Technical Efficiency in
Active Portfolio Management
Leon Korte
The University of South Dakota School of Business
Vermillion, South Dakota
November 2001
Most individuals and institutions invest in a portfolio of assets. Commercial banks invest in many different types of financial assets when they make loans to consumers and businesses. Diversification can be achieved by investing is a set of securities that have different risk-return characteristics. The amount of risk reduction achieved through diversification depends on the degree of correlation between the returns of the individual securities in the portfolio. Because most securities are positively correlated with returns in the securities market in general, it is usually not possible to eliminate all risk in a portfolio of securities. As the economic outlook improves, returns on most individual securities tend to increase; as the economic outlook deteriorates, individual security returns tend to decline. In spite of this "co-movement" among the returns of individual securities, each security experiences some "unique" variation in its returns unrelated to the underlying economic factors that influence all securities. In other words, there are two types of risk inherent in each security: systematic, or non-diversifiable, risk and unsystematic, or diversifiable, risk.
Systematic risk refers to that portion of the variability of an individual security's returns caused by factors affecting the market as a whole; as such it can be thought of as being non-diversifiable. Systematic risk accounts for 25 to 50 percent of the total risk of any security. Some of the sources of systematic risk, which cause the returns from all securities to vary more or less together, include interest rate changes, inflation and changes in investor expectations about the overall performance of the economy.
Unsystematic risk is unique to the firm. It is the variability in a security's return caused by such factors as management capabilities and decisions, the unique effects of government regulations, and the particular levels of financial and operating leverage the firm employs. Since unsystematic risk is unique to each firm, an efficiently diversified portfolio of securities can successfully eliminate most of the unsystematic risk inherent in the individual securities. A cost of a diversified portfolio is the effort required to understand and control the diverse assets. A specialized portfolio requires specialized knowledge in a narrower area of portfolio management.
Banks report loan portfolio categories including real estate loans, loans to deposit institutions, agricultural production and farming, commercial and industrial, loans to individuals and other loans. Banks were identified as holding a specialized [non-diversified] loan portfolios if agricultural production and farming loans accounted for 60 percent or more of the bank's loan portfolio. Banks were identified as holding diverse portfolios if no category accounted for more than 40 percent of the bank's total loan portfolio.
Data for the years ended December 31, 1995, 1996, 1997, 1998 and 1999 were collected. A bank was included in the sample if it was categorized consistently for all five years. Sixteen banks with 80 observations were included in the sample.
The banks included in the specialized portfolio sample reported an average of 78.9 percent of their respective loan portfolios in agricultural production and farming related loans. The largest concentration was 95.15 percent of the total loan portfolio in agriculture related loans. The smallest concentration was 66.82 percent in agriculture related loans. Banks included in the diversified portfolio sample reported an average distribution ranging from 17.2 percent of their portfolio as loans to individuals to 31.3 percent of their portfolio as commercial and industrial loans.
The observations included in the specialized portfolio sample are located in smaller, more rural communities than is the case for the diversified portfolio observations. The average total assets for the specialized portfolio observations was $18.882 million (s = $8.931 million). The diversified portfolio observations averaged $156.900 million (s = $129.198 million) in total assets. The difference in average total assets was statistically significant.
A common and simple partial productivity measure in the banking industry relates outstanding deposits or loans to number of employees. In this study the average earning assets per employee for the specialized portfolio observations was $2,005,410 (s = $457,290); the average earning assets per employee for the diversified portfolio observations was $2,069,590 (s = $438,320). The difference between the two groups was not statistically significant (T = 0.6374; a = 0.4742).
Data envelopment analysis was first set forth by Farrell (1957) in a special case single input/single-output technical efficiency model. Charnes, Cooper and Rhodes (1978) generalized the special case model by applying mathematical programming to construct a single “virtual” input and a single “virtual” output from multiple variables. This non-parametric approach calculates a discrete piecewise frontier for each observation rather than optimizing a single regression plane for all the data. The focus of data envelopment analysis is on individual observations in contrast to the emphasis on averages associated with other statistical approaches.
As a financial intermediary, a bank collects deposits from customers and translates the available funds into credit for others and other investment instruments. The model variables capture the necessary input allocation and product mix decisions needed to acquire deposits and make loans and investments. The banking industry has changed, but the functions of financial intermediaries have remained relatively constant.
The investment model incorporates six input variables. The variables reflecting input resources include:
1. Full-time employees
2. Employee compensation expenses (salaries and benefits)
3. Expenses related to premises and fixed assets
4. Other non-interest expense
5. Core deposits
6. Purchased funds
Management’s decisions relative to staffing levels reflect the efficiency of operations. Full-time equivalent employees represent a productive resource that may or may not be used efficiently. Employee compensation costs reflect market conditions necessary to acquire the employees.
Expenses related to premises and fixed assets include depreciation and/or rent of banking facilities, lease costs for computing services and other costs of occupancy and operations. These costs reflect management decisions about the leasing or ownership of buildings and other long-term assets.
The cash or money position of a bank may be managed through either the purchase or sale of assets or through borrowing. Assets purchased or sold may include Treasury bills, short-term government securities, bankers’ acceptances, and Federal funds. Borrowing may take the form of buying Federal funds through the Federal funds market or direct borrowing from the Federal Reserve. Maintaining a net borrowed or purchased position in Federal funds is thought to be a less conservative management approach.
Management determines the number of employees needed to perform operating function at a desired level of service. They establish salary levels, determine the types and locations of facilities and the policies and procedures for furnishings and operations. Market forces determine some of these factors, but management makes the decisions regarding the overall level of expenses that can affect activities such as past-due collections, portfolio quality decisions or deposit servicing. Furthermore, management determines the non-interest expenses incurred by the firm such as legal and administrative costs.
Core deposits and purchased funds are two additional input variables. Core deposits are stable deposits not typically withdrawn over short periods of time and are not highly rate sensitive. An estimate of core deposits includes the sum of demand deposits, NOWs, MMDAs, savings deposits, and small deposits.
Purchased funds represent funds needed in addition to deposits to service investments and provide liquidity. This category includes federal funds purchased and securities sold under agreement to repurchase, demand notes issued to the United States Treasury, other borrowed money, time certificates of $100,000 or more, and open-account time deposits of $100,000 or more.
The variables reflecting banking outputs include:
1. Earnings Assets
2. Total interest income
Earning assets include performing loans (total loans less loans 90 days or more past due and non-accrual loans). For purposes of this study earning assets included loans for construction and development, farmland, non-agricultural real estate, agriculture production loans, commercial and industrial loans, and credit card loans. These six groups were consolidated into a single variable to minimize observations with zero values. It is further assumed that loan-servicing activities do not significantly vary across the six categories.
Total interest income is the interest earned on the loans mentioned. Management decides where to invest funds as well as determines the relative quality and risk of each asset in which it invests. The amount of interest income thus serves as a proxy for the diversification of the various loan portfolios.
Output variables for the investment model are interest income and earning assets. Interest income reflects the revenues generated by the investments selected by bank management. Earning assets reflect investments and loans that are current and accruing interest.
To model the essential functions of banking a multiple variable model is necessary to capture the complexities of the process. Single factor ratios do not capture the interactions of the bank activities relative to gathering deposits and making investments. To measure managerial efficiency the multiple-variable relationships must be modeled. An evaluation technique that measures transformational efficiency relative to peer institutions controls for environmental conditions that are not influenced by managerial actions and allows for a inter-firm comparison of management efficiency.
A preliminary research question is whether the relative efficiencies observed in the two groups is different when observed from a macro perspective. Assuming the efficiency scores are not normally distributed, the hypothesis that the two groups are equal was tested using the Mann-Whitney test for rank order. The null hypothesis is that the sum of ranks for the specialized observations is not statistically different from the sum of the rank order of the diversified observations when the efficiency scores are calculated from a pooled set of observations. Mathematically, the hypothesis may be written:
The eighty observations comprising the five years were pooled and evaluated using the DEA methodology. The relative efficiency scores were ranked in descending order so that more efficient observations were assigned lower ordinal values in the rank order. The sum of the ranks for the specialized observations (n = 45) was 1731 (m = 38.47). The sum of the diversified observations (n = 35) was 1509 (m = 43.11). The difference was not statistically significant using the Mann-Whitney large sample test (z = 0.88742); the mean rank order for eighty observations is 405.
The rank orders of the individual years were compared to determine if the hypothesis held for the individual years as well as the pooled data. The efficiency scores calculated using the pooled data were segregated into individual years and then ranked from most efficient to least efficient for each year. Using a small-sample case of the Mann-Whitney test, the null hypothesis is rejected if the sum of the ranks of the specialized class is either less than 58 or greater than 95. The differences in the sum of the rank order values were not statistically significant when evaluated using the Mann-Whitney small sample test for any of the five years of the study period. The mean rank for the specialized portfolios was less than the mean rank of the diversified portfolios in four of the five years, the exception being 1998. In 1998 the diversified portfolios were relatively more efficient than the specialized portfolios, suggesting a possible weakening in the underlying operations of the agriculture sector of the economy. Again, the apparent reversal in rankings reflected the non-significance of the difference between the two groups for the five years of the study period.
For a third analysis the relative efficiency scores were divided by class, ranked and analyzed by year to see there was any differences in the ranking of observations across time. The scores for the two classes cannot be compared as the ranks were calculated for each class separately, however the trends of the ranks suggest that the two groups followed relatively similar patterns during the five years included in the study period. The trends are reflected in Table 3 and the corresponding graph. Similarly because the ranks were calculated for five years for each class it is difficult to calculate statistical significance for the differences between years. In each group the sum of the rank orders decreased from 1995 to 1997 suggesting an increase in relative efficiency for each group (scores were ranked in descending order). The sum of the ranks increased in 1998 reflecting a decline in relative efficiency in each group in that year. The decline in relative efficiency for the specialized portfolios was more pronounced than was apparent for the diversified portfolios in 1998. The sum of the ranks again declined for both groups in 1999 reflecting an apparent increase in relative efficiency in the last year included in the study period. As in the preceding year the changes in relative efficiency for the specialized portfolios was more pronounced in 1999 than was apparent for the diversified portfolios.
Portfolio management efficiency is a function of the abilities of the individual managers and the policy constraints imposed by the characteristics of the investment portfolio. To control for the possible differences created by the differing characteristics of the portfolios each group was analyzed separately to identify possible differences among the individual observations within each group. The observations were divided into specialized or diversified samples and again subjected to the DEA methodology. The DEA efficiency scores of this second analysis were compared to the scores from the pooled data for the same observations to gain some insight as to possible differences in relative efficiencies depending on the composition of the potential reference set.
In each case the efficiency scores for the separate classes were higher than calculated for the pooled data. This may suggest that relative efficiency is influenced by the factors present in the individual observations that are unique to each group of observations. The higher relative efficiency scores within the two groups suggest there is more difference between groups than within groups. Portfolio management efficiency can be assumed to be more consistent within the respective groups and the subsequent projections to the efficiency frontier in the next analysis does not materially misstate the managerial abilities reflected in the respective observations.
There were no differences in the relative rankings of the observations included in the specialized portfolio group. This suggests that the efficiency frontiers for the specialized observations are dominated by observations from the same class. The diversified portfolio observations showed less uniformity in relative rankings when comparing the efficiency scores calculated from the pooled data and the scores calculated using only the diversified portfolio observations. This appears consistent with the conclusions that specialized portfolio observations dominated the efficiency frontiers for the pooled data. Comparing the scores for the diversified portfolio observations for the pooled analysis and the separate group analysis it again appears that there is more uniformity within the diversified group of observations that is found in the pooled data.
To test for possible differences between programs it was first necessary to control for variations resulting from the differences in the management of the individual observations. This was accomplished in three steps. In the first step DEA models were run for each observation in comparison with observations of the same group and virtual observations were created by projecting the observations to the efficiency frontier. The virtual observation reflects the existing input or output relationships in relation to the efficient reference set for each observation. This step was completed using both an input orientation and an output orientation. Later analysis suggests that although the projections to the virtual observation differs depending on the orientation, the efficiency scores are not affected.
In the second step the virtual observations from the two groups were pooled together and DEA models were run on the pooled data. The third step was to test the hypothesis that the efficiency distributions from the virtual observations were identical between the specialized lenders and the diversified lenders. As in the first analysis, the Mann-Whitney tests were used to assess the differences between the two distributions.
The evaluation of managerial efficiency suggested that there was less difference within groups than between groups and that the specialized portfolio observations were more likely to define the efficiency frontier for the pooled data when using the actual data. It can be hypothesized that projecting the individual observations to the efficiency frontiers for the respective groups will reinforce the relative efficiency of the specialized portfolio observations. The alternative hypothesis may be offered that the specialized portfolios reflect higher relative efficiencies than are found in diversified portfolios when controlling for variations in the abilities of management of the individual portfolios. The null hypothesis is that the sum of ranks for the specialized observations is not statistically different from the sum of the rank order of the diversified observations when the efficiency scores are calculated from a pooled set of observations. Mathematically, the null hypothesis may be written:
The eighty virtual observations comprising the five years were pooled and evaluated using the DEA methodology. The relative efficiency scores were ranked in descending order so that more efficient observations were assigned lower ordinal values in the rank order. The sum of the ranks for the specialized observations (n = 45) was 1361 (m = 30.24). The sum of the diversified observations (n = 35) was 1879 (m = 53.69). The difference was statistically significant using the Mann-Whitney large sample test (z = -4.4759). The null hypothesis that the two groups are identical was rejected.
The efficiency scores for the specialized lenders included forty virtual observations that defined the efficiency frontier (q = 1.0000) and five observations with efficiency scores between 1.0000 and 0.99876. The efficiency scores for the diversified lenders included twenty virtual observations that defined the efficiency frontier, four observations between 0.9750 and 1.0000, two observations between 0.9500 and 0.9750, two observations between 0.9250 and 0.9500 and seven observations below 0.9250.
Using a limited sample of banks in a rural environment this study concludes that specialized lending practices yield greater management efficiencies than practices that lead to more diversified loan portfolios. This conclusion is drawn from statistical analyses of virtual observations projected from actual data. These virtual observations reflect what is possible under a given program. One limitation to what is possible is the assumption that each observation can be made relatively efficient. This assumption may not be practical given the realities of staffing and experience. Additional investigation of specific observations is necessary to determine whether improvement to the efficient frontier is possible or feasible.
Concluding that specialized lending is more efficient that diversified loan portfolios does not reduce the unsystematic risk inherent in such lending practices. Indeed it may in fact increase the amount of systematic risk that follows from a lack of diversification. Different results may be found in periods when economic conditions put increased earnings pressure on the agricultural sector of the economy. The underlying factors that appear to lead to the observed relative efficiencies derived from specialized lending include specific knowledge in the area of specialization, in this case, the agriculture sector. By reducing the learning curve it may be possible to improve efficiency relative to other observations. In other areas of apparent specialization (i.e., credit card servicing) any possible efficiencies may arise from customer diversification which shifts the risk from the unsystematic to systematic.
Using a sample of sixteen commercial banks and eighty observations the present study concludes that managing a specialized loan portfolio is relatively more efficient than managing a diversified loan portfolio. This conclusion is tempered with an understanding that management resources are an important factor in converting the theory into practice. Using a nonparametric methodology and nonparametric statistical tests, it was found that observations reflecting specialized loan portfolios were significantly more efficient than observations reflecting diversified loan portfolios after controlling for the effect management resources. Without controlling for the effect of management resources there were no statistically significant differences in the relative efficiency of the two groups.
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