Residual Income Model - PowerPoint

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					Investing with a Stock Valuation Model




      Zhiwu Chen, Yale University
      Ming Dong, Ph.D. candidate, OSU
                                                        Purpose
 Models:
     The stock valuation model      developed by Bakshi & Chen (1998)
      and extended by Dong (1998)

     The residual-income model       implemented in Lee-Myers-
      Swaminathan (1997)




 To compare their performance to traditional stock-selection

   measures: book/market, P/E, momentum, size, and so on
             Motivation: why not expected-return models?
 The CAPM, APT and other multi-factor models all focus on
  EXPECTED FUTURE RETURNs

 Stock-Selection Idea: if the actual expected return on IBM is higher
  than its deserved expected return, then IBM is a buy (hence, Jensen’s
   Aplha)


 But, what is IBM’s actual expected 1-yr-forward return today?     -----
  You cannot observe it!

 Conclusion: you cannot really apply such expected-return models.
                  Motivation: why stock-valuation models?
 There is always a market price for each stock !

 Stock-Selection Idea: if IBM’s market price is lower than its model
  price (fair value), then IBM is a buy (hence, undervalued stocks)

 Conclusion: stock valuation modeling is the way to go.



 But, is there a “good” equity-valuation model?
            Motivation: existing stock valuation models

 Variants of the Gordon model: too many unrealistic assumptions           (e.g.,
   a constant and flat term structure, constant dividend growth forever)


 Multi-stage dividend/earnings/cashflow discount models:

     No structural parameterization of the firm’s business

     No attention paid to how the stock has historically been valued by market

     Fair values determined by these models are too often below market price.
             The Bakshi-Chen-Dong (BCD) Model

 Fundamental Variables:          current EPS, expected future EPS, and 30-yr bond yield

 Firm-specific parameters:
     EPS growth volatility
     Long-run EPS growth rate
     Duration of business-growth cycle
     Systematic or beta risk of the firm
     Correlation between the firm's EPS and the interest-rate environment


 30-yr Treasury yield’s parameters:
     Its long-run level
     Interest-rate volatility
     Duration of interest-rate cycle
                    Comparison
• The BCD Model                            • The Residual-Earnings Model
                                             (e.g., Lee, Meyer and Swaminathan (1998))

   – Detailed parameterization of EPS
                                              – Two parameters: beta and
     processes and interest-rate process
                                                dividend-payout ratio
     Parameters to be estimated from
     past data

   – Closed-form stock valuation              – No closed-form valuation formula.
     formula                                    Requires ad hoc approximation of
                                                the stock’s future price at end of
                                                forecasting horizon
   – Past data are used to estimate
     parameters
     So, valuation reflects both past
     valuation standard for the stock         – Valuation is independent of past
     and the stochastic discounting of          valuation standard for the stock
     future prospects
                                                              Data

 I/B/E/S, CRSP, and Compustat

 Future EPS forecasts: consensus analyst estimates

 Period covered: Jan. 1979 - Dec. 1996

 Stock universe: about 2500 U.S. stocks (mostly large cap)
        What Constitutes a Good Stock-Selection Measure?




 Mean-reverting,        so that if too low, you can buy the stock, counting on
   the measure to go back to its norm.


 Not too persistent,       e.g., if book/market ratio is too persistent, you will
   not want to buy a stock just because it has a high B/M ratio. You would
   like fast mean-reversion


 High predictive power of future stock performance
                      Behavior of Book/Market Ratio over Time

•         This figure shows the average B/M ratio path for each quartile obtained by sorting all stocks
          according to their B/M ratios as of January 1990.


                                                         Average B/M by Quartile
           2
                                                                                                                                          Q1 (low )
                                                                                                                                          Q2
                                                                                                                                          Q3
    B/M




           1                                                                                                                              Q4(high)



           0
               7901
                      7912
                             8011
                                    8110
                                           8209
                                                  8308
                                                          8407
                                                                 8506
                                                                        8605
                                                                               8704
                                                                                      8803
                                                                                             8902
                                                                                                    9001
                                                                                                           9012
                                                                                                                  9111
                                                                                                                         9210
                                                                                                                                9309
                                                                                                                                       9408
                                                                                                                                              9507
                                                                                                                                                     9606
                                                                                  Date
                                     Behavior of LMS Value/Price over Time

   •                 This figure shows the average Lee-Myers-Swaminathan V/P ratio path for each quartile obtained by
                     sorting all stocks according to their V/P as of January 1990.
                                                                                                                                                                                                     Q1(low)
                                                                                     Part A: Average V/P Ratio by Quartile                                                                           Q2
                                                    2
                                                                                                                                                                                                     Q3

                                                                                                                                                                                                     Q4(high
                                                                                                                                                                                                     )
                                           V/P




                                                    1




                                                    0
                                                        7902
                                                                8001
                                                                       8012
                                                                              8111
                                                                                      8210
                                                                                              8309
                                                                                                          8408
                                                                                                                 8507
                                                                                                                        8606
                                                                                                                               8705
                                                                                                                                      8804
                                                                                                                                             8903
                                                                                                                                                    9002
                                                                                                                                                           9101
                                                                                                                                                                  9112
                                                                                                                                                                         9211
                                                                                                                                                                                9310
                                                                                                                                                                                       9409
                                                                                                                                                                                              9508
                                                                                                                                                                                                       9607
                         Part B:V/P Autocorrelation for the Lowest Quartile                                                       Date
                    1
Autocorrelation




                  0.5

                    0
                         1
                             5
                                 9
                                     13
                                          17
                                               21
                                                    25
                                                           29
                                                                  33
                                                                        37
                                                                              41
                                                                                     45
                                                                                             49
                                                                                                     53
                                                                                                            57




                  -0.5
                                               Number of Months Lagged
                                                                                           Behavior of E/P Ratio

•   This figure shows the average E/P ratio path for each quartile obtained by sorting all stocks according
    to their E/P ratios as of January 1990.
•   You would like to see the qartiles crossing each other over time. Yes, they do to some extent.


                                                     Part A: Average E/P by Quartile
                                                                                                                                    Q1(low )
                         0.2
                                                                                                                                    Q2
                        0.15                                                                                                        Q3
                                                                                                                                    Q4(high)
            E/P Ratio




                         0.1
                        0.05
                           0
                        -0.05
                         -0.1
                                7901

                                       8002
                                              8103

                                                      8204
                                                             8305

                                                                    8406

                                                                           8507
                                                                                  8608

                                                                                          8709

                                                                                                 8810

                                                                                                        8911

                                                                                                               9012
                                                                                                                      9201

                                                                                                                             9302

                                                                                                                                    9403
                                                                                                                                           9504

                                                                                                                                                  9605
                                                                                         Date
                  BCD Model Mispricing
 Step 1: use past 2-yr data to estimate model parameters for
  the stock

 Step 2: use current EPS, 1-yr-forward EPS forecast and 30-yr
  yield, plus the estimated parameters, to compute the stock’s
  current model price (out of sample)

 Mispricing = [market price - model price] / model price

 Thus, a negative mispricing means an undervalued stock, and
  so on.
                                                        Behavior of BCD Model Mispricing

•                    This figure shows the average BCD Model mispricing path, for each quartile obtained by sorting all
                     stocks according to their mispricing levels as of January 1990.
•                    The quartiles switch from over- to undervalued, and vice versa, every few years!


                                    Figure 2: Reversals of Mispricing Across Quartiles
                                                                                                                                               Q1 (undervalued)
                                                                                                                                               Q2
                      35                                                                                                                       Q3
                                                                                                                                               Q4 (overvalued)
                      25
    Mispricing (%)




                      15

                       5

                       -5

                     -15

                     -25
                            7901
                                   7911
                                          8009
                                                 8107
                                                        8205
                                                               8303
                                                                      8401
                                                                             8411
                                                                                    8509
                                                                                           8607
                                                                                                  8705
                                                                                                         8803
                                                                                                                8901
                                                                                                                       8911
                                                                                                                              9009
                                                                                                                                     9107
                                                                                                                                            9205
                                                                                                                                                   9303
                                                                                                                                                          9401
                                                                                                                                                                 9411
                                                                                                                                                                        9509
                                                                                                                                                                               9607
                                                                                                    Date
                                            Persistence of BCD Model Mispricing

                                      Part A: Mispricing Autocorrelation
                                     for the Most Undervalued Quartile
                    1
Autocorrelation




                  0.6


                  0.2


                  -0.2


                  -0.6
                         1

                             5

                                 9

                                       13

                                            17

                                                 21

                                                      25

                                                           29

                                                                33

                                                                     37

                                                                          41

                                                                               45

                                                                                    49

                                                                                                             53

                                                                                                                  57
                                                 Number of Months Lagged                                              Part B: Distribution of Mispricing Mean-Reversion Time
                                                                                                                                             Full Sample

                                                                                                             10
                                                                                                              9
                                                                                         Percent of Stocks    8
                                                                                                              7
                                                                                                              6
                                                                                                              5
                                                                                                              4
                                                                                                              3
                                                                                                              2
                                                                                                              1
                                                                                                              0
                                                                                                                  3
                                                                                                                      5
                                                                                                                          7
                                                                                                                              9
                                                                                                                                  11
                                                                                                                                       13
                                                                                                                                            15
                                                                                                                                                 17
                                                                                                                                                      19
                                                                                                                                                           21
                                                                                                                                                                23
                                                                                                                                                                     25
                                                                                                                                                                          27
                                                                                                                                                                               29
                                                                                                                                                                                    31
                                                                                                                                                                                         33
                                                                                                                                                                                              35
                                                                                                                                                                                                   37
                                                                                                                                                                                                        39
                                                                                                                                                                                                             41

                                                                                                                                                                                                                  43
                                                                                                                                            Mean-Reversion Time in Months
                                A Small Summary
 BCD Model mispricing is the least persistent over time and
  mean-reverting the fastest

     It takes about 1.5 years for a group of stocks to go from most
      over- to most underpriced, or the reverse


 P/E ratio is the second least persistent.

     High P/E stocks do not always have the highest P/E.


 B/M and V/P are the most persistent.
     Stocks with the highest B/M seem to be always so. Low B/M
      stocks seem to always have low B/M.
Try to Understand the Measures Again
Panel A: Mispricing portfolios (based on Misp)

                    MP1       MP2        MP3      MP4      MP5     All Stocks
   Misp (%)        -19.63     -4.96      2.58    10.59    30.67       3.86
       V/P           1.00      1.00      0.96     0.90     0.78       0.93
  ME ($Millions)   1118.6    1703.9     1975.4   1966.0   1450.8    1643.3
      B/M            0.89      0.81      0.75     0.71     0.69       0.77
   Ret-6 (%)        -7.51      3.03      9.26    15.61    27.86       9.65
   Ret+1 (%)         2.04      1.83      1.53     1.31     1.18       1.67
   Ret+6 (%)         9.21    10.20       9.44     8.96    10.12       9.59
      Beta           1.25      1.05      1.02     1.05     1.22       1.12

Panel B: V/P portfolios

                    VP1       VP2        VP3      VP4      VP5     All Stocks
       V/P          0.41      0.69       0.89     1.11      1.54      0.93
   Misp (%)         9.92      5.78       3.11     1.49     -0.97      3.86
  ME ($Millions)   1189.4    1841.8     2187.1   1958.2   1343.8    1643.3
      B/M           0.58      0.61       0.70     0.84      1.03      0.77
   Ret-6 (%)       15.74     11.31       9.21     7.74      5.18      9.65
   Ret+1 (%)        1.33      1.27       1.50     1.59      1.87      1.67
   Ret+6 (%)        9.10      8.66       9.16     9.48    10.60       9.59
      Beta          1.50      1.31       1.14     0.93      0.70      1.12
  Try to Understand the Measures                One More Time
Panel E: Momentum portfolios (based on Ret-6)

                   MO1       MO2       MO3       MO4      MO5     All Stocks
  Ret-6 (%)       -18.79     -1.95     7.66     18.00    43.32       9.65
  Misp (%)         -8.92     -1.41     3.24      8.10    18.26       3.86
      V/P           0.93      0.98     0.97      0.92     0.82       0.93
 ME ($Millions)   1020.9    1681.4    1975.6    2084.1   1452.8    1643.3
     B/M            0.94      0.82     0.77      0.71     0.60       0.77
  Ret+1 (%)         1.51      1.56     1.52      1.44     1.86       1.67
  Ret+6 (%)         7.64      9.02     9.36      9.70    12.22       9.59
     Beta           1.25      1.06     1.02      1.04     1.21       1.12

Panel D: B/M portfolios

                   BM1       BM2       BM3       BM4      BM5     All Stocks
     B/M           0.25      0.45      0.66      0.89     1.61       0.77
  Misp (%)         9.86      4.52      2.89      1.72     0.30       3.86
      V/P          0.67      0.83      0.97      1.09     1.11       0.93
 ME ($Millions)   2357.1    1924.9    1512.5    1386.9   1036.3    1643.3
  Ret-6 (%)       19.42     12.48      9.01      6.28     1.11       9.65
  Ret+1 (%)        1.52      1.48      1.37      1.56     1.95       1.67
  Ret+6 (%)        9.41      9.38      8.91      9.39    10.84       9.59
     Beta          1.29      1.21      1.10      0.97     1.02       1.12
      Predictive Power for Future Returns

 From the regression tables,

     BCD Model Mispricing has the highest predictive power (for
      future 1-month, 6-month and 12-month returns)


     Momentum comes second (defined on past 6-month or 12-month
      returns)

     Size is the third most significant (the smaller the firm, the higher
      the future return)

     Last comes B/M & V/P
 Regressions of 1-month-forward Stock Returns on predictive variables


No.   Intercept   Misp       V/P      Size     B/M      Ret-6    Ret-12   Adj-R2   No.
                                                                                   Obs.
1      2.404      -0.029             -0.142    0.130    0.021             0.051    216
       (4.82)     (-8.97)            (-2.79)   (1.16)   (5.91)

2      2.357                         -0.138    0.162    0.009             0.042    216
       (4.62)                        (-2.69)   (1.42)   (2.48)

3      2.475      -0.031             -0.151    0.275             0.019    0.054    216
       (4.92)     (-9.17)            (-2.96)   (2.53)            (7.99)

4      2.485                         -0.152    0.292             0.012    0.044    216
       (4.81)                        (-2.96)   (2.68)            (4.90)
9      2.278      -0.029    0.211    -0.126    0.175             0.018    0.059    215
       (4.78)     (-7.71)   (2.21)   (-2.62)   (1.72)            (7.77)

10     2.356                0.319    -0.135    0.157             0.012    0.048    215
       (4.81)               (3.45)   (-2.79)   (1.51)            (4.84)

11     1.629                0.291                                         0.010    215
       (5.29)               (2.49)
            Do they perform differently across months:
                                                      Month-of-the-Year Effect

 Month      Intercept   Misp       Size      B/M      Ret-12    Adj-R2   No.
                                                                         Obs
 January     8.961      -0.062    -0.811    0.440      0.011    0.076    18
             (5.91)     (-6.14)   (-9.16)   (1.89)     (1.22)

February     4.229      -0.034    -0.208    0.544      0.019    0.065    18
             (1.82)     (-2.03)   (-1.07)   (1.11)     (2.25)

 March       3.727      -0.026    -0.357    0.580      0.022    0.050    18
             (2.61)     (-2.44)   (-2.69)   (1.62)     (3.15)

  April      2.571      -0.019    -0.170    0.301      0.021    0.049    18
             (1.46)     (-1.84)   (-0.77)   (1.82)     (2.93)

  May        3.792      -0.039    -0.317    0.249      0.013    0.044    18
             (2.69)     (-3.44)   (-1.88)   (0.73)     (2.23)

  June       2.231      -0.017    -0.060    0.564      0.022    0.046    18
             (1.91)     (-1.73)   (-0.49)   (1.59)     (2.28)

  July       1.389      -0.029    -0.083    0.160      0.023    0.055    18
             (0.98)     (-2.33)   (-0.50)   (0.44)     (3.50)

 August      1.980      -0.048    0.125     0.101      0.012    0.060    18
             (0.60)     (-3.69)   (0.61)    (0.22)     (1.62)

September    2.042      -0.023    -0.221    0.042      0.008    0.057    18
             (1.41)     (-3.02)   (-1.65)   (0.09)     (0.69)

 October     -0.417     -0.013    0.092     0.163      0.032    0.046    18
             (-0.26)    (-1.13)   (0.68)    (0.47)     (4.16)

November     -0.036     -0.031    -0.067    -0.019     0.022    0.062    18
             (-0.01)    (-2.43)   (-0.25)   (-0.04)    (2.30)

December     0.226      -0.028    0.127     0.173      0.024    0.041    18
             (0.18)     (-3.21)   (0.94)    (0.56)     (2.64)
           Forming 2-dimensional Portfolios

 Take mispricing - size quintile portfolios as an example

 Step 1: for each month, sort all stocks into 5 quintiles
  according to their Mispricing levels. Independently, sort all
  stocks into 5 firm-size quintiles.

 Step 3: intersections of the 5 Mispricing and 5 size quintiles
  result in 25 portfolios, for each month.

 Step 3: average monthly return and volatility are then
  calculated for each Mispricing-size sorted portfolio.

 All sorting and portfolio formations are out of sample.
Investment Performance by Mispricing & Size
              Monthly Returns on Mispricing--Size Sorted Portfolios




                                                                                                  2.5



                                                                                                2




                                                                                                        Monthly Return (%)
                                                                                                1.5


                                                                                               1


                                                                                               0.5

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Investment by Mispricing & Book/market

   Monthly Returns on Mispricing--Book/Market Sorted Portfolios




                                                                                             3


                                                                                             2.5




                                                                                                    Monthly Return (%)
                                                                                            2

                                                                                            1.5


                                                                                            1


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Investment by Mispricing & Momentum
     Monthly Returns on Mispricing--Momentum Sorted Portfolios



                                                                                          3.5

                                                                                        3




                                                                                                Monthly Return (%)
                                                                                        2.5

                                                                                       2

                                                                                       1.5

                                                                                       1

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           Alpha & Beta: for Mispricing & Momentum portfolios
•   All the portfolios here are same as in preceding chart, based on Mispricing &
    Momentum.


                                                                                                2

                                                                                                1.5

                                                                                                1




                                                                                                       Monthly Alpha (%)
                                                                                                0.5

                                                                                               0

                                                                                               -0.5

                                                                                               -1

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                                LMS Mispricing & Momentum
•   Fair value in the V/P ratio is determined by the LMS residual-income model, where

    book value, EPS estimates and CAPM-based expected returns are used as the basis.
                     Monthly Returns on LMS V/P Ratio--Momentum Sorted Portfolios



                                                                                                  3


                                                                                               2.5




                                                                                                      Monthly Return (%)
                                                                                               2


                                                                                              1.5


                                                                                              1


                                                                                              0.5
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         Investment by Mispricing & Sharpe Ratio
Sharpe ratio is based on the stock’s past-5-yr average return divided by its volatility. It measures
the risk-return tradeoff offered by the stock, hence representing “quality”. Not shown in this
figure is that in each given Mispricing group, the higher the Sharpe ratio, the lower the portfolio’s
volatility.
                          Monthly Returns on Mispricing--Sharpe Ratio Sorted Portfolios


                                                                                                              4

                                                                                                          3.5

                                                                                                          3




                                                                                                                    Monthly Return (%)
                                                                                                          2.5

                                                                                                          2

                                                                                                          1.5

                                                                                                          1

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                                                                       )
                            g




                                                                                                   Sh
       Forecasting the Stock Market
The “% of Undervalued Stocks” path indicates the then-current percentage of stocks that were
undervalued at the time, relative to the entire stock universe. The other path is the then-1-yr-
forward return on the S&P 500 index.

                                                                                                      % of Stocks Undervalued
100%
                                                                                                      1-Yr. Forw ard S&P 500 Return

70%

40%

10%

-20%

-50%
           7911
                  8010
                         8109
                                8208
                                       8307
                                              8406
                                                     8505
                                                            8604
                                                                   8703
                                                                          8802
                                                                                 8901
                                                                                        8912
                                                                                               9011
                                                                                                        9110
                                                                                                               9209
                                                                                                                      9308
                                                                                                                             9407
                                                                                                                                    9506
                                                                                                                                           9605
                                                                     Date
                 Concluding Remarks
 BCD Mispricing is strongly mean-reverting

     overvalued => undervalued => overvalued => undervalued …..


 BCD Mispricing shows persistent winner-loser reversals (once
  every 1.5 years or so)

 The winning strategy:


     “ BCD Valuation + Momentum + Size ”

				
DOCUMENT INFO
Description: Residual Income Model document sample