Chapter 8 Stocks,Stocks Valuation, and Stock Market Equilibrium

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Chapter 8 Stocks,Stocks Valuation, and Stock Market Equilibrium Powered By Docstoc
					     Chapter 2
Discounted Dividend
     Valuation
             Challenges


 Defining and forecasting CF’s
 Estimating appropriate discount rate
           Basic DCF model

   An asset’s value is the present value of
    its (expected) future cash flows

             
            CFt
V0  
     t 1 (1  r ) t
    Comments on basic DCF
         model
 Flat term structure of discount rates
  versus differing discount rates for
  different time horizons
 Value of an asset at any point in time is
  always the PV of subsequent cash flows
  discounted back to that point in time.
 Three alternative definitions of cash flow


 Dividend discount model
 Free cash flow model
 Residual income model
Dividend discount model

 The DDM defines cash flows as
  dividends.
 Why? An investor who buys and holds a
  share of stock receives cash flows only
  in the form of dividends
 Problems:
     Companies that do not pay dividends.
     No clear relationship between dividends
      and profitability
DDM (continued)

 The DDM is most suitable when:
     the company is dividend-paying
     the board of directors has a dividend policy
      that has an understandable relationship to
      profitability
     the investor has a non-control perspective.
Free cash flow

 Free cash flow to the firm (FCFF) is cash
  flow from operations minus capital
  expenditures
 Free cash flow to equity (FCFE) is cash
  flow from operations minus capital
  expenditures minus net payments to
  debtholders (interest and principal)
Free cash flow

 FCFF is a pre-debt cash flow concept
 FCFE is a post-debt cash flow concept
 FCFE can be viewed as measuring what
  a company can afford to pay out in
  dividends
 FCF valuation is appropriate for
  investors who want to take a control
  perspective
FCF valuation

 PV of FCFF is the total value of the
  company. Value of equity is PV of FCFF
  minus the market value of outstanding
  debt.
 PV of FCFE is the value of equity.
 Discount rate for FCFF is the WACC.
  Discount rate for FCFE is the cost of
  equity (required rate of return for equity).
FCF (continued)

 FCF valuation is most suitable when:
     the company is not dividend-paying.
     the company is dividend paying but
      dividends significantly differ from FCFE.
     The company’s FCF’s align with
      company’s profitability within a reasonable
      time horizon.
     the investor has a control perspective.
 FCF valuation is very popular with
  analysts.
Residual income

 RI for a given period is the earnings for
  that period in excess of the investors’
  required return on beginning-of-period
  investment.
 RI focuses on profitability in relation to
  opportunity costs.
 A stock’s value is the book value per
  share plus the present value of expected
  future residual earnings
          Residual income (continued)

 RI valuation is most suitable when:
   the company is not dividend-paying, or as an
    alternative to the FCF model.
   the company’s FCF is negative within a comfortable
       time horizon.
      the investor has a control perspective.
 RI valuation is also popular. The quality of
  accounting disclosure can make the use of RI
  valuation error-prone.
 Which is best, DDM, FCF, or
             RI?
 One model may be more suitable for a
  particular application.
 Analyst may have more expertise with
  one model.
 Availability of information.
 In practice, skill in application, including
  the quality of forecasts, is decisive for
  the usefulness of an analyst’s work.
Discount rate determination

 Jargon
     Discount rate: any rate used in finding the
      present value of a future cash flow
     Risk premium: compensation for risk,
      measured relative to the risk-free rate
     Required rate of return: minimum return
      required by investor to invest in an asset
     Cost of equity: required rate of return on
      common stock
Discount rate determination

     Weighted average cost of capital (WACC):
      the weighted average of the cost of equity,
      after-tax cost of debt, and cost of preferred
      stock
Two major approaches for cost of
            equity
 Equilibrium models:
     Capital asset pricing model (CAPM)
     Arbitrage pricing theory (APT)
 Bond yield plus risk premium method
  (BYPRP)
CAPM

 Expected return is the risk-free rate plus
  a risk premium related to the asset’s
  beta:
 E(Ri) = RF + i[E(RM) – RF]


 The beta is i = Cov(Ri,RM)/Var(RM)
 [E(RM) – RF] is the market risk premium
  or the equity risk premium
             CAPM

 What do we use for the risk-free rate of return?
   Choice is often a short-term rate such as the 30-day T-bill
    rate or a long-term government bond rate.
   We usually match the duration of the bond rate with the
       investment period, so we use the long-term government
       bond rate.
      Risk-free rate must be coordinated with how the equity
       risk premium is calculated (i.e., both based on same bond
       maturity).
            Equity risk premium

 Historical estimates: Average difference between
  equity market returns and government debt returns.
     Choice between arithmetic mean return or geometric
      mean return (see Table 2-2 p. 50)
     Survivorship bias
     ERP varies over time
     ERP differs in different markets (see Table 2-3 p. 51)
            Equity risk premium

 Expectational method is forward looking instead of
  historical
 One common estimate of this type:
     GGM equity risk premium estimate
       = dividend yield on index based on year-ahead dividends
         + consensus long-term earnings growth rate
         - current long-term government bond yield
        Arbitrage Pricing Theory (APT)

 CAPM adds a single risk premium to the risk-free
  rate. APT models add a set of risk premiums to the
  risk-free rate:
 E(Ri) = RF + (Risk premium)1
  + (Risk premium)2 + … + (Risk premium)K
 (Risk premium)i = (Factor sensitivity)i × (Factor risk
  premium)i
        Arbitrage Pricing Theory (APT)

 Factor sensitivity is asset’s sensitivity to a
  particular factor (holding all other factors constant)
 Factor risk premium is the factor’s expected return
  in excess of the risk-free rate.
APT models

 One popular model is the Fama-French
 three factor model using company-
 specific attributes:
     RMRF – return on equity index minus 30
      day T-bills
     SMB (small minus big) – return on small
      cap portfolio minus return on large cap
      portfolio
     HML (high minus low) – return on high
      book-to-market portfolio minus return on
      low book-to-market portfolio
APT models

 The Burmeister, Roll, and Ross (BIRR)
  model uses five macroeconomic factors
     Confidence risk
     Time-horizon risk
     Inflation risk
     Business-cycle risk
     Market timing risk
Using BIRR model

 Use BIRR model to calculate required
   return on the S&P 500 (data in example
   2-4, p 53)
 The required return is:
r = 5.00% + (0.27×2.59%) – (0.56×0.66%)
       – (0.37×4.32%) + (1.71×1.40%)
       +(1.00×3.61%)
r = 9.74%
      Sources of error in using
              models
 Three sources of error in using CAPM or
  APT models:
     Model uncertainty – Is the model correct?
     Input uncertainty – Are the equity risk
      premium or factor risk premiums and risk-
      free rate correct?
     Uncertainty about current values of stock
      beta or factor sensitivities
BYPRP method

 The bond yield plus risk premium
  method finds the cost of equity as:
  BYPRP cost of equity
    = YTM on the company’s long-term debt
     + Risk premium

 The typical risk premium added is 3-4
  percent.
        Build-up method

 Cost of equity is the risk-free rate plus one or more
  risk premiums, one or more of which is usually
  subjective rather than theoretically sound.
 For example, cost of equity is risk-free rate + equity
  risk premium +/- company-specific risk premium
 BYPRP is an example of this.
 Buildup method sometimes used for stocks that are
  not publicly traded.
              Dividend discount models
                      (DDMs)
         Single-period DDM:

         D1         P1        D1  P1
V0                      
          r )1 1  r for (1  r )1
       (1 Rate of(return)1 single-period DDM


   D1  P1      D1 P1  P0
r         1     
     P0         P0   P0
            More DDMs

             Two-period DDM:

            D1             D2                   P2                      D1            D2  P2
V0                                                                            
       (1  r )  1
                  (1  r )   (1  r )
            Multiple-period DDM:
                                    2                      2
                                                                   (1  r )   1
                                                                                      (1  r )   2




                         D1                   Dn                   Pn
             V0                                        
                     (1  r )   1
                                            (1  r )   n
                                                               (1  r ) n
        n
             Dt       Pn
V0                
     t 1 (1  r ) (1  r ) n
                  t
        Indefinite HP DDM

         For an indefinite holding period, the PV
           of future dividends is:
         D1                 Dn
V0                                
       (1  r )1         (1  r ) n

           
             Dt
V0                 .
     t 1 (1  r )
                   t
Forecasting future dividends

 Using stylized growth patterns
     Constant growth forever (the Gordon
      growth model)
     Two-distinct stages of growth (the two-
      stage growth model and the H model)
     Three distinct stages of growth (the three-
      stage growth model)
Forecasting future dividends

 Forecast dividends for a visible time
  horizon, and then handle the value of the
  remaining future dividends either by
     Assigning a stylized growth pattern to
      dividends after the terminal point
     Estimate a stock price at the terminal point
      using some method such as a multiple of
      forecasted book value or earnings per
      share
Gordon Growth Model

 Assumes a stylized pattern of growth,
  specifically constant growth:
     Dt = Dt-1(1+g)
Or
     Dt = D0(1 + g)t
       Gordon Growth Model

        PV of dividend stream is:

     D0 (1  g ) D0 (1  g ) 2     D0 (1  g ) n
V0                                          
      (1  r )    (1  r ) 2
                                    (1  r ) n

        Which can be simplified to:



         D0 (1  g )    D1
    V0              
          rg          rg
        Gordon growth model

 Valuations are very sensitive to inputs. Assuming
  D1 = 0.83, the value of a stock is:

                    g = 3.45% g = 3.70%   g = 3.95%

        r = 5.95%    $33.20    $36.89      $41.50

        r = 6.20%    $30.18    $33.20      $36.89

        r = 6.45%    $27.67    $30.18      $33.20
Other Gordon Growth issues

 Generally, it is illogical to have a
  perpetual dividend growth rate that
  exceeds the growth rate of GDP
 Perpetuity value (g = 0):     D
                           V0       1
                                    r
 Negative growth rates are also
  acceptable in the model.
  Expected rate of return

   The expected rate of return in the
    Gordon growth model is:

   D0 (1  g )     D1
r             g    g
       P0          P0
   Implied growth rates can also be derived
    in the model.
        PV of growth opportunities

 If a firm has growing earnings and dividends, it
  can be worth more than a non-growing firm:
 Value of growth = Value of growing firm – Value
  of assets in place (no growth)
 OR



               E
           V0   PVGO
               r
      Gordon Model & P/E ratios

       If E is next year’s earnings (leading P/E):

 P0 D1 / E1 (1  b)
                
       rg           r  earnings (trailing P/E):
 E1  If E is this year’s g


P0 D0 (1  g ) / E0 (1  b)(1  g )
                  
E0      rg              rg
Strengths of Gordon growth model

 Good for valuing stable-growth,
  dividend-paying companies
 Good for valuing indexes
 Simplicity and clarity, also helps
  understanding of relationships between
  V, r, g, and D
 Can be used as a component in more
  complex models
Weaknesses of Gordon growth
model
 Calculated values are very sensitive to
  assumed values of g and r
 Is not applicable to non-dividend-paying
  stocks
 Is not applicable to unstable-growth,
  dividend paying stocks
           Two-stage DDM
 The two-stage DDM is based on the multiple-period
  model:

           n
              Dt           Pn
  V0                
       t  (1  r       (1  r
                    t          n
 Assume1the first ) dividends)grow at gS and dividends
                    n
  then grow at gL. The first n dividends are:




    Dt  D0 (1  g S )        t
        Two-stage DDM (cont)

 Using Dn+1, the value of the stock at t=n is

       D0 (1  g S )n (1  g L )
  Pn 
              r  gL
 The value at t = 0 is




          n
             D0 (1  g S ) D0 (1  g S ) (1  g L )
                         t              n
   P0                   
        t 1  (1  r ) t
                            (1  r )n (r  g L )
Two-stage DDM example

 Assume the following values
     D0 is $1.00
     gS is 30%
     Supernormal growth continues for 6 years
     gL is 6%
     The required rate of return is 12%
                Two-stage DDM example

                                                               Present Values
Time    Value   Calculation                         Dt or Vt   Dt/(1.12)t or Vt/(1.12)t
1       D1      1.00(1.30)                             1.30           1.161
2       D2      1.00(1.30)2                            1.69           1.347
3       D3      1.00(1.30)3                            2.197          1.564
4       D4      1.00(1.30)4                            2.856          1.815
5       D5      1.00(1.30)5                            3.713          2.107
6       D6      1.00(1.30)6                            4.827          2.445
6       V6      1.00(1.30)6(1.06) / (0.12 – 0.06)     85.273         43.202
Total                                                                53.641
          “Shortcut” two-stage DDM
          (not in the book)
           If gS is constant during stage 1, this
             works:
      D0 (1  g S )  (1  g S )n  D0 (1  g S ) n (1  g L )
 P0                1          n 
                                     
       r  gS           (1  r )     (1  r )n (r  g L )

     1.00(1.30)  (1.30)6  1.00(1.30)6 (1.06)
V0              1 
                  (1.12)6   (1.12)6 (0.12  0.06)
     0.12  0.30          
                           
           For gS=30%, gL=6%, D0=1.00 and r=12%



V0  7.222  1.4454  
                            85 .274
                                    6
                                       10 .439  42 .202  53 .64
                            (1.12 )
Using a P/E for terminal value

 The terminal value at the beginning of
  the second stage was found above with
  a Gordon growth model, assuming a
  long-term sustainable growth rate.
 The terminal value can also be found
  using another method to estimate the
  terminal value at t = n. You can also use
  a P/E ratio, applied to estimated
  earnings at t = n.
Using a P/E for terminal value

 For DuPont, assume
     D0 = 1.40
     gS = 9.3% for four years
     Payout ratio = 40%
     r = 11.5%
     Trailing P/E for t = 4 is 11.0
 Forecasted EPS for year 4 is
     E4 = 1.40(1.093)4 / 0.40 = 1.9981 = 4.9952
                Using a P/E for terminal value

Time    Value   Calculation                            Dt or Vt        Present Values
                                                                  Dt/(1.115)t or Vt/(1.115)t
1       D1      1.40(1.093)1                            1.5302             1.3724
2       D2      1.40(1.093)2                            1.6725             1.3453
3       D3      1.40(1.093)3                            1.8281             1.3188
4       D4      1.40(1.093)4                            1.9981             1.2927
4       V4      11  [1.40(1.093)4 / 0.40]             54.9472            35.5505
                = 11  [1.9981 / 0.40] = 11  4.9952
Total                                                                     40.88
       Valuing a non-dividend paying
       stock
 This can be viewed as a special case of the two-
  stage DDM where the dividend in stage one is zero:


                n
                  length P
 Forecasting the Dt  ofn stage one and the
        V 0  (1 in) stage rtwo are the challenges.
  dividend pattern r
               t 1
                      t
                          (1  )
                             n
The H model

 The basic two-stage model assumes a
 constant, extraordinary rate for the
 super-normal growth period that is
 followed by a constant, normal growth
 rate thereafter.
The H model

 Fuller and Hsia (1984) developed a
  variant of the two-stage model where the
  growth rate begins at a high rate and
  declines linearly throughout the super-
  normal growth period until it reaches the
  normal growth rate at the end. The
  normal growth rate continues thereafter.
           The H model
 The value of the dividend stream in the H model is:

            D0 (1  g L ) D0 H ( g S  g L )
      P                 
             r  gL             r L
   V0 =0value per share at time zero g
 D0 = current dividend
 r = required rate of return on equity
 H = half-life of the high growth period (i.e., high growth period = 2H
  years)
 gS = initial short-term dividend growth rate
 gL = normal long-term dividend growth rate after year 2H
          H model example

 For Siemans AG, the inputs are:
     Current dividend is €1.00.
     The dividend growth rate is 29.28%, declining linearly over a
      sixteen year period to a final and perpetual growth rate of
      7.26%.
     The risk-free rate is 5.34%, the market risk premium is 5.32%,
      and the Siemens beta, estimated against the DAX index, is
      1.37.
     The required rate of return for Siemens is:
      r = rf + bi(rm – rf) = 5.34% + 1.37(5.32%) = 12.63%.
               H model example

                Using the H model, the value of the
                   company is:
       D0 (1  g L ) D0 H ( g S  g L )    1.00 (1.0726 )   1.00 (8)( 0.2928  0.0726 )
V0                                                     
                            gL           32.80 = €52.77.1263  0.0726
        r  g L V =r 19.97 + 0.1263  0.0726
                      0
                                                                 0.

                If Siemens experienced normal growth
                   starting now, its value would be €19.97.
                   The extraordinary growth adds €32.80 to
                   its value, which results in Siemens being
                   worth a total of €52.77.
Three-stage DDM

 There are two popular version of the
  three-stage DDM
     The first version is like the two-stage model, only
      the firm is assumed to have a constant dividend
      growth rate in each of the three stages.
     A second version of the three-stage DDM
      combines the two-stage DDM and the H model. In
      the first stage, dividends grow at a high, constant
      (supernormal) rate for the whole period. In the
      second stage, dividends decline linearly as they do
      in the H model. Finally, in stage three, dividends
      grow at a sustainable, constant rate.
   Three-stage DDM with three
         distinct stages
 Assume the following for IBM:
     Required rate of return is 12%
     Current dividend is $0.55
     Growth rate and duration for phase one
      are 7.5% for two years
     Growth rate and duration for phase two are
      13.5% for the next four years
     Growth rate in phase four is 11.25%
      forever
        Three-stage DDM with three
              distinct stages

                                                                        Present values
Time    Value                  Calculation                   Dt or Vt    Dt/(1.12)t or
                                                                          Vt/(1.12)t
1       D1      0.55(1.075)                                    0.5913        0.5279
2       D2      0.55(1.075)2                                   0.6356        0.5067
3       D3      0.55(1.075)2(1.135)                            0.7214        0.5135
4       D4      0.55(1.075)2(1.135)2                           0.8188        0.5204
5       D5      0.55(1.075)2(1.135)3                           0.9293        0.5273
6       D6      0.55(1.075)2(1.135)4                           1.0548        0.5344
6       V6      0.55(1.075)2(1.135)4(1.1125)/(.12 – .1125)   156.4620      79.2685
Total                                                                      82.3897
       Spreadsheet modeling

 Spreadsheets allow the analyst to build very
  complicated models that would be very
  cumbersome to describe using algebra.
 Built-in functions such as those to find rates of
  return use algorithms to get a numerical answer
  when a mathematical solution would be
  impossible or extremely complicated.
       Spreadsheet modeling


 Because of their widespread use, several
  analysts can work together or exchange
  information through the sharing of their
  spreadsheet models.
          Finding rates of return for any
          DDM
           For a one-period DDM
       D1  P       D1 P  P0
    r       1
               1     1
       0PFor the P0      P0
                    Gordon model

      D0 (1  g )the H-model
        For  g  D1  g
   r
          P0           P0



     D0 
r    ((1  g L )  H ( g S  g L ))  g L
     P0 
Finding rates of return for any
DDM
 For multi-stage models and spreadsheet
  models it can be more difficult to find a
  single equation for the rate of return.
     Trial and error is used instead of an
      equation.
     Using a computer or trial and error, the
      analyst finds a discount rate such that the
      present value of future expected dividends
      equals the current stock price.
       Finding r with trial & error

 Johnson & Johnson’s current dividend of $.70 to
  grow by 14.5 percent for six years and then grow
  by 8 percent into perpetuity. J&J’s current price is
  $53.28. What is the expected return on an
  investment in J&J’s stock?
       Finding r with trial & error

 For a good initial guess, we can use the expected
  rate of return formula from the Gordon model as a
  first approximation: r = ($0.70  1.145)/$53.28 + 8%
  = 9.50%. Since we know that the growth rate in the
  first six years is more than 8 percent, the estimated
  rate of return must be above 9.5 percent.
 Let’s use 9.5 percent and 10.0 percent to calculate
  the implied price.
          Finding r with trial & error

The present value of the terminal value
  = V6 / (1+r)6 = [D7/(r-g)]/(1+r)6
The calculations for 9.5% and 10.0% are shown in the
  table. Actual r is 9.988%.

                          Present Value of Dt and V6   Present Value of Dt and V6
       Time t    Dt
                                  at r = 9.5%                 at r = 10.0%
       1        $0.8015             $0.7320                      $0.7286
       2        $0.9177             $0.7654                      $0.7584
       3        $1.0508             $0.8003                      $0.7895
       4        $1.2032             $0.8369                      $0.8218
       5        $1.3776             $0.8751                      $0.8554
       6        $1.5774             $0.9151                      $0.8904
       7        $1.7035
       6                         $65.8838                     $48.0805
       Total                     $70.8085                     $52.9245
       Strengths of multistage DDMs

 Can accommodate a variety of patterns of future
  dividend streams.
 Even though they may not replicate the future
  dividends exactly, they can be a useful
  approximation.
 The expected rates of return can be imputed by
  finding the discount rate that equates the
  present value of the dividend stream to the
  current stock price.
       Strengths of multistage DDMs

 Because of the variety of DDMs available, the
  analyst is both enabled and compelled to evaluate
  carefully the assumptions about the stock under
  examination.
 Spreadsheets are widely available, allowing the
  analyst to construct and solve an almost limitless
  number of models.
       Strengths of multistage DDMs

 Using a model forces the analyst to specify
  assumptions (rather than simply using subjective
  assessments). This allows analysts to use common
  assumptions, to understand the reasons for
  differing valuations when they occur, and to react to
  changing market conditions in a systematic
  manner.
           Weaknesses of multistage
                   DDMs
 Garbage in, garbage out. If the inputs are not
  economically meaningful, the outputs from the
  model will be of questionable value.
 Analysts sometimes employ models that they do
  not understand fully.
 Valuations are very sensitive to the inputs to the
  models.
          Weaknesses of multistage
                  DDMs
 Subjective assessments may be better than
  systematic, quantitative assessments in some
  cases.
 Programming and data errors in spreadsheet
  models are very common. These models must be
  checked very thoroughly.
           Weaknesses of multistage
                   DDMs
 The choice of model should be made very carefully.
  There is a tendency to grab a model, put in the
  data, get the results, and use them without carefully
  justifying the logic of the underlying model and the
  appropriateness and realism of the values inserted
  into the model.
    Equity durations
    (not in the book)
     Duration is a measure of the interest rate
      risk of fixed income securities. The
      concept of duration can also be adapted
      to equities.
     The mathematical definition of duration
      is
    1 dP    dP / P
D      
    The percentage change in price is
    P dr      dr

dP / P  D  dr
   Gordon model duration
   (not in the book)
    The stock price is
     c1
P
    g derivative with respect to r is
   r The


dP  The1 duration is
         c
   
dr    (r  g )2


    1
D
   rg
Forecasting growth rates

 There are three basic methods for
  forecasting growth rates:
     Using analyst forecasts
     Using historical rates (use historical
      dividend growth rate or use a statistical
      forecasting model based on historical data)
     Using company and industry fundamentals
         Finding g

 The simplest model of the dividend growth rate is:
     g = b x ROE
     where g = Dividend growth rate
     b = Earnings retention rate (1 – payout ratio)
     ROE = Return on equity.
            Finding g

             The ROE, found with the duPont model
               is:
           Net Income         Sales            AverageTotal Assets
   ROE                                   
             Sales      AverageTotal Assets Average Stockholders ' Equity


             The growth rate can also be expressed
               as:

   Net income - Dividends Net income Sales         Assets
g                                        
          Net income        Sales     Assets Shareholders' equity
        DDMs and portfolio selection

 Investment managers have used DCF models,
  including dividend discount models as part of a
  systematic approach to security selection and
  portfolio formation.
 If a manager just chooses the most undervalued
  securities without any risk discipline, his selections
  might concentrate on a particular (or a few) risk
  factors. He might often fail to meet his risk
  objective. A risk control discipline must be used.
       DDMs and portfolio selection

 Sort stocks into groups according to the risk control
  methodology. For example, put stocks into groups
  of similar beta risk.
 Rank stocks by expected return within each group
  using a DCF methodology. Rank stocks from
  highest to lowest expected return within each
  sector grouping.
       DDMs and portfolio selection

 Select portfolio from the highest expected return
  stocks consistent with the risk control methodology.
  All selected securities are equal weighted, but more
  important sectors have a larger number of
  securities; the result is approximate sector
  neutrality.
        DDMs and portfolio selection

 Six analysts follow a universe of 250 stocks.
 Company uses a three-stage, H-model.
 For each, an analyst estimates 1) the initial growth
  rate, 2) the length of the initial phase, and 3) the
  length of the transitional phase.
 Initial growth rate estimated with duPont model.
       DDMs and portfolio selection

 Length of initial phase and transitional phase based
  on fundamental analysis.
 Growth rate for maturity phase assumed to be the
  same for all stocks.
 Stocks assigned to five beta quintiles.
       DDMs and portfolio selection

 Company invests in the top return quintile in each
  beta quintile (10 stocks in each beta quintile).
 Method had superior returns for several years.

				
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