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1、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 businessNo attention pa
2、id to how the stock has historically been valued by marketFair 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 gro
3、wth rate Duration of business-growth cycle Systematic or beta risk of the firm Correlation between the firms EPS and the interest-rate environment 30-yr Treasury yields parameters:Its long-run level Interest-rate volatility Duration of interest-rate cycle,Comparison,The BCD ModelDetailed parameteriz
4、ation of EPS processes and interest-rate processParameters to be estimated from past dataClosed-form stock valuation formulaPast data are used to estimate parametersSo,valuation reflects both past valuation standard for the stock and the stochastic discounting of future prospects,The Residual-Earnin
5、gs Model(e.g.,Lee,Meyer and Swaminathan(1998)Two parameters:beta and dividend-payout ratioNo closed-form valuation formula.Requires ad hoc approximation of the stocks future price at end of forecasting horizonValuation is independent of past valuation standard for the stock,Data,I/B/E/S,CRSP,and Com
6、pustatFuture EPS forecasts:consensus analyst estimatesPeriod covered:Jan.1979-Dec.1996Stock 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
7、 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-reversionHigh predictive power of future stock performance,Behavior of Book/Market Ratio over Time,This figure shows the average B/M ratio path for e
8、ach quartile obtained by sorting all stocks according to their B/M ratios as of January 1990.,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.,Behavior
9、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.,BCD Model Mispricing,Step 1:use past 2-yr data to e
10、stimate model parameters for the stockStep 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 priceThus,a negative mispricing means an undervalued stock,and so on.
11、,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!,Persistence of BCD Model Mi
12、spricing,A Small Summary,BCD Model mispricing is the least persistent over time and mean-reverting the fastestIt takes about 1.5 years for a group of stocks to go from most over-to most underpriced,or the reverseP/E ratio is the second least persistent.High P/E stocks do not always have the highest
13、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,Try to Understand the Measures One More Time,Predictive Power for Future Returns,From the regression tables,BCD Model Mispricing h
14、as 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 pr
15、edictive variables,Do they perform differently across months:Month-of-the-Year Effect,Forming 2-dimensional Portfolios,Take mispricing-size quintile portfolios as an exampleStep 1:for each month,sort all stocks into 5 quintiles according to their Mispricing levels.Independently,sort all stocks into
16、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 Per
17、formance by Mispricing&Size,Investment by Mispricing&Book/market,Investment by Mispricing&Momentum,Alpha&Beta:for Mispricing&Momentum portfolios,All the portfolios here are same as in preceding chart,based on Mispricing&Momentum.,LMS Mispricing&Momentum,Fair value in the V/P ratio is determined by t
18、he LMS residual-income model,where book value,EPS estimates and CAPM-based expected returns are used as the basis.,Investment by Mispricing&Sharpe Ratio,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,he
19、nce representing“quality”.Not shown in this figure is that in each given Mispricing group,the higher the Sharpe ratio,the lower the portfolios volatility.,Forecasting the Stock Market,The“%of Undervalued Stocks”path indicates the then-current percentage of stocks that were undervalued at the time,re
20、lative to the entire stock universe.The other path is the then-1-yr-forward return on the S&P 500 index.,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”,
