infinite number of outcomes
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Measuring Total Risk The standard deviation

• The standard deviation, sk, measures the
  dispersion around the expected value of an
  assets risk.

Variance, ?2measures the variability of outcomes
Standard deviation, ?


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The standard deviation - Example
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The coefficient of variation

• The coefficient of variation, CV, is a measure
  of relative dispersion that is useful in
  comparing various assets with differing risks
  and expected returns.

• Coefficient of variation Risk
  s
• 
  Return k

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Risk aversion and Required Returns

• Assuming that all investors are risk averse,
  that investor will ALWAYS choose to invest in
  portfolios with lower returns but with lower risk
  as well.
• Risk averse investors will demand higher expected
  returns for riskier investments
• Investors will hold a diversified portfolio of
  assets because the investor will diversify away a
  portion of the risk that is inherent in putting
  all your eggs in one basket.

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Relationship between required rates of return and
Risk for Risk Averse Investors
k kRF RP
Risk Premium RP
kRF
Risk-Free Return kRF

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Portfolio Risk and Return
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Rate of Return distributions for perfectly
positively and negatively correlated stock


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Correlation Coefficient


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Effects of Portfolio Size on Portfolio Risk for
Average Stocks
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Relevant Irrelevant Risk

• Relevant risk is the risk that cannot be reduced
  or diversified away (systematic, or market risk)
• Irrelevant risk is the portion of total risk
  can be reduced through diversification
  (firm-specific, or unsystematic risk)

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Relevant Risk

Risk Premium based on systematic risk


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The Capital Asset Pricing Model (CAPM)
The CAPM is a model developed to determine the
required rate of return for an investment that
considers the fact that some of the total risk
associated with the investment can be diversified
away in essence, the model suggests that the
risk premium associated with an investment should
only be based on the risk that cannot be
diversified away rather than the total risk
investors should not be rewarded for not
diversifyingthat is, they should not be paid for
taking on risk that can be eliminated through
diversification.


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The concept of Beta
The market, or systematic, risk can be
measured by comparing the return on an investment
with the return on the market in general, or an
average stock the resulting measure is called
the beta coefficient, and is identified using the
Greek symbol ß graphically, ß can be determined
as follows



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The concept of Beta
The beta coefficient shows how the returns
associated an investment move with respect to the
returns associated the market because the market
is very well diversified, its returns should be
affected by systematic risk onlyunsystematic
risk should be completely diversified away in a
portfolio that contains all investments in the
market thus, the beta coefficient is a measure
of systematic risk because it gives an indication
of the degree of movement in returns associated
with an investment relative to the market, which
contains only systematic risk for example, an
investment with ß 2.0 generally is considered
twice as risky as the market, such that the risk
premium associated with the investment should be
twice the risk premium on the market.


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Relative volatility of Assets S, R
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Beta Coefficients for Selected Stocks
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Interpreting Beta

• The beta value of a company j stock is an index
  of the amount of company js systematic risk
  relative to that of the market portfolio
• The beta value of a company j stock indicates the
  degree of responsiveness of expected return on
  the stock relative to movements in expected
  return of the market
• The beta of a the stock j indicates the relative
  magnitude of the change in the stocks risk
  premium as a result of a change in risk premium
  of the market portfolio

Beware Beta does not indicate the degree of
total volatility that can be expected on an
investments return but only the extent to which
expected return is likely to react to overall
market movements
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Portfolio Beta Coefficients

• A portfolios beta, ?p is a function of the betas
  of the individual investments in the portfolio
• A portfolio beta is the weighted average of the
  betas associated with the individual investments
  contained in the portfolio

wj of total funds invested in asset j ?j
asset js beta coefficient
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Relationship between Risk and Rates of Return

• Return Risk-free rate Risk Premium
• kj kRF RPInvest
• kRF (RPM)ßj
• kRF (kM - kRF)ßj
• Capital Asset Pricing Model (CAPM)

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Relationship between Risk and Rates of Return

• Market risk premium RPM kM - kRF
• where RPM is the return associated with the
  riskiness of a portfolio that contains all the
  investments in the market. RPM is based on how
  risk averse investors are on average. Because an
  investments beta coefficient indicates
  volatility relative to the market, we can use ß
  to determine the risk premium for an investment.
  Investment risk premium RPInvest RPM x
  ßInvest A more volatile investmentthat is, an
  investment with a high ßwill earn a higher risk
  than a less volatile investment

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The Security Market Line (SML)
The CAPM Graph
Security Market Line, SML
RPM

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CAPM - Example

• Calculate the required return for Federal
  Express assuming it has a beta of 1.25, the rate
  on US T-bills is 5. , and the expected return
  for the SP 500 is 15.

ki 5 1.25 15 - 5 ki 17.5
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Sensitivity to risk-aversion / betas
ki
SML
17.5
15.0
assets risk premium (12.5)
market risk premium (10)
RF 5
bi
1.25
1.0