Risk and Returns

1
Risk and Returns

• Return and Risk for Individual Securities
• Return and Risk for Portfolios
• Systematic and unsystematic risk
• Capital Asset Pricing Model

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You can either sleep well or eat well. -- An old
saying on Wall Street
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Expected Returns

• Expected returns are based on the probabilities
  of possible outcomes
• In this context, expected means average if the
  process is repeated many times
• The expected return does not even have to be a
  possible return

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Expected Return

• What are the expected returns of the stock?

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Variance and Standard Deviation

• Variance and standard deviation still measure the
  volatility of returns
• Using unequal probabilities for the entire range
  of possibilities
• Variance is the weighted average of squared
  deviations
• Standard Deviation is the square root of variance

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Variance and Standard Deviation

• What are the variance and standard deviation of
  the stock?

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Question

• Given the following information, what is the
  standard deviation for this stock?
• Probability
• State of of State of Rate of
• Economy Economy Return
• Boom .10 .18
• Normal .50 .09
• Recession .40 -.08
• a. 6.91 percent
• b. 7.13 percent
• c. 7.27 percent
• d. 8.09 percent
• e. 9.43 percent

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Portfolios

• A portfolio is a collection of assets
• An assets risk and return is important in how it
  affects the risk and return of the portfolio
• The risk-return trade-off for a portfolio is
  measured by the portfolio expected return and
  standard deviation, just as with individual assets

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Portfolio Weights

• Suppose you have 15,000 to invest and you have
  purchased securities in the following amounts.
  What are your portfolio weights in each security?
• 2000 of DCLK
• 3000 of KO
• 4000 of INTC
• 6000 of KEI

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Portfolio Expected Returns

• The expected return of a portfolio is the
  weighted average of the expected returns for each
  asset in the portfolio
• You can also find the expected return by finding
  the portfolio return in each possible state and
  computing the expected value as we did with
  individual securities

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Portfolio Expected Return
If you put 50 of your money in stock A and 50
in bond B, what is the expected return of your
portfolio?
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Portfolio Variance

• Compute the portfolio return for each stateRP
  w1R1 w2R2 wmRm
• Compute the expected portfolio return using the
  same formula as for an individual asset
• Compute the portfolio variance and standard
  deviation using the same formulas as for an
  individual asset

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Portfolio Variance
If you put 50 of your money in stock A and 50
in bond B, what is the standard deviation of your
portfolio?
14
Question

• put 30 in Asset A and 70 in Asset B
• State of the Probability Return Return
• economy of state on A on B
• Boom 0.40 30 -5
• Bust 0.60 -10 25
• 1.00
• What is the expected return and the standard
  deviation of
• 1) asset A
• 2)asset B
• 3)the portfolio?

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Expected versus Unexpected Returns

• Realized returns are generally not equal to
  expected returns
• There is the expected component and the
  unexpected component
• At any point in time, the unexpected return can
  be either positive or negative
• Over time, the average of the unexpected
  component is zero

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Systematic and Unsystematic Risk

• Systematic risk
• A risk that influences a large number of assets.
• Also known as non-diversifiable risk or market
  risk
• Includes such things as changes in GDP,
  inflation, interest rates, etc.
• Unsystematic risk
• Risk factors that affect a limited number of
  assets
• Also known as unique risk and asset-specific risk
• Includes such things as labor strikes, part
  shortages, etc.

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Question

• Which one of the following is considered an
  example of systematic risk?
• a. a higher inflation rate than predicted
• b. lower company sales than predicted
• c. resignation of a firms chief financial
  officer
• d. an increase in overseas sales for a
  conglomerate, such as General Electric
• e. higher company profits than those forecasted

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Diversification

• Portfolio diversification is the investment in
  several different asset classes or sectors
• Diversification is not just holding a lot of
  assets
• For example, if you own 50 internet stocks, you
  are not diversified
• However, if you own 50 stocks that span 20
  different industries, then you are diversified

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The Principle of Diversification

• Diversification can substantially reduce the
  variability of returns without an equivalent
  reduction in expected returns
• This reduction in risk arises because worse than
  expected returns from one asset are offset by
  better than expected returns from another
• However, there is a minimum level of risk that
  cannot be diversified away and that is the
  systematic portion

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Portfolio Diversification (Figure 13.1)
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Diversifiable Risk

• The risk that can be eliminated by combining
  assets into a portfolio
• Often considered the same as unsystematic, unique
  or asset-specific risk
• If we hold only one asset, or assets in the same
  industry, then we are exposing ourselves to risk
  that we could diversify away

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Question

• Diversifying a portfolio of equity securities
  across sectors and markets will tend to
• a. increase the required risk premium.
• b. reduce the beta of the portfolio to zero.
• c. reduce the standard deviation of the portfolio
  to zero.
• d. eliminate the market risk.
• e. reduce the firm-specific risk.

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Systematic Risk Principle

• There is a reward for bearing risk
• There is not a reward for bearing risk
  unnecessarily
• The expected return on a risky asset depends only
  on that assets systematic risk since
  unsystematic risk can be diversified away

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Measuring Systematic Risk

• How do we measure systematic risk?
• We use the beta coefficient to measure systematic
  risk
• What does beta tell us?
• A beta of 1 implies _______________
• A beta lt 1 implies _______________
• A beta gt 1 implies _______________

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Portfolio Beta

• Amount PortfolioStock Invested Weights Beta
• (1) (2) (3) (4) (3) ? (4)
• Haskell Mfg. 6,000 50 0.90 _____
• Cleaver, Inc. 4,000 33 1.10 _____
• Rutherford Co. 2,000 17 1.30 _____
• Portfolio 12,000 100 _____
• Simple!!

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Question
What is the expected return on this portfolio?
What is the beta of this portfolio? Does this
portfolio have more or less systematic risk than
an average asset?
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Portfolio Expected Return and Portfolio Beta

• Consider a portfolio made up of asset A and the
  risk-free asset. asset A has an expected return
  of E(RA)20 and a beta of 1.6. The risk free
  rate is 8. What is the portfolio expected return
  and portfolio beta if 30 of the money is
  invested in asset A and 70 of the money is in
  the risk-free asset?

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Portfolio Expected Return and Portfolio Beta

• Portfolio Expected return

Asset A
Portfolio beta
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Two portfolios

• Portfolio Expected return

Asset A
Asset B
Portfolio beta
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Reward-to-Risk Ratio

• The reward-to-risk ratio is the risk premium on
  an asset divided by the assets beta.

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Market Equilibrium

• The reward-to-risk ratio must be the same for all
  the assets in the market and they all must equal
  the reward-to-risk ratio for the market

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Reward-to-Risk Ratio

• Asset A has an expected return of 12 and a beta
  of 1.40. Asset B has an expected return of 8 and
  a beta of 0.80. Are these assets valued correctly
  relative to each other if the risk-free rate is
  5?
• a. For A, (.12 - .05)/1.40 ________
• b. For B, (.08 - .05)/0.80 ________
• What would the risk-free rate have to be for
  these assets to be correctly valued?

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Question

• If a group of securities are correctly priced,
  then the reward-to-risk ratio
• a. for the entire group must equal 1.0.
• b. for each security must equal 1.0.
• c. for each security must equal 0.
• d. is equal for each security.
• e. of the combined group is equal to that of a
  risk-free security.

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Security Market Line

• The security market line (SML) is the
  representation of market equilibrium
• The slope of the SML is the reward-to-risk ratio
  (E(RM) Rf) / ?M
• But since the beta for the market is ALWAYS equal
  to one, the slope can be rewritten
• Slope E(RM) Rf market risk premium

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The Security Market Line (SML)
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Capital Asset Pricing Model

• Expected return on an individual security

Market Risk Premium
This applies to individual securities held within
well-diversified portfolios.
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Capital Asset Pricing Model

• The capital asset pricing model (CAPM) defines
  the relationship between risk and return
• E(RA) Rf ?A(E(RM) Rf)
• If we know an assets systematic risk, we can use
  the CAPM to determine its expected return
• This is true whether we are talking about
  financial assets or physical assets

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Question

• The Capital Asset Pricing Model
• a. can be applied both to individual securities
  and to portfolios of securities.
• b. computes the compensation an investor should
  receive based on the total risk of an individual
  security.
• c. has limited use because it does not consider
  the pure time value of money.
• d. when plotted takes the shape of a bell.
• e. ignores the fact that risk-free rates of
  return vary over time.

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Capital Asset Pricing Model

• Suppose the risk-free rate is 4, the market risk
  premium is 8.6, and a particular stock has a
  beta of 1.3. based on CAPM, what is the expected
  return on this stock?
• Suppose the risk-free rate is 8, the expected
  return on the market is 14. If a particular
  stock has a beta of 0.60, what is its expected
  return based on CAPM?