Calculate Expected Rate of Return on Stockholders' by yek12436

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                 CHAPTER 8
           Risk and Rates of Return


   Stand-alone risk (statistics review)

   Portfolio risk (investor view) --
    diversification important

   Risk & return: CAPM/SML (market
    equilibrium)
      Risk is viewed primarily from the                    2

          stockholder perspective
   Management cares about risk because
    stockholders care about risk.
   If stockholders like or dislike something about a
    company (like risk) it affects the stock price.
   Risk affects the discount rate for future returns --
    directly affecting the multiple (P/E ratio)
   Thus, the concern is still about the stock price.
   Stockholders have portfolios of investments –
    they have stock in more than just one company
    and a great deal of flexibility in which stocks they
    buy.
                                            3



           What is investment risk?

   Investment risk pertains to the
    uncertainty regarding the rate of return.
   Especially when it is less than the
    expected (mean) return.
   The greater the chance of low or
    negative returns, the riskier the
    investment.
                                                 4



Return = dividend + capital gain or loss

   Dividends are relatively stable
   Stock price changes (capital gains/losses)
    are the major uncertain component
   There is a range of possible outcomes and
    a likelihood of each -- a probability
    distribution.
                                          5

        Expected Rate of Return



   The mean value of the probability
    distribution of possible returns

   It is a weighted average of the
    outcomes, where the weights are the
    probabilities
                                  6
  Expected Rate of Return
          (k hat)


ˆ
k  p1k1  p2 k 2  ... pn k n
     n
    pi k i
    i 1
                                                            7


            Investment Alternatives


Economy      Prob.   T-bill   HT     Coll    USR     MP

Recession     0.1    8.0% -22.0% 28.0% 10.0% -13.0%
Below avg     0.2     8.0     -2.0   14.7    -10.0   1.0
Average       0.4     8.0     20.0   0.0      7.0    15.0
Above avg     0.2     8.0     35.0   -10.0   45.0    29.0
Boom          0.1     8.0     50.0   -20.0   30.0    43.0

              1.0
                             8
      Why is the T-bill
    return independent
     of the economy?



     Will return be 8%
regardless of the economy?
                                      9


  Do T-bills really promise a
 completely risk-free return?

No, T-bills are still exposed to
the risk of inflation.
However, not much unexpected
inflation is likely to occur over a
relatively short period.
                                           10
     Do the returns of HT and Coll.
      move with or counter to the
               economy?


 High Tech: With. Positive correlation.
  Typical.

 Collections: Countercyclical.

 Negative correlation. Unusual.
                                 11

Calculate the expected rate of
 return for each alternative:
^ = expected rate of return
k

             n

      k =  k i pi
      ^

             i=1

^ = (-22%)0.1 + (-2%)0.20
kHT
     + (20%)0.40 +
(35%)0.20
     + (50%)0.1 = 17.4%
                                               12

       Calculate others on your own

                          ^
                          k
       HT               17.4%
       Market           15.0
       USR               13.8
       T-bill            8.0
       Coll.             1.7

HT appears to be the best, but is it really?
                                   13

What‟s the standard deviation
of returns for each alternative?
 = standard deviation

 =    Variance     =    
                             2



        n
  =  (ki  k i
            ˆ )2 p
       i =1
                      14



Normal Distribution
                                        15

In a sample of observations
   One often assumes that data are from
    an approximately normally distributed
    population. then
   about 68.26% of the values are at
    within 1 standard deviation away from
    the mean,
   95.46% of the values are within two
    standard deviations and
   99.73% lie within 3 standard
    deviations.
                                                                                    16

                       n
              =               ^2
                       (k i  k) Pi
                      i=1




 HT = [- 22 - 17.4 2 0.1 + - 2 - 17.4 2 0.2  20 - 17.4 2 0.4 + 35 - 17.4 2 0.20
 50  17.4 2 0.1]0.5  [403]0.5  20.0748599


      T-bills = 0.0%.
         HT = 20.0%.                   Coll = 13.4%.
                                        USR = 18.8%.
                                         M = 15.3%.
                                    17




   Standard deviation (i)
    measures total, or stand-
    alone, risk.
   The larger the i , the lower
    the probability that actual
    returns will be close to the
    expected return.
                                            18



       Expected Returns vs. Risk:
Security           Expected       Risk, 
                    return
High Tech           17.4%          20.0
Market               15.0          15.3
US Rubber            13.8*         18.8*
T-bills               8.0           0.0
Collections           1.7*         13.4*

*Return looks low relative to 
                                     19



  Coefficient of variation (CV):

Standardized measure of dispersion
about the expected value:

           Std dev   
      CV =         =
            Mean     
                     k

   Shows risk per unit of return.
                               20



  Portfolio Risk & Return

Assume a two-stock portfolio
with $50,000 in HighTech and
$50,000 in Collections.


     Calculate kp and p.
                                      21

                             ^
            Portfolio Return,kp
        ^
        kp is a weighted average:

                      n
               ˆ          ˆ
               kp =  w i k i .
                    i =1

^
kp = 0.5(17.4%) + 0.5(1.7%) = 9.6%
    ^                ^            ^
    kp is between kHT and kCOLL.
                                                       22

Alternative Method:


                             Estimated Return
 Economy       Prob.       HT       Coll.      Port.
 Recession      0.10     -22.0%     28.0%      3.0%
 Below avg.     0.20       -2.0      14.7      6.4
 Average        0.40      20.0       0.0       10.0
 Above avg.     0.20      35.0      -10.0      12.5
 Boom           0.10      50.0      -20.0      15.0

    ^
    kp = (3.0%)0.1 + (6.4%)0.20 + (10.0%)0.4
         + (12.5%)0.20 + (15.0%)0.1 = 9.6%
                                                        23



      3.0 - 9.6 0.1  6.4  9.6 0.20
                                                 1/ 2
                2                 2
                                             
                                            
 P =  10.0  9.6 0.4  12.5  9.6 0.20
                     2                  2

                                            
       15.0  9.6 0.1
                     2
                                            
                                             

                               = 3.3%

                  3.3%
            CVP =      = 0.34.
                  9.6%
                                              24



 p = 3.3% is much lower than that of
    either stock (20% and 13.4%).
   p = 3.3% is also lower than avg. of HT
    and Coll, which is 16.7%.
   Portfolio provides avg. return but
    lower risk.
   Reason: diversification.
   Negative correlation is present
    between HT and Coll but is not
    required to have a diversification
    effect
                                      25



     General Statements about risk:

   Most stocks are positively
    correlated. rk,m  0.65.
   You still get a lot of
    diversification effect at .65
    correlation
   35% for an average stock.
   Combining stocks generally
    lowers risk.
                                    26
 What would happen to the
    riskiness of a 1-stock
 portfolio as more randomly
selected stocks were added?


   p would decrease because the
    added stocks would not be
    perfectly correlated
                                                    27



p %
 35    Company Specific risk

                  Total Risk, P
 20

             Market Risk
 0
        10   20      30    40      ......   1500+
                            # stocks in portfolio
                                          28




   As more stocks are added, each
    new stock has a smaller risk-
    reducing impact.
   p falls very slowly after about 40
    stocks are included. The lower
    limit for p is about 20% = M .
                                                                 29
          Decomposing Risk—Systematic (Market) and
            Unsystematic (Business-Specific) Risk

   Fundamental truth of the investment world
     – The returns on securities tend to move up and
       down together
        • Not exactly together or proportionately
   Events and Conditions Causing Movement in
    Returns
     – Some things influence all stocks (market risk)
        • Political news, inflation, interest rates, war, etc.
     – Some things influence only particular firms
       (business-specific risk)
        • Earnings reports, unexpected death of key
          executive, etc.
     – Some things affect all companies within an
       industry
        • A labor dispute, shortage of a raw material
                                   30


Total = Market + Firm specific
risk     risk         risk

 Market risk is that part of a
 security‟s risk that cannot be
 eliminated by diversification.
 Firm-specific risk is that part
 of a security‟s risk which can
 be eliminated with
 diversification.
                                  31




   By forming portfolios, we
    can eliminate nearly half
    the riskiness of individual
    stocks (35% vs. 20%).
   (actually35% vs. 20% is a
    43%reduction)
                               32

   CAPM -- Capital Asset
      Pricing Model

If you chose to hold a one-
stock portfolio and thus are
exposed to more risk than
diversified investors, would
you be compensated for all
the risk you bear?
                                  33


   NO!
   Stand-alone risk as
    measured by a stock‟s 
    or CV is not important to
    well-diversified investors.
   Rational, risk averse
    investors are concerned
    with p , which is based
    on market risk.
   Beta measures a stock‟s       34

    market risk. It shows a
    stock‟s volatility relative
    to the market.
   Beta shows how risky a
    stock is when the stock is
    held in a well-diversified
    portfolio.
   The higher beta, the
    higher the expected rate
    of return.
                                  35



      How are betas calculated?
   Run a regression of past
    returns on Stock i versus
    returns on the market.
   The slope coefficient is
    the beta coefficient.
                                                         36
     Illustration of beta = slope:


                                     Regression line

ki    20                      .
      15                  .           Year
                                       1
                                             kM
                                             15%
                                                   ki
                                                   18%
                                       2     -5    -10
      10                               3     12    16
       5


-5     0      5      10       15      20           kM
      -5
                     ki = -2.59 + 1.44 kM
.     -10
                                          37



                Find beta:

   “By Eye.” Plot points, draw in
    „regression‟ line, get slope as
     b = Rise/Run. The “rise” is the
    difference in ki , the “run” is the
    difference in kM . For example,
    how much does ki increase or
    decrease when kM increases
    from 0% to 10%?
                                            38
 Computer: statistics program or
  spreadsheet regression program
 Calculator. Enter data points, and
  calculator does least squares
  regression: ki = a + bkM = -2.59 +
  1.44kM . r = corr. coefficient = 0.997.
 Find someone‟s estimate of beta
  for a given stock on the web
 In the real world, we would use
  weekly or monthly returns, with at
  least a year of data, and would
  always use a computer.
                                         39


   If beta = 1.0, average risk stock. (The
    „market‟ portfolio has a beta of 1.0.)
   If beta > 1.0, stock riskier than
    average.
   If beta < 1.0, stock less risky than
    average.
   Most stocks have betas in the range
    of 0.5 to 1.5.
   Some ag. related companies have
    betas less than 0.5
                                     40




   =1, get the market expected
    return
   <1, earn less than the market
    expected return
   >1, get an expected return
    greater than the market
                                    41



     Can a beta be negative?
   Answer: Yes, if the
    correlation between ki and kM
    is negative.
   Then in a “beta graph” the
    regression line will slope
    downward.
   Negative beta -- rare
                                              42


ki
                           b = 1.29
                 HT
      40


                                       b=0
      20
                             T-bills

-20    0    20              40
                                         kM

                                  Coll
      -20             b = -0.86
                                             43




                  Expected           Risk
Security           Return           (Beta)
HighTech           17.4%             1.29
“Market”             15.0            1.00
US Rubber            13.8            0.68
T-bills              8.0             0.00
Collections          1.7            -0.86

     Riskier securities have higher
     returns, so the rank order is O.K.
                                              44
Given the beta of a stock, a theoretical
    required rate of return can be
             calculated.
   The Security Market Line (SML) is used.
   SML: ki = kRF + (kM - kRF)bi

                           MRP

MRP= market risk premium
                          45




ki = kRF + (kM - kRF)bi
                                                    46



              For Term Projects

   Use KRF = 2.5%; this is the 10 year treasury
    rate. Often it is argued to use a shorter
    term rate, but we are going to use 2.5%.
   Use MRP = 5%
   The historical average MRP is about 5%.
   Find your own beta from the web
   On Yahoo Finance look up your company
    and then the “key statistics” tab on the left
    will give you their beta
                                         47


       Use the SML to calculate
the required returns (for the example)

       SML: ki = kRF + (kM - kRF)bi .


   Assume kRF = 8%.
                   ^
   Note that kM = kM is 15%.
   MRP = kM - kRF = 15% - 8% = 7%
                                              48



         Required rates of return:

kHT      = 8.0% + (15.0% - 8.0%) 1.29
         = 8.0% + (7%)1.29
         = 8.0% + 9.0%        = 17.0%
kM       =   8.0% + (7%)1.00      =   15.0%
kUSR     =   8.0% + (7%)0.68      =   12.8%
kTbill   =   8.0% + (7%)0.00      =   8.0%
kColl    =   8.0% + (7%)(-0.86)   =   2.0%
                                         49


Calculate beta for a portfolio with
   50% HT and 50% Collections:
            Portfolio Beta

bP =      weighted average of the
  betas of the stocks in the portfolio
     =    0.5(bHT) + 0.5(bColl)
     =    0.5(1.29) + 0.5(-0.86)
     =    0.22 .
Weights are the proportions invested
  in each stock.
                                                 50


     The required return on the HT/Coll.
                portfolio is:

kP     =    Weighted average k
       =    0.5(17%) + 0.5(2%) =       9.5% .

Or use SML for the portfolio:

kP     =    kRF + (kM - kRF) bP
       =    8.0% + (15.0% - 8.0%) (0.22)
       =    8.0% + 7%(0.22)       =     9.5% .
                                                           51
Using Beta—The Capital Asset Pricing
           Model (CAPM)

   The CAPM helps us determine how stock prices
    are set in the market
     Developed in 1950s and 1960s by Harry
       Markowitz and William Sharpe
   The CAPM's Approach
     People won't invest unless a stock's expected
       return is at least equal to their required return
     The CAPM attempts to explain how investors'
       required returns are determined
                                     52


Has the CAPM been verified through
         empirical tests?


     Not completely. Because
      statistical tests have
      problems which make
      verification almost
      impossible.
                                          53




   Investors seem to be concerned with
    both market risk and total risk.
    Therefore, the SML may not produce
    a correct estimate of ki:

      ki = kRF + (kM - kRF)b + ?
                                      54


   Also, CAPM/SML concepts are
    based on expectations, yet
    betas are calculated using
    historical data. A company‟s
    historical data may not reflect
    investors‟ expectations about
    future riskiness.

								
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