1	Appraising the US Stock Market With PB-ROE
2	If A Bubble, What Kind Was It? Irrational exuberance? Exaggerated accounting profits? Temporary high profitability?
3	What The Gurus Said -- I The momentum gets rolling: Jeremy Siegel (1994) – “increasing recognition by investors of the superior past performance of equities.” Alan Greenspan (1996) -- “How do we know when irrational exuberance has unduly escalated asset values….” David Dreman (1996) – There is an impressive and growing body of evidence demonstrating that investors and speculators don’t necessarily learn from experience.” Marty Zweig (1997) – “The major direction of the market is dominated by Federal Reserve policy and the movement of interest rates….” “Never fight the tape.”
4	What The Gurus Said -- II Momentum tops out: Jeremy Siegel (1999) – JPM article “The Shrinking Equity Premium.” Elaine Garzarelli (2000) – predicts Dow 12500 in 6 months because of loosening of interest rates by the Federal Reserve. Ed Yardeni (2000) – “[Dow] 15000 by 2005 looks like a fairly unambitious forecast at this point.” Byron Wien (2000) – “there is too much complacency. People say they are worried, but nobody is doing anything about it.”
5	What The Gurus Said -- III After some decline: Jeremy Siegel (2001) -- “I think we can think of March and April as the bottom.” With interest rates going down, I wonder where investors are really going to put their money.” The Motley Fool (2001) – “We’re going to buck up in the hopes that 2002 will certainly be better.” Abby Cohen (Jan 2002) – “The bear market is over for all intents and purposes.”
6	What The Gurus Said -- IV After more decline: Warren Buffett (2002) – “If there is a special place in hell they’re saving for anyone, I think they ought to use it up on the people that really got very rich and all their investors have their savings wiped out.” Barton Biggs (2002) -- “My guess is that the bearishness and selling have been somewhat overdone.” David Dreman (2002) – “I think we’ve come out of the worst bubble in history, including the classic ones that have been written about like the tulip mania.
7	The Big Picture Not just an inability to forecast… But valuation models that are too simplistic (normal p/e, some EVA), Or with uncertain, unmeasurable ingredients (most DDM’s), Or too detailed to estimate with available data (some EVA and CFROI models?), Leaving enormous uncertainty as to how much of price moves are based on market psychology and deceptive profit reporting.
8	A PB-ROE Model …
9	A Stock Valuation Model is Good … For control When we just need to know cause and effect Application: government, corporate policy For prediction To separate causes you can predict from those you can not predict Application: research focus To identify residuals that have predictive value for returns Application: trades
10	Wilcox’s History of PB-ROE I used it in the late 1970’s as a management consulting tool for companies interested in improving their stock price. Developed derivation only after noticing occasional linear relationships between P/B and ROE. 1984 FAJ article proposed PB-ROE as a means of focusing investment research. From early 1990’s used by several investment firms to exploit negative autocorrelation in cross-sectional residuals as a stock or country selection ingredient. This is my first effort to apply it to S&P500 time series. There is now enough available data.
11	The Industry Cross-sectional Case: (log PB often near-linear with ROE)
12	Before Tackling Our Market Analysis, Note For Effective Use of PB-ROE: Must get over thinking book value is less accurate than reported earnings! R-Squared irrelevant, look at dispersion of pricing errors. Approximate linear relationship between PB and expected return on equity. Instead, we measure current and past ROE. Dividend, required return and investment horizon are additional variables. PB-ROE models work best where range of complicating variables is tight: Required return based on risk characteristics and interest rate levels Investment horizon before return on equity reverts to mean Dividend policy Differences between current and expected ROE, as within an homogeneous industry.
13	Understanding PB-ROE’s Pros and Cons for Time-Series For time-series use, note that required return changes dramatically with inflation and real interest rates. Also, we will not have an industry context to provide a large-sample frame of reference. Derivation Documentation of PB-ROE: 1) At any point in time, k = ΔP/P + D/P Where k is required expected shareholder return P is price, D is dividend 2) We can choose any measurable accounting entity, in this case B, book value, to decompose ΔP. B has better growth forecasting properties than does earnings. 3) ΔP = ΔB * (P/B) + B * Δ(P/B) + ΔB * Δ(P/B) The compound difference on the right will vanish as we go to a differential equation form.
14	Derivation Documentation – II Differential Equation from 1) & 3): 4) (P/B)(k-g) = d (P/B)/ dt + δ Where δ is D/B and g is expected growth in B Note expected return on equity is r = g + δ. Boundary Condition: 5) At a time horizon t=T, g + δ assumed to revert to a normal value k, having been constant until that time, and P/B will have reached a normal value N. Exact Solution: 6) P/B = [δ/(k-g)][1 - e^(g-k)T] + N e^(g-k)T Where e is the natural constant 2.718 ….
15	Derivation Documentation – III In contrast to the Gordon model δ/(k-g), here we can express the exponential on the left as an infinite Taylor series and divide out the troublesome (k-g): 7) P/B = δ[T + (g-k)T²/2 + …] + Ne^(g-k)T The functional relationship of P/B to δ + g, or r, is nearly the same if we assume P/B at time T is N=1. Expressing the right-hand exponential as a second Taylor series, and combining: 8) P/B = 1 + (r-k)T + (r-k)(g-k)T²/2 + …. Again, if δ, or r-g, is small, step 8) approximates the Taylor series for: 9) P/B = e^(r-k)T
16	Empirical Measurement - I Unlike past earnings growth as a measure of expected earnings growth, accounting ROE is a fair indicator of future ROE and thus of r. Consequently … The slope of a cross-sectional regression line between log P/B and ROE can be used as a measure of typical time horizon T. Horizontal scatter from this best fit line can tell us about specific ROE-r. Differences in the intercept may tell us something about changes in required shareholder return k.
17	S&P 500 Time-Series Study Data Sources Barra: S&P500 monthly total returns, S&P500 monthly P/B, cap-weighted E/P, cap-weighted B/P, cap-weighted ROE, where net income E and ROE are based on 12 month net income before extraordinary items. St. Louis Federal Reserve: 12-month CPI inflation rate, seasonally adjusted, Moody’s seasoned Aaa corporate bond yield. Value Line Database: individual stock pricing and fundamental data.
18	Excess Aggregate GAAP Net Income Before GAAP Extraordinary Items
19	Empirical Measurement -- II Given PB-ROE’s assumptions, increasing disparity of individual company expected ROE’s … Will increase the market value of the aggregate, Even though there is no change in aggregate income or aggregate book value. The appropriate aggregate ROE estimate is intermediate between capitalization-weighted and book-weighted ROE averages.
20	Increasing Profitability Concentration
21	ROE Measure Should Reflect Growing Profit Inequality
22	What Required Shareholder Return?
23	Estimated Excess Profit Inputs
24	Statistical Challenges Same Variables on Both Sides Book value in P/B, ROE. Some change in P/B implied in EstROE weighting. Really need iterative model. Autocorrelation of Residuals Inevitable for an irrational bubble, but sign of missing variables. Multicollinearity between inflation and real interest. PB-ROE applied to time-series market valuation: Useful measures of statistical significance and confidence intervals require non-parametric methods. Absent these, estimated model structure requires strong prior if used to guide research. Expanding window residuals can be rigorously tested as return predictors. EstROE is superior to book-weighted ROE.
25	Full Sample Regression
26	Full Sample Explanation
27	Expanding Window Models Based on 2 Year Start-Up Period
28	Evidence of Rising Norms
29	Lagged Residual Has Modest Monthly Return Predictive Power
30	The Correlation Is Robust
31	Conclusion -- I PB-ROE & The S&P500 The PB-ROE valuation model can be successfully used to better understand market valuation time-series for use both in regulation and investment research focus. For market-timers, even when all forward-looking information is removed, it has a modest monthly predictive power. Comparisons with the various “Fed” models are welcomed.
32	Conclusion – II, Bubble Anatomy Most of the “bubble” can be explained by fundamentals of GAAP reported ROE (before true extraordinary items), interest rate and inflation rates. The big bubble may lie in a cycle of unsustainable reported profits, as well as temporary extremes of profit inequality. However, superimposed were: A long-term upward trend in valuation that may have been based on declining risk or lower effective taxation, possibly through use of pension funds and 401K plans. Unexplained aggregate excess pricing on the order of 35% from 1999 through mid-2002. Overall excess pricing during a period of decline was striking. It is this part that seems a market psychology, or speculative, bubble. As of early 2003, there is no longer significant evidence of speculative over-valuation or under-valuation relative to GAAP reporting and current interest rates and inflation.