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# Required Rate of Return by mnmgroup

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```									Required Rate of
Return
RISK

 How  to measure risk
(variance, standard deviation, beta)
 How to reduce risk
(diversification)
 How to price risk
(security market line, CAPM)
For a Treasury security, what is
the required rate of return?

Required
rate of =
return
For a Treasury security, what is
the required rate of return?

Required   Risk-free
rate of = rate of
return     return

Since Treasury’s are essentially free of default
risk, the rate of return on a Treasury
security is considered the “risk-free” rate of
return.
For a corporate stock or bond, what is
the required rate of return?

Required
rate of =
return
For a corporate stock or bond, what is
the required rate of return?

Required   Risk-free
rate of = rate of
return     return
For a corporate stock or bond, what is
the required rate of return?

Required   Risk-free
rate of = rate of
Risk
+
Premium
return     return

How large of a risk premium should we
require to buy a corporate security?
Returns

 Expected  Return - the return that an
investor expects to earn on an asset,
given its price, growth potential, etc.

 Required Return - the return that an
investor requires on an asset given
its risk.
Expected Return

State of     Probability           Return
Economy          (P)      Orl. Utility Orl. Tech
Recession       .20           4%         -10%
Normal           .50          10%         14%
Boom             .30          14%         30%
For each firm, the expected return on the
stock is just a weighted average:
Expected Return

State of     Probability           Return
Economy          (P)      Orl. Utility Orl. Tech
Recession       .20           4%         -10%
Normal           .50          10%         14%
Boom             .30          14%         30%
For each firm, the expected return on the
stock is just a weighted average:

k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn
Expected Return

State of  Probability          Return
Economy      (P)      Orl. Utility Orl. Tech
Recession    .20          4%         -10%
Normal       .50          10%         14%
Boom         .30          14%         30%

k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn

k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%
Expected Return

State of  Probability          Return
Economy      (P)      Orl. Utility Orl. Tech
Recession    .20          4%         -10%
Normal       .50          10%         14%
Boom         .30          14%         30%

k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn

k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%
Based only on your
expected return
calculations, which
stock would you
prefer?
Have you considered
RISK?
What is Risk?
 The possibility that an actual return
will differ from our expected return.
 Uncertainty in the distribution of
possible outcomes.
What is Risk?
 Uncertainty in the distribution of
possible outcomes.

Company A
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
4      8     12

return
What is Risk?
 Uncertainty in the distribution of
possible outcomes.

Company A                               Company B
0.5
0.2
0.45                     0.18
0.4
0.16
0.35
0.14
0.3
0.12
0.25
0.1
0.2
0.08
0.15                     0.06
0.1
0.04
0.05
0.02
0
4      8     12     0
-10   -5   0   5   10   15   20   25   30

return                              return
How do we Measure Risk?

 Toget a general idea of a stock’s
price variability, we could look at
the stock’s price range over the
past year.
How do we Measure Risk?
A  more scientific approach is to examine
the stock’s STANDARD DEVIATION of
returns.
 Standard deviation is a measure of the
dispersion of possible outcomes.
 The greater the standard deviation, the
greater the uncertainty, and therefore ,
the greater the RISK.
Standard Deviation

s = S (ki - k)
n
2
P(ki)
i=1
s           S
n           2
=             (ki - k) P(ki)
i=1

Orlando Utility, Inc.
s
n

S
n            2
=            (ki - k) P(ki)
i=1
i=1

Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
s         S
n           2
=           (ki - k) P(ki)
i=1

Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
s         S
n           2
=           (ki - k) P(ki)
i=1

Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
s          S
n             2
=             (ki - k) P(ki)
i=1

Orlando Utility, Inc.
( 4% - 10%)2 (.2) =     7.2
(10% - 10%)2 (.5) =     0
(14% - 10%)2 (.3) =     4.8
Variance         =      12
s       S
n            2
=          (ki - k) P(ki)
i=1

Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance         =    12
Stand. dev. = 12 = 3.46%
s         S
n            2
=            (ki - k) P(ki)
i=1

Orlando Technology, Inc.
s         S
n           2
=           (ki - k) P(ki)
i=1

Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
s         S
n           2
=           (ki - k) P(ki)
i=1

Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) =      0
s         S
n           2
=           (ki - k) P(ki)
i=1

Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) =      0
(30% - 14%)2 (.3) = 76.8
s         S
n           2
=           (ki - k) P(ki)
i=1

Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) =      0
(30% - 14%)2 (.3) = 76.8
Variance      =        192
s        S
n            2
=          (ki - k) P(ki)
i=1

Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) =      0
(30% - 14%)2 (.3) = 76.8
Variance      =        192
Stand. dev. = 192 = 13.86%
Which stock would you prefer?
How would you decide?
Which stock would you prefer?
How would you decide?
Summary

Orlando     Orlando
Utility   Technology

Expected Return         10%         14%

Standard Deviation     3.46%      13.86%
 It   depends on your tolerance for risk!
It depends on your tolerance for risk!

Return

Risk

Remember there’s a tradeoff between risk
and return.
Portfolios
 Combining   several securities in a
portfolio can actually reduce overall
risk.
 How does this work?
 Suppose we have stock A and stock B.
The returns on these stocks do not tend
to move together over time (they are
not perfectly correlated).

rate
of
return

time
 Suppose we have stock A and stock B.
The returns on these stocks do not tend
to move together over time (they are
not perfectly correlated).

rate                                 kA
of
return

time
 Suppose we have stock A and stock B.
The returns on these stocks do not tend
to move together over time (they are
not perfectly correlated).

rate                                 kA
of
return

kB

time
 Suppose we have stock A and stock B.
The returns on these stocks do not tend
to move together over time (they are
not perfectly correlated).

rate                                 kA
of
return                              kp

kB

time
 What has happened to the variability
of returns for the portfolio?

rate                                kA
of
return                              kp

kB

time
Diversification
 Investing  in more than one security
to reduce risk.
 If two stocks are perfectly
positively correlated,
diversification has no effect on risk.
 If two stocks are perfectly
negatively correlated, the portfolio
is perfectly diversified.
 Ifyou owned a share of every stock
traded on the NYSE and NASDAQ,
would you be diversified?
YES!
 Would you have eliminated all of
your risk?
NO! Common stock portfolios still
have risk. (Remember the October
1987 stock market “crash?”)
Some risk can be diversified
away and some can not.

 Market   Risk is also called Non
diversifiable risk. This type of risk
can not be diversified away.
 Firm-Specific risk is also called
diversifiable risk. This type of risk
can be reduced through
diversification.
Market Risk

 Unexpected   changes in interest rates.
 Unexpected changes in cash flows
due to tax rate changes, foreign
competition, and the overall business
cycle.
Firm-Specific Risk

A   company’s labor force goes on
strike.
 A company’s top management dies
in a plane crash.
 A huge oil tank bursts and floods a
company’s production area.
As you add stocks to your
portfolio, firm-specific risk is
reduced.
As you add stocks to your
portfolio, firm-specific risk is
reduced.
portfolio
risk

number of stocks
As you add stocks to your
portfolio, firm-specific risk is
reduced.
portfolio
risk

Market risk
number of stocks
As you add stocks to your
portfolio, firm-specific risk is
reduced.
portfolio
risk

Firm-
specific
risk
Market risk
number of stocks
Do some firms have more
market risk than others?
Yes. For example:
Interest rate changes affect all firms,
but which would be more affected:

a) Retail food chain
b) Commercial bank
Do some firms have more
market risk than others?
Yes. For example:
Interest rate changes affect all firms,
but which would be more affected:

a) Retail food chain
b) Commercial bank
 Note
As we know, the market compensates
investors for accepting risk - but
only for market risk. Firm-specific
risk can and should be diversified
away.

So - we need to be able to measure
market risk.
This is why we have BETA.

Beta: a measure of market risk.
Specifically, it is a measure of how an
individual stock’s returns vary with
market returns.

It’s a measure of the “sensitivity” of an
individual stock’s returns to changes in
the market.
The market’s beta is 1

A   firm that has a beta = 1 has average
market risk. The stock is no more or
less volatile than the market.
 A firm with a beta > 1 is more volatile
than the market (ex: computer firms).
 A firm with a beta < 1 is less volatile
than the market (ex: utilities).
Calculating Beta
XYZ Co. returns
15

10

5
S&P 500
returns
-15   -10     -5 -5      5    10   15

-10

-15
Calculating Beta
XYZ Co. returns
15
.. .
.. . .
10 . . . .
.. . .
.. . .
5
S&P 500                        .. . .
returns
-15     -10
.. . 5
-5 -5
.     10   15
.. . .
. . . . -10
.. . .
.
. . . -15
Calculating Beta
Beta = slope
XYZ Co. returns           = 1.20
15
.. .
.. . .
10 . . . .
.. . .
.. . .
5
S&P 500                        .. . .
returns
-15     -10
.. . 5
-5 -5
.     10    15
.. . .
. . . . -10
.. . .
.
. . . -15
Summary:

 We know how to measure risk, using
standard deviation for overall risk and beta
for market risk.
 We know how to reduce overall risk to only
market risk through diversification.
 We need to know how to price risk so we will
know how much extra return we should
require for accepting extra risk.
What is the Required Rate of
Return?
 Thereturn on an investment
required by an investor given the
investment’s risk.
Required
rate of =
return
Required   Risk-free
rate of = rate of     +
return     return
Required   Risk-free
rate of = rate of
Risk
+
Premium
return     return
Required   Risk-free
rate of = rate of
Risk
+
Premium
return     return

Market
Risk
Required   Risk-free
rate of = rate of
Risk
+
Premium
return     return

Market         Firm-specific
Risk              Risk
Required   Risk-free
rate of = rate of
Risk
+
Premium
return     return

Market            Firm-specific
Risk                 Risk
can be diversified
away
Required
rate of
Let’s try to graph this
return
relationship!

Beta
Required
rate of
return

12%    .

Risk-free
rate of
return
(6%)

1   Beta
Required
rate of        security
return         market
line
12%    .    (SML)

Risk-free
rate of
return
(6%)

1    Beta
This linear relationship between risk
and required return is known as
the Capital Asset Pricing Model
(CAPM).
Required                                 SML
rate of        Is there a riskless
return         (zero beta) security?

12%                    .

Risk-free
rate of
return
(6%)

0               1           Beta
Required                                      SML
rate of        Is there a riskless
return         (zero beta) security?

12%                    .         Treasury
securities are
as close to riskless
Risk-free
rate of
as possible.
return
(6%)

0               1                Beta
Required                                  SML
rate of        Where does the S&P 500
return         fall on the SML?

12%                   .

Risk-free
rate of
return
(6%)

0             1              Beta
Required                                  SML
rate of        Where does the S&P 500
return         fall on the SML?

12%                   .
The S&P 500 is
a good
Risk-free                     approximation
rate of                      for the market
return
(6%)

0             1              Beta
Required                       SML
rate of
return
Utility
Stocks
12%                   .

Risk-free
rate of
return
(6%)

0             1   Beta
Required        High-tech    SML
rate of
stocks
return

12%            .

Risk-free
rate of
return
(6%)

0      1        Beta
The CAPM equation:
kj = krf + b j (km - krf)
where:
kj = the Required Return on security j,
krf = the risk-free rate of interest,
b j = the beta of security j, and
km = the return on the market index.
Example:
 Suppose  the Treasury bond rate is
6%, the average return on the S&P
500 index is 12%, and Walt Disney
has a beta of 1.2.
 According to the CAPM, what
should be the required rate of
return on Disney stock?
kj = krf + b (km - krf)

kj = .06 + 1.2 (.12 - .06)
kj = .132 = 13.2%

According to the CAPM, Disney
stock should be priced to give a
13.2% return.
Required                                SML
rate of
Theoretically, every
return         security should lie
on the SML

12%                     .

Risk-free
rate of
return
(6%)

0               1          Beta
Required                                     SML
rate of
Theoretically, every
return         security should lie
on the SML

12%                     .     If every stock
is on the SML,
investors are being fully
Risk-free                compensated for risk.
rate of
return
(6%)

0               1               Beta
Required                                  SML
rate of        If a security is above
return         the SML, it is
underpriced.
12%                    .

Risk-free
rate of
return
(6%)

0              1             Beta
Required                                    SML
rate of        If a security is above
return         the SML, it is
underpriced.
12%                    .
If a security is
below the SML, it
Risk-free                     is overpriced.
rate of
return
(6%)

0                              Beta
1
Practice Problem:
 Find the intrinsic value of a common stock with
the following information:
 ROE = 20%
 50% retention of earnings
 Beta = 1.4
 recent dividend = \$4.30
 Treasury bond yield = 7.5%
 Return on the S&P 500 = 12%
 Market price for common stock = \$100
 Should you buy the stock?

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