A Value at Risk Analysis of State & Local Government Pension Funds 

William G. Albrecht
The University of North Carolina at Pembroke

Hannarong Shamsub
RMIT Internationa University

Kishore Raga
Nelson Mandela Metropolitan University

Introduction

     This paper reports results of estimating Value at Risk (VaR) from an investigation of 127 large state and local government pension funds in the United States. The estimation data cover year 2000 and were obtained from the Public Pension Coordinating Council’s 2001 Survey of State and Local Government Retirement Systems.¹ The examination parallels Gupta, Stubbs, and Thambiah (2000) in terms of an analytic approach and employs a parametric technique outlined by Butler (1999) for computing VaR. VaR estimates are provided using five different criteria: census region, system administration, system size (as measured by assets), equity allocation, and financial performance.
     The VaR statistics computed are annual percentage numbers measuring the worst expected loss that a system can expect over a given time interval under both normal and extreme market conditions at a 95% percent confidence level. In practice VaR can be used either diagnostically or prescriptively to determine whether or not a particular system’s risk level is appropriate to existing circumstances. For example, pensions with funding levels in excess of 100% might be expected or advised to take less risk so as to ensure the longevity of existing surpluses. Correspondingly, systems with shortfalls could potentially expose assets to higher levels of risk in order to capitalize on existing risk premiums.
     In addition to the applications listed above, VaR estimates can be used for tracking changes to risk profiles due to shifts in asset allocation patterns versus varying market conditions. Beyond this aspect VaR calculations allow for standardized peer comparisons of overall risk profiles.
     Illustrating the latter aspect is the overall purpose of this paper and the remainder of the article proceeds as follows. First, a brief discussion of methodology and interpretation is given along with descriptive VaR statistics for all pension systems in the sample. VaR estimates are then provided according to the first four criteria listed earlier. The relationship between VaR and subsequent financial performance is then examined before comparing results with a prior empirical study. The paper concludes with a general summary of findings.

Value at Risk: Methodology and Interpretation

     We use previously reported asset allocations and ten years of quarterly data on asset class returns to compute the Diversified VaR (DVaR) for each of 127 public pension systems for which information concerning portfolio composition and other relevant criteria are available.² The assumption underlying a DVaR statistic is that the correlation between assets is not always equal to one and that portfolio risk can be reduced through combinations of risky assets. Tables 1 and 2 in Appendix A give descriptive statistics concerning asset allocation patterns and quarterly market risk index assumptions, respectively.
     In addition, we also compute Undiversified VaR (UVaR) for each system under the assumption that there is no benefit from diversifying a system’s portfolio; that is the correlation coefficient rij = +1 for all combinations of assets i and j. While our measures do not adjust for managerial level characteristics, prior research demonstrates that approximately ninety percent of market risk in a typical fund comes from the volatility of the underlying asset classes (e.g., Gupta, Stubbs, and Thambiah, 2000: p. 65). Therefore, our estimated “partial” VaRs can be considered as reasonable approximations of actual values utilizing manager level data.
     Following Bulter (1999) we use the portfolio distribution for each system to compute the asset-side Value at Risk.³ The overall median DVaR for the sample is 13.82% and the 127 values range from 3.52% to 21.66%. This suggests that a one-time-out-of-twenty market year could cost the median pension approximately 14% of system assets. The magnitude of this number indicates that such an occurrence is likely to downgrade the status of a fully funded state and local government pension system to that of underfunded.⁴ By comparison the overall median UVaR is 17.4% and the 127 values range from 3.52% to 23.66%.

VaR by Census Region and Jurisdiction⁵

     Table 1 presents a breakdown of state and local pensions by major census region and system administration. The upper portion of the table indicates that approximately 64% of all systems are either in the Midwest or Southern regions of the United States and that the Northeastern region has the fewest. The lower half of the table suggests that most of the day to day administration is conducted by the state and that approximately two-thirds of pensions have local jurisdictions involved with fund management. Furthermore, supervision by counties or other forms of community government (e.g., special districts) are least present for all systems.

[See Table 1]

     Figure 1 presents median VaR estimates by census region. Our prior expectation is that geographical areas with the highest system counts should have the highest dispersion but our findings do not support this expectation. While the Midwestern and Southern regions have DVaR ranges of approximately 12% and 8%, respectively, the Western region has a range slightly in excess of 12% on the same measure. By comparison the DVaR range statistic for the Northeast region is 4%. While larger in absolute magnitude, the ranking of regions by dispersion continues to hold for the UVaR measure as well.

[See Figure 1]

     Due to the rather wide dispersion an overall conclusion is that state and local government pension systems in similar geographic areas do not tend to mimic the norms or investment allocation patterns of their peers. In essence, the risk profiles of these institutional investors appear to be substantially different within census regions even though the median systems have relatively similar VaR estimates.
     Figure 2 reports identical information for system administration. Results indicate that pensions governed by cities/towns and states have relatively similar VaRs in terms of median estimates. However, the identical minimum DVaR and UVaR of 3.52% for cities and towns is substantially below that for systems with state administration.⁶ At the same time the maximum DVaR of 21.66%  and UVaR of 23.16% for pensions under state administration are in excess of that for cities and towns which is 15.62% and 18.76%, respectively. Again, this suggests that risk taking is not very similar on this dimension.

[See Figure 2]

     By comparison, the 57 funds administered independently or by counties and special districts also have median DVaR and UVaR estimates which are similar to that for the entire sample. However, the range for each of these classifications is narrower than either that of states or cities/towns. This suggests that pension systems with non-state or non-city/town administrative jurisdictions are more homogeneous in their risk profiles than those which are managed by states or cities.

VaR by Plan Assets⁷

     Figure 3 shows median pension assets by census region for 125 systems reporting this measure. The middle system in the Southern geographic location leads with more than $1,391 million in assets followed by the Western region with $1,241 million. Median assets over all systems are $1,185 million of which both the Northeastern and Midwestern regions are below this measure of central tendency.

[See Figure 3]

     Figure 4 presents VaR estimates by system size and suggests that risk taking propensities (as measured by the median VaR) increases incrementally with size.⁸ However, the distinction between actual median VaRs are greatest for those pensions with between $100 and $999 million or less than $100 million in assets (approximately 1.29% for UVaR and 1.35% for DVaR). The range of differences in risk taking is greatest for systems with less than $100 million and those between $1.0 billion and $9.9 billion.

[See Figure 4]

     The most restricted range is found in middle sized funds-those with $100-$999 million and those with assets in excess of $10 billion. This is interesting in light of the fact that 50% of all systems are within these categorical classifications. Such a finding suggests that as state and local government pensions grow in magnitude their asset allocations at first become more similar to those of their “financial” peers. However, after a certain point the trend appears to reverse and funds once again assume greater levels of individuality in their portfolio composition decisions. As size continues to increase state and local government pension funds once again converge in terms of an overall risk profile. Further information is given in Appendix B which reports the distribution of pensions by assets and census region.

VaR by Equity Allocation⁹

     Table 2 details equity allocations for the 127 systems considered in this study. The information suggests that more than 70% of pensions have equity allocations between 50% and 70%. Fifteen percent are conservative on this measure while approximately 12% are comparatively aggressive in their asset allocation decisions.

[See Table 2]

     Figure 5 is consistent with the prior expectation that VaR estimates should increase with proportions of the portfolio devoted to equity investments. The overall differences in median VaR statistics reflect the underlying volatility of this asset class. Furthermore, the differences in DVaR verses UVaR underscore the benefits that can be attributable to diversification when assets are not assumed to be perfectly positively correlated.

[See Figure 5]
VaR and Public Pension Financial Performance

     Figure 6 presents the medians and ranges of the annual total rate of return on system assets by census region for 104 systems reporting annual financial performance. Median rates of return are similar by geographic area except for the Midwest which is in excess of 9% for this measure of central tendency. The South has the widest range (25%) in terms of dispersion with a low of -4% and a high of 21%.

[See Figure 6]

     Differences within regions primarily reflect different asset allocation patterns among pensions. To the extent that public retirement systems enjoy higher rates of return participants are more secure in their future and taxpayers may benefit as residual claimants of potential surpluses. However, capturing higher returns often entails assuming greater levels of risk as well.
     Figures 7 and 8 present the annual financial performance of systems plotted against VaR estimates. Both graphs reveal that there is no substantive relationship between total rate of return and either measure of VaR (DVaR r = -.06, p = NS; UVaR r = -.13, p = NS). This finding is significant as such a result suggests that pension systems which take on higher risks do not necessarily earn higher rates of return. In fact, as both figures demonstrate, the best and worst performing state and local government pension systems have similar DVaRs and UVaRs which are near the median levels of 13.82% and 17.4% respectively.¹⁰

[See Figures 7 and 8]
Comparison to a Prior Empirical Study

     Prior to this investigation the Value at Risk for state and local government retirement systems on any dimension has not been examined. Therefore, direct comparisons with other studies on this exact unit of analysis are not possible at this time. However, Gupta, Stubbs, and Thambiah’s (2000) exploration of the same topic in relation to corporate pensions does provide some imperfect information for public-private sector comparisons on a parallel DVaR measure. ¹¹ The authors’ estimation data cover 1998.
     In their investigation the authors noted above found an overall median DVaR of 17.3% with a range of 9.5% to 28.3% for 162 of the largest defined benefit plans in the United States.¹² The calculated measure of central tendency is approximately 4% “higher” than the 13.4% found during the course of this study and the minimum and maximum values are both higher than the minimum and maximum values reported here (3.52% and 21.66%). Overall, time periods notwithstanding, this suggests that corporate pension portfolios are probably riskier than that of state and local government pensions. This may reflect competitive verses public steward attitudes between the two sectors when making asset allocation decisions.¹³ Another possibility is that constitutional investment restrictions may essentially govern the amount of system resources that public pensions can place in a particular asset class. Either way, differences in long run levels of financial performance for public verses corporate defined benefits are likely to be affected by levels of risk taking between the two sectors.
     Two other criteria used in both studies offer some further types of imperfect comparisons. In relation to the first, equity allocations, the positive relationship between percentage of the portfolio in equity investments and DVaR is similar to the results described here. Concerning the second, Gupta, Stubbs, and Thambia (2000) find that corporate pension aggressiveness increases with plan size up to about $5 billion and then levels off. Figure 4 appears to show a similar scenario for public sector retirement systems up to $999 million.

Conclusion

     This paper provides Value at Risk estimates for 127 large public pension funds in the United States. Results indicate that the median system for the entire sample has a DVaR of 13.82%-suggesting the fund’s asset side could drop by approximately 14% in a one-in-twenty worst market year. The range in DVaR is fairly substantive-from a minimum of 3.52% to a maximum of 21.66%. By comparison, the overall median UVaR is 17.4% and the 127 values range from 3.52% to 23.66%. In either case the conservative end of the continuum roughly corresponds to a portfolio of very safe fixed income investments while the aggressive end has risk characteristics resembling a moderate to aggressive growth equities portfolio.
     Overall, average aggressiveness (in terms of risk taking) increases with system size; funds managing $10 billion are the most aggressive with a median DVaR of 14.09% and a median UVaR of 18%. In terms of investment tactics, the notion of aggressiveness continues when examining VaR in relation to the proportion of a system’s portfolio allocated to equity investments. Thus, the results in Figure 5 are consistent with prior expectations.
     In terms of examining VaR by other specific criteria, the analysis here shows that risk profiles are fairly broad both within census regions and governing jurisdictions. This suggests that state and local government retirement funds do not tend to mimic their “peers” in relation to these two types of criteria. One exception might be said to exist with non-state or non-city/town administrative jurisdictions which appear to be more homogeneous in their risk profiles than those which are managed by states or cities. Results also indicate that there is a no relationship between risk taking and annual financial performance.
     Finally, a comparison of these “best available” results with that of another study in relation to corporate pensions suggests that state and local government retirement systems have a lower overall VaR both in terms of central tendency and dispersion. However, the results are not disparate enough to draw dissimilar overall conclusions for each sector. In fact a general consideration with potential implications for public policy exists for both: A one-time-out-of-twenty market year would most likely downgrade the status of a fully funded pension to that of underfunded.

References

Butler, C. (1999). Mastering value at risk. London: Prentice Hall.
Harris, J. D. (2002).  2001 survey of state and local government employee retirement systems [Electronic Version]. Public pension
       Coordinating Council Survey Report. Available: http://ppcc.grsnet.com/.
Government Finance Officers Association (2000). 2000 survey of state and local government employee retirement systems: Survey
       report. Chicago: Public pension Coordinating Council.
Gupta, F., Stubbs, E., and Y. Thanmbia (2000). U.S. corporate pension plans: A value at risk analysis. The Journal of Portfolio
       Management (Summer), 65-72.

Tables

Table 1: Pension Systems by Major Census Region and System Administration

Table 2: Pension Systems by Equity Allocation

Figures

Appendix A
Table 1: Descriptive Raw Statistics of 127 Defined Benefit Public Pension Systems

*Median value is $1,185 million and the range is $104,667 million.

Table 2: Quarterly Market Index Assumptions*

*Note: The “other” category consists of other investments and alternative investments (including private equity) as listed in the 2001 Survey of State and Local Government Employee Retirement Systems Database User’s Guide on page 4. The “other” category is indexed by the NCREIF property index and the Mortgage Index is based on a 30 year fixed rate. Standard deviations and correlations are computed using ten years of quarterly data ending 4Q00. The sources for the indexes are as follows: S&P 500, M. L. Corp/Gov., MSCI EAFE, and the M. L. Global Gov. are from http://www.globalfindata.com. Wilshire Real Estate is from http://www.wilshire.com. “Other” is from http://www.ncreif.org.

Appendix B

Footnotes

1. As of this writing the 2001 survey is the most recent available.
2. There are 171 systems reporting in the survey. We analyze systems offering defined benefit plans only and exclude 21 systems which do not meet this criterion. Fourteen systems are also excluded as the data reported is not for fiscal year 2000. Nine systems are excluded due to insufficient reporting of portfolio distributions. This leaves 127 systems remaining for analysis. The text of the article notes other minor instances of missing information.
3. The procedure involves calculating a quarterly standard deviation for a portfolio of assets using a Z-score of 1.645 as a scalar adjustment to the volatility. The annual figures are then calculated by using the “root of time rule” which involves multiplying the quarterly VaR by the square root of four. The annual VaR is two times that of a quarterly VaR (Guptia, Stubbs, and Thambia, 2000: 65).
4. One way of supporting this statement is to note that for fiscal year 2000 25% of state and local government pension plans were actuarially more than 110% funded (Harris, 2002: 13).
5. The decision to examine VaR by census region is based on the Government Finance Officers Association’s (GFOA) 2000 Survey Report which indicates that geographic location influences pension system investment practices (p. 9). The decision to examine VaR by jurisdiction is based on the same report which indicates that the type of administrative jurisdiction may affect the amount of resources available to the system (p. 12).
6. The 3.52% calculation is a result of two systems which allocate 100% of assets to cash investments.
7. The decision to examine VaR by assets is based on the Government Finance Officers Association’s (GFOA) 2000 Survey Report which indicates that the amount of assets that a system holds may affect the distribution of investments among the major types of securities or asset classes (p. 10-11).
8. The categorization of the continuous size variable follows the classifications in the GFOA 2000 Survey of State and Local Government Employee Retirement Systems Survey Report.
9. The categorization of the continuous equity variable follows that employed by Gupta, Stubbs, and Thambia (2000).
10. The mean total return statistic for the 104 systems is 6.2%.
11. On page 65 of their work the authors note their use of “proprietary analytics.” This confounds any attempt at a direct comparison as VaR methodologies are not necessarily consistent. Different VaR models will give different VaR findings (Butler, 1999, 5).
12. The authors do not specifically use the label DVaR. However, their published annual market index risk assumptions indicate that they do not consider UVaR (p. 71). The authors use 3 years of monthly data ending 3Q98.
13. According to Gupta, Stubbs, and Thambia (2000) pensions may use financial performance success to reduce personnel costs or to improve income and balance sheets. Private sector funds able to capitalize on such an opportunity would be expected to derive a competitive advantage (p. 69).