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Appeal from the United States District Court for the Eastern District of Michigan at Detroit. Nos. 2:23-cv-11092; 2:23-cv-11096—George Caram Steeh III, District Judge.

Argued: December 12, 2024

Decided and Filed: August 6, 2025

Before: BATCHELDER, MOORE, and BUSH, Circuit Judges.

Page 2ARGUED: David J. Selwocki, ASHERKELLY, PLLC, Southfield, Michigan, for the Trustees of the Operating Engineers Local 324 Pension Fund. Kevin M. Williams, LAW OFFICE OF KEVIN WILLIAMS, Louisville, Kentucky, for Ace-Saginaw Company. ON BRIEF: David J. Selwocki, Jacquelyne M. Zolynsky, ASHERKELLY, PLLC, Southfield, Michigan, for the Trustees of the Operating Engineers Local 324 Pension Fund. Kevin M. Williams, LAW OFFICE OF KEVIN WILLIAMS, Louisville, Kentucky, Paul E. Robinson, SULLIVAN & LEAVITT, P.C., Northville, Michigan, for Ace-Saginaw Company.

JOHN K. BUSH, Circuit Judge. This case is about pension funds, actuaries, and the Employee Retirement Income Security Act (ERISA). But we can analogize it to a chat about a basketball game. Imagine asking a professional oddsmaker to give his best estimate of how many points the Louisville Cardinals will give up in their next game. And assume there are no extenuating circumstances. Last season, the Cardinals allowed 70 points on average, and they never surrendered more than 93.¹ The oddsmaker predicts 100-what a seemingly odd forecast. But then he adds, “by the way, I think there’s a 77–95% chance the Cardinals will give up fewer points than that.” Now the oddsmaker is just rude; perhaps he doesn’t think so poorly of the Cardinals’ chances, but he certainly didn’t give his best estimate when he predicted 100 points for the other team.

In the current dispute, ERISA told an actuary to give his best estimate of the withdrawal liability of Ace-Saginaw Paving Company (Ace). Instead, he gave an estimate that he believed would overcount Ace’s withdrawal liability 77–95% of the time. Because he did not give his best estimate, we affirm the district court and hold that his estimate violated 29 U.S.C. § 1393(a)(1).

The Operating Engineers Local 324 Pension Fund (the Fund) is a multiemployer pension fund, meaning it manages pension payments for multiple employers who pool their funds. The Fund, like other pension funds, needs to make two key predictions: how much it will owe pensioners in the future, and how much employers need to contribute to satisfy these obligations.

Pension funds do not collect from employers the exact amounts that they forecast needing to pay out in future years; if a fund expects to pay a given worker $1 million during his or her retirement, it does not collect $1 million from the employer. This is because of the time value of money: a dollar received today almost certainly has more present value than a dollar received ten years from now because the earlier dollar can earn interest in the interim. United Mine Workers of Am. 1974 Pension Plan v. Energy W. Mining Co. , 39 F.4th 730, 735 n.3 (D.C. Cir. 2022). So instead, the fund collects a smaller amount from the employer and invests it, forecasting that investment returns will make up the difference between what the employer contributed and what the fund will pay pensioners. See Masters, Mates & Pilots Pension Plan v. USX Corp. , 900 F.2d 727, 733 (4th Cir. 1990).

It is the job of the fund's actuary to calculate what each employer needs to contribute according to ERISA’s guardrails. See 29 U.S.C. §§ 1082–84. Imagine a fund that will owe $100 million to its pensioners 20 years from now. If things go according to plan, the fund will collect from employers a little bit each year for the next 20 years, and the sum of these amounts (plus the investment returns) will equal $100 million. To calculate this, the fund (through its actuary) needs to predict its investments' rate of return. This rate of return is incorporated into the 'minimum funding interest rate,' which helps determine the minimum amount the employers must contribute each year to cover the fund’s future benefits to pensioners.

Of course, it’s impossible to predict investment returns with complete accuracy. So, if by year 15 it appears that the fund will overshoot its goal because the return has been better than predicted, the fund can adjust and tell employers to pay smaller contributions during the remaining five years. If the return has been worse than expected, the fund can tell employers to Page 4contribute more. In this latter scenario, when the fund anticipates running out of money, the portion of its benefits that the employers have failed to cover is called the fund's unfunded vested benefits (UVBs). 29 U.S.C. § 1393(c). The fund's actuary periodically reassesses the minimum funding rate to ensure the fund stays on track and avoids accumulating UVBs. Because pension funds do not have a defined end date, they accrue pension obligations and receive contributions continuously. By ensuring that the actuary's estimates are consistently assessed and updated, the fund should have enough money on hand to cover its pension obligations as they come due and not have to deal with UVBs.

Against that background, we now turn to the issue before us. This case is about what happens when an employer wants to 'withdraw,' or exit, from a fund. ERISA requires a withdrawing employer to be assessed its share of any accumulated UVBs upfront.² See 29 U.S.C. § 1391(b). The statute requires the fund's actuary to compute the employer's “withdrawal liability.” That is the sum an employer must pay today that will, together with the investment return on that sum, equal the employer’s share of the fund’s UVBs. See 29 U.S.C. § 1381(b)(1) (defining an employer’s withdrawal liability as its “allocable amount of unfunded vested plan benefits”). Withdrawal liability must be calculated “by a plan actuary . . . on the basis of . . . actuarial assumptions and methods which, in the aggregate, are reasonable (taking into account the experience of the plan and reasonable expectations) and which, in combination, offer the actuary's best estimate of anticipated experience under the plan.' 29 U.S.C. § 1393(a)(1).

The sole dispute in this case regards an actuary's prediction of this investment return, which the parties have called the withdrawal interest rate.³ This is 'arguably the most important assumption' in the withdrawal liability calculation. Concrete Pipe & Prod. of Cal., Inc. v. Constr. Laborers Pension Tr. for S. Cal. , 508 U.S. 602, 633 (1993). “A small adjustment in the Page 5interest rate assumption can lead to a major change in the withdrawal liability calculation.” Bd. of Trs., Mich. United Food & Com. Workers Union v. Eberhard Foods, Inc. , 831 F.2d 1258, 1260 (6th Cir. 1987).

We consider this actuarial prediction as it applied to one employer that partially withdrew from the Fund in December 2018, Ace-Saginaw Paving Company. Ace believed it should owe $6,297,833, based on its calculation incorporating a 7.75% withdrawal interest rate, the same as the Fund’s minimum funding interest rate. But the Fund’s actuary, Jonathan Feldman, told Ace it owed $16,386,924, based on a calculation using a 2.27% withdrawal interest rate, a rate calculated by the Pension Benefit Guaranty Corporation (PBGC) to approximate the return of a certain set of annuities. See Sofco Erectors, Inc. v. Trs. of Ohio Operating Eng’rs Pension Fund , 15 F.4th 407, 419 (6th Cir. 2021). The calculated contribution amounts are so different because a 7.75% annual growth rate is more than three times a 2.27% growth rate. A higher interest rate assumption means fewer dollars are needed upfront to account for the Fund’s UVBs because, presumably, there will be a greater sum of investment returns to cover the difference.

Ace sued the Fund over this discrepancy between the two contribution amounts. The parties entered arbitration, which ERISA requires. 29 U.S.C. § 1401(a)(1). The arbitrator concluded that Feldman’s 2.27% interest rate assumption violated § 1393(a)(1) by not offering the actuary’s best estimate of anticipated experience under the plan. The arbitrator ordered the Fund to recalculate Ace’s withdrawal liability using a withdrawal interest rate that complies with § 1393(a)(1). The district court agreed with the findings of the arbitrator and granted summary judgment to Ace on whether the Fund violated § 1393(a)(1). Ace-Saginaw, Paving Co. v. Operating Eng’rs’ Loc. 324 Pension Fund , No. 23-CV-11092, 2024 WL 1223532, at *7 (E.D. Mich. Mar. 20, 2024). Ace asked the district court to change the arbitrator’s remedy; it wanted the court to order the Fund to recalculate its withdrawal liability using the Fund's minimum funding interest rate, 7.75%. The district court rejected this request and affirmed the arbitrator’s remedy.

The Fund appeals the finding that it illegally calculated Ace’s withdrawal liability, and Ace appeals the arbitrator's choice of remedy. Ace also asks this court to grant it costs and Page 6attorneys’ fees for defending this appeal. Ace’s argument for that award relies on Federal Rule of Appellate Procedure 38 and 29 U.S.C. § 1451(e), one of ERISA’s fee-shifting provisions.

In the type of arbitration that ERISA mandates, an actuary’s determination of withdrawal liability receives deference unless the challenging party shows by a preponderance of the evidence 'that the actuarial assumptions and methods used in the determination were, in the aggregate, unreasonable (taking into account the experience of the plan and reasonable expectations), or the plan’s actuary made a significant error in applying the actuarial assumptions or methods.” Sofco , 15 F.4th at 416–17 (quoting 29 U.S.C. § 1401(a)(3)(B)).

Because we review a grant of summary judgment de novo, we are essentially reviewing the arbitrator’s decision. Energy West , 39 F.4th at 737. We review the arbitrator’s legal findings de novo. Sofco , 15 F.4th at 420 ('What is acceptable under ERISA and controlling Supreme Court caselaw is a question of law.”). As to the arbitrator’s factual findings, ERISA directs us to presume that “findings of fact made by the arbitrator [are] correct” unless the challenging party can rebut them by a 'clear preponderance of the evidence.' 29 U.S.C. § 1401(c). We have interpreted this standard to provide for 'clear error' review, 'which means that we will only disturb the arbitrator’s findings if, after reviewing the entire record, we are left with the definite and firm conviction that a mistake has been committed.' Sherwin-Williams Co. v. N.Y. State Teamsters Conf. Pension Ret. Fund , 158 F.3d 387, 393 (6th Cir. 1998).

The Fund has not established by a 'clear preponderance of the evidence' that a withdrawal liability calculation premised on a 2.27% interest rate was the actuary's best estimate. The arbitrator found that Feldman chose the PBGC discount rate even though he recognized and acknowledged that it was not his best estimate for the fund’s future performance. We agree. Based on an analysis of Feldman’s testimony and two letters he sent to the Fund’s trustees, we conclude that Feldman violated § 1393(a)(1) by assuming an interest rate that was untethered from his expectations for the fund’s performance and driven by concerns inappropriate for his actuarial role.

Page 7Section 1393 'establishes a two-part test for actuarial assumptions: (1) they must be reasonable; and (2) they must be the actuary’s best estimate.” Sofco , 15 F.4th at 421 (quoting Rhoades, McKee & Boer v. United States , 43 F.3d 1071, 1073 (6th Cir. 1995)).

For the reasonability test, we ask whether a reasonable actuary, if he or she accounted for the experience and reasonable expectations of the Fund, see 29 U.S.C. § 1393(a)(1), would have found 'the combination of methods and assumptions employed in the calculation' to be “acceptable,” Concrete Pipe , 508 U.S. at 635. 'In practical terms it is a burden to show something about standard actuarial practice, not about the accuracy of a predictive calculation.” Id. A single expert witness testified at the arbitration hearing, Dr. Ethan Kra. Based on his analysis of the Fund, Dr. Kra testified that it was reasonable and within standard actuarial practice for Feldman to calculate Ace’s withdrawal liability using the PBGC interest rate.⁴ Since we are not actuaries, we hesitate to disagree with Dr. Kra based solely on our own analysis of the Fund or the argument of Ace’s counsel. See Vinson & Elkins v. C.I.R. , 7 F.3d 1235, 1238 (5th Cir. 1993) ('Congress intended to give actuaries some leeway and freedom from secondguessing.”); Combs v. Classic Coal Corp. , 931 F.2d 96, 100 (D.C. Cir. 1991) (ERISA's reasonableness test “permits the actuary wide latitude in determining withdrawal liability.”).

So, we turn to the best-estimate test. “An actuarial determination that violates ERISA by not being based on the actuary’s best estimate is unreasonable, hence reversible.” Chicago Truck Drivers Union (Indep.) Pension Fund v. CPC Logistics, Inc. , 698 F.3d 346, 357 (7th Cir. 2012). The best-estimate test is procedural in that we do not assess whether the actuary made “the most accurate predictive calculation.' Sofco , 15 F.4th at 421 (cleaned up). Instead, the actuary's chosen assumptions and methods will pass this test so long as they, in combination, “offer the actuary’s best estimate of anticipated experience under the plan.” 29 U.S.C. § 1393(a)(1).

One way a withdrawal liability calculation can fail the best-estimate test is if “the chosen assumptions” represent “the dictates of plan administrators or sponsors” instead of “the actuary’s Page 8own judgment.” Rhoades , 43 F.3d at 1075. In short, the “estimate” must be the “actuary’s.” 29 U.S.C. § 1393(a)(1).

A calculation can also fail this test if the interest rate is not 'based on the unique characteristics of the plan.” Sofco , 15 F.4th at 422 (quoting Eberhard , 831 F.2d at 1263). “[A]n actuary must choose a rate that reflects 'anticipated experience under the plan'. . . . A fund's determination is not insulated from review when an actuary uses otherwise reasonable assumptions to estimate the wrong thing.” Sofco , 15 F.4th at 423 (quoting § 1393(a)(1)). Thus, in Sofco we rejected a fund's calculation of withdrawal liability that applied a standard, fixed formula that “was not tailored to the unique characteristics of the plan.” Sofco , 15 F.4th at 421 (quotation omitted).

These two provisos cover the phrases “actuary’s . . . estimate” and “anticipated experience under the plan' in the statute. But a fund can also violate § 1393(a)(1) if its assumptions and methods do not offer the actuary's 'best' estimate. See Fischer v. United States , 603 U.S. 480, 486 (2024) (“We must give effect, if possible, to every clause and word of the statute.” (cleaned up)). This is still a procedural test—we do not inquire into whether the actuary’s assumptions and methods in fact lead to the most accurate calculation of withdrawal liability. Rather, we ask whether the actuary thought his assumptions and methods would do so. Vinson & Elkins , 7 F.3d at 1238 (“The statute refers to the actuary ’s best estimate, not that of a court or of outside experts.”). An actuary fails this test if he chooses an interest rate that he does not believe will lead to the most accurate withdrawal liability calculation.

That is what Feldman did. The arbitrator correctly concluded that Feldman based his estimate on factors that have nothing to do with accurately calculating withdrawal liability. The arbitrator pointed to two key pieces of evidence that guided his decision, and they guide ours as well: Feldman's 2012 letter to the Fund's trustees justifying his change from a withdrawal interest rate matching the minimum funding rate to one matching the PBGC interest rate, and his 2019 letter to the trustees affirming that decision.

In 2012, the newly hired Feldman conducted his first annual assessment of the Fund. The Fund had used a 7.75% interest rate assumption for both the minimum funding and withdrawal Page 9liability calculations. While Feldman believed this assumption was still appropriate for minimum funding, he asserted that it would be more appropriate to use the PBGC rate, which at the time was about 4%, for withdrawal liability.

Feldman outlined his reasons for making this change in a letter to the Fund's trustees dated March 9, 2012. It would have been appropriate for him to have made this change if he believed a 4% rate of return best estimated the amount that a withdrawing employer needed to contribute to cover its share of the Fund’s UVBs as they came due. But the reasons listed in the letter show that Feldman had something else in mind: discouraging employers from leaving the plan. Feldman told the trustees that the plan was underfunded—70% of current-year employer contributions went to covering previously accrued benefits and only 30% went to covering current-year benefits. He then wrote:

It is vital that the Plan retain as many employers as possible to maintain its contribution base.

To put this last point in another perspective, for each dollar that is not received from a withdrawing employer, the remaining employers will collectively need to contribute an additional $0.70 to help pay off the Plans['] unfunded liabilities. Once an employer has withdrawn and been assessed, the Plan cannot go after additional money from that employer—there are no second chances.

Note that since the Plan is a construction industry plan, construction industry employers that withdraw from the Plan and do not continue covered operations within the jurisdiction of the Plan will not have to pay withdrawal liability.

We do understand that this change may make it more difficult to get new employers to participate in the Plan. However, given the current decline in the construction industry, the outlook for attracting new employers is already dim . . . . As actuaries to the Plan, our primary responsibility is the well-being of the Plan and its participants. . .

R. 14-8, PageID 1128.

This letter reflects a misunderstanding of the role that § 1393 gives an actuary. Calculating withdrawal liability is an objective task, which explains why Congress gave the job to actuaries, who are 'trained professionals subject to regulatory standards' and 'not, like the trustees, vulnerable to suggestions of bias or its appearance.” Concrete Pipe , 508 U.S. at 632.

Page 10When calculating withdrawal liability, it is not the actuary’s role to enact a “policy proposal” to discourage employers from withdrawing. Cf. Sofco , 15 F.4th at 422.

The letter openly reveals that Feldman changed the interest rate for policy reasons. He weighed the benefit that fewer employers would withdraw against the cost that the plan would become less attractive to prospective employers. He concluded that changing the withdrawal interest rate was worth the risk because there were fewer and fewer potential participants, i.e., employers entering the construction industry.⁵ This is the same policy tradeoff that dogged the trustees and actuary in CPC Logistics , leading the trustees to choose an interest rate assumption that did not lend itself to the actuary’s best estimate of withdrawal liability. See 698 F.3d at 35557. The only difference here is that Feldman apparently took the initiative himself to factor those considerations into his assumptions. Cf. Vinson & Elkins , 7 F.3d at 1238 (explaining that a goal of the best-estimate test is to ensure that the “assumptions truly came from the plan actuary” and were not “chosen by plan management for tax planning or cash flow purposes”). In sum, Feldman appears to have changed the interest rate assumption to make it unattractive for employers to leave the Fund, not to create a more accurate appraisal of withdrawal liability.

The Fund argues on appeal that it was fine for Feldman to prioritize the Fund’s remaining employers over its withdrawing ones—the goal of ERISA, the Fund argues, is to protect funds and pensioners, not withdrawing employers. Even assuming that is so, the Fund falls into the fallacy of presuming that Congress intended to pursue a statute's objectives to every possible extent. Rodriguez v. United States , 480 U.S. 522, 525–26 (1987) (per curiam). The Fund also fails to recognize that withdrawal liability, on its own, makes it harder for employers to withdraw. “Congress established employer withdrawal liability both to provide a disincentive to withdrawals and to mitigate their effect by requiring a withdrawing employer to pay its fair share of a pension plan's unfunded vested benefits liabilities.' Eberhard , 831 F.2d at 1259Page 11 (emphasis added); see also Sofco , 15 F.4th at 415-16 (same). The Fund does not present evidence that Congress did more than require a withdrawing employer to pay its fair share of the Fund’s UVBs. As we explain below, Feldman required withdrawing employers (such as Ace) to pay far more than their “fair share.”

Feldman's 2019 letter to the trustees furthers our skepticism that withdrawal liability calculated with the PBGC rate was his best estimate. Feldman wrote this letter for the plan year in which Ace partially withdrew from the Fund. He noted that the Fund had become even more underfunded than it was in 2011. And he gave two new justifications for using the PBGC rate as the withdrawal interest rate.

First, Feldman wrote that the Actuarial Standards of Practice allowed actuaries to use the PBGC rate to calculate withdrawal liability for any plan. We rejected this argument in Sofco because that actuarial practice contradicts ERISA's directive to base withdrawal liability calculations on the anticipated experience of the plan. Sofco , 15 F.4th at 423 (“ERISA does not yield to the Actuarial Standards of Practice; the standards must succumb to the statutory requirements.”).

Second, Feldman explained that '[t]here is a transfer of risk from employers who withdraw from the Plan to those employers who remain in the plan . . . . [E]ven when determining the present value of vested benefits using PBGC interest rates, there is still some transfer of risk.” R. 14-8, PageID 1133. Using anything higher than the PBGC rate, Feldman argued, would 'result[] in a transfer of an unreasonable amount of investment risk from withdrawing employers to the Plans['] continuing employers[.]' Id. In his testimony at arbitration, Feldman elaborated on why this transfer of risk was a problem that called for using the PBGC interest rate. He explained that an employer who withdraws is not subject to the ongoing risk of the plan’s future performance because the withdrawn employer’s liability is fixed regardless of future events-if Feldman's assumptions proved to be too optimistic, the withdrawing employer could not be compelled to pay any extra to compensate. Remaining employers, on the other hand, would have to cover the shortfall—they are exposed to the risk.

Page 12Feldman’s solution was to choose an interest rate that gave the remaining employers a lower chance of getting stuck having to pay extra in the future: the PBGC rate of 2.27%.

It's important to understand how Feldman arrived at this rate. Feldman was not an employee of the Fund. He was an outside consultant employed by a firm called Horizon Actuarial Services. In 2018, Horizon compiled a survey of asset managers to project how well the Fund’s portfolio would perform ten and twenty years into the future. The 2019 letter and Feldman’s testimony suggest that he trusted Horizon’s estimates, adopted them as his own, and thought they were meaningful in both the minimum funding and withdrawal liability contexts. Indeed, the arbitrator concluded that Feldman 'simply looked at the Horizon survey' and “selected the PBGC rates” because of what he saw in it. R. 14-8, PageID 1159.

The 2019 letter reveals that Feldman focused on a statistic from the survey estimating the likelihood of the Fund's investments exceeding a given level of annual return over the next twenty years. For the minimum funding rate, 7.75%, the average survey respondent thought that the Fund’s investments had a 45% chance of exceeding that rate of return. This meant there was a 55% chance of performing worse than 7.75%. To put this in context, if we assume that a given actuary thinks that a survey is perfectly accurate and that it encompasses every factor he wants to consider, then the actuary would pick the rate with a 50% chance-an equal likelihood of overestimating as underestimating the employer’s withdrawal liability.

But Feldman chose the PBGC rate of 2.27%. The Horizon survey had a statistic for achieving 2.3% annual returns over a twenty-year time horizon. According to the survey, a conservative portfolio manager would predict exceeding a 2.3% annual return 77% of the time and an optimistic manager would predict exceeding that rate of return 95% of the time. By adopting the findings of this survey, Feldman recognized and acknowledged that Ace would pay more than its share of withdrawal liability between 77% and 95% of the time. Like the arbitrator, we cannot conclude Feldman gave his best estimate of Ace's withdrawal liability when he believed that this estimate would cause Ace to overpay 77–95% of the time.

The Fund characterizes the 77–95% range as reflecting a higher degree of certainty rather than a higher likelihood of overpayment-the Fund can be 77-95% sure that the remaining Page 13employers will not be left with a shortfall. This degree of caution, according to the Fund, was necessary because of the Fund’s “dire condition.” 6 Appellant's Reply Br. at 22 ('Simply put, an interest rate with only a 50/50 probability of exceeding the returns creates a probability of loss that this Fund cannot withstand.”). But Ace bears the risk of inaccurate actuarial estimates, too. If Feldman errs by overestimating the rate (and thus the performance of the Fund’s investments), then the Fund will suffer a shortfall and, conversely, if Feldman errs by underestimating the performance of the Fund’s investments, then Ace will have contributed more than necessary, and the Fund will not refund the difference. See Combs , 931 F.2d at 102. Both are at risk from the possibility of the actuary’s misestimate, but—pointing to its “dire condition”—the Fund would have Ace bear more of that risk.

If the Fund were in such dire straits, one would think this should lead to an increase in the minimum funding requirement just as it apparently must lead to an increase in withdrawal liability. No, says the Fund-withdrawal liability is different from minimum funding. 'With minimum funding, the interest rate can change, the asset portfolio can be changed, contributions can increase . . . . Things can be done over decades, or year-by year, to budget for ongoing liability. With withdrawal liability, once it is calculated, it cannot be changed regardless of adverse effects or experiences of the Fund.” Appellant’s Reply Br. at 22–23. But this is just making the same argument in a different way—the Fund believes we should shift the bulk of this risk to the withdrawing employer, Ace.

It is not the role of the actuary to consider these policy issues. Congress made the applicable policy choices when it enacted § 1393. In doing so, it removed policy considerations from the equation by requiring the 'apparently unbiased' actuary to calculate withdrawal liability, and by prohibiting trustees from influencing the assumptions and methods used to do so. Concrete Pipe , 508 U.S. at 635. The actuary's fidelity is owed to the statute, not to a particular party. See CPC Logistics , 698 F.3d at 355 (in the context of withdrawal liability, the 'actuary is a professional, assumed to be neutral and disinterested'). When calculating withdrawal liability, the role of the actuary is to take into account the anticipated experience of Page 14the plan and objectively give his or her best estimate of how much the withdrawing employer needs to contribute to cover its share of the fund’s UVBs as they come due. Ideally, this estimate should be one with an equal risk of overestimating as underestimating: 50/50.

Let us be clear about how to tell whether the actuary has given his or her best estimate. An arbitrator should not ask whether the actuary’s assumptions and methods will produce the best estimate of an employer’s withdrawal liability. Vinson & Elkins , 7 F.3d at 1238. Instead, the arbitrator is to ask whether the actuary believes those assumptions and methods will produce the best estimate. In other words, the question is whether the calculation represents the actuary’s best estimate of anticipated experience under the plan. If an actuary dismisses his own 50/50 best estimate in favor of a different estimate, then the actuary has violated the best-estimate test. So too if a fund dismisses the actuary’s best estimate. CPC Logistics , 698 F.3d at 357; Vinson & Elkins , 7 F.3d at 1238. '[F]actoring in a discount for conservatism,' as the Fund argues we should allow, “after an actuary has arrived at his or her best estimate of anticipated experience would be contrary to the statutory mandate.” Sofco , 15 F.4th at 422 (quoting Wachtell, Lipton, Rosen & Katz v. C.I.R. , 26 F.3d 291, 296 (2d Cir. 1994)).

That said, let us be equally clear that an actuary need not accept the results of a thirdparty's estimate, as Feldman did. Feldman could have taken the Horizon survey, adjusted it reasonably according to his actuarial judgment, and made his own 50/50 estimate that satisfied the reasonableness and best-estimate tests.

Further, an actuary has no reason to worry when that process results in an interest rate assumption on the conservative end of the reasonableness spectrum. Courts have upheld the conservative interest rate assumptions of actuaries who, for example, thought that a fund’s recent investment success would not continue. See Eberhard , 831 F.2d at 1262-63 (interest rate assumption based on a belief “that future rates are more likely to approximate long-term rates than the high rates prevailing during the last decade”); USX , 900 F.2d at 733–34 (same); Vinson & Elkins , 7 F.3d at 1239–40 (same); Wachtell , 26 F.3d at 296 (to predict future returns for a plan with only two years of investment data, the actuary dismissed that data as too little to be helpful and instead relied on long-term market trends). Because the best-estimate test is procedural Page 15rather than substantive, it does not offend § 1393(a)(1) “when an actuary chooses an assumption that is within the range of reasonable assumptions, even when the assumption is at the conservative end of that range, provided the chosen assumption is the actuary’s best estimate of anticipated plan experience.” Wachtell , 26 F.3d at 296.

In sum, though we recognize that actuaries have wide latitude to choose assumptions and methods under the reasonableness test, their choices will violate the best-estimate test if they do not offer (1) the actuary’s estimate, (2) the actuary's best estimate, and (3) the actuary's best estimate of anticipated experience under the plan . We conclude that Feldman failed to give his best estimate because he chose an interest rate that he determined would lead Ace to pay too much in withdrawal liability 77–95% of the time.

Moving to the remedy, Ace cites Sofco for the proposition that we must order the actuary to recalculate Ace's withdrawal liability using the minimum funding interest rate, 7.75%. Indeed, this was the remedy in Sofco . But the Sofco district court ordered this relief without significant discussion aside from finding the actuary’s original calculation unreasonable. Sofco Erectors, Inc. v. Trs. of Ohio Operating Eng'rs Pension Fund , No. 2:19-cv-2238, 2020 WL 2541970, at *10 (S.D. Ohio May 19, 2020). And the Sofco appellate panel affirmed the district court in full without discussing the remedy. Sofco therefore did not create precedent on this issue. Wright v. Spaulding , 939 F.3d 695, 702 (6th Cir. 2019) (“For a court’s conclusion about an issue to be part of its holding . . . it must be clear that the court considered the issue and consciously reached a conclusion about it.”).

Considering the issue as a matter of first impression, we affirm the district court's decision to give the Fund another chance to calculate Ace's withdrawal liability. True, an actuary’s statutory responsibilities in calculating minimum funding and withdrawal liability are similar. Compare 29 U.S.C. § 1084(c)(3) with 29 U.S.C. § 1393(a)(1). Consequently, we have found it reasonable for an actuary to use the same interest rate assumption for calculating minimum funding and withdrawal liability. Eberhard , 831 F.2d at 1262.

Page 16But it is also permissible for the two assumptions to diverge. See id. ; Energy West , 39 F.4th at 742. That is because some factors unique to withdrawal liability might cause an adjusted interest rate assumption to result in a more reasonable calculation. See Concrete Pipe , 508 U.S. at 633 (“[T]he assumptions used by the Plan in its other calculations may be supplemented by several actuarial assumptions unique to withdrawal liability.” (quotation omitted)). At the same time, there is a limit to the kinds of adjustments an actuary can make. See id. at 632-33 (Congress’s use of similar statutory language “to describe the actuarial assumptions and methods to be used in these different contexts tends to check the actuary’s discretion in each of them.”).

Dr. Kra, the expert witness, testified to one such adjustment that our case law has recognized as striking the right balance. He said that actuaries calculate withdrawal liability on a different time horizon than minimum funding, and that this factor allows the use of a different interest rate assumption. We have said as much. See Eberhard , 831 F.2d at 1262. It is permissible for an actuary to account for different time horizons because, crediting Dr. Kra's testimony, doing so enables an actuary to more accurately forecast how much an employer would need to contribute upfront to pay for its share of its fund’s UVBs as they come due. On the other hand, it is impermissible to incorporate a differentiating factor that serves a purpose other than accuracy, like the policy considerations Feldman cited. Doing so arouses skepticism because “the opportunity for manipulation and bias is particularly great where funds use different interest rate assumptions for withdrawal liability and minimum funding purposes.' Nat'l Ret. Fund on Behalf of Legacy Plan of Nat’l Ret. Fund v. Metz Culinary Mgmt., Inc. , 946 F.3d 146, 152 (2d Cir. 2020).

So, when the Fund calculates Ace's withdrawal liability on remand, its actuary may deviate from the assumptions and methods used to calculate minimum funding for the relevant plan year. But that discretion is limited to differentiating factors that improve the accuracy of the withdrawal liability calculation, meaning they provide a more accurate estimate of the amount that Ace had to contribute as of the time of its partial withdrawal to pay for its share of the Fund’s UVBs as they come due.

Page 17Finally, Ace seeks an award of attorney's fees pursuant to Federal Rule of Appellate Procedure 38 and 29 U.S.C. § 1451(e). Ace has limited its request to the cost of litigating this appeal—it does not ask us for fees covering the cost of the entire dispute. We cannot award fees under Rule 38 because Ace has not filed a separate sanctions motion, which the rule requires when an appeals court does not raise the issue on its own. Moreover, this appeal was not frivolous. See Larry E. Parrish. P.C. v. Bennett , 989 F.3d 452, 457–58 (6th Cir. 2021).

We assess a § 1451(e) request for fees using a five-factor balancing test. The factors are “(1) The degree of the opposing party's culpability or bad faith; (2) The ability of the opposing party to satisfy an award of attorney’s fees; (3) Whether an award of fees against the opposing party would deter others from acting in similar circumstances; (4) Whether the party requesting fees sought to benefit all participants and beneficiaries of a multiemployer plan or to resolve a significant legal question; and (5) The relative merits of the parties’ position.” Cent. States, Se. & Sw. Areas Pension Fund v. 888 Corp. , 813 F.2d 760, 767 (6th Cir. 1987).

Our calculus tracks that in Sofco . Like the litigation in Sofco , this appeal 'involved complicated legal questions without clear answers. Each party prevailed on some issues. There is no evidence of bad faith from either party. . . . And neither parties’ positions were frivolous.” Sofco 15 F.4th at 433. Further, Ace appealed the district court's ruling, just as the Fund did. And neither side has succeeded in its challenge. So, Ace and the Fund share responsibility for this appeal. As in Sofco , we award no fees.

We affirm the judgment of the district court and remand for the Fund's actuary to recalculate Ace’s withdrawal liability using assumptions and methods that comply with ERISA.