Managing concentration risk in receivables

Managing concentration risk in receivables

Borgman, Richard H

The management of accounts receivable can be a complicated task, with direct implications for the firm’s bottom line. The credit manager must identify sources of risk and balance potential sales with potential losses when setting credit policy. The firm’s business type, financial position, approach to risk, and customer profiles must all be considered when establishing the firm’s risk preference. However, all firms can reduce receivable risk by applying the principle of diversification. This article describes an analytic tool that measures the level of diversification in a portfolio of receivables. The concentration ratio measures concentration risk, the degree that a pool of receivables is concentrated in a relatively few accounts.

The benefits of diversification are familiar and generally accepted, as long as payoff prospects are not perfectly (positively) correlated, the risk of the aggregate payoff can be reduced by diversifying over many financial assets. Having a number of customer accounts in and of itself does not ensure diversification. Often, a more complex application of this diversification principle to accounts receivable is problematic because information about customers’ payoff probabilities and correlations is generally unavailable or difficult to estimate.It is possible, however, for managers to calculate a summary measure of portfolio concentration which incorporates both number and size of accounts. Further, understanding the measure allows a manager to take steps to improve the level of concentration risk. The following sections describe and define the concentration ratio, and then apply it to estimate the concentration of a large sample of public firms.

The Concentration Ratio

The concentration ratio has a venerable history as a measure of industrial and international trade concentration, and has been applied to bank loan portfolios.2In all cases, it indicates relative diversification, whether of competitors within an industry (i.e., monopoly), of trade with foreign countries, of bank loans, or here, of accounts receivable.

A simple example will help illustrate. Say a firm has five customers with accounts receivable balances. Customer A owes $80, B and C owe $100, D owes $400, and E owes $600. The total accounts receivable balance is $1,280. The amount of receivable dollars concentrated in customer A is 80/1280 or 6.25%; similarly, the amount of receivable dollars in B and C is 7.81% each, in D is 31.25%, and in E is 46.9/o. The concentration ratio for this portfolio of receivables is calculated by weighting each individual dollar concentration by its importance to the portfolio, by its relative dollar value and then summing. Thus, the process that arrives at the concentration ratio is to square the individual dollar concentrations and sum to form a weighted average of dollar concentrations. The concentration ratio for this firm’s receivables (firm 1) is 0.333 or 1/3. The results are summarized in Table 1.

More formally, the concentration ratio (C) is defined as: where Si is the dollar amount of receivables from customer i, N is the number of customers, and S is total receivables. C can range from a minimum of just over 0 to a maximum of 1. Given a set of borrowers, C indicates the extent of diversification versus a naive optimal diversification of an equal sized credit to each borrower.3 The higher the ratio, the more concentration. The reciprocal of the concentration ratio, called the diversification quotient (Q), signifies the number of equal sized loans which would generate the same concentration ratio. It is what Adelman (1969) calls a “numbers-equivalent.” Thus the diversification quotient is an indicator of how diversified a firm’s accounts receivable actually are.

For firm 1, the maximum potential diversification, and the minimum concentration ratio, occurs when the receivables are equally allocated across the five firms. Then C = 1/N = 1/5 = 0.2. Firm 1 is less diversified that it could be potentially. The diversification quotient for firm 1 is the reciprocal of C, or 3. Despite a portfolio of 5 customers, this firm’s receivables are as diversified as a portfolio of 3 equal sized accounts. In other words, the relatively large accounts (D and E) increase the concentration of the firm’s receivables from the potential minimum of 0.2 to 0.33. Similarly, the diversification has been diminished from a potential maximum of 5 (lN) to 3.

Compare this firm with firms 2 and 3 (also summarized in Table 1), each with receivables totaling $1,280. Firm 2 reflects better diversification. The concentration ratio is 0.25 and the diversification quotient is 4. It is diversified as well as a portfolio of 4 equal sized credits. Firm 3 is the least diversified. Most of its risk is concentrated in a single large receivable. C is 0.5 and Q is 2.

The concentration ratio has real value to a credit manager. It is a single summary measure that links number and proportion. Even without knowing individual customer risks with a high degree of accuracy, and even without knowing correlations among customer risks, all things being equal, a reduction in the concentration ratio will reduce the firm’s overall exposure to credit risk in its receivables portfolio and increase the firm’s effective diversification.

In fact, it is possible to determine the optimal size of a new account receivable if the desire is to reduce concentration. The optimal size is the fraction C of the current total accounts receivable dollars. For firm 1, the optimal size of a new account receivable would be $426 (i.e., 0.333 x $1,280) which will reduce concentration to 0.25 and increase the diversification quotient by 1 to 4 (note that the an optimal sized new customer account will always increase the diversification quotient by 1). In contrast, the optimal sized new account for the more diversified firm 2 is $320, which will result in a new diversification quotient of 5, and $640 for the least diversified firm 3.

The maximum sized new account receivable that will not increase concentration is 2 – ( CC) times the current accounts receivable total amount. For firm 1, that turns out to be $1,280, the current size of total accounts receivable. For firm 2, the largest new customer account would be $853 and for firm 3 it is $2,560.

The Concentration of Accounts Payable of Public Firms

To better illustrate the use of the concentration ratio and the characteristics of concentrations in the real world, accounts payable totals for a large sample of public non-financial firms were collected from the Compustat database.4 These accounts payable would, of course, show as accounts receivable for many other firms. From the entire database, there were 7001 firms with accounts payable information. Typically because a relatively small number of firms do most of the business, there is not an even distribution of payables. The largest 14 firms (in terms of accounts payable), for example, represent just over 20% of all payables in the sample. (Table 2)

The concentration ratio captures this imbalance in payables. If all these accounts payables were the receivables of just one firm, that firm would have a concentration ratio in receivables of 0.005, which inverts to a diversification quotient of 200. That is, despite the existence of 7001 accounts, because some firms are much larger and owe much more than others, this portfolio is as diversified as a portfolio of 200 equal sized credits. What is clear from this illustration is that it is not simply the number of accounts (customers) that provides diversification, it is the proportion of dollars in those accounts that is very important. What is also clear is that the manager of accounts receivable faces serious concentration problems if his firm’s clients reflect at all the imbalance in the economy as a whole.

Table 3 presents concentrations by industry. As a rough way to differentiate, the sample of 7001 firms was divided by SIC codes into 14 groups. Note the number of firms per industry varies widely using this criteria, from 23 personal services firms to 3,443 manufacturing firms. All segments, not surprisingly, exhibit significant concentrations. For example, the payables of the 417 mining firms are as diversified as an equal sized pool of 25.

One additional calculation (last column of Table 3) indicates the relative degree of concentration across industry. The measure of relative diversification is each industry’s diversification quotient divided by N, the number of firms, all multiplied by 100. Thus this measure is scaled from 0 to 100, with a higher score indicating greater diversification in that industry, a lower number indicating greater concentration. The most diversified industry is the smallest – personal services. With 23 firms and a diversification quotient of 5.67, the industry’s accounts payables are almost 25% as diversified as is potentially possible. The least diversified is business services, whose 646 firms have a diversification quotient of only 6.4, and a relative diversification measure of only 0.98 or just about 1% of what would be possible with equal sized firms.


The concentration ratio presented in this article is a practical measure that considers the number and size of customer accounts to help credit managers assess the level of diversification in their accounts receivable. Of course, while measuring diversification is important, it is only one aspect of an effort to manage credit risk exposure. But the concentration ratio is a simple tool that can tell managers the relative level of receivable concentration, provide guidance as to the characteristics that will reduce concentration, and over time indicate improvement or deterioration in accounts receivable diversification. On the other hand, it is clear that receivable managers face a formidable task. Accounts payable volume among public firms is concentrated overall and by industry.

1 Pierce and Chase (1988), for example, point out that “diversification is a simple concept whose implementation is complex.”

Two men – acting independently – are acknowledged with the development of the concentration ratio: Albert O. Hirschman in his 1945 study National Power and the Structure of Foreign Trade and O.C. Herfindahl in his 1950 doctoral dissertation Concentration in the U.S. Steel Industry. Paroush (1992) and Ford (1995-96) have applied the ratio to bank portfolio concentrations

The strategy is naive because it assumes all firms are equally likely to default and each firm’s likelihood is independent of other firms.

4 The data are from year end 1995.


Adelman, MA., February 1969, “Comment on the “H” Concentration Measure as a Numbers-Equivalent,” Review of Economics and Statistics, 51, 99-101.

Ford, John K, Winter 1995-96, “The Effect of a New Loan on Portfolio Concentration” Commercial Lending Review.

Herfindahl, Orris C., 1950, Concentration in the U.S. Steel Industry, Doctoral Dissertation, Columbia University.

Hirschman, Albert O., 1945, National Power and the Structure of Foreign Trade, Berkeley: University of California Press.

Paroush, Jacob, 1992, “Credit Risk Measurement,” International Review of Economics and Finance, 1(1), 3341.

Pierce, James L., and Samuel B. Chase, July 1988, The Management of Risk in Banking, Washington D.C.: Association of Reserve City Bankers

Richard H. Borgman, PhD. is an Assistant Professor of Finance and John K Ford PhD. is a Professor of Finance at the Maine Business School of the University of Maine.

Copyright Credit Research Foundation Second Quarter 1998

Provided by ProQuest Information and Learning Company. All rights Reserved