Corporate balance sheet data are important building blocks of quantitative-fundamental (“quantamental”) investment factors. However, accounting terms are easily misunderstood and confused with economic concepts. Accounting is as much driven by assessment of risk as it is by economic value. For example, earnings are recognized only when receipt of cash is highly certain. Investment spending is recognized as such only when there is a high probability of related payoffs. Acknowledging links to risk and the double-entry system, accounting data can be combined into factors that capture the information that they jointly convey. For example, earnings yields become a more meaningful indicator when also considering return on equity and expended investment ratios.

Penman, Stephen. and Xiao-Jun Zhang (2021), “Accounting for Asset Pricing Factors”

The below are quotes from the paper. Emphasis, headings, and text in brackets have been added for clarity.

This post ties in with this site’s summary on fundamental value estimates.

### Principles for using accounting measures as trading factors

“Accounting numbers are governed by accounting principles that connect…to risk and expected return [and] depart from economic ideal”

“Accounting numbers [such as] book value, investment, return on equity, and other profitability measures…appear in standard [factor] models, but often from data mining without a clear explanation of why they indicate investment risk…__Rather than entering as the separate, additive factors…adding to the ‘factor zoo,’ [accounting] numbers should be combined parsimoniously into factors that capture the information that they jointly convey about risk and return__ in the double-entry system.”

“A ‘debit’ always requires a matched ‘credit.’…The accountant cannot recognize earnings without a corresponding effect on the balance sheet, and the two convey information jointly…The double-entry system that has often been marveled at for its other properties can also be utilized in constructing factor models.”

“[This] begins with the recognition that, in theory, the __expected return is given by the expected future earnings yield on current price, for which the current earnings-to-price [earnings yield] is a predictor__. However, it is an imperfect predictor, for current earnings are typically disturbed by accounting principles that convey the risk to expected earnings…[a deficiency that can be mitigated by __taking into consideration return on equity and expensed investment__].”

### Common misunderstandings

**“Investment** is measured as the change in total assets on the balance sheet. However, this number is __not a firm’s investment but rather the investment that accountants book to the balance sheet__. Considerable investment is expensed against earnings, including research and development (R&D), investment in software, brand building with advertising expenditures, expenditures on customer loyalty programs, building supply chains and distribution systems, human capital, and more. Indeed, in recent times investment is typically in these intangible’ assets rather than tangible assets booked to the balance sheet.”

“**Book value** (net assets by the balance sheet equation) in the book-price ratio [B/P] factor is not ‘assets in place’…nor does B/P indicate the value of growth opportunities over those from assets in place. Rather, it is an accounting number that depends on the extent to which accountants recognize those assets on the balance sheet and subsequently amortize them. __For the modern corporation with relatively few assets on the balance sheet, B/P is quite low, not only due to the market’s pricing of assets but also because assets are not on the balance sheet__.”

“**Return of equity** [ROE] and other measures in profitability factors are interpreted as economic profitability…But ROE is an accounting measure that __not only omits assets in the book-value denominator but also reduces earnings in the numerator with the expensing of investment__; investment that produces earnings is charged against earnings. That is a seeming perversion, confusing investment with return to investment. Further, leverage also affects ROE, compounding the interpretation.”

### Clues for integrating accounting information

“Given the no-arbitrage dividend discount model (with constant discount rates for simplicity) and clean surplus accounting under which earnings add to book value and dividends are paid out of book value…__the price [of a stock] in the infinite-horizon dividend discount model…is [equal to the] expected cumulative future earnings with dividends reinvested at the risk-free rate, [discounted] at the required return__…[In equilibrium] the required return is given by expected future cum-dividend earnings relative to the current price that is discounted for the risk to the expected earnings. This [maeans that] the expected earnings yield…is related to risk and return.”

“The governing principle for booking earnings and the corresponding balance sheet involves an **assessment of risk**: __earnings are recognized only when uncertainty is resolved. Until that point, the recognition of earnings is deferred__. Thus, while a firm’s market price may rationally incorporate future earnings expectations, the accounting informs that those earnings are still at risk…

- Earnings is revenue minus expenses…Under the so-called
**revenue realization principle**,__revenue is not booked until…receipt of cash is ‘highly certain__.’ Only then is revenue added to the income statement and, correspondingly, to book value in the balance sheet, usually with a receivable or cash…In asset pricing terms, revenue and additions to book value are recognized only when a firm can book a low-beta asset, cash or a near-cash receivable…The accountant then recognizes expenses incurred to gain revenues, so-called matched expenses to report net value added from revenues. - [Under
**conservative accounting**] investments where the outcome is particularly uncertain are not booked as assets…__Many investments, often referred to as intangible assets, are not so booked but rather are expensed against earnings__in the income statement under…So, R&D expenditures into a possible drug where there is no product as yet, let alone customers and revenues is distinguished from a plant producing a product with revenues and from the inventory that is the product itself that yields revenues.”

“[One can] connect the two principles—the revenue realization principle and conservative accounting for investment—to the discount factor in a general, no-arbitrage asset pricing model [and evaluate relations through regression]:

- The
__mean coefficient on [accounted] investment [in respect to future stock returns] is reliably negative__…consistent with the realization principle in accounting investment booked to the balance sheet indicates a higher probability of realizing earnings, thus conveying lower expected returns…In contrast, the mean coefficient on*expensed*investment is not significantly different from zero.

__Accounting principles thus explain the negative relation between balance-sheet investment and forward returns__… Investment booked to the balance sheet indicates a higher probability of realizing payoffs, projecting lower risk and return… Risk declines as firms convert risky growth options to ‘assets in place,’ and that is recognized in the accounting treatment. __The book-price ratio is positively related to returns__… Book-to-price is ubiquitous in asset pricing, with higher book-to-price said to indicate higher risk and thus the basis for an [investment] factor…[However, there are] earnings expected in price relative to that not yet recognized by the accounting. Those unrecognized earnings are earnings yet to be realized [at times compromising the information value of the ratio and to be considered in investment strategies]- With conservative accounting for investment, earnings in the numerator of return on equity (ROE) is reduced by expensed investment, and consequently, this investment is missing from its denominator…Thus an
__accounting return on investment is not real profitability, and conjectures that higher accounting ROE results from a higher hurdle rate are off base__, as are those that embrace the accounting ROE as measuring the productivity of investment…[Our regression] reports a slightly negative correlation… of ROE with returns. __Earnings yield is positively associated with returns in many empirical tests__…The forward earnings yield gains its legitimacy as an indicator of the expected return from the equation.”

### An example for a structured account factor

“The starting point is the recognition…that the expected return is given by the expected cum-dividend earnings yield…Investors buy expected earnings but those unrealized earnings are at risk, requiring a discount…Accordingly, information that conveys the expected earnings yield indicates the expected return.”

“This suggests factor construction along the following lines.

- With earnings-to-price as a starting point,
__distinguish low versus high ROE for a given earnings yield__. That incorporates the effect of conservative accounting on earnings (via the ROE numerator) but also the effect on book value (via the denominator); a high ROE indicates earnings realized on previously expensed investment that produced the low book value—risk resolved—and__a low ROE indicates risky expensed investment with future earnings still at risk, yet to be realized__. - But a low ROE can also be due to poor ex-post performance. So,
__within those ROE groups, identify the extent to which ROE is affected by the current expensing of investment__.”

“So, each year at March 31, firms are sorted into four portfolios, one with all negative earnings yield and three from a ranking on positive earnings yield, 1/3 each. Then, within each of those portfolios, firms are sorted on ROE, with the top and bottom third designated high and low. Finally, within each of those earnings yield-ROE portfolios, firms are sorted on expensed investment to price with the top and bottom third again designated high and low. Importantly, these are nested sorts to capture the joint accounting effects for the same set of firms, not the independent sorts of extant models.”

“[We] report means annual excess returns over years for portfolios formed from the first two sorts, on earnings yield and then ROE. The returns are increasing in earnings yield, though those for negative earnings yield are higher than the low positive earnings yield. __For a given earnings yield, returns are decreasing in ROE; ROE adds to information about expected returns to that in earnings yield__.”

“The panel reports (at the far right) the mean return difference between the high positive earnings yield portfolio each year with low ROE and the low positive earnings yield portfolio with high ROE… The mean return spread (with zero net investment) is a significant 7.6%, indicating payoffs to risk differences in the portfolios.”