The two main sources of uncertainty are:

• The amount of state education aid that will be appropriated. This has a historical standard deviation of $778,950
• The budget-to-actual variance for expenses. This has a historical standard deviation of $452,323 (based on UCOA expense data)

Assuming state education aid and expense budget variance are independent, their sum has a standard deviation of $900,755 (the square root of the sum of the squares of the individual standard deviations).

Nineteen times out of 20, we expect the deviation from the mean to be less than or equal to the half-width of a 95% confidence interval for the quantity being estimated.

For normally distributed data, the half-width of a 95% confidence interval is two standard deviations, or $1,801,510.

In the worst-case scenario for the underlying distribution, Chebyshev’s theorem gives a half-width of 4.47 standard deviations, or $4,028,298.

So a $3 million fund balance falls roughly in the middle of the range between the half-width for the normal distribution and the worst case.

Some recommendations, such as the ones proposed by the Government Finance Officers Association (GFOA) are in the range of 15-17% of operating expenses.

Rhode Island school district budget-to-actual variances based on UCOA expense data would not appear to justify tying up this much capital.

I suspect the reason the percentage is so high is that tax rate stabilization is listed as one of the purposes of fund balance.

For example, the Scituate school department recently reported a fund balance in excess of $20 million, but their fund balance policy explicitly states that fund balance can be used to reduce the tax transfer from the town.

Since 90% of the movement in the tax rate is due to the real estate market and revaluation cycles, you need a much higher percentage of operating costs if you expect to dampen oscillations in the tax rate.

Some relief is provided by the state in the form of categorical aid, which is determined as follows:

• Each LEA calculates expenses for individual special education students, and reports those that exceed twice the sum of the Core Instruction Amount ($11,050 for 2023) and the Student Success Factor ($4,420 for 2023). Although reimbursement occurs only for the portion that exceeds 5 times this sum, RIGL 16-7.2-6(a) requires RIDE to compute the amounts for two, three, and four times the sum, which dictates the reporting requirement.
• The Rhode Island Department of Education reimburses school districts dollar-for-dollar for amounts exceeding five times the sum ($77,350 for 2023)
• If the total requested exceeds the amount appropriated ($4.5 million for 2023), the statute specifies that the amounts are pro-rated.
• Although the numbers are not published, I was told in a private conversation with RIDE that in recent years the appropriated High Cost Special Education Categorical Aid has turned out to be one-third to one-half of the total amount requested.

High Cost Special Education Categorical Aid was established in 2013.

RIDE supplied me with the 2013 and 2014 data, and I manually entered the numbers for 2015-2023 from their website to produce a complete history of the High Cost Special Education Categorical Aid.

Note that the High Cost Special Needs Categorical Aid for East Greenwich is $46,000 less than last year's.

The Finance Subcommittee has been considering a dedicated fund balance category to reduce the effect of fluctuations in these costs.

Large expenditures can be problematic due to the 4% levy cap if all of the expense lands in one year.

The Finance Subcommittee has been considering establishing a fund balance category for known future capital expenditures.

It appears that this is a common practice for Rhode Island LEAs.

Examples include replacement of the turf field, which has a projected useful life of 10 years, and technology updates that will be required in four or five years that are laid out in Dr. Arnoff’s technology plan.

Each of these will cost roughly $1 million, which represents something over 2% of the operating budget, so they probably cannot be absorbed in a single budget year given the typical statutory and mandated increases.

While approval of the town administration and Town Council is not strictly required, a workable fund balance policy will require collaboration between and among the Town Council, the School Committee, and the administrations. 

I recently had a conversation with a former member of the Town Council about how they handled fund balance, and he told me the town and school department were arguing over the same issues then that we are today. 

This tells me that resolving these issues will not be a trivial matter, but I am optimistic that this can be achieved with the current composition of the administrations and elected bodies.

Society of Actuaries Exam SRM: Statistics for Risk Modeling.

Society of Actuaries Exam SRM: Statistics for Risk Modeling September 2022 Syllabus with learning outcomes and readings.

Society of Actuaries Statistics for Risk Modeling (SRM) Sample problems and solutions.

Society of Actuaries Exam P: Probability.

Society of Actuaries Exam P: Probability September 2022 Syllabus with learning outcomes and readings.

Society of Actuaries Exam P: Probability Sample exam

Harvard Statistics 110 (covers the material on Exam P)

Harvard Statistics 110 textbook (Blitzstein and Hwang)

Harvard Statistics 110 Lecture Videos (YouTube)