Stock Selection Models Slides

8/8/2019 Stock Selection Models Slides

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Investing with a Stock Valuation Model

Zhiwu Chen, Yale University

Ming Dong, Ph.D. candidate, OSU


2/30

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


3/30

Motivation: why not expected-return models? The CAPM, APT and other multi-factor models all focus on

EXPECTED FUTURERETURNs

Stock-Selection Idea: if the actual expected return on IBM is higher

than its deserved expected return, then IBM is a buy (hence, JensensAplha)

But, what is IBMs actual expected 1-yr-forward return today? -----

You cannot observe it!

Conclusion: you cannot really apply such expected-return models.


4/30

Motivation: why stock-valuation models? There is always a market price for each stock !

Stock-Selection Idea: if IBMs 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?


5/30

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 firms 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.


6/30

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 yields parameters:

Its long-run level

Interest-rate volatility

Duration of interest-rate cycle


7/30

Comparison The BCD Model

Detailed parameterization of EPS

processes and interest-rate process

Parameters to be estimated from

past data

Closed-form stock valuation

formula

Past data are used to estimate

parameters

So, valuation reflects both past

valuation standard for the stock

and the stochastic discounting of

future prospects

The Residual-Earnings Model(e.g., Lee, Meyer and Swaminathan (1998))

Two parameters: beta anddividend-payout ratio

No closed-form valuation formula.

Requires ad hoc approximation of

the stocks future price at end offorecasting horizon

Valuation is independent of past

valuation standard for the stock


8/30

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)


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What Constitutes a Good Stock-Selection Measure?

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

Not too persistent, e.g., if book/market ratio is too persistent, you willnot 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


10/30

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

0

1

2

7901

7912

8011

8110

8209

8308

8407

8506

8605

8704

8803

8902

9001

9012

9111

9210

9309

9408

9507

9606

Date

B/M

Q1 (low)

Q2

Q3

Q4(high)


11/30

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.

Part A: Average V/P Ratio by Quartile

0

1

2

7902

8001

8012

8111

8210

8309

8408

8507

8606

8705

8804

8903

9002

9101

9112

9211

9310

9409

9508

9607

Date

V/P

Q1(low)

Q2

Q3

Q4(high

Part B:V/P Autocorrelation for the Lowest Q uartile

-0.5

0

0.5

1

1 5 913

17

21

25

29

33

37

41

45

49

53

57

Number of Months Lagged

Au

tocorre

lat

ion


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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

-0.1

-0.05

0

0.05

0.1

0.15

0.2

7901

8002

8103

8204

8305

8406

8507

8608

8709

8810

8911

9012

9201

9302

9403

9504

9605

Date

E/P

Ratio

Q1(low )Q2Q3Q4(high)


13/30

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 stocks

current model price (out of sample)

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

Thus, a negative mispricing means an undervalued stock, and

so on.


14/30

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

-25

-15

-5

5

15

25

35

7901

7911

8009

8107

8205

8303

8401

8411

8509

8607

8705

8803

8901

8911

9009

9107

9205

9303

9401

9411

9509

9607

Date

Mispric

ing(

Q1 (undervalued)

Q2

Q3

Q4 (overvalued)


15/30

Persistence of BCD Model Mispricing

Part A: Mispricing Autocorrelation

for the Most Undervalued Quartile

-0.6

-0.2

0.2

0.6

1

1 5 913

17

21

25

29

33

37

41

45

49

53

57

Number of Months Lagged

Autocorrelation

Part B: Distribution of Mispricing Mean-Reversion Time

Full Sample

0

1

2

3

4

5

6

7

8

9

10

3 5 7 911 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Mean-Reversion Time in Months

PercentofStock


16/30

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.


17/30

Try to Understand the Measures AgainPanel A: Mispricing portfolios (based on Misp)

MP1 MP2 MP3 MP4 MP5 All Stocks

Misp (%) -19.63 -4.96 2.58 10.59 30.67 3.86V/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 1643.3B/M 0.89 0.81 0.75 0.71 0.69 0.77Ret-6 (%) -7.51 3.03 9.26 15.61 27.86 9.65Ret+1 (%) 2.04 1.83 1.53 1.31 1.18 1.67Ret+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 0.93Misp (%) 9.92 5.78 3.11 1.49 -0.97 3.86

ME ($Millions) 1189.4 1841.8 2187.1 1958.2 1343.8 1643.3B/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 9.65Ret+1 (%) 1.33 1.27 1.50 1.59 1.87 1.67Ret+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


18/30

Try to Understand the Measures

One More TimePanel 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 9.65Misp (%) -8.92 -1.41 3.24 8.10 18.26 3.86

V/P 0.93 0.98 0.97 0.92 0.82 0.93ME ($Millions) 1020.9 1681.4 1975.6 2084.1 1452.8 1643.3B/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 1.67Ret+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: /M portfolios

BM1 BM2 BM3 BM4 BM5 All Stocks

B/M 0.25 0.45 0.66 0.89 1.61 0.77Misp (%) 9.86 4.52 2.89 1.72 0.30 3.86

V/P 0.67 0.83 0.97 1.09 1.11 0.93ME ($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 9.65Ret+1 (%) 1.52 1.48 1.37 1.56 1.95 1.67Ret+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


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Predictive Power for Future Returns

From the regression tables,

BCD Model Mispricing has the highest predictive power (forfuture 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


20/30

Regressions of 1-month-forward Stock Returns on predictive variables

No. Intercept Misp V/P Size B/M Ret-6 Ret-12 Adj-R 2 No.Obs.

1 2.404(4.82)

-0.029(-8.97)

-0.142(-2.79)

0.130(1.16)

0.021(5.91)

0.051 216

2 2.357(4.62)

-0.138(-2.69)

0.162(1.42)

0.009(2.48)

0.042 216

3 2.475(4.92)

-0.031(-9.17)

-0.151(-2.96)

0.275(2.53)

0.019(7.99)

0.054 216

4 2.485(4.81)

-0.152(-2.96)

0.292(2.68)

0.012(4.90)

0.044 216

9 2.278(4.78) -0.029(-7.71) 0.211(2.21) -0.126(-2.62) 0.175(1.72) 0.018(7.77) 0.059 215

10 2.356(4.81)

0.319(3.45)

-0.135(-2.79)

0.157(1.51)

0.012(4.84)

0.048 215

11 1.629(5.29)

0.291(2.49)

0.010 215


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Do they perform differently across months:

Month-of-the-YearEffect

M o n t h I n t e r c e p t M i s p S i z e B / M R e t - 1 2 A d j - R 2 N o .O b s

J a n u a r y 8 . 9 6 1

( 5 . 9 1 )

- 0 . 0 6 2

( - 6 . 1 4 )

- 0 . 8 1 1

( - 9 . 1 6 )

0 . 4 4 0

( 1 . 8 9 )

0 . 0 1 1

( 1 . 2 2 )

0 . 0 7 6 1 8

F e b r u a r y 4 . 2 2 9( 1 . 8 2 )

- 0 . 0 3 4( - 2 . 0 3 )

- 0 . 2 0 8( - 1 . 0 7 )

0 . 5 4 4( 1 . 1 1 )

0 . 0 1 9( 2 . 2 5 )

0 . 0 6 5 1 8

M a r c h 3 . 7 2 7( 2 . 6 1 ) - 0 . 0 2 6( - 2 . 4 4 ) - 0 . 3 5 7( - 2 . 6 9 ) 0 . 5 8 0( 1 . 6 2 ) 0 . 0 2 2( 3 . 1 5 ) 0 . 0 5 0 1 8

A p r i l 2 . 5 7 1( 1 . 4 6 )

- 0 . 0 1 9( - 1 . 8 4 )

- 0 . 1 7 0( - 0 . 7 7 )

0 . 3 0 1( 1 . 8 2 )

0 . 0 2 1( 2 . 9 3 )

0 . 0 4 9 1 8

M a y 3 . 7 9 2

( 2 . 6 9 )

- 0 . 0 3 9

( - 3 . 4 4 )

- 0 . 3 1 7

( - 1 . 8 8 )

0 . 2 4 9

( 0 . 7 3 )

0 . 0 1 3

( 2 . 2 3 )

0 . 0 4 4 1 8

J u n e 2 . 2 3 1( 1 . 9 1 )

- 0 . 0 1 7( - 1 . 7 3 )

- 0 . 0 6 0( - 0 . 4 9 )

0 . 5 6 4( 1 . 5 9 )

0 . 0 2 2( 2 . 2 8 )

0 . 0 4 6 1 8

J u l y 1 . 3 8 9

( 0 . 9 8 )

- 0 . 0 2 9

( - 2 . 3 3 )

- 0 . 0 8 3

( - 0 . 5 0 )

0 . 1 6 0

( 0 . 4 4 )

0 . 0 2 3

( 3 . 5 0 )

0 . 0 5 5 1 8

A u g u s t 1 . 9 8 0( 0 . 6 0 )

- 0 . 0 4 8( - 3 . 6 9 )

0 . 1 2 5( 0 . 6 1 )

0 . 1 0 1( 0 . 2 2 )

0 . 0 1 2( 1 . 6 2 )

0 . 0 6 0 1 8

S e p t e m b e r 2 . 0 4 2( 1 . 4 1 )

- 0 . 0 2 3( - 3 . 0 2 )

- 0 . 2 2 1( - 1 . 6 5 )

0 . 0 4 2( 0 . 0 9 )

0 . 0 0 8( 0 . 6 9 )

0 . 0 5 7 1 8

O c t o b e r - 0 . 4 1 7

( - 0 . 2 6 )

- 0 . 0 1 3

( - 1 . 1 3 )

0 . 0 9 2

( 0 . 6 8 )

0 . 1 6 3

( 0 . 4 7 )

0 . 0 3 2

( 4 . 1 6 )

0 . 0 4 6 1 8

N o v e m b e r - 0 . 0 3 6( - 0 . 0 1 )

- 0 . 0 3 1( - 2 . 4 3 )

- 0 . 0 6 7( - 0 . 2 5 )

- 0 . 0 1 9( - 0 . 0 4 )

0 . 0 2 2( 2 . 3 0 )

0 . 0 6 2 1 8

D e c e m b e r 0 . 2 2 6

( 0 . 1 8 )

- 0 . 0 2 8

( - 3 . 2 1 )

0 . 1 2 7

( 0 . 9 4 )

0 . 1 7 3

( 0 . 5 6 )

0 . 0 2 4

( 2 . 6 4 )

0 . 0 4 1 1 8


22/30

Forming 2-dimensional Portfolios

Take mispricing - size quintile portfolios as an example

Step 1: for each month, sort all stocks into 5 quintilesaccording 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.


23/30

Investment Performance by Mispricing & Size

MP1(und

ervalued)

MP3

MP5(ove

rvalued) S1(sm

all)

S2

S3

S4

S5(large)

0

0.5

1

1.5

2

2.5

MonthlyReturn(%

Mispricing

Size

Monthly Returns on Mispricing--Size Sorted Portfolios


24/30

Investment by Mispricing & Book/market

MP1(und

ervalued)

MP3

MP5(ove

rvalued)

BM1(low

)

BM2

BM3

BM4

BM5(high)

0

0.5

1

1.5

2

2.5

3

MonthlyReturn(%

Mispricing

B/MRa

tio

Monthly Returns on Mispricing--Book/Market Sorted Portfolios


25/30

Investment by Mispricing & Momentum

MP1(und

ervalued)

MP3

MP5(ove

rvalued) M

O1(low

)

MO2

MO3

MO4

MO5(high)

0

0.5

1

1.5

2

2.5

3

3.5

MonthlyReturn(%)

Mispricing

Momentu

m

Monthly Returns on Mispricing--Momentum Sorted Portfolios


26/30

Alpha & Beta: for Mispricing & Momentum portfolios

All the portfolios here are same as in preceding chart, based on Mispricing &

Momentum.

MP1(un

dervalue

d)

MP3

MP5(ove

rvalued)

MO1(

low)

MO2

MO3

MO4

MO5(high)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

MonthlyAlpha(

Mispricing

Momentu

m


27/30

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.

VP1(l w

)

VP3VP5

(hih)

O1(l

w)

OO3

MO

MO5(hi

h)

5

1

1.5

2

2.5

3

MonthlyReturn(

V/P

Ratio

Momentu

m

Monthly Returns on LMS V/P Ratio--Momentum Sorted Portfolios


28/30

Investment by Mispricing & Sharpe Ratio

MP1(und

ervalued

)

MP3

MP5(ove

rvalued)

SP1(lo

w)

SP2

SP3

SP4

SP5(h

igh)

0

0.5

1

1.5

2

2.5

3

3.5

4

MonthlyReturn(%

Misp

ricingSh

arpeR

atio

Monthly Returns on Mispricing--Sharpe Ratio Sorted Portfolios

Sharpe ratio is based on the stocks 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 portfolios

volatility.


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Forecasting the Stock MarketThe % 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.

-50%

- 0%

10%

0%

0%

100%

11

010

1 0 0 0 0

505

0 0 0 01

1011

110

0 0 05 0 0

5

Date

% of Stocks Undervalued

1-Yr. Forw ard S&P 500 Return


30/30

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

Documents

Stock Selection Models Slides