## Stock and Flow Essentials

Grasping the difference between stock and flow variables is essential to understanding and analyzing financial and economic data. Mathematically speaking, a flow variable is a vector, a two-dimensional measurement. One of these dimensions is time. The other is the quantity of the variable in question that was tabulated over the specified period. By contrast, a stock variable is a one-dimensional measure. It is an instantaneous measure, taken at a precise moment in time. As a result, stock variables often are referred to as snapshot values.

Income statements are collections of flow variables. Balance sheets contain stock variables.

## The Time Element

Since audited financial statements typically are produced on both a quarterly and an annual basis, these are the most common time dimensions encountered in dealing with flow variables in finance. For internal management reporting purposes; however, financial reports often are produced on a monthly, weekly and even daily basis. Indeed, in much of the financial services industry, especially in securities firms, daily closure of the books is customary, largely due to regulatory requirements.

Noting the time dimension associated with a given flow variable is critical to the correct interpretation thereof, including using historical data to develop financial forecasts and projections for future time periods.

Because stock variables are a point in time observations, their values may not be representative of a company's normal financial position over a longer period, such as during an entire fiscal quarter or fiscal year. This can be due either to random events or to the deliberate manipulation of financial results by the company; a process traditionally referred to as window dressing. This can include temporarily removing certain debts or loans from the company's balance sheet as of the reporting date, thereby enhancing the apparent financial strength of the firm. Using the point in time stock variables on a balance sheet thus have potentially serious limitations as indicators of financial condition.

## Apple Inc. Example

Apple Inc. (AAPL) reported \$233.7 billion in net sales revenue on its income statement for the fiscal year 2015, which ended on Sept. 26, 2015 (per page 39 of its 2015 Form 10-K, as can be found on Apple's investor relations page). As should be the case with the flow variables on income statements, this figure equals the sum of the net sales revenue figures on the four quarterly financial statements for the same fiscal year:

74.6 + 58.0 + 49.6 + 51.5 =  \$233.7 billion

Note, however, that the audited figures in a firm’s annual report may not equal the sum of previously released unaudited quarterly data for the same fiscal year. Adjustments made by the auditors can produce discrepancies. In the case of Apple’s 2015 reporting, the auditors do not seem to have made any material adjustments, at least not to numbers that are rounded to the nearest million dollars. The income statement figures in the unaudited quarterly reports add to the numbers in the audited annual report.

Turning to the stock variables on Apple’s balance sheet, take long-term debt as an example. A figure of \$53.463 billion is the snapshot taken on September 26, 2015. This same figure is reported on Apple’s 10-K and 10-Q reports for that point in time. The closing value for fiscal 2014 was \$28.987 billion. Deriving an average value of long-term debt for fiscal 2015 can be done two ways.

A quick method is a two-point average of the closing values for fiscal years 2014 and 2015:

(28.987 + 53.463) / 2 = \$41.225 billion

A more detailed method is a five-point average, also taking account of the closing values for the three intervening fiscal quarters:

(28.987 + 32.504 + 40.072 + 47.419 + 53.463) / 5 = \$40.489 billion

Even this latter method, which uses three additional data points, is at best an approximation. As with the two-point average, the five-point average presumes that the book value of Apple’s long-term debt grew smoothly between observations, which may or may not have been the actual case. Nonetheless, in the absence of publicly available data showing the actual day-to-day changes, these are the best approximations that an analyst can make.

## Economic Data

Time periods of a year and a calendar quarter are typical for most flow variables. Unlike financial flow variables, when economic flow variables are reported for periods of less than a calendar year, the numbers usually are annualized and seasonally adjusted.

For example, as reported by the Bureau of Economic Analysis (BEA) of the U.S. Department of Commerce, Gross Domestic Product (GDP) for the calendar year 2014 was \$17.348 trillion. The quarterly GDP figures for 2014, also in trillions, were \$16.984, \$17.270, \$17.522 and \$17.616, respectively. The annual GDP figure for 2014 thus is the average, rather than the sum of the four quarterly numbers:

(16.984 + 17.270 + 17.522 + 17.616) / 4 = \$17.348 trillion

Seasonal adjustments remove the impact of recurring patterns in economic activity that manifest themselves at roughly the same time each year. Most notably, economic activity in the U.S. is markedly weakest in the first calendar quarter. In particular, retail sales suffer a huge fall after the Christmas shopping season, and construction activity is impaired by winter weather in much of the country. As explained in the Federal Reserve Bank of San Francisco Economic Letter “The Puzzle of Weak First-Quarter GDP Growth,” in recent years unadjusted GDP has tended to fall by about 10% in the first quarter and rise by about 20% in the second quarter. Removing seasonal fluctuations that repeat every year is designed “to reveal underlying cyclical and trend movements in the economy."

## Seasonality at Apple

Returning to the analysis of Apple Inc. above, you can see an obvious pattern of seasonality in its net sales revenue. The first fiscal quarter of 2015, which ended on December 27, 2014, produced 32% of that fiscal year’s sales revenue (\$74.6 million out of \$233.7 million), indicating the importance of the Christmas shopping season to this consumer products company. In fact, analysis of quarterly net sales revenue for fiscal 2013 through 2015 reveals a remarkably stable seasonal sales pattern:

32% of the annual total in the first quarter of each year

25% in the second quarter of each year

20% to 21% in the third quarter

22% to 23% in the fourth quarter

## The Bottom Line

In working with financial or economic data, it is critical to understand whether the measure in question is a stock or flow variable, as well as the point in time or time period associated with its measurement. Additionally, economic flow variables are frequently reported as seasonally adjusted annual rates, which has key implications for the interpretation thereof.