Managerial Finance: Chapter 13—Return, Risk & the Security Market Line

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Managerial FinanceChapter 13Return, Risk the
Security Market Line

• OVU-ADVANCE
• Notes prepared by D. B. Hamm
• Updated January 2006

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Expected Return (1)
Most investments carry some degree of risk.
Generally only U.S. securities (specifically
T-bills) are considered risk free Rf because
the Federal government can raise taxes or borrow
as necessary to avoid default.
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Expected Return (2)

• Suppose Investment A has probable returns as
  follows
• In the previous "go-go" market, it had earned
  12.
• In the recent market slump, it earned only 4.
• If we project a 60 probability of renewed boom
  and a 40 probability of bust, then the
  expected return of A E(RA) is as follows
•  
• E(RA) (.60 x .12) (.40 x .04)
• .072 .016
• .088 or 8.8

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Risk Premium
Risk Premium is the difference between the
expected return on the proposed investment and
the risk free rate. If U.S. security G is
earning 4 then the risk premium for investment A
(from previous slide, E(R) 8.8) is   RiskA
E(RA) - Rf .088 - .04
.048 or 4.8
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Variance Standard Deviation
The Variance, or squared deviations from the
expected return gives us a measurement of how
much risk movement is in an investment. For
Investment A ?2A prob1 x (return1 - E(RA)2
prob2 x (return2 - E(RA)2 ?2A .60
x (.12 - .088)2 .40 x (.04 -
.088)2 .60 x .001024
.40 x .002304
.00036864
.0009216 .00129024   The Standard
deviation is the square root of the variance.
For A ?A SQRT of .00129024 -0.03592
or - 3.59   This gives some idea of the
potential movement in Investment A
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Investment Portfolios
A portfolio of investments enables us to
diversify and therefore minimize the portion of
risk that relates to "surprises" or unexpected
movement in individual securities. A portfolio
won't remove risk related to the market as a
whole ("market risk").
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Portfolio Illustration
Suppose we mix a portfolio of 40 in Investment A
(previous) 40 in Investment B, which may earn
only 7 in a good market but booms to 14 in a
recession, and we put the other 20 in government
investment G earning 4. Portfolio Expected
Return for Portfolio "P"   E(RP) .40 x
E(RA) .40 x E(RB) .20 x E(RG)
  Where E(RA) 8.8 , E(RB) 9.8 , and
E(RG) 4 (the risk-free rate)   E(RP) ( .40
x .088) (.40 x .098) (.20 x .04) E(RP)
.0824 or 8.24  
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Portfolio Illustration (continued)
Note The percentage weights are based on the
total dollars invested in each security. If we
invested 100,000 as follows 40,000 in A,
40,000 in B, and 20,000 in G, then we would
have the 40-40-20 mix above.     The variance
of this portfolio is 0.00000434062 and the
standard deviation is .0020736 or about or -
2/10 of 1. In other words, diversifying
eliminated almost all of the diversification risk
or unexpected return.  
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Risk Beta (1)

• Total risk of any investment both
• the market risk (which can't be diversified) and
  
• the diversifiable risk, which can be minimized
  or eliminated by diversification in a portfolio.
  
• The market risk is called systematic and the
  diversifiable risk is called unsystematic.
•  
• Total risk Systematic risk Unsystematic
  risk
• (market risk)
  (diversifiable risk)

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Risk Beta (2)
Total risk Systematic risk Unsystematic
risk   (market)
(diversifiable) The unsystematic risk is
asset-specific and relates to individual
investments which can be minimized through
diversification. The systematic risk, or market
risk, can affect all market investments. A
recession or a war, for example, might impact all
investments in a portfolio. Since we can
usually eliminate the unsystematic risk, we focus
primarily on the systematic risk.   Expected
return of any asset , or E(Rasset), depends only
on the asset's systematic risk. We measure the
systematic risk by the beta coefficient, or ?.
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Risk Beta (3)
The Beta of an asset Covariance of asset
returns with
The market index portfolio
Variance with the market portfolio   I don't want
to figure that out--do you? There are people on
this planet who live for this stuff and do that
for most publicly traded assets. (Your
facilitator is NOT one of them!) Therefore we
will assume the Beta is given for any investment
we work with. The general rule for ? is as
follows If ? 1.0 then the investment
has "normal" market risk If ? lt 1.0 then
the investment has below normal market risk
(for example U.S. securities' ?
0 or zero risk) If ? gt 1.0 then the
investment has a greater than normal
market risk (higher risk)
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Some Sample Betas (as of 1/31/07)

• Ford Motor Co (recent financial concerns, stock
  has dipped from 13.17 to 8.08/share over 2 yrs)
  1.83
• Wal-Mart (solid, 47.19/sh) 0.17
• GE (also solid, 36.11/sh) 0.51
• CVS Corp. (near mkt average, 33.31/sh) 0.94
• Microsoft (solid, but rolling out Windows Vista,
  30.41/sh) 0.71
• Trump Entertainment Resorts (considerable
  fluctuation, 17.57/sh) 1.96
• NutriSystem, Inc. (also wildly fluctuates,
  45.83/sh) 2.06 (stock has recently endured a
  12 drop)

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Portfolio Beta
If we have the Beta coefficient for each of the
individual investments in our portfolio, we can
evaluate the overall risk in our entire
portfolio. Using the earlier example, let's make
the following assumptions 40
40 20 Portfolio P Investment
A Investment B Investment G ?A 1.40
?B .90 ?G 0 (risk
free)   ?P (.40 x 1.40) (.40 x .90)
(.20 x 0) .56 .36
0 .92 (slightly below
normal systematic risk) (As we calculated
earlier, the expected return E(R) on portfolio P
E(RP) 8.24. Since the portfolio Beta is
slightly lt 1, we assume its E(R) to be slightly
lt the market rate)
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The Security Market Line (SML)
When we mix a portfolio of assets, we find a
linear ( positive correlation) relationship
between the individual assets' expected returns
and their Betas. Assets with a higher Beta
generally have a higher expected return to
compensate for the higher systematic (market)
risk. (General concept of risk vs. return--the
higher the potential return, the higher the
potential risk.)  
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The Security Market Line (SML) (2)
  This linear relationship between expected
return and Beta is called the Security Market
Line (SML). The slope of the SML is as
follows   E(RA) -
Rf Slope of SML for Asset A ?A Or
the difference between expected return and risk
free return divided by the beta coefficient.
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Security Market Line (SML) (3)
E(RA) - Rf Slope of SML
for Asset A ?A
.088 - .04 For our
Investment A 1.40 .0343 or
3.4   For our Investment B .098 - .04
.90
.0644 or 6.4   This is the
reward-to-risk ratio. Here investment B is more
attractive, although neither is particularly high
in a bull market ( remember B was better in a
bear market).
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Security Market Line (SML) (4)
In an organized market, this difference in
reward-to-risk would not persist because buyers
and sellers would bid up investment B over
investment A which would lower B's return and
increase A's return.   We therefore assume the
reward to risk ratio is the same for all assets
in the market and can therefore be plotted on the
SML.  
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Market Risk Premium
If we create a theoretical portfolio of all
securities in the market, which would therefore
have a Beta of the market average ?M 1.0 we
can evaluate the entire market risk premium as
  Market Risk Premium E(RM) - Rf Risk
premium Expected market return risk free rate

Example If the going market rate were 11.5
and the T-bill (risk free) rate were 4, then the
market risk premium is the difference of 7.5
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Capital Asset Pricing Model (CAPM)
If we select any asset "i" in this market and
assume that trading in the market's assets has
"normalized" the expected return so that it
equals the same reward to risk, then the equation
for the SML of any asset "i" in the market
is Expected return risk free rate (risk
premium x Beta) E(Ri) Rf E(RM) - Rf x
?i.   This is called the Capital Asset Pricing
Model or CAPM.
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CAPM Illustration (1)
If the Rf 4 and the E(RM)11.5 Suppose we
select an asset "i" with a ?i .7 The expected
return on this asset is therefore (using
CAPM)   E(Ri) Rf E(RM) - Rf x ?i
.04 .115 - .04 x .7 .04
(.075 x .7) .04 .0525
.0925 or 9.25  Because the Beta is
low risk (less than market), the expected return
is less than the market rate.
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CAPM Illustration (2)
Expected Return risk free rate (risk premium)
x Beta E(Ri) Rf E(RM) - Rf x
?I (Where Rf 4,
E(RM) 11.5) If the ? 1.0 then the expected
return 11.5 (the market
rate) If the ? 1.5 then the expected return
15.25 If the ? 2.0 then the expected return
19 (this is double the
market risk!) If the ? .5 then the expected
return 7.75 If the ? 0 then the
expected return 4 (the
risk-free rate)
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CAPM (3)

• As long as we have the following variables
• The risk free rate
• The current market rate
• The assets Beta
• Then we can estimate the expected return for any
  asset (investment).
• If we have the E(R) of an asset and any two of
  the above, we can work backward and find the
  missing variable. Example-if we knew the return
  on an asset over time, we could estimate what its
  Beta should be.

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CAPM (conclusion)

• Assumptions of the Capital Asset Pricing Model
  (CAPM)
• The pure time value of money This is the risk-
  free rate, or the rate you could expect to earn
  over time if you accepted no (zero) risk (govt.
  securities)
• The reward for bearing systematic risk, or the
  risk premium (asset rate in excess of the risk
  free rate)
• The amount of systematic risk in the market, or
  the Beta value

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Cartoon
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Pause here for class case before going to chapter
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