A New Model for Stock Valuation

Zhiwu ChenProfessor of Finance, Yale University

Co-Chairman, ValuEngine Inc.

The ValuEngine™ Stock-Valuation Model

Based on recent research by Bakshi & Chen (1997), Chang, Chen & Dong (1998) …

Applying the methodology from bond valuation & options pricing (e.g., the Vasicek, the Cox-Ingersoll-Ross models, the Black-Scholes, …)

The ValuEngine™ 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

The Formula

Research Findings

Mispricing Distribution Across Stocks

0%

5%

10%

15%

20%

25%

-55% -45% -35% -25% -15% -5% 5% 15% 25% 35% 45% 55%Under- to overvaluation

Model Valuation and Average Return

0%

10%

20%

30%

40%

Ave

rage

Ret

urn

-55%

-45%

-35%

-25%

-15% -5%

5% 15%

25%

35%

45%

55%

Mispricing

Understanding Valuation Measures

Behavior of Book/Market Ratio over Time

Average BE/ME by Quartiles

0

1

2

7901

7912

8011

8110

8209

8308

8407

8506

8605

8704

8803

8902

9001

9012

9111

9210

9309

9408

9507

9606

Date

BE/M

E

Q1 (low )Q2Q3Q4(high)

• 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.

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.

Average E/P Ratios by Quartiles

-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)

Behavior of ValuEngine Model Mispricing

• This figure shows the average ValuEngine 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!

Reversals of Mispricing Across Quartiles

-40

-20

0

20

40

60

7901

8003

8105

8207

8309

8411

8601

8703

8805

8907

9009

9111

9301

9403

9505

9607

Date

Mis

pricin

g(%

)||

Q1 (undervalued)Q2Q3Q4 (overvalued)

Q1

Q4

Q1

Q4Q1

Q4

Q1

Q4

Applying ValuEngine™ : Back-Test Results

ValuEngine™ Strategy One: focus on absolute valuation

• Buy stocks that are undervalued by more than 10% and with a momentum rank higher than 70.

• Sell a stock if it becomes at least 10% overvalued or has a momentum rank below 60.

ValuEngine™ vs S&P 500

-20%

0%

20%

40%

60%

80%

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

Year

Ann

ual R

etur

n

Valu-Engine

S&P 500

Investment Styles and Performance

24%

28%26%

19%

23%21%

15%

24%

20%

17%

20%19%

17% 18% 17%

0%

20%

40%

1980s 1990s 1980s-1990s

Year

Ave

rage

Ret

urn

Valu-EngineLow P/ESmall CapTop MomentumS&P 500

Investment Styles and Growth

$0

$5

$10

$15

$20

$25

$30

1982 1984 1986 1988 1990 1992 1994 1996 1998

Year

Dol

lars

(in

Mill

ions

)

Valu-Engine

Low P/E

Small Cap

Top Momentum

S&P 500

ValuEngine™ Strategy Two: focus on relative-valuation

• Buy Criteria: stock must have a mispricing rank and a momentum rank greater than 70 (on a 1-100 scale).

• Sell Criteria: mispricing or momentum rank falls below 60.

Style One: combining ValuEngine™ mispricing with size

0

0.5

1

1.5

2

2.5

Mo

nth

ly R

etu

rn (

%)

Monthly Returns on Mispricing--Size Sorted Portfolios

Style 2: combining ValuEngine™ mispricing with Book/Market

0

0.5

1

1.5

2

2.5

3

Mo

nth

ly R

etu

rn (

%)

Monthly Returns on Mispricing--Book/Market Sorted Portfolios

Style 3: combining ValuEngine™ mispricing with momentum

0

0.5

1

1.5

2

2.5

3

3.5

Mo

nth

ly R

etu

rn (

%)

Monthly Returns on Mispricing--Momentum Sorted Portfolios

Alpha & Beta: for Mispricing & Momentum portfolios

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

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Mo

nth

ly A

lph

a (

%)

Residual-Income Model Mispricing & Momentum

Mispricing in this chart is determined by the residual-earnings model as implemented in Lee, Myers and Swaminathan (1998), where book value, EPS estimates, and CAPM-like expected returns are used as the basic inputs. Then, the mispricing quintiles are constructed and sorted accordingly.

0

0.5

1

1.5

2

2.5

3

Mo

nth

ly R

etu

rn (

%)

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

Using ValuEngine™ to Forecast the Stock Market

Percentage of Undervalued Stocks vs 1-Year-Forward S&P 500 Returns

-50%

-20%

10%

40%

70%

100%79

11

8010

8109

8208

8307

8406

8505

8604

8703

8802

8901

8912

9011

9110

9209

9308

9407

9506

9605

Date

% of Stocks Undervalued

1-Yr. Forw ard S&P 500 Return

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.

Conclusions

– The best investment strategy:

Combine ValuEngine valuation with momentum!

– Hot and Cold stock groups switch every few

years

ValuEngine Inc.

• Specializing in putting theory to investment practice

• Providing stock valuation and equity analytical tools

ValuEngine Inc.Two Stamford Plaza, Suite 1550281 Tresser Blvd.Stamford, CT 06901(203) 335-0550