diversity of the credit portfolio, The

Abstract

The cheapest and easiest approach to managing the loan or receivables poq/61io is to invest every dollar in one credit. Of course this strategy carries the risk of a single default destroying the entire value of the porfolio. The objective of diversification is to spread portfolio dollars over a number of loans and reduce the probability of a catastrophic loss.

The Concentration Ratio

The concentration ratio is a useful tool that allows a credit manager to measure the diversity of the portfolio. The overall concentration ratio for the portfolio is simply the sum of the squared proportions of each credit. For example, suppose a portfolio consists of four loans in the proportions 49%, 21%, 16% and 14%. The concentration ratio is [(.49)2+(.21 ) 2+(. 16) 2+(. 14) 2] or 33%. This measure accounts for both the number of credits and their relative sizes. The portfolio has four loans but the large size of one produces the same overall concentration ratio as a portfolio with three loans of equal size [(.33)2+(.33)2+(.33)2] or 33%.

The possible values of the concentration ratio range from zero to one with smaller values indicating a more diverse portfolio. An easy interpretation of the concentration ratio is the weighted average of the concentrations of the individual loans. As shown below, the concentration of each loan in the portfolio is weighted by its importance in the portfolio.

(.49)(.49)+(.21)(.21) +(.16)(.16) +(.14)(.14) = .33

The concentration ratio is also the probability that two dollars drawn at random from the portfolio will be from the same loan. Obviously the higher the concentration of the portfolio, the higher the probability.

The concentration ratio conveys useful information but it can only deal with one dimension of diversification at a time. For instance, assume a portfolio consists of four equal loans to firms in different industries. This portfolio is clearly more diversified than one with four equal loans to firms in the same industry but both portfolios have a concentration ratio of [(.25)2+( .25)2+( .25)2+( .25)2] or 25%. The concentration ratio captures only the diversification across firms and not the diversification across industries. The following discussion describes a new measure that considers many aspects of diversification simultaneously. The similarity ratio allows the credit manager to include several dimensions of diversity in a single measure. Calculating The Similarity Ratio

The last column in the table above is a similarity ratio for each loan in the portfolio. The overall similarity ratio for the portfolio (S) is the weighted average of these figures. The equation below weights the similarity ratio for each loan by the relative importance of the loan in the portfolio.

S = (.40)(.70) + (.30)(.65) + (.20)(.60) + (.10)(.55) = .65

The similarity ratio for the portfolio indicates the average similarity of portfolio dollars and can take on values between zero and one. The lower the value, the less similar the loans, and the greater the diversity of the portfolio.

Increasing Diversification Across Firms

A credit manager can use the similarity ratio to assess the impact of changes in the portfolio on the level of diversification. The portfolio in the above example is relatively concentrated because there is one large loan that accounts for 40% of the portfolio. Spreading portfolio dollars evenly over four firms would increase the diversification of the portfolio.

S = (.25)(.625) + (.25)(.625) + (.25)(. 625) + (.25)(. 625) = .625 Increasing Diversification Across Industries

The equation below shows that diversifying across industries reduces the similarity ratio for the entire portfolio to (0.25).

S = (.25)(.25) + (.25)(.25) + (.25)(.25) + (.25)(.25) = .25

A portfolio concentrated in a single loan would have a similarity ratio of one. The calculations above show that diversifying evenly across four firms in the same industry reduces the similarity ratio from one to (0.625). Further diversification by spreading the portfolio evenly over four firms in different industries reduces the similarity ratio from (0.625) to (0.25).

This example shows the equal effects of diversification by firm and diversification by industry. The initial diversification by firm reduces the similarity ratio by (0.375) from one to (0.625). The subsequent diversification by industry produces an identical reduction in the similarity ratio of (0.375) from (0.625) to (0.25).

This example also illustrates that the concentration ratio is a special case of the similarity ratio. These two measures yield the same result when there is no similarity among loans. This relationship provides a useful interpretation of the similarity ratio. For example, a similarity ratio of (0.20) indicates the portfolio has the same diversification as a portfolio spread evenly over five loans to completely different firms.

Conclusion

The analysis of commercial credit has two distinct aspects. The first is the evaluation of individual borrowers using tools such as cash flow forecasting and the analysis of financial statement ratios. The second is the evaluation of the overall credit portfolio using tools like the concentration ratio and the similarity ratio. Both of these aspects of financial analysis have an important role to play in credit administration. It is important both to select good borrowers and to build a diversified portfolio.

Richard H. Borgman is Assistant Professor of Finance and John K. Ford is Nicolas Salgo Professor of Business Administration at the Maine Business School, University of Maine, Orono, ME 04469

Copyright Credit Research Foundation Fourth Quarter 2000
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