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Managerial Finance:

Chapter 13—Return, Risk & theSecurity Market Line

OVU- ADVANCE

Notes prepared by D. B. HammUpdated 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 [R f ] 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(R A) ] is as follows:

E(R A) = (.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:

Risk

A= E(R

A) - R

f

= .088 - .04 = .048 or 4.8%

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Variance & Standard Deviation

The Variance, or squared deviations from the expectedreturn gives us a measurement of how much risk movement

is in an investment. For Investment A:

σ2A

= [prob1 x (return1 - E(R A)2] + [prob2 x (return2 - E(R

A)2]

σ2A

= [.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:

σA

= 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(R P) = [.40 x E(R

A)] + [.40 x E(R

B)] + [.20 x E(R

G)]

Where E(R A) =8.8% , E(R

B) =9.8% , and E(R

G) = 4%

(the risk-free rate)

E(R P) = ( .40 x .088) + (.40 x .098) + (.20 x .04)

E(R P) = .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, canaffect 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(R asset

), depends

only on the asset's systematic risk. We measure the

systematic risk by the beta coefficient, or β .

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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 tradedassets. (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 β is as follows:

If β = 1.0 then the investment has "normal" market risk

If β < 1.0 then the investment has below normal market risk

(for example U.S. securities' β = 0 or zero risk)

If β > 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 hasdipped 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 individualinvestments 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 Gβ

A= 1.40 β

B= .90 β

G= 0 (risk free)

β

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(R P) = 8.24%. Since the portfolio Beta is

slightly < 1, we assume its E(R) to be slightly < the market

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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. (Generalconcept 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(R A) - R

f

Slope of SML for Asset A = βA

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(R A) - R

f

Slope of SML for Asset A = βA

.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 andincrease A's return.

We therefore assume the reward to risk ratio is

the same for all assets in the market and cantherefore 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

βM = 1.0 we can evaluate the entire marketrisk premium as

Market Risk Premium = E(R M

) - R f

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 theequation for the SML of any asset "i" in the

market is

Expected return = risk free rate + (risk premium x Beta)E(R

i) = R

f + [E(R

M) - R

f ] x β

i.

This is called the Capital Asset Pricing

Model or CAPM.

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CAPM Illustration (1):

If the R f = 4% and the E(R

M)=11.5%

Suppose we select an asset "i" with a βi= .7

The expected return on this asset is therefore

(using CAPM)

E(R

i)= R

f + [E(R

M) - R

f ] x β

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(R i)= R

f + [E(R

M) - R

f ] x β

I

(Where Rf= 4%, E(R M

)= 11.5%)

If the β = 1.0 then the expected return = 11.5%

(the market rate)

If the β = 1.5 then the expected return = 15.25 %

If the β = 2.0 then the expected return = 19%(this is double the market risk!)

If the β = .5 then the expected return = 7.75%

If the β = 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 asset’s 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 youaccepted 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 theBeta value

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Cartoon

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Pause here for class case before

going to chapter 15

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