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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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