Motivation: Motivation: existing stock valuation existing stock valuation modelsmodels

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

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

No structural parameterization of the firm’s businessNo structural parameterization of the firm’s business

No attention paid to how the stock has historically been valued No attention paid to how the stock has historically been valued

by marketby market

Fair values determined by these models are too often below Fair values determined by these models are too often below

market price. market price.

The Bakshi-Chen-Dong (BCD) The Bakshi-Chen-Dong (BCD) ModelModel

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

Firm-specific parameters:Firm-specific parameters: EPS growth volatility EPS growth volatility

Long-run EPS growth rate Long-run EPS growth rate

Duration of business-growth cycle Duration of business-growth cycle

Systematic or beta risk of the firm Systematic or beta risk of the firm

Correlation between the firm's EPS and the interest-rate environmentCorrelation between the firm's EPS and the interest-rate environment

30-yr Treasury yield’s parameters:30-yr Treasury yield’s parameters: Its long-run levelIts long-run level

Interest-rate volatility Interest-rate volatility

Duration of interest-rate cycleDuration of interest-rate cycle

ComparisonComparison

The BCD ModelThe BCD Model

• Detailed parameterization of Detailed parameterization of EPS processes and interest-EPS processes and interest-rate processrate processParameters to be estimated Parameters to be estimated from past datafrom past data

• Closed-form stock valuation Closed-form stock valuation formulaformula

• Past data are used to Past data are used to estimate parametersestimate parametersSo, valuation reflects both So, valuation reflects both past valuation standard for past valuation standard for the stock and the stochastic the stock and the stochastic discounting of future discounting of future prospectsprospects

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

• Two parameters: beta and Two parameters: beta and dividend-payout ratiodividend-payout ratio

• No closed-form valuation No closed-form valuation formula. Requires ad hoc formula. Requires ad hoc approximation of the approximation of the stock’s future price at end stock’s future price at end of forecasting horizonof forecasting horizon

• Valuation is independent of Valuation is independent of past valuation standard for past valuation standard for the stockthe stock

DataData

I/B/E/S, CRSP, and CompustatI/B/E/S, CRSP, and Compustat

Future EPS forecasts: consensus analyst estimatesFuture EPS forecasts: consensus analyst estimates

Period covered: Jan. 1979 - Dec. 1996Period covered: Jan. 1979 - Dec. 1996

Stock universe: about 2500 U.S. stocks Stock universe: about 2500 U.S. stocks (mostly large (mostly large cap)cap)

What ConstitutesWhat Constitutes a a Good Stock-Selection Good Stock-Selection MeasureMeasure??

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

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

High predictive power of future stock performanceHigh predictive power of future stock performance

Behavior of Book/Market Ratio over Behavior of Book/Market Ratio over TimeTime

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

Average B/M by Quartile

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Behavior of LMS Value/Price over Behavior of LMS Value/Price over TimeTime

This figure shows the average Lee-Myers-Swaminathan V/P ratio path for each 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. quartile obtained by sorting all stocks according to their V/P as of January 1990.

Part A: Average V/P Ratio by Quartile

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Part B:V/P Autocorrelation for the Lowest Quartile

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Behavior of E/P RatioBehavior of E/P Ratio

This figure shows the average E/P ratio path for each quartile obtained by 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. 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 You would like to see the qartiles crossing each other over time. Yes, they do to some extent.some extent.

Part A: Average E/P by Quartile

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BCD Model MispricingBCD Model Mispricing

Step 1: Step 1: use past 2-yr data to estimate model use past 2-yr data to estimate model parameters for the stockparameters for the stock

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

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

Thus, a negative mispricing means an undervalued stock, and so Thus, a negative mispricing means an undervalued stock, and so on.on.

Behavior of BCD Model MispricingBehavior of BCD Model Mispricing

This figure shows the average BCD Model mispricing path, for each quartile 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 obtained by sorting all stocks according to their mispricing levels as of January 1990. 1990.

The quartiles switch from over- to undervalued, and vice versa, every few years!The quartiles switch from over- to undervalued, and vice versa, every few years!

Figure 2: Reversals of Mispricing Across Quartiles

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Persistence of BCD Model MispricingPersistence of BCD Model Mispricing

Part A: Mispricing Autocorrelation for the Most Undervalued Quartile

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Part B: Distribution of Mispricing Mean-Reversion Time Full Sample

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A Small SummaryA Small Summary

BCD Model mispricing is the least persistent over BCD Model mispricing is the least persistent over time and mean-reverting the fastesttime and mean-reverting the fastest

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

P/E ratio is the second least persistent. P/E ratio is the second least persistent.

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

B/M and V/P are the most persistent. B/M and V/P are the most persistent. Stocks with the highest B/M seem to be always so. Low B/M Stocks with the highest B/M seem to be always so. Low B/M

stocks seem to always have low B/M.stocks seem to always have low B/M.

Try to Understand the Measures Try to Understand the Measures AgainAgain

Panel A: Mispricing portfolios (based on Misp)

MP1 MP2 MP3 MP4 MP5 All StocksMisp (%) -19.63 -4.96 2.58 10.59 30.67 3.86

V/P 1.00 1.00 0.96 0.90 0.78 0.93ME ($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 0.77Ret-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 StocksV/P 0.41 0.69 0.89 1.11 1.54 0.93

Misp (%) 9.92 5.78 3.11 1.49 -0.97 3.86ME ($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 0.77Ret-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

Try to Understand the MeasuresTry to Understand the Measures One More One More TimeTime

Panel E: Momentum portfolios (based on Ret-6)

MO1 MO2 MO3 MO4 MO5 All StocksRet-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 1643.3

B/M 0.94 0.82 0.77 0.71 0.60 0.77Ret+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: B/M portfolios

BM1 BM2 BM3 BM4 BM5 All StocksB/M 0.25 0.45 0.66 0.89 1.61 0.77

Misp (%) 9.86 4.52 2.89 1.72 0.30 3.86V/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 1643.3Ret-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

Predictive Power for Future Predictive Power for Future ReturnsReturns

From the regression tables, From the regression tables,

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

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

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

Last comes B/M & V/PLast 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(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

Do they perform differently across months: Do they perform differently across months:

Month-of-the-Year EffectMonth-of-the-Year Effect

Month Intercept Misp Size B/M Ret-12 Adj-R2 No.Obs

January 8.961(5.91)

-0.062(-6.14)

-0.811(-9.16)

0.440(1.89)

0.011(1.22)

0.076 18

February 4.229(1.82)

-0.034(-2.03)

-0.208(-1.07)

0.544(1.11)

0.019(2.25)

0.065 18

March 3.727(2.61)

-0.026(-2.44)

-0.357(-2.69)

0.580(1.62)

0.022(3.15)

0.050 18

April 2.571(1.46)

-0.019(-1.84)

-0.170(-0.77)

0.301(1.82)

0.021(2.93)

0.049 18

May 3.792(2.69)

-0.039(-3.44)

-0.317(-1.88)

0.249(0.73)

0.013(2.23)

0.044 18

June 2.231(1.91)

-0.017(-1.73)

-0.060(-0.49)

0.564(1.59)

0.022(2.28)

0.046 18

July 1.389(0.98)

-0.029(-2.33)

-0.083(-0.50)

0.160(0.44)

0.023(3.50)

0.055 18

August 1.980(0.60)

-0.048(-3.69)

0.125(0.61)

0.101(0.22)

0.012(1.62)

0.060 18

September 2.042(1.41)

-0.023(-3.02)

-0.221(-1.65)

0.042(0.09)

0.008(0.69)

0.057 18

October -0.417(-0.26)

-0.013(-1.13)

0.092(0.68)

0.163(0.47)

0.032(4.16)

0.046 18

November -0.036(-0.01)

-0.031(-2.43)

-0.067(-0.25)

-0.019(-0.04)

0.022(2.30)

0.062 18

December 0.226(0.18)

-0.028(-3.21)

0.127(0.94)

0.173(0.56)

0.024(2.64)

0.041 18

Forming 2-dimensional PortfoliosForming 2-dimensional Portfolios

Take mispricing - size quintile portfolios as an exampleTake mispricing - size quintile portfolios as an example

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

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

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

All sorting and portfolio formations are out of sample.All sorting and portfolio formations are out of sample.

Investment Performance by Investment Performance by Mispricing & SizeMispricing & Size

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Investment by Mispricing & Investment by Mispricing & Book/marketBook/market

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Monthly Returns on Mispricing--Book/Market Sorted Portfolios

Investment by Mispricing & Investment by Mispricing & MomentumMomentum

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Monthly Returns on Mispricing--Momentum Sorted Portfolios

Alpha & Beta: Alpha & Beta: for Mispricing & for Mispricing & Momentum portfoliosMomentum portfolios

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

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LMS Mispricing & MomentumLMS Mispricing & Momentum

Fair value in the V/P ratio is determined by the LMS residual-income Fair value in the V/P ratio is determined by the LMS residual-income model, where book value, EPS estimates and CAPM-based expected model, where book value, EPS estimates and CAPM-based expected

returns are used as the basis.returns are used as the basis.

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

Investment by Mispricing & Investment by Mispricing & Sharpe RatioSharpe Ratio

MP1 (undervalued)

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Mispricing

Sharpe Ratio

Monthly Returns on Mispricing--Sharpe Ratio Sorted Portfolios

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.

Forecasting the Stock MarketForecasting 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.

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Concluding RemarksConcluding Remarks

BCD Mispricing is strongly mean-reverting

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

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

The winning strategy: The winning strategy:

“ “ BCD Valuation + Momentum + Size ”BCD Valuation + Momentum + Size ”