### WHAT DOES THE EARNINGS NUMBER MEASURE?

#### by

Jack L. Treynor

Editor, *Financial Analysts Journal*

April 30,1981

[Introductory note: Jack L. Treynor is editor of
*Financial Analysts Journal.* A trustee of the Financial Analysts
Research Foundation and a member of the board of the Institute for
Quantitative Research in Finance, he is also a director of the American
Finance Association, a member of the Investment Advisory Council
to the City of New York. He is a director of eleven mutual funds
and general partner in two partnership funds. He is the author of
articles in *Harvard Business Review, The Journal of Business,
and Financial Analysts Journal.* He is senior author of *The
Financial Reality of Pension Funding Under ERISA,* published
by Dow-Jones Irwin, Homewood, Illinois (1976).]

One of the most influential college physics texts of modern times
is *Foundations of Physics* by Lindsay and Margenau. The book
is unusual among physics texts in its emphasis on the philosophy and
underlying physics -- a philosophy that was pushed ahead rapidly in
the first decades of the twentieth century by Edington, Jeanes and,
of course, Einstein. Lindsay and Margenau point out that every variable
in physics has two definitions -- one that explains how it is measured
and one that explains how it is used: "The very idea of symbolism
implies ... that a symbol must represent a concept transcending the
particular operation which it is used to represent."

The necessity of these two definitions is not, of course, unique
to physics. Indeed, it applies wherever we use numbers to try to understand
the real world. It even applies in accounting. When we attempt to
apply Lindsay and Margenau's dictum to accounting, however, we immediately
run into a curious problem: The people who derive accounting numbers
and the people who use them are two different groups of people. According
to both the Trueblood Report and the Objectives Statement of the Financial
Accounting Standards Board, the primary user of accounting numbers
is the outside user. Perhaps it is for this reason that the two kinds
of definitions of such accounting numbers as earnings are rarely considered
simultaneously.

On one hand, if you ask an accountant for the meaning of earnings,
he will very likely (as I noted in "The Trouble with Earnings")
tell you how an earnings number is derived from the accrual process.
If, on the other hand, you ask an outside user what the earnings number
means, three possible answers are available to him: (1) a rationalized
proxy for cash flow, (2) the change over the accounting period in
the value of the firm and (3) a proxy for the value of the firm. Many
outside users seem to be subscribing to the first definition of earnings
in the way they use earnings numbers. Perhaps unfairly, Hicks is usually
held responsible for the second. Fischer Black has recently offered
us the third.

Although Black's definition proceeds from a consideration of how
professional investors use published earnings, it raises some questions.
One has to do with the way in which the earnings series is generated
from the bookkeeping process. How does a bookkeeping process that
operated in a predictable manner on input time series that are themselves
not random walks (levels of employment, output, sales, etc.) produce
a random walk?

How can an outside user combine his insights and information with
an accountant's estimate of value (i.e., the published earnings figure)
to produce an improved estimate of value? If Black's definition of
the earnings number is the correct one, then the accountant is, in
effect, saying to the outside user: "Take it or leave it. Use
my estimate of value or your own, but don't try to use mine to derive
yours."

Before the accounting profession can move forward from the observation
of the Trueblood Report and the Objectives Statement that accounting
standards should reflect the needs of outside users, it must determine
which of these three definitions of the earnings concept is the correct
one.

*A Theory of Earnings*

What if the accountant producing the earnings measure wanted it to
be as useful as possible to the outside user? Taking a leaf from the
Objective Statement, what the outside user wants to do is predict
future cash flows. If the accountant undertook to predict the entire
stream of future flows x(t), such a prediction would replace both
the income statement and the balance sheet. (Owen and Brief made this
point in their *Financial Analysis Journal* article, "The
Role of the Accountant in Investment Analysis," in the January-February
1975 issue.) Periodic accounting reports would update predictions
of the cash flow stream, so that over time the outside user would
accumulate a series of predictions.

x(t,1),

x(t,2),

...

x(t,T).

Focusing on the series of predictions for the rate of cash flow at
a particular point in future time, we observe that, if these predictions
are as good as they can be (i.e., as free as possible of extraneous
noise), then they will have an important statistical property. One
of the most general theorems proved by Howard Raiffa and Robert Schlaifer
in their famous book, *Applied Statistical Decision Theory,*
was one which, translated into words, says that when you are making
a series of predictions of the same future event, the best current
prediction of a future prediction is your current prediction of the
event. (To get technical for a moment, your forecast at any point
in time of the event -- or indeed, of any future prediction of the
event -- will be a probability distribution. The word "prediction"
in this statement refers to the expected value associated with the
probability distribution.) But this means that your current prediction
of any future prediction, including the next one, will imply zero
change from the current prediction, and your next prediction will
imply zero change in the prediction after that and so forth. The result,
of course, is what we have come to call a random walk. Any time series
of such predictions that is not a random walk is either (1) not fully
reflecting information as soon as it is available or (2) is mixing
noise in with the information content in the time series.

An array of successive predictions of the future cash flow stream
is an awesome thing to contemplate. Every prediction in the series
contains subpredictions for every future point in time. A new set
of such predictions is issued at the end of each accounting period.
After a while, the outside user has accumulated an embarrassment of
riches. Fortunately for both the outside user and the reporting accountant,
such predictions are largely redundant information. There is an important
class of transformations on the cash flow series that are essentially
costless, reversible and capable of being undertaken at any time at
the option of management. These are, of course, exchanges of cash
flow across time executed at market interest rates. Because management
can achieve such transformations so readily (and so costlessly) that
they cannot be predicted, a prediction of the future cash flow stream
purports to contain a great deal more information than it really can.

Attention has traditionally focused on one particular member of this
transformation class -- namely, that cash flow series that concentrates
all its value at time zero. Since all the members of the class contain
equal information about the future of the company, a fortiori, this
member -- the so-called "present value" -- contains all
the useful information in the entire cash flow series. No matter what
capital market transformations management way have elected, the present
value of the cash flow stream will be the same. Raiffa and Schlaifer
might be tempted to call it a "sufficient statistic" on
the future cash flow stream.

Since the present value of the cash flow stream depends linearly
on the individual cash flows, predictions of future present values
of the stream will have the same property as predictions of the individual
cash flows -- namely, the random walk property.

It follows from these considerations that if the accountant is attempting
to report information about the future cash flow stream as soon as
possible and adulterated with as little noise as possible, he has
little choice but to report the present value of the stream. (He could,
of course, report the implied value five or ten years hence, but the
choice of time horizon would introduce unnecessarily arbitrary elements
into the reporting scheme.) This begins to sound a lot like Black's
concept. It also sounds a lot like "permanent earnings"
as described, for example, in Bill Beaver's new book. But this is
getting ahead of the story.

The accountant's objective in recognizing individual transactions
that he *predicts* will have no present value impact on the firm
will be to prevent them from doing so. He must acknowledge simultaneously
all ultimate cash flow implications of such transactions. Such present
value preserving acknowledgements are, of course, called accrual accounting.
The purpose of accrual accounting is to prevent transactions from
introducing spurious information into the accountant's predictions.(1)

In practice, of course, accrual accounting goes further than that.
It treats transactions that by themselves are ambiguous -- that may
or may not contain information -- as if they had none. The accountant
waits until he has in hand all the transactions in a cycle to see
whether in the aggregate they have present-value consequences, and
then makes a once-and-for-all present value adjustment. Transactions
-- and only transactions -- acknowledged by the accountant to contain
new information are permitted to alter the present value of the cash
flow stream. Others are treated as if they were precisely the kind
of present-value- preserving transformations just discussed.(2)

If the completed cycle has present value implications, however, then
the accountant must acknowledge those implications. At this point
accrual accounting introduces two sophisitications: 1) it makes present
value adjustments for the last transactions in the cycle, whether
or not they have any net present value effect; 2) it makes these adjustments,
whether or not their net effect was expected. Taken together, these
sophistications enable the accountant to accumulate all sales revenue
and all expense for a period.

The second sophistication would clash with the basic rule that only
unexpected cash flow is reflected in present value adjustments, were
it not for the fact that at the same time the accountant records actual
revenues and expenses he makes a contrary present value adjustment
to remove the expected effect.

Let's recapitulate in more familiar terms: The present value of the
firm's net cash flow is its *equity.* The net effect on present
value over the accounting period of the transactions I have been describing
is, of course, *income.* Transactions containing (potential)
information are *revenue* and *expense* transactions. The
adjustment to remove from present value the expected contribution
of current-period transactions is accomplished by depreciation (which,
as we shall see, also accomplishes something else).(3)

We have already noted that transactions in inefficient markets are
virtually certain to result in gains or losses. What is less clear
is whether it is rational to *expect* a gain (or loss) from such
transactions in the future -- i.e., to expect to be able to gain consistently
from trading in such markets. Nor is it clear that if the firm's employees
have this ability they won't charge the firm for it. If they do not,
then the only source of expected contributions to net present value
is economic rents. Indeed, we can define an asset as something whose
services arc sufficiently scarce to justify an expectation of future
rents -- hence to contribute to present value. Obviously, an asset
doesn't have to be tangible. Given this definition, expected future
cash flows will derive entirely from scarcity rents on the firm's
assets.

We can put these concepts into perspective by examining the economic
content of Hick's definition of earnings -- considering how time and
changing expectation interact in altering the present value of the
firm. Let x(t,u) be the cash flow series, t being equal to or greater
than zero and less than infinity. This stream will have a present
value at each future point in time, T, of:

It has, of course, rates of change with respect to u and T. For the
change with respect to u we have:

Since T appears in both the lower limit and the integrand we have:

At future time T, of course, the second expression has the value
-x(T,u), since the discount factor equals one.

Using the expressions for the two partial derivatives, we can write
the total differential:

This is the total differential of the remaining cash flow stream.
As real time elapses, of course, the future cash stream is being realized,
converted into actual cash and (presumably) invested at the market.
Thus the way in which the present value of the firm will change over
time, starting from now, involves a term that is missing from this
total differential -- namely, the cash flows already realized. As
noted, the accountant focuses on present value surprise by treating
the stream as the expected cash stream and the contribution to the
present value of the firm that this expression leaves out as the *actual*
cash flow. Let us now write an augmented expression for the total
differential of the present value of the firm including the actual
contribution of cash currently involved.

In the expression

X(u,T) is the expected rent at T -- i.e., the expected difference
between sales income and cost of sales. Thus the total expression
breaks down into *operating income*

and the *change in expectations*

The subexpression

is depreciation -- i.e., the expected decline in value of the assets.
Depreciation acknowledges that, with elapsing real time, the present
value of the remaining cash flow future stream 1) Appreciates at the
market rate and 2) depreciates at the instantaneous cash flow rate.
Under this view, operating profit is market return plus surprise in
realized rents. Surprise in rents doesn't necessarily imply either
a) market inefficiency or b) contributions (good or bad) by management.(4)
Market return is a capital market phenomenon. It has to do with return
investors require based on liquidity, risk and tax considerations
(aside from luck, the sole cause of rapidly rising PV).

Operating income deals entirely with the past; the change in expectations
deals with the future. The rules governing the accrual process relate
entirely to the first element. The second element is judgmental, constrained
only by what the accountant can do with reserves, etc., under GAAP.

The key point is that "operating income" and "adjustment
for changing expectations" are mutually exclusive. Any logical
connections between a surprise in operation income and altered expectations
about the driving variables that collectively make up "n"
are entirely outside the accounting process. Any disciplines in "measurement"
and manipulations of measured numbers accountants impose on accounting
for operating income constrain these connections not at all.

One is tempted to suspect, simply because accounting provides no
formal apparatus for changing expectations, that accountants employ
none. If so, then accountants who can define earnings in terms of
the first kind of definition ("It's what you get when you take
the journal entries, etc., etc.") but not the second are navigating
without any compass whatever. Estimating the value of this second
term cannot realistically be described in such terms as "measuring"
or "reporting."

*What the Evidence Tells Us*

Although it ignores the effect of changing expectations, conventional
bookkeeping is loosely consistent with the Hicksian notion of income,
though not with Black-Beaver: Operating income is an element in the
change in permanent income, rather than in permanent income itself.

Variability in value is far less than variability in change in value.
(The latter has an almost infinite coefficient of variation.) Thus
the adjustments to reserves required to report value are far less
than those required to report change in value; then, too, the resulting
time series is "smoother." Thus accountants' desire to smooth
the reputed series is a powerful force toward reporting value and
away from reporting changes in value.

The obvious test of whether *reported* income is permanent income
or the change in permanent income is the role of changing expectations.
In 1965, Paul Samuelson published a paper entitled "Proof that
Property Anticipated Prices Fluctuate Randomly." In a rational
market, share value will fluctuate randomly. And if value fluctuates
randomly, then the second definition -- the change in value over the
accounting period -- cannot fluctuate randomly. The first difference
of a random walk is not a random walk. The difference between the
time series character of a random walk and its first difference is
very large -- virtually impossible to overlook in the statistical
evidence. (See Appendix
B)

Will anyone deny that price is a superb surrogate for permanent income,
or that change in price is a surrogate for change in permanent income?
No? Then we have merely to examine behavior of income time series
in relation to share price time series to answer, once and for all,
whether reported income attempts to reflect permanent income or change
in permanent income. Price change approximates a random walk. Do changes
in reported income approximate a random walk? If so, do they correlate
with price changes? If the answers to these questions are "yes,"
then reported earnings is an attempt to capture permanent earnings,
rather than its first difference.

There is an abundance of evidence on the time series properties of
earnings. In England, Little and Raynor, and in the United States,
Lintner and Glauber, have found that changes in earnings approximate
a random walk. One of the most exhaustive examinations of the evidence
is that of Beaver. I quote from his "concluding remarks"
to Chapter 5:

"Earnings changes and price changes show a significant, positive
correlation. Obviously, value (permanent earnings) and change in
value should have no correlation.

Although significant, the relationship is not simply one-to-one.
This occurs in part because prices act as if earnings are perceived
to contain a transitory component." (*Financial Reporting
: An Accounting Revolution*, Englewood Cliffs, NJ, Prentice-Hall,
1981).

One possible source of a "transitory component" in reported
earnings is operating income that constrains companies from reporting
what they want to report -- namely, permanent earnings. In view of
the fact that operating income is an element in the change in permanent
earnings, rather than in permanent earnings, it wouldn't be surprising
if companies encountered such constraints.

*Enter Creative Accounting*

Illustration 1 is
a picture of what the evidence seems to me to imply about the total
accounting process. Let's start with the estimates of your prototypical
security analyst. He or she makes some estimate of value and, as a
result, clients buy and sell and price is affected. The accountant
makes his own judgment about what the value of the firm should be
and compares that estimate with price. Based on that comparison, he
says, "That price is too low or too high." He determines
an earnings number he hopes will guide analysts in the proper directions.
And that earnings number then feeds back into the thinking of the
analyst. At the same time, the bookkeeper is going through the double
entry bookkeeping process, estimating changes in value that have nothing
whatever to do with what the accountant is trying to provide the analyst.
Inevitably, when you compare the changes in value that come out of
the bookkeeping process with the value-related numbers the accountant
is feeding the analyst, you get differentials -- sometimes large differentials.

These differentials require creative accounting. Accountants write
off assets, create reserves for future losses, shift from pooling
to purchase, shift from LIFO to FIFO, shift from 30 year depreciation
lives to 15 year depreciation lives -- whatever it takes to make certain
that the earnings number that's fed back to the analyst is the Fischer
Black type of number rather than the double entry bookkeeping number.

The number contributed by creative accounting is a residual. The
bookkeeping inputs consequently have no effect whatever on the earnings
number that's fed to the analyst. If it did, the earnings number couldn't
behave the way the evidence shows it does behave-namely, as a random
walk. All the bookkeeping number does is determine the residual contribution
that has to be made in closing entires in order for the earnings number
to satisfy Fischer Black prescription -- namely, an estimate (to a
constant factor) of value.

**ILLUSTRATION
1**

*The Dynamics of Creative Accounting*

Let's consider for a moment the human dynamics of this process. One
way the process can operate is the one I cited initially. The accountant
forms his own opinion about value and then changes the inputs feeding
back to the analyst every time he sees the analyst gets off the track.
This is clearly what the Accounting Principles Board did when they
prohibited the pooling treatment of business combinations. They decided
stock prices of conglomerates were entirely too high. They were going
to do something about the stock prices by changing the earnings numbers
fed to the analysts and they did it by prohibiting an accounting practice
that resulted in high earnings. The same thing can happen at the level
of the individual company in the closing transactions of the company's
accountant.

Another way this process can operate is to buy credibility for the
accountant. The accountant can look at the actual current market price
of the company shares and feed back an earnings number that accords
with that price. When he does that investors will say, "Gee,
that company must be reporting their earnings pretty accurately."

Because accountants' value to a reporting firm depends on their credibility
with the outside user, it wouldn't be surprising if they behaved this
way most of the time. But it would be surprising if they behaved this
way all the time, because then, of course, they'd never have the opportunity
to cash in on that credibility. So the third way in which this process
can operate is for the firm to tell its accountant what value the
accountant ought to be encouraging outside users to arrive at, independently
of what the accountant thinks the value ought to be. I think that
happens too from time to time.

To summarize: Outsiders use earnings to improve their estimates
of value. But value deals entirely with the future. Numbers that alter
users' view of the future are not objective (for example) merely because
they are based on the past. There is no other basis for *any*
numbers affecting judgments about the future. ("I know not what
my future foot steps may be guided by, except the lantern of the past."
-- Patrick Henry.)

No meaningful theory of accounting can be erected on a consideration
of how accounting deals with the past. To understand accounting --
and its principal product, the earnings number -- we must consider
how it deals with the future. The central problem in accounting is
not how to measure but how to forecast. Thus the question posed at
the beginning of this paper is sterile and unproductive. The earnings
number doesn't "measure" anything.

The double entry bookkeeping process actually has no impact whatever
on earnings as reported to outside users. All it affects is the adjusting
entries that have to be made to the results of that process in order
to produce the desired earnings number which, as Black has pointed
out, is a measure of value, and not change in value.

*Appendix A*

To prove: Depreciation of an asset with value V(t) is given by:

**Appendix B**

To prove: The first difference of a random walk is not a random walk.
The second difference of a random walk is the first difference of
the first difference of a random walk. The question is: does the first
difference of the first difference of a random walk have distinctive
statistical properties of a first difference of a random walk? If
not, then the first difference of a random walk is not a random walk.

Define the backward shift operator b as shifting backward one unit
in time any time series to which it is applied. Consider a random
-- walk series with first difference x, such that:

**E [x b x] = o = E [x] **

and define second difference x such that