This paper examines the dimensions and “forces” found in common-size financial statements in both the vertical and horizontal forms.  The analysis looks at the financial metrics, trends, and insights that can be gained from comparing statements in the vertical and horizontal directions.  The paper concludes with a discussion of Melse (2008) and addresses the research question and conclusions made in the article titled, “Accounting in three dimensions: A case for momentum revisited.”

Horizontal Analysis

            Analyzing financial statements in a horizontal form refers to comparing similar line items of the balance sheet and income statement across relevant time intervals.  Common-size financial statements describe the conversion of values to percentages or ratios to key benchmarks such as top-line revenue on the income statement and total assets on the balance sheet.  This conversion to percentages allows for direct comparison between time intervals and other firm performance metrics in the same time periods (Gibson, 2012).

In the example of Exxon Mobil Corp. a three year consolidated income statement is presented using progress from 2004 as the benchmark for growth in revenue and reduction goals statement1across expense categories.  The horizontal analysis shows that Exxon revenue increased 23.2% in 2005 and 25.5% in 2006 from levels of $291 billion in 2004.  This type of analysis provides trending data that clearly shows Exxon revenue is growing at more than 20% per year and allows for additional trend comparisons of expenses and net income line items.  In a combination of horizontal and vertical analysis one significant insight is that the total revenues are growing at 24.4% and 26.7% while total costs are only growing at 21.2% and 20.8% in comparable periods.  Common-size financial statements provide clarity and a means for direct comparison that allow for measurements of performance against prior years, other firms, and average performances within and across business sectors (Gibson, 2012).

In another financial example using a horizontal analysis of a balance sheet from 2007 to 2008 the differences between the two years are computed in percentages.  The benchmark is thestatement2 year 2007 and comparisons of growth or decline are clearly illustrated in positive or negative percentages.  This conversion allows an analyst to quickly observe that only three line items are increasing: current assets, retained earnings, and total stockholder’s equity.  The current assets are growing while long-term PP&E declined in the comparable periods.  The total liabilities show a decrease of 30% that reflects a strong reduction in obligations that may be beneficial for the business.  These trends give historical insight into the performance of a business and allow for comparisons of growth rates across categories in a vertical analysis as well.  Studies have shown that consistent trends across time greatly increase investor interest in a firm and increase the perception of management credibility on future decisions (Koonce & Lipe, 2010). While the common-size approach allows for broad comparisons, the value of horizontal analysis depends on comparing similar time periods; otherwise the rates of change being compared are misleading and incompatible for analysis.

Vertical Analysis

            Analyzing financial statements in a vertical form refers to comparing items on the same income or balance sheet in proportion to key statement benchmarks in the same time period such as total revenue or total assets.  Using an example of vertical analysis from an Exxon Mobil Corp. statement3balance sheet the conversion to common-size percentages occurs in a vertical calculation of proportions to total assets, total liabilities and shareholder’s equity.  For example, the cash and cash equivalents in 2005 represent 13.8% of the total assets of Exxon Mobil.  PP&E represent 51.4% of Exxon Mobil’s assets in the same period.  Comparisons of these components work well with a pie chart illustration of percentages of each asset line item that comprise the whole.  It is important to recognize the distinction between vertical and horizontal comparisons using common-size financial statements.  For example in analyzing total current assets that comprise 35.2% of assets in 2005 and 34.6% of assets in 2006 this does not represent a change in rate over time.  Even though the current assets in 2006 are a smaller 34.6% proportion of the total assets for Exxon Mobil relative to 2005, the actual $75.8 billion in current assets in 2006 is larger than the $73.3 billion in 2005.  The purpose of a vertical analysis is to observe which components of the balance sheet are increasing or decreasing in relation to the asset or liability benchmark within each time period.  It is another tool to clearly observe when values become disproportional relative to each other on the same financial statement and time period.  Insights managers could use with the vertical analysis includes setting guidelines that liquid assets need to comprise more than 12% of total assets in order to cover short-term variances with a greater cushion of cash on hand.  It is a valuable tool for internal business metrics and tracking category increases or decreases relative to primary business benchmarks.

From the perspective of the income statement a similar vertical analysis can be made between components and the total sales for each period.  In the following comparative income statement statement4the gross profit in 2008 represents 30.4% of total sales and 31.7% in 2007.  Again, despite a larger percentage of gross profit in 2007 the actual gross profit is $75,000 less than actual values in 2008.  Represented in the vertical is how the proportion to sales has changed over time so the view on those items becomes clearer for decisions and analysis.  In the horizontal the percentage increase represents growth of actual value over time relative to prior equal time periods.  In the vertical the percentage increase represents growth of actual value relative to other components on the financial statement in the same period.

Review of Melse (2008)

            Eric Melse introduces a different perspective on analyzing financial statements titled, “Accounting in three dimensions: A case for momentum.”  Borrowing on themes from physics he describes a type of vector analysis as an applicable means for examining financial statements with better understanding.  Melse describes a triple-entry framework with three dimensions that incorporates capacity into a more robust growth picture that he calls momentum.  He explains how this momentum is analogous to a dashboard on a car and how financial statements represent the odometer in continuity or “now,” the odometer period or “how,” and a speedometer or “why” (p. 335).  In vector analysis a similar representation is known as magnitude, velocity, and direction. The point Melse makes is that businesses have a financial motion that can be described and explained through balance sheets, income statements, and changes in wealth.   He classifies data based on magnitudes, cash flows, and changes over time.  He suggests components of accounting wherein Force is a derivative of Momentum and Momentum a derivative of Wealth and this framework is captured using triple-entry accounting.

This accounting perspective is fully consistent with other studies related to the momentum effect anomaly that explains how company stock prices that do well in prior years continue to do well in future years (Fama & French, 2012).  These unusually high returns over time simulate momentum in physics and show high correlation with inertia from fundamental values and strong financial ratios.  The stock prices accelerate as good results are reported and slow as financial reports disappoint or slow from previous reported periods.

The Melse study then classifies different financial statements into the three “dimensions” of accounting as well as the financial ratios that correspond to each of the financial statements.  The intent of the methodology is to provide an improved perspective on the financial criteria that put businesses in motion and sustain the direction and velocity over time.  Melse describes a number of benefits of the methodology, such as predicting stock price movement, balancing investment portfolio risk, and gaining a deeper understanding what the accounting data represents.  Analyzing the complex motion of business fluctuations using concepts of physics makes sense as different sizes, incomes, liabilities, debt, and returns on assets comprise distinct forces that contribute to acceleration or decay of a firm over time.  That these financial statement “forces” have predictive market aspects that can be used to anticipate stock price movement and risk is consistent with many studies (Konchitchki & Patatoukas, 2014).  Scholars and investors appreciate the value in looking at financial statements from many perspectives and in multi-dimensional ways to improve understanding.


Fama, E. F. & French, K. R. (2012). Size, value, and momentum in international stock returns. Journal of Financial Economics, 105(2012), 457-472.

Gibson, C. H. (2011).  Financial reporting & analysis: Using financial accounting information. Mason OH:   South-Western.   ISBN: 9781439080603

Melse, E. (2008).  Accounting in three dimensions: A case for momentum revisited. The Journal of Risk Finance, 9(4), 334-350. doi: 10.1108/15265940810895007

Konchitchki, Y. & Patatoukas, P. N. (2014).  Taking the pulse of the real economy usingfinancial statement analysis: Implications for macro forecasting and stock valuation.  The Accounting Review, 89(2), 669-694.  doi: 10.2308/accr-50632

Koonce, L. & Lipe, M. G. (2010). Earnings trend and performance relative to benchmarks: How consistency influences their joint use.  Journal of Accounting Research, 48(4), 859-884. doi: 10.1111/j.1475-679X.2010.00377.x