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Required Business Performance ® Methodology Bjorn N. Jorgensen Columbia Business School February 26, 2008 * Duplication or dissemination prohibited without prior written permission. FOR INTERNAL USE ONLY FOR INVESTMENT PROFESSIONAL USE ONLY

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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

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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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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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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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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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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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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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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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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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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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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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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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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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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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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(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.

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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.

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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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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

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

BOffice Depot

100.0%

80.0% 90.0%

40.0% 50.0% 60.0% Probability 70.0%

30.0%

10.0% 20.0%

0.0%

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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)

Prob

abili

ty

11/19/07 Probability11/20/06 ProbabilityE (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)

Prob

abili

ty

11/19/07 Probability11/20/06 ProbabilityE (11/19/07 P b bilit )

A

BC

D

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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

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Figure 7: Sensitivity of RBPP to changes in weighted Average Cost of Capital (WACC) for Microsoft

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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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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)

Prob

abili

ty

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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

FOR INTERNAL USE ONLY

Page 1:

Required Business Performance® (RBP®) is a methodology that determines the revenue needed for a given company to support

its current stock price, based on the company’s past performance. RBP® probability is a methodology that measures the

likelihood that a company can deliver the performance necessary to support the current price of its stock. The RBP

and RBP

probability methodologies are the subject of a Transparent Value LLC patent application filed with the United States Trademark and Patent Office.

Please note that “RBPP” is used as an abbreviated reference for the RBP probability throughout the Harvard Business School Case Study of Transparent Value LLC. “RBPP” is not the accurate abbreviated name for RBP probability.

Due to legal changes in the Dow Jones and Wilshire relationship, the Dow Jones Wilshire U.S. Large‐Cap Indexes currently operate under the name of “Dow Jones U.S. Large‐Cap Total Stock Market Index ”.

“Dow Jones ”, “Dow Jones Indexes” and “Dow Jones RBP Indexes” are service marks of Dow Jones & Company, Inc. (“Dow Jones”). Dow Jones does not sponsor, endorse, sell or promote investment products based on its indexes, including, the Dow Jones RBP Indexes, and Dow Jones makes no representation regarding the advisability of investing in any such products. Inclusion of a company in the Dow Jones RBP Indexes and additions to and deletions from such indexes do not in any way reflect an opinion on the investment merits of such company.

Microsoft is a registered trademark of Microsoft, Inc. The products and services offered by Transparent Value, LLC are not in any way endorsed by, sponsored by, approved by, or affiliated with Microsoft, Inc.

Page 9: Office Depot is a registered trademark of Office Depot, Inc. The products and services offered by Transparent Value, LLC are not in any way endorsed by, sponsored by, approved by, or affiliated with Office Depot, Inc.

Page 10: Google is a registered trademark of Google, Inc. The products and services offered by Transparent Value, LLC are not in any way endorsed by, sponsored by, approved by, or affiliated with Google, Inc.

Disclosures: This material is intended to inform you of products and services offered by Transparent Value and not an offer to buy or sell, or a solicitation of an offer to buy or sell, any security or fund interest. No claim is made that RBP can, in and of itself, be used to determine which securities to buy or sell, or when to buy or sell them. The opinions, estimates and investment strategies and views expressed in this document constitute the judgment of Transparent Value’s investment strategies, based on past, hypothetical or current market conditions. The views and strategies described herein may not be suitable for all investors. There is no guarantee that the Transparent Value investment methodology will produce positive investment results. All investments are subject to the risk of loss. Transparent Value, LLC (“Transparent Value”) is a subsidiary of Guggenheim Partners, LLC. Transparent Value , RBP , Required Business Performance , and the Transparent Value logo are registered trademarks of Transparent Value, LLC or one of its subsidiaries. "See the market clearly" is a trademark of Transparent Value, LLC and its affiliates. Other featured words or symbols used to identify the source of goods and services may be the trademarks of their respective owners.

Transparent Value did not compensate Columbia University, or an affiliate thereof, or receive compensation for the publication of this document.

Use of a reprint containing this performance information and rankings, as applicable, would be prohibited if it implied something about or caused a reader to draw an inference concerning (i) the experience of advisory clients, (ii) the possibility of a prospective client having an investment experience similar to that of prior clients, or (iii) Transparent Value’s competence, when there are additional facts that, if disclosed, would imply different results from those suggested in the article.

Transparent Value Funds are distributed by ALPS Distributors, Inc.

Guggenheim Funds Distributors, Inc. is the marketing agent for Transparent Value Mutual Funds. Transparent Value, LLC and

Guggenheim Funds Distributors, Inc. are subsidiaries of Guggenheim Partners, LLC.

© 2011 Transparent Value, LLC. All rights reserved. TVA000184 04/2012

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