FINC 3310

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FINC 3310

• Chapter Thirteen
• Risk, Return, and the Security Market Line

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I. Expected Returns and Risk

• The quantification of risk and return is a
  crucial aspect of modern finance. It is not
  possible to make good (i.e., value-maximizing)
  financial decisions unless one understands the
  relationship between risk and return.
• And, rational investors like returns and dislike
  risk.
• Here, we are looking to the future, at the
  possible returns and the riskiness associated
  with them. A tractable way to look at things is
  the use of "states of nature" and probabilities,
  kind of like scenario analysis.

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Using expectations

• The expected return is defined as
• And the variance of expected returns is
• That is, from E(R) and s2(R) we can look at
  riskiness of expected return on an asset.

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Using expectations An Example

• Stock A Prob. Return Weighted Return
• Optimistic .2 .50 .10
• Expected .6 .20 .12
• Pessimistic .2 -.15 -.03
• .19 E(RA)
• Stock B Prob. Return Weighted Return
• 0ptimistic .2 .05 .01
• Expected .6 .20 .12
• Pessimistic .2 .35 .07
• .20 E(RB)
• Now, calculate s2 of each...

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Using expectations An Example

• Stock A Prob. Return E(RA) ( )2
  Weighted
• 0ptimistic .2 .5 .19 .09610 .01922
• Expected .6 .2 .19 .0001 .00006
• Pessimistic .2 -.15 .19 .11560 .02312
• s2.04240
• s2 .04240 so sA.20591
• Stock B Prob. Return E(RB) ( )2
  Weighted
• 0ptimistic .2 .05 .2
  .0225 .0045
• Expected .6 .2 .2 0 0
• Pessimistic .2 .35 .2
  .0225 .0045
• s2.009
• s2 .009 so sB .09487

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Returns and Risk in Portfolios

• Let weights be 50/50 on A B
• State Prob. Return Weighted
• O .2 (.5)(.50)(.5)(.05) .275 .055
• E .6 (.5)(.2)(.5)(.20) .20 .12
• P .2 (.5)(-.15)(.5)(.35) .10 .02
• .195
• What about portfolio variance?

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Returns and Risk in Portfolios

• State Prob. Rps E(Rp) ( )2 Weighted
• O .2 .275 .195 .0064 .00128
• E .6 .20 .195 .000025 .000015
• P .2 .10 .195 .009025 .0018051
• s2.00310
• s2 .00310 so s .055678
• NOTICE
• (.5)(.20591).5(.09487).15039
• which is NOT s2(Rp)...WHY?

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Returns and Risk in Portfolios

• What happens when assets are combined into a
  portfolio?
• The expected return of the portfolio is a
  weighted average of the expected returns of the
  individual assets.
• The standard deviation of returns is not a
  weighted average of the assets' standard
  deviations.
• Lets look at why this is so...

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Announcements, Surprises, and Expected Returns

• What affects an assets return? We must
  consider
• systematic risk
• unsystematic risk
• And, for both of these, the key to risk is the
  idea that unanticipated information is what leads
  to price changes. Consider the components of an
  assets actual return
• R E(R) U
• and U

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Announcements, Surprises, and Expected Returns

• Look at U again
• R E(R) m e
• and m and e are
• What happens to e as more assets are added to
  the portfolio?

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Portfolio Diversification
Average annualstandard deviation ()
Diversifiable risk
Nondiversifiablerisk
Number of stocksin portfolio
1
10
20
30
40
1000
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Systematic Risk and Expected Returns

• KEY ECONOMIC ARGUMENT 1 Because unsystematic
  risk can be diversified away, there should be no
  compensation (reward) for bearing that risk.
  This can be restated very directly - an asset's
  expected return depends only on its systematic
  risk.
• Our measure of systematic risk an asset's beta,
  or b

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Defining Beta

• What does beta measure? The relationship of an
  asset's returns to the returns on the "market
  portfolio". More explicitly, beta is defined as
• b 1.0 is the "average" or market beta

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Systematic Risk and Expected Returns

• KEY ECONOMIC ARGUMENT 2 In equilibrium, the
  risk premium per unit of systematic risk must be
  equal across assets. That is, the price of risk
  is a market wide phenomenon, not an
  asset-specific one. This relationship is given
  as

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Systematic Risk and Expected Returns

• How can we use this to determine any asset's
  return as a function of its risk? First, let
  asset j above be the market portfolio. What is
  its beta? Let Rj be the return on the market,
  and rewrite the relationship above as
• and rearrange to obtain
• E(Ri) Rf biE(Rm) - Rf
• This is the equation of the Security Market Line
  (SML), derived from the Capital Asset Pricing
  Model (CAPM).

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Risk, Returns, and the CAPM

• The Capital Asset Pricing Model (CAPM) - an
  equilibrium model of the relationship between
  risk and return.
• What determines an assets expected return?
• The risk-free rate - the pure time value of money
• The market risk premium - the reward for bearing
  systematic risk
• The beta coefficient - a measure of the amount of
  systematic risk present in a particular asset

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Using CAPM Some examples

• Asset Invested b E(Ri)
• A 10,000 1.7 ?
• B 15,000 .65 ?
• C 25,000 1.2 ?
• If Rf 6 and Rm 11, what are the E(Ri)?
  And, what is bp and E(Rp)?

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Using CAPM Some examples

• E(RA) 61.7(11-6)14.5
• E(RB) 60.65(11-6)9.25
• E(RC) 61.2(11-6)12.0
• OR, use bp and the CAPM
• and E(Rp)61.135(11-6)11.675

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Using the SML in Capital Budgeting

• We know that for a project or investment to be
  attractive what must be true?
• How does this relate to CAPM and the SML?

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Using the SML in Capital Budgeting

• Assume Rf 6, Rm 12
• Project b IRR RRR
• X 1.1 14 ?
• Y 0.8 10.5 ?
• Z 1.4 17 ?
• Think of RRR like E(R) from CAPM.

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Using the SML in Capital Budgeting

• Over the line Þ positive NPV (why?)