1. Required Business Performance®
Methodology
Bjorn N. Jorgensen
Columbia Business School
February 26, 2008
*
Duplication or dissemination prohibited without prior written permission.
FOR INTERNAL USE ONLYFOR INVESTMENT PROFESSIONAL USE ONLY
2. 1. Outline
This paper describes how Transparent Value derives Required Business Performance
(RBP) and RBP Probability (RBPP), which measures the likelihood that future sales will
grow to the level implied from current stock price. The next section briefly summarizes
the literature on valuation and intrinsic equity value estimates. Section 3 describes price-
implied expectations: knowing that prices aggregate diverse sources of public and private
information, investors can use prices to impute expected future performance of key value
drivers. Section 4 describes the process that leads to the RBPP which expresses price-
implied expectations of future sales as a risk-adjusted probability. Section 5 reports
sensitivity analyses for three case studies. Section 6 demonstrates the effect of using the
RBPP for two indexes based on companies in Dow Jones Wilshire 750. Appendix A
provides additional details regarding the methodology and shows the process for
Microsoft. Appendix B demonstrates that an index of RBPP weighting of the Dow 30
companies outperforms the value-weighted Dow 30 index.
2. Intrinsic Firm Value Estimates
Investors can make portfolio choice decisions in many ways: They may (i) generate
measures of intrinsic value of the firm, (ii) base their investment strategy on technical
analysis, or (iii) rely on price momentum or other fundamental signals such as accounting
earnings momentum to guide their investments.1
The intrinsic value approach estimates
what the firm is worth without reference to current stock market value. This intrinsic
value approach presumes that price is what you pay but value is what you get. If intrinsic
firm value exceeds (falls below) current market value, one interpretation is that the firm
is undervalued (overvalued). This section reviews some common ways to derive intrinsic
value of equity.
Estimates of intrinsic value of equity can be derived from dividends, free cash flows,
accounting book values or accounting earnings. First, intrinsic value of equity might be
derived from the expected discounted value of all future dividends of the firm. Many
1
The list of fundamental signals is large as documented by Ou and Penman (1989), Lev and Thiagarajan
(1993) and Abarbanell and Bushee (1997, 1998).
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3. implementations of the dividend discount model presume a terminal value date and
require measuring the anticipated value that a shareholder receives when selling the
shares. Other implementations do not explicitly require a terminal value estimate but
instead make assumptions about dividends in the long run. One common way to capture
terminal value is the Gordon growth model which assumes that earnings grow at the same
rate in perpetuity. Under the Gordon growth model, intrinsic value or terminal value of
equity becomes the ratio of future dividends divided by the difference between the
discount rate and the growth rate. To apply this approach to equity valuation, only the
firm’s discount rate and the firm’s growth rate in dividends need to be estimated. The
Gordon growth model, however, cannot immediately be applied to firms that have yet to
pay any dividends, e.g., Microsoft. Since dividends are not a primitive measure of value
creation, a firm could be profitable without paying any dividends. Instead of paying
dividends, these firms reinvest all their earnings in its operations leading to stock price
increases to the benefit of equity investors. Consequently, value of equity is often
derived from free cash flows or accounting earnings.
As an alternative to measuring intrinsic value of equity as the expected discounted value
of all future dividends, intrinsic value of equity can be estimated as the expected
discounted value of all future free cash flows. Again, the Gordon growth model is
typically invoked by assuming constant growth rates of free cash flows beyond the
forecast horizon. Intrinsic value of equity is then derived from estimated firm value by
deducting the current market value of debt. Since analysts do not usually offer forecasts
of future free cash flows, this approach calculates forecasts of future free cash flows from
rolling forecasts of future income statements, future capital expenditures, and future
balance sheets, among others.
In addition, intrinsic value of equity could be estimated from accounting measures. One
such accounting-based approach, the residual income valuation model, generates firm
value estimates from accounting-based valuation as the sum of current accounting book
value and the expected discounted sum of future abnormal earnings.2
There are three
2
Abnormal earnings are also referred to as residual income or Economic Value Added®. See Ohlson
(1995).
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4. common implementations of the residual income valuation models that each makes
different mutually exclusive assumptions about future earnings beyond the analysts’
forecast horizon. First, Return-On-Equity (ROE) may be expected to remain constant in
perpetuity. Second, analysts forecast of Return-On-Equity may be expected to move
after the forecast horizon linearly towards the industry median ROE by the twelfth year
after which the residual incomes remain constant in perpetuity. Third, analysts forecast
of Return-On-Equity may be expected to continue to grow at some constant rate.3
An alternative accounting-based approach ignores book value and relies on analysts
earnings forecasts.4
One example of this approach is the Price-Earnings-to-Growth
(PEG) ratio defined as the forward price-earnings ratio divided by the percentage long
term growth rate in projected earnings per share forecasts.
In theory, identical estimates of intrinsic value of equity should result based on dividends,
free cash flows, or accounting earnings.5
In practice, however, the different implicit
assumptions in the common implementations of these valuation models, in particular
regarding terminal values – the evolution of future Return-On-Equity after the forecast
horizon – can lead to differences in the accuracy of estimates of intrinsic value of equity.
3. Price-implied Expectations
Rappaport and Mauboussin (2001) introduce the idea of price-implied expectations.
They argue that the approach of deriving intrinsic value of the firm ignores important
information embedded in current stock prices. They, therefore, propose to compute the
implied parameters from current market value. This section next briefly summarizes
what other information might be reflected in current market prices and then outlines how
one can impute parameters from market prices. Finally, Required Business Performance
is introduced.
3
Examples of the first approach includes Frankel and Lee (1998), Liu, Nissim, and Thomas (2002), and
Ali, Hwang, and Trombley (2003). Examples of the second approach include Lee, Myers, and
Swaminathan (1999) and Gebhardt, Lee, and Swaminathan (2001). Finally, Claus and Thomas (2001) take
the third approach by assuming that the long term growth rate in 3% below the risk free rate.
4
See Ohlson and Juettner-Nauroth (2005).
5
See Francis, Olsson and Oswald (2000) and Lundholm and O’keefe (2001).
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5. 3.1 Information in Current Prices
Whatever the view on efficient markets, most agree that prices reflect, albeit imperfectly,
publicly available information as well as private information. While individual investors
can differ in their views on the firm value, they can be more or less bullish on any given
stock, the market price observed at any point in time reflects the views of many different
investors. The source of individuals’ disagreement in assessment of value is their
interpretation of public information and possibly any private information that they may
have.
There are multiple sources of public information. First, the financial statements of the
firm are one source of public information. On the one hand, financial statements gain
perceived reliability and credibility because they are audited while on the other hand they
may not be timely. Based on financial statements – including the balance sheet, income
statements and statement of cash flows – investors can predict future dividends or,
equivalently, predict the future free cash flows. This process generates an individual
investors’ estimate of firm value. Second, stock market participants also interpret other
public information about the firm. For example, patent approval is likely favorable news
while executives divesting equity may be viewed as unfavorable news. Each new piece
of public information is weighted by some investors in reassessing firm value. Third,
analysts that cover a firm or industry may issue analyst reports that summarize their
views on the firm. Such reports often include quarterly earnings forecasts and a target
price, the price level at which the analyst expects firm value at some future date.6
Other
information intermediaries, like credit rating agencies may also affect some investors’
assessment of firm value, and hence the stock price of the firm. Finally, the media or
casual communications on internet news boards among investors may affect
interpretations.
In addition, individual investors may possess private information. It is possible that
observed market prices reflect transactions by insiders who illegally trade based on
private information. More benevolently, investors and analysts may expend resources on
6
See Bradshaw (2002).
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6. collecting private information that might facilitate superior interpretation of the publicly
available information.7
3.2 Derivation of Price-implied Expectations
Observed market prices are a function of a multitude of factors labeled generically as
either public information or private information:
( )nInformatioprivatenInformatiopublicfP ;=
P f
( )nInformatioprivatenInformatiopublicotherVfP ;,=
( )nInformatioprivatenInformatiopublicotherPgV ;,=
1−
t
where is the stock price per share and represents a generic function. Based on the
discussion in section 3.1 above, the public information is publicly observable and
includes the firm’s financial statements from all previous years, while the private
information is unobservable. One way to re-express how prices are formed is as follows:
t
(1)tt
where V is an unobservable variable that is critical for assessing the future performance
of the firm. Rappaport and Mauboussin’s concept of price-implied expectations (PIE)
implies that investors can infer what the market expects. They derive:
t
tt (2)
using the inverse function , with slight abuse of notation. Since how investors
assess the market value of equity is generally quite complex, the price-implied
expectations are derived through a complicated numerical procedure.
= fg
8
Nonetheless, to
illustrate Rappaport and Mauboussin’s concept of price-implied expectations (PIE)
through two simplistic examples: The PEG model and the Gordon growth model. In each
example, these models are presumed to correctly capture what is important to investors,
such that the observed market price should equal our intrinsic value of equity. From this
the market’s implied expectations towards a variable can be imputed.
7
See Coval and Moskowitz (1999), among others.
8
For example, chapter 5 of Rappaport and Mauboussin (2001) derive the price implied expectations
towards the forecast horizon through a numerical procedure.
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7. 3.2.1 PEG Ratio Example
The PEG ratio is defined as:
G
PEG
*100
=
EPSP /
G EPS
EPS
G
)
, where is the price per share, is the
forward Earnings Per Share, and is the percentage growth rate in . Suppose that
one is a natural level for the PEG ratio (one rule of thumb is that such PEG ratios result in
hold recommendations from analysts). If the observed market prices are correct when
PEG ratios are at this benchmark of one, investors can again infer from the forward price-
earnings ratio the price-implied expectations towards the percentage growth rate in ,
. That is G can be imputed.
P EPS
3.2.2 Gordon Growth Model Example
The Gordon growth model measures intrinsic value of equity as
( gr −
Div
Div g
per share, where
represents the per share total dividends, is the growth rate in dividends which is
assumed constant, and r the (appropriately risk-adjusted) cost of equity capital. If
capital markets are fully efficient, observed market price per share, , is correct and
should be equal to the intrinsic value of equity per share. Investors can readily observe
the market price per share at any point in time. If further investors are confident about
the expected dividends and the cost of capital, then they can solve for the implied growth
rate.
P
g
9
As stock prices increase (decrease), the investors’ implied growth rate would also
increase (decrease). Thus, price-implied expectations approach allows each investor to
infer what constant dividend growth rate a marginal investor anticipates at any point in
time.
Consider an investor calculating both (i) the price-implied expectations (PIE) towards the
growth rate in EPS, G , based on the PEG model and (ii) the PIE towards the growth rate
in dividends per share, , based on the Gordon growth model. Of course, the PIE from
9
The resulting price-implied expectations of the growth rate is:
P
Divrg −= .
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8. different models will differ. The reason is that these models impose different views on
the firm’s future profitability.
Continuing with the Gordon growth model, suppose instead investors were certain about
both the expected dividends and the growth rate, but investors were uncertain about the
appropriately risk-adjusted cost of capital. In that case, investors would instead solve for
the implied cost of equity capital. As stock prices increase (decrease), the price-implied
expectations regarding the risk-adjusted cost of equity capital would decrease (increase).
4 Required Business Performance
Transparent Value extends the price-implied expectations’ approach to generate a risk-
adjusted probability called Required Business Performance Probability (RBPP). The
RBPP is the result of a two stage process. The first stage identifies the required business
performance (RBP); the revenue necessary to support a given stock price for a given
company. RBP methodology is a reverse discounted free cash-flow analysis using a
company’s stock price, income, balance sheet and cash-flow statements to determine
what the stock’s current price implies in terms of future free cash flow and revenue.
RBP is used as a benchmark against which to measure management’s ability to perform
in the future. The second stage then assesses the probability of the firm achieving the
RBP. The RBPP is the likelihood that the management of a company, based upon its past
performance in business, will meet its RBP.
The first stage is based on the methodology that is founded on the principal that the stock
price of a company must be transparently linked to management’s ability to perform.
Rather than calculating the value of the stock using the traditional DCF formula, the RBP
methodology reverses the DCF process and works backwards to solve for the required
business performance (revenue and business model growth rates) to defend a particular
valuation.
The second stage of this process initially estimates the empirical distribution of gross
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9. change in sales over the most recent 12 quarters. Changes in sales revenues10
are
assumed to be log-normally distributed. This distributional assumption is compelling for
multiple reasons. First, similar to stock price, sales revenues are non-negative variables.
Second, sales revenues have been assumed log-normally distributed in the accounting
literature. One reason is that sales revenues is the product of two components – the
output quantities sold and the sales prices per unit – each of these components could also
be viewed as log normally distributed.11
This means that price-implied forecasted sales
naturally decompose into quantity effects and price effects. Finally, the assumption that
stock prices are log normally distributed is standard in finance and implicit in the Black
and Scholes option pricing model. Consequently, making the log normal assumption for
underlying fundamental variables generates a natural link between fundamentals and
observed market prices.12
Once the best log-normal distribution has been fitted to the historical data of gross sales
increases, the PIE sales forecast is located at some percentage between 0% and 100% in
this distribution. This percentage is the RBPP. Since this process that leads to RBPP is
complex, the next section tests intuition by presenting three case studies.
5 Sensitivity Analysis
This section reports the result of sensitivity analyses on the price-implied probability
measure, RBPP. The purpose is twofold: First, we illustrate the sensitivity of the RBPP
to hypothetical changes in the inputs; Second, we confirm our intuition about the
direction and magnitude of these hypothetical changes. We report the results from three
separate sensitivity analyses with respect to per share stock price, discount rate, and
operating margin. As one would expect, the implied probability of sustaining
performance decreases when ceteris paribus (i) the stock price increases, (ii) risk goes up,
as measured by the weighted average cost of capital, and (iii) the operating margin ratio
declines. We present the analysis for three separate companies to illustrate that these
10
Changes in sales revenues are defined as quarterly sales divided by sales of the same quarter in the
previous fiscal year.
11
See Hilliard and Leitch (1975).
12
Note that the price-implied sales revenues are risk-adjusted because the discount rate is risk adjusted,
similar in spirit to risk-neutralized distributions used in finance.
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10. hypothetical analyses rely on firm-specific inputs whose variability is different between
these companies. Nonetheless, the results exhibit striking similarities that appear
representative of the methodology.
5.1 Sensitivity to Stock Price Changes
In this section, we report the results with varying stock prices to create hypothetical
scenarios of what the RBPP would have been if ceteris paribus only the stock prices had
been different. We present these graphs in figures with RBPP in percent on the vertical
axis and stock prices on the horizontal axis. From these hypothetical experiments, three
common patterns are as expected and evident from casual inspection. First, the RBP
varies as a smooth non-linear curve that is monotonically decreasing in the stock price.
Second, as the hypothetical stock price decreases towards zero, the RBPP goes to one.
Third, as the hypothetical stock price increases sufficiently, the RBPP goes to zero. As a
result, all graphs are inverted S-shapes.
Consider Office Depot Inc. (“Office Depot”) which had a stock price of $18.80 per share
as of November 19, 2007. Based on that stock price – and also based on WACC and
other financial statement data available on that date – the actual RBPP was 92.30%. This
is indicated by the point B in Figure 1. Holding all other inputs fixed, we then decreased
and increased the stock price up to 25%. This created the softly downwards sloping blue
curve. From this experiment, it appears that a hypothetical one percent marginal increase
in the stock price from its actual 2007 of $18.80 level would lead to a 2% decrease in the
RBPP.13
We repeated this experiment for Office Depot using the stock price of $41.44
per share as of November 20, 2006 and using the appropriate WACC and financial
statement information for that date. Based on that stock price – and also based on
WACC and other financial statement data available on that date – the actual RBPP was
38.00%. This is indicated by point A in Figure 1. Again, by varying the stock price
hypothetically away from its actual level by increasing and decreasing up to 25%, we see
a red downwards sloping curve going through point A, similar to the blue curve for 2007.
As expected, the inverted s-curve has shifted towards the left as the stock price declined
13
This represents the approximate slope – or sensitivity - of the blue curve at point B.
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11. between 2006 and 2007. From this experiment, a hypothetical one percent marginal
increase in the stock price from its 2006 level of $41.44 appears to result in a 1%
decrease in the RBPP. While the marginal sensitivity of implied probabilities to stock
price changes is lower in 2006 than in 2007, this is not automatic since other fundamental
inputs have also changed. Put differently, if the blue line had been extended to include
$41.44, its slope would have been even lower than the red line.
Consider next Google Inc. (“Google”) trading at $625.85 and $495.05 and price per share
as of November 19, 2007 and November 20, 2006, respectively. The implied
probabilities were 98.82% and 99.9% for November 2007 and 2006 respectively. The
information is indicated by the points A and B for 2006 and 2007, respectively. Figure 2
reports the results of hypothetical scenario analyses. We see that the implied
probabilities appear extremely insensitive to changes in Google’s stock price and remain
similar from 2006 to 2007. Specifically, a hypothetical one percent marginal increase in
the stock price from its actual level results in a 0.1% decrease in the RBPP for both 2006
and 2007.
Third, consider Microsoft Corporation (“Microsoft”) which was trading at $33.96 with an
actual RBPP of 78.75% on November 19, 2007, as indicated by the point B in Figure 3.
Similarly, Microsoft’s actual price per share of $29.89 and actual RBPP of 38.3% on
November 20, 2006, are indicated by the point A and the dotted red lines in Figure 3. We
find that a hypothetical one percent marginal increase in the stock price from its actual
level would have resulted in a .3% and 1% decrease in the RBPP in 2007 and 2006,
respectively.
It is worth reiterating that RBPP changes result from price movements as well as from the
arrival of other information. Comparing 2006 to 2007, we see that Microsoft’s stock
price increased by 14% while the RBPP more than doubled increasing by 206%. We
separate the 206% increase in RBPP into two effects: change in price and change in other
information, where the latter includes new financial statement information and changes in
WACC. To quantify these two effects, we consider the hypothetical benchmark where
only stock price changed while all other information used for calculating RBPP remains
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12. the same. In this hypothetical benchmark case where RBPP is calculated on November
20, 2006 using the price as of November 19, 2007, the hypothetical RBPP would have
been 25.29%. This hypothetical benchmark is indicated by the point C in Figure 4. As
expected the hypothetical RBPP is lower because the higher stock price leads to higher
price implied sales which in turn are less likely to be attainable. Comparing points A and
C, observe see that the increase in stock price would have led to a 34% decline in the
RBPP. Second, comparing points C and D, we can gauge the effect on RBPP of all other
information holding the stock price fixed at its level as of November 19, 2007. This
second comparison reveals that RBP would have been higher by 211% due to new non-
price information used for calculating RBPP. In summary, the above analysis attributes
the 206% increase in Microsoft’s RBPP during 2007, which corresponding to moving
from points A to B in Figure 4, into two components: 66% price effect and 311%
information effect.14
While stock price movements do lead to revisions in Microsoft’s
RBPP, the arrival of other information also leads to material revisions in RBPP.
5.2 Sensitivity to Changes in Discount Rates
In this section, we report the results of varying the discount rate to investigate the
hypothetical effect on the implied probabilities holding all other factors constant. We
present these results in figures with implied probabilities on the vertical axis and the
WACC on the horizontal axis. From these hypothetical experiments, three common
patterns arise as expected and appear evident from casual inspection. These three
patterns are the same as for the hypothetical changes in stock price. First, the WACC is a
smooth non-linear curve that is monotonically decreasing in the stock price.15
Second, as
the hypothetical WACC decreases towards zero, the RBPP goes to one. Third, as the
hypothetical WACC increases sufficiently, the RBPP goes to zero. As a result, all graphs
are inverted S-shapes.
14
That is, 206% = (1 - 34%) * (1 + 211%). = 66% * 311%. Note that an alternative decomposition using
point D in Figure 4 the hypothetical benchmark suggests a less pronounced price effect for Microsoft
during 2007.
15
As is well-known, it is theoretically possible that an increase in the discount rate can have a non-
monotonic effect on the present value of future cash flows when the signs of the future cash flows alternate.
This would require negative correlation in future free cash flows over time which is uncommon in practice.
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13. Consider Office Depot which on November 19, 2007, had a WACC of 9.4% and an
actual RBPP was 92.30%, as indicated by the two black lines in Figure 5. Holding all
other inputs fixed, we then decreased and increased the WACC up to 25% to calculate
hypothetical RBPP, resulting in the blue downwards sloping curve. From this
hypothetical experiment, we find that a hypothetical one percent marginal increase in the
WACC from its actual 2007 level of 9.4% would lead to a 3% decrease in the RBPP.
We repeated this experiment for Google, using as starting point their WACC of 11.4%
and actual RBPP of 98.82% as of November 19, 2007, as indicated in Figure 6.
Performing similar hypothetical calculations, results in the blue curve and we find that a
hypothetical one percent marginal increase in the WACC of Google from its actual 2007
level of 11.4% would lead to a 1% decrease in the RBPP.
Repeating this analysis for Microsoft, we start with their WACC of 9.5% and actual
RBPP of 78.75% as of November 19, 2007, as indicated in Figure 7. For Microsoft, we
find by moving along the blue curve, that a hypothetical one percent marginal increase in
the WACC of Microsoft from its actual 2007 level of 9.5% would lead to an approximate
3.5% decrease in the RBPP.
5.3 Sensitivity to Changes in Operating Margins
In this section, we report the results of varying the operating margin to create
hypothetical scenarios of the implied probabilities. As above, we present graphs in
figures with implied probabilities (RBPP) on the vertical axis and operating margins on
the horizontal axis. From these hypothetical experiments, three common patterns emerge
exactly as expected and evident from casual inspection. First, the RBPP is a smooth non-
linear curve that is monotonically increasing in the operating margins, that is, higher
operating margins render it more likely that the firm can meet the performance implicit in
its current market value. Second, as the hypothetical operating margins decreases
towards zero, the RBPP goes to zero. Third, as the hypothetical operating margins
increases sufficiently, the RBPP goes to one. As a result, all graphs are S-shapes.
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14. Consider Office Depot which had an operating margin ratio of 4.8% as of November 19,
2007. Based on the actual inputs as of that date, the RBPP was 92.3% same as reported
above and indicated by the dotted lines. The hypothetical effect of alternative operating
margins results in the S-shaped pattern in Figure 8. Further, the graph reveals that a
hypothetical one percent marginal increase in the operating margin ratio of Office Depot
from its actual 2007 level of 4.8% would lead to a 5% increase in the RBPP.
Again, we repeated this experiment for Google and Microsoft. For Google, we use as
starting point the actual operating margin ratio of 31.4% and actual RBPP of 98.82% as
of November 19, 2007. Figure 9 reveals that a hypothetical one percent marginal
increase in the WACC of Google from its actual 2007 level of 31.4% would lead to a .4%
increase in the RBPP. Repeating this analysis Microsoft, we start with their actual
operating margin ratio of 36.9% and actual RBP of 78.75% as of November 19, 2007, as
indicated by the dotted blue line in Figure 10. For Microsoft, we find that a hypothetical
one percent marginal increase in the operating margin ratio of Microsoft from its actual
2007 level of 36.9% would lead to a 2% increase in the RBPP.
6. Portfolio Index based on RBPP
This section evaluates the performance of two “RBPP portfolio” indexes using stocks in
the Dow Jones Wilshire 750 (The Dow Jones Wilshire Large Cap 750 Index). Portfolio
weights for these RBPP portfolios are adjusted at the beginning of each quarter.
The first analysis considers a RBPP portfolio index and uses the Dow Jones Wilshire 750
index as a benchmark. While the Dow Jones Wilshire 750 index assigns market weights,
the first RBPP portfolio uses the relative implied risk-adjusted probabilities as the
weights. That is, the portfolio weight of each stock is its RBPP calculated at the
beginning of each quarter divided by the sum of RBPPs for all stocks in the index. Since
each RBPP is between zero and one, all stocks receive non-negative weights in both
portfolios.
The second analysis considers the performance of an index which combines an equally-
weighted long position in the 30 stocks with the highest RBPP and an offsetting equally-
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15. weighted short position in the 30 stocks with the lowest RBPP. The specific 60
companies which are included in this long/short portfolio changes at the beginning of
each quarter.
The sample period for statistical testing in this section covers 756 trading days over 12
quarters from Friday November 12, 2004 to Wednesday November 14, 2007. During this
period, the Dow Jones Wilshire 750 increased by 27.26% from 2,675.60 to 3,404.84.
The RBPP at the beginning of each quarter is positively correlated with the following
quarter’s stock returns for firms included in Dow Jones Wilshire 750.16
This positive
correlation is consistent with higher RBPP firms outperforming lower RBPP firms. That
is, the higher the RBPP, the larger the margin of outperformance.
6.1 Dow Jones Wilshire 750 Portfolio Index based on RBPP vs. Value-weighted
The RBPP portfolio index uses the same 750 firms each quarter but changes their weight
from value-weights to relative RBPP. To facilitate this comparison, the RBPP portfolio
index was normalized without loss of generality to also start at 2,675.60 on Friday
November 12, 2004. Figure 11 represents the time-series of both indexes. Overall, both
indexes tend to increase over the time period. To evaluate the difference in performance
between these portfolios, we first calculate for each day the returns on the RBPP portfolio
in excess of the Dow Jones Wilshire 750. This measure of relative performance yields a
mean excess return of 1.29%. Further, the minimum, median, and maximum excess
returns are 64.11%, 1.35%, and 58.89%, respectively. Consistent with a positive median
return, the histogram for these excess returns in Figure 12 reveals that the peak of the
distribution is well above zero at the bin between 5 and 10 bps. A variety of statistical
tests reveal statistically significant differences in daily excess returns. First, a two-sided
t-test of the null hypothesis that excess returns have zero mean results in a t-statistic of
2.00 with an associated p-value of 0.0454 which is statistically significant at a 5%
confidence level. Colloquially, this means that the mean daily excess returns are
statistically significantly positive. Second, the RBPP-based index outperforms the
16
Specifically, a regression of quarterly stock return on beginning of quarter RBPP shows that RBPP is
significantly correlated (at 0.01 p-levels) with quarterly stock returns after controlling for both
autocorrelation and time-fixed effects.
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16. (value-weighted) Dow Jones Wilshire 750 in 403 out of 756 days. This difference is
statistically significant with a p-value of 0.0747. Third, a Wilcoxon signed rank test
documents with a p-value of 0.0381 which is significant at a 5% confidence level.
Overall, these results support that the RBPP portfolio outperforms the Dow Jones
Wilshire 750.
6.2 Index of Leading vs. Lagging Firms in Dow Jones Wilshire 750 Portfolio
We now compare the performance of two equally weighted portfolios: one is based on
the 30 companies with the highest RBPP in Dow Jones Wilshire 750 (Leading 30) while
the other consists of the 30 companies with the lowest RBPP in Dow Jones Wilshire 750
(Lagging 30). Figure 13 presents the time-series performance of these two indexes.
Casual inspection reveals that these indexes diverge more towards the end of the period.
This is consistent with the Leading 30 index outperforming the Lagging 30 index.
To evaluate the difference in performance between the Leading 30 portfolio and the
Lagging 30 portfolios, we calculate for each day the returns of Leading 30 less the
Lagging 30, which represents the return from a long/short portfolio that takes equally
weighted long (short) positions in companies with the 30 highest (lowest) RBPP. Figure
14 reveals that this portfolio has increasing cumulative returns. The mean (median) daily
return on this long/short portfolio is 5.98% (4.19%) with a minimum and maximum of -
291.03% and 162.69%, respectively. Consistent with a positive median, the Leading 30
portfolio outperforms the Lagging 30 on most days.17
More importantly, the Leading 30
portfolio outperforms the Lagging 30 by higher margins: The mean daily excess return
of 5.98% is highly statistically significant with a p-level of 0.0038, well below commonly
used confidence levels.18
When accumulating consistently small daily excess returns
over longer periods, large differences will arise as evident from the cumulative excess
returns for the whole sample period in Figure 14.
17
The returns on this long/short portfolio are positive on 406 out of 756 trading days. A non-parametric
sign test reveals that this difference is statistically significant at a 0.038 p-level.
18
This is based on a two-sided Student’s t-test of the null hypothesis that excess returns have mean zero.
The null hypothesis is rejected with a t-statistic of 2.90 and an associated p-value of 0.0038 which is highly
statistically significant. Further, a non-parametric signed rank test result in a p-value of 0.0021 that is
statistically significant at the 1% level.
15
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17. Thus, a portfolio that goes long (short) in the Leading 30 (Lagging 30) companies in the
Dow Jones Wilshire 750 generates statistically significant positive average returns.
Appendix B reports other statistically-based tests that use the companies in the Dow
Jones Industrial Average. Overall, these findings are consistent with superior
performance from firms with higher RBPP.
7. Summary
Transparent Value applies a systematic method to identify an implied risk-adjusted
probability measure, Required Business Performance Probability (RBPP), which
represents the likelihood that a firm’s future sales can meet the expected sales implied by
the observed market prices. The sensitivity analyses illustrate three characteristics of
RBPP: Ceteris paribus, a stock price decrease leads to an increase in the RBPP. Second,
an exogenous decrease in the risk adjusted discount rate leads to an increase in the RBPP.
Third, improved operating margins lead to an increase in the RBPP. The magnitude of
the sensitivities of RBPP varies across firms depending on, among others, their industry
and life cycle as illustrated by the three sensitivity analyses.
Various statistics-based tests support that companies with higher RBPP on average
outperform companies with lower RBPP. First, RBPP are positively correlated with the
subsequent quarter’s stock returns for the firms in Dow Jones Wilshire 750. Second,
RBPP-weighted portfolio index outperforms the value-weighted portfolio index for Dow
Jones Wilshire 750 and DJIA. Third, an equally weighted long/short portfolio based on
the highest/lowest RBPP firms in Dow Jones Wilshire 750 earns positive returns. These
results suggest that an index that exclusively involves long positions should, on average,
underperform relative to an augmented index based on 130 long and 30 short, which
appropriately uses RBPP rankings to determine in which firms to take additional 30%
long positions and 30% short positions.
16
FOR INTERNAL USE ONLY
18. References:
Abarbanell, J., and B. Bushee. 1997. Fundamental analysis, future earnings, and stock
prices. Journal of Accounting Research 35: 1-24.
Abarbanell, J., and B. Bushee. 1998. Abnormal stock returns to a fundamental analysis
strategy. The Accounting Review 73: 19-45.
Ali, A., L. Hwang, and M. Trombley. 2003. Residual-income-based valuation predicts
future stock returns: Evidence on mispricing vs. risk explanations. The Accounting
Review 78: 377-396.
Botosan, C., and M. Plumlee. 2005. Assessing alternative proxies for the expected risk
premium. The Accounting Review 80: 21-53.
Bradshaw, M. 2002. The use of target prices to justify sell-side analysts' stock
recommendations. Accounting Horizons 16: 27-41.
Bradshaw, M. 2004. How do analysts use their earnings forecasts in generating stock
recommendations? The Accounting Review 79: 25-50.
Claus, J., and J. Thomas. 2001. Equity premia as low as three percent?: Evidence from
analysts’ earnings forecasts for domestic and international stock markets. Journal of
Finance 56: 1629-1666.
Coval, J., and T. Moskowitz. 1999. Home bias at home: local equity preference in
domestic portfolios. Journal of Finance 54: 1–39.
Fama, E., and K. French. 1997. Industry costs of equity. Journal of Financial Economics
43: 153-193.
Francis, J., P. Olsson, and D. Oswald. 2000. Comparing the accuracy and explainability
of dividend, free cash flow, and abnormal earnings equity value estimates. Journal of
Accounting Research 38: 45-70.
Frankel, R., and C. Lee. 1998. Accounting valuation, market expectation and cross-
sectional stock returns. Journal of Accounting and Economics 25: 283-319.
Gebhardt, W., C. Lee, and B. Swaminathan. 2001. Toward an implied cost of capital.
Journal of Accounting Research 39: 135-176.
Hilliard, J. E., and R. A. Leitch. 1975. Cost-volume-profit analysis under uncertainty: a
log normal approach. The Accounting Review 50: 69-80.
Lee, C., J. Myers, and B. Swaminathan. 1999. What is the intrinsic value of the Dow?
Journal of Finance 54: 1693-1741.
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19. 18
Lev, B., and S. R. Thiagarajan. 1993. Fundamental information analysis. Journal of
Accounting Research 31: 190-215.
Liu, J., D. Nissim, and J. Thomas. 2002. Equity valuation using multiples. Journal of
Accounting Research 40: 135-171.
Lundholm, R. J., and T. O'keefe. 2001. Reconciling value estimates from the discounted
cash flow value model and the residual income model. Contemporary Accounting
Research 18: 1-26.
Lyon, J. D., B. M. Barber, and C-L. Tsai. 1999. Improved methods for tests of long-run
abnormal stock returns. The Journal of Finance 54: 165-201.
Ohlson, J. A. 1995. Earnings, book values, and dividends in securities valuation.
Contemporary Accounting Research 11: 661-687.
Ohlson, J. A., and B. Juettner-Nauroth. 2005. Expected EPS and EPS growth as
determinants of value. Review of Accounting Studies 10: 349-365.
Ou, J. A., and S. H. Penman. 1989. Financial statement analysis and the prediction of
stock returns. Journal of Accounting and Economics 11: 295-330.
Penman, S. H. 1992. Return to fundamentals. Journal of Accounting, Auditing and
Finance 7: 465-482.
Penman, S., and T. Sougiannis. 1998. A comparison of dividend, cash flow, and earnings
approaches to equity valuation. Contemporary Accounting Research 15: 343-383.
Rappaport, A., and M. J. Mauboussin. 2001. Expectations Investing: Reading Stock
Prices for Better Returns. Harvard Business School Press.
Sougiannis, T., and T. Yaekura. 2001. The accuracy and bias of equity values inferred
from analysts earnings forecasts. Journal of Accounting, Auditing and Finance 16: 331-
362.
FOR INTERNAL USE ONLY
20. Figure 1: Sensitivity of RBPP to changes in price for Office Depot
Figure 2: Sensitivity of RBPP to changes in price for Google
$782.3$751.0$719.7
Google Inc.
90.0%
91.0%
92.0%
93.0%
94.0%
95.0%
96.0%Probability
97.0%
98.0%
99.0%
100.0%
$371.3 $396.0 $420.8 $445.5 $469.4 $470.3 $495.1 $500.7 $519.8 $532.0 $544.6 $563.3 $569.3 $594.1 $594.6 $618.8 $625.9 $657.1 $688.4
Stock price (5% incremental change)
11/20/06 11/20/06
A
B
11/19/07 Probabilities11/20/06 Probabilities
Stock price (5% incremental change)
$51.8$49.7$47.7$45.6$14.1 $15.0 $16.0 $16.9 $17.9 $18.8 $19.7 $20.7 $21.6 $22.6 $23.5 $31.1 $33.2 $35.2 $37.3 $39.4 $41.4 $43.5
A
B
Office Depot
100.0%
80.0%
90.0%
40.0%
50.0%
60.0%Probability
70.0%
30.0%
10.0%
20.0%
0.0%
FOR INTERNAL USE ONLY
19
21. Figure 3: Sensitivity of RBPP to changes in price for Microsoft.
Microsoft
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
$22.4 $23.9 $25.4 $25.5 $26.9 $27.2 $28.4 $28.9 $29.9 $30.6 $31.4 $32.3 $32.9 $34.0 $34.4 $35.7 $35.9 $37.4 $37.4 $39.1 $40.8 $42.5
Stock price (5% incremental change)
Probability
11/19/07 Probability
11/20/06 Probability
E (11/19/07 P b bilit )
B
A
Figure 4: Sensitivity of RBPP to changes in price for Microsoft.
Microsoft
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
$22.4 $23.9 $25.4 $25.5 $26.9 $27.2 $28.4 $28.9 $29.9 $30.6 $31.4 $32.3 $32.9 $34.0 $34.4 $35.7 $35.9 $37.4 $37.4 $39.1 $40.8 $42.5
Stock price (5% incremental change)
Probability
11/19/07 Probability
11/20/06 Probability
E (11/19/07 P b bilit )
A
B
C
D
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22. Figure 5: Sensitivity of RBPP to changes in weighted Average Cost of Capital (WACC)
for Office Depot
Figure 6: Sensitivity of RBPP to changes in weighted Average Cost of Capital (WACC)
for Google
21
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23. Figure 7: Sensitivity of RBPP to changes in weighted Average Cost of Capital (WACC)
for Microsoft
22
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24. Figure 8: Sensitivity of RBPP to changes in operating margins for Office Depot
Figure 9: Sensitivity of RBPP to changes in operating margins for Google
Office Depot
0.0%
‐15.0% ‐12.0% ‐9.0% ‐6.0% ‐3.0% 0.0% 3.0% 6.0% 9.0% 12.0% 15.0%
Change in Operating Margin (3% incremental change)
‐15.0% ‐12.0% ‐9.0% ‐6.0% ‐3.0% 0.0% 3.0%
Change in Operating Margin (3% incremental change)
Google Inc.
100.0%
90.0%
80.0%
70.0%
60.0%Probability
50.0%
40.0%
30.0%
20.0%
10.0%
100.0%
90.0%
80.0%
70.0%
60.0%Probability
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
9.0%6.0% 12.0% 15.0%
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25. Figure 10: Sensitivity of RBPP to changes in operating margins for Microsoft
Microsoft
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
-15.0% -12.0% -9.0% -6.0% -3.0% 0.0% 3.0% 6.0% 9.0% 12.0% 15.0%
Change in Operating Margin (3% incremental change)
Probability
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26. FOR INTERNAL USE ONLYFOR INVESTMENT PROFESSIONAL USE ONLY
Statement of Accuracy
Columbia White Paper
Information presented in this accompanying statement to the Columbia White Paper for
the study of Transparent Value, LLC (Transparent Value) and its investment methodology
reflects updated facts and dates, as well as content clarifications as of .
The information and material presented in this document are provided to you for
illustrative and information purposes only and should not be considered as an offer or the
solicitation of an offer to buy or subscribe for securities or other financial instruments.
For educational and research purposes, Columbia University solicited the permission and
advice of Transparent Value for the production of this document.
Please note you are receiving the Columbia White Paper in an abbreviated version from its
original form.
April 12, 2011
