As mentioned in a prior post, Apportioning Discretionary Appropriations for Expected WIFIA Portfolio Funding Losses, I think it is possible to develop a credit subsidy estimate model for predictable funding losses in WIFIA loans. It would also seem to be required for compliance with OMB Circulars A-11 and A-129, as recently discussed here and here, respectively.
This post outlines how I think it could be done, or at least the main elements involved. The goal is to demonstrate that modelling WIFIA funding cost might be relatively straightforward and can produce usable results.
The Central Factor: US Treasury Rates
US Treasury interest rates are the central factor in a model of WIFIA funding cost:
- The WIFIA loan commitment rate is set at the yield, plus one basis point, on the day of closing of the UST security most closely matched to the weighted average life of the loan. In practice, for a typical WIFIA loan amortization schedule, the WAL is about 20 years, and so the UST security will be the UST 20Y.
- The discount rates in OMB’s Credit Subsidy Calculator are also based on UST yields, but in a more complicated way. The CSC uses a Treasury ‘zero curve’ that exactly matches the WIFIA loan’s entire debt service schedule, a precise methodology widely used for interest rate swap transactions and able to accurately capture the economic value of the payment stream, as FCRA intended. Fortunately for simplification, the resultant discount rate used by the CSC, known as the ‘Single Effective Rate’ or SER, is also very close to the UST 20Y for WIFIA loans with a 20-year WAL, plus or minus a few basis points. We’ll assume they’re the same for this exercise. On commitment closing day, therefore, both the WIFIA rate and the SER are essentially equal to the then-current UST 20Y rate. When the loan is disbursed, however, the WIFIA rate is the ‘old’ UST 20Y while the SER on that day (which will evaluate the cost of funding the disbursement) now reflects the then-current ‘new’ UST 20Y. The divergence between the ‘old’ and ‘new’ UST 20Y is the cause of loan funding gains (the old rate is higher than the new) and losses (vice versa) [1].
- For WIFIA’s highly rated Aa3/AA- water system borrowers (the vast majority), the rates on their tax-exempt bond financing alternatives are also closely correlated with the UST curve. That factor will be important in a such a borrower’s decision to apply to WIFIA in the first place, but for this exercise, it matters most in their next decision — whether to draw on a WIFIA loan commitment or not, depending on their long-term financing alternatives.
- Finally, a borrower’s short-term financing rates will also be correlated to the UST curve, at least most of the time. The curve is usually positively sloped, so when UST 20Y rates are falling, short-term rates are most likely to fall too, and vice-versa.
UST 20Y Variation Between Loan Commitment and Disbursement
As noted above, the divergence between the UST 20Y at loan commitment and at disbursement is the cause of funding gains and losses, so that’s the first and most important parameter we need to predict.
- Note that we’re not trying to predict the direction, up or down, of the divergence — that’s effectively impossible for the multi-year time frames involved in an infrastructure loan drawdown period. Instead, the focus is on the long-term historical pattern of the variation itself, which may be expected to continue for the foreseeable future.
- A typical WIFIA loan will have a 5-year period after commitment during which the loan will be disbursed in amounts corresponding to eligible construction expenditures completed to date. For simplicity, assume the loan can be disbursed exactly every 12 months, up to 60 months from loan commitment. We can look at the historical pattern of how much the UST 20Y changed from the rate at commitment on those anniversary dates. The chart above shows the pattern for 12 months and 60 months from 3/1995 to 3/2026. For most of the 30 years, the range of variation seems relatively constant for both anniversaries, within about 2%. (The last few years were a bit anomalous for the 60-month variation — more on that in the next-but-last section below.)
The statistics for all five anniversaries (table below) tell roughly the same story. The averages are slightly negative but close to zero (especially for the shorter anniversaries), reflecting the slow overall fall in the UST 20Y rate for most of this specific period. The standard deviation values are also low (the maximum UST market swing was less than 4% percentage points even in five years, after all) and increase gradually as expected (the longer the time, the greater the variation).
Translating Historic Variation into Predictive Probability
Now come the major assumptions. As noted, UST 20Y rates fell on average for most of the last 30 years. Imagine a ‘mirror image’ of the chart at the top of this post, so that rates rose on average by exactly the same amount. The averages in the above table would flip signs — but the standard deviation values would remain the same.
We’re not trying to predict whether rates will rise or fall on average for estimating the funding cost of future WIFIA loan disbursements — that’s not possible. But if we know something about the likely variation in UST 20Y rates within the typical timeframe of WIFIA loan disbursements after commitment, then at least we can estimate the range of expected variation in UST 20Y over years 1-5.
- First big assumption: That the historical variation pattern (specifically, the Standard Deviation or StdDev) observed over the last 30 years in the Treasury market is assumed to continue for timeframes relevant to estimating WIFIA loan funding cost, say the next ten years. This assumption is based on the size and centrality of this market, the long-established processes and institutional participants in trading, and the importance of UST rates throughout the world economy.
- Second big assumption: That a sample of this variation, such as described above, can be the basis of a normal probability distribution that is sufficiently accurate for our purposes. The UST 20Y is bought and sold on a huge Treasury market where many price transactions, each executed by independent actors, are accurately recorded each day. Despite the abstract quality, it is in fact an ‘organic’ process in which human beings are expressing their sophisticated perceptions of an unknowable future, all aiming at maximizing their own independent self-interest. It’s worth noting that the Black Scholes option model, now standard in financial markets for pricing many options and option-like products is also based on normal distribution assumptions [2].
- Third big assumption: That the average or mean of the variation for our purposes can be assumed to be zero. As noted above, we’re not trying to predict where Treasury rates will go, up or down, over the next few years. In theory, over the long run, there is an average rate around which the market will cycle, always reverting to mean eventually. The variation around that ‘Platonic’ mean will average zero. In practice, we see that mean reversion in our samples reflected in the low average values above. A zero mean assumption also underscores what the model is for in FCRA credit subsidy terms — we’re solely trying to estimate the impact of predictable variation of UST 20Y rates on the funding cost of a WIFIA loan, not the unpredictable rise or fall of those rates. I think this is consistent with the principles outlined in the 1967 Budget Commission Report, FCRA law and OMB budget processes.
Normal distributions calculated from mean and StdDev reflect probability density for all possible outcomes within the range. For our purposes, we can simplify that by using one basis point (.01%) intervals, since that’s the way the credit subsidy will be calculated (e.g., a change from 4.50% to 4.51% will be included, but not a hypothetical change from 4.50% to 4.501%) and we can use a frequency distribution instead.
The curves above show the results for the five 12-month periods. As you’d expect, some variation within about +/- 1% from the WIFIA loan commitment rate for a disbursement 12 months after closing is pretty likely. For longer periods, the variation widens, but the vast majority of outcomes will be +/- 3%. This looks realistic — exactly the sort of thing I think FCRA law intended to be included in credit subsidy estimates.
Translating UST 20Y Variation into PV of Typical WIFIA Loan
Next, we need to estimate what impact on WIFIA loan present value (PV) that a predicted variation in the UST 20Y will have. The difference between the PV of the WIFIA loan and the PV of the Treasury funding at disbursement determines, per FCRA law and OMB’s CSC, the loan’s funding cost (an upward re-estimate) or gain (a downward re-estimate).
This part is straightforward. The PV of Treasury funding (based on the ‘outgoing’ government cash flows) is by definition equal to 100% of the loan disbursement amount. The PV of the WIFIA loan disbursement (based on the ‘incoming’ government cash flow paid by the borrower) will vary depending on the discount rate derived from the UST curve on the day of disbursement, which here we assume to be the UST 20Y, as noted above.
Imagine a typical $100m WIFIA loan commitment (35-year term, level amortization for simplicity) with a 4.50% interest rate, close to current rates. If at disbursement the UST 20Y is still exactly 4.50%, the PV of loan disbursement will be $100m and the net present value (NPV) compared to Treasury’s $100m PV will be zero — no gain or loss. If rates have risen to say 5.00%, the loan’s PV will be only about $90m — a $10m loss. If OTOH rates have fallen to 4.00%, the loan’s PV will be $110m — a $10m gain. And so on.
The above chart summarizes the NPV impact on this typical WIFIA loan from variation (relative to the rate at closing) in UST 20Y rates, ranging from plus or minus 4.50%, which (per the probability curves above) covers all the material outcomes.
Note that the NPV impact is specific to each loan, depending on its term, amortization and deferral patterns. Each WIFIA loan will have its own NPV impact chart, which can be fully calculated at commitment, since all the relevant facts are known at that point (e.g., the commitment rate and the repayment pattern). This is very straightforward and highly mechanical — for every variation (in one basis point intervals) in the UST 20Y rate from the loan’s commitment rate, the NPV impact (in effect, the upward or downward re-estimate) can be calculated with certainty. The only factor missing is the probability of any particular variation occurring — that’s where the probability curves described above come in.
Combining NPV and UST 20Y Probability: Expected Loss, Gain in ‘Must Draw’ Disbursement Case
Combining a WIFIA loan’s NPV impact chart with the UST 20Y variation probabilities is also straightforward. For each basis point in the variation range, the probability of that variation (say, a 0.48% rise has a 0.29% chance of occurring) is multiplied by the NPV impact at the corresponding interest rate for the WIFIA loan (the loan’s commitment rate plus or minus the variation, or 0.48% plus 4.50%, 4.98%, for a NPV loss of little less than $10m in the above $100m loan example). The expected loss due to the 0.48% rise is therefore about $29k (0.29% times $10m). This is repeated for all the rates in the range — the sum of losses is about $5m and the exact same amount in gains.
The chart above shows the results for the typical WIFIA loan described above. The pattern is intuitive. Variations close to zero are most likely, but they’ll have little NPV impact, so their expected impact on loan funding cost is low. In contrast, wide variations up or down will have a big NPV impact, but their probabilities are slight, and their expected impact of loan funding cost will also be low. In the middle — the trough and peak — are where NPV impact and probability are both meaningful and there are material results. The sum of all probability-weighted impacts is the expected outcome for this loan.
Here’s a critical observation — in the above chart, all outcomes assume that borrower draws on the loan, regardless of how the UST 20Y rate has changed since commitment. In effect, the borrower has no option but to draw, either by loan contract or by the lack of any financing alternatives. In this case, expected NPV losses will exactly equal expected NPV gains (as can be seen from the chart), and the net expected result for the loan’s funding cost at loan commitment is zero. That means that the loan’s credit subsidy estimate at commitment with respect to funding cost (even when fully analyzed, as we’ve been doing here) is also validly zero.
In practice for the vast majority of federal credit, where borrowers qualify primarily by having no cost-effective alternatives and must draw the money, the funding cost impact on interest rate variations between commitment and disbursement can simply be ignored.
I think such ‘must-draw disbursement’ cases are exactly what FCRA law and OMB budgeting procedures were designed to deal with. Of course, the drafters of the law and procedures understood that whenever there’s a delay between loan commitment and disbursement, there will be variation in the Treasury-based discount rate — the NPV of the loan will change. But over the long run, if the disbursements are not influenced by rate changes (true for most federal borrowers), gains and losses will balance out. Any particular funding losses or gains from variation is therefore just budget ‘noise’ and should be efficiently accommodated without affecting the real budget ‘signal’. Hence, automatic permanent indefinite authority to incur mandatory appropriations (for losses) or a simple dump back to the program’s budget (for gains) should be seen as an efficient ‘bookkeeping’ system for minor variations, not as a central feature of what FCRA was intended to do or a de facto entitlement mechanism for highly rated public water systems.
All correct, I think, and our model would seem to confirm the validity of the approach. But the model is also demonstrating the centrality of the must-draw disbursement assumption. Interest rate variation is inevitable and big NPV impacts are likely for long-term, fixed-rate loans, as shown by the distinct trough and peak in the above chart. Only by assuming must-draw disbursement can the net impact be ignored because gains and losses will eventually balance. For cases where that assumption clearly does not apply, the story is very different.
Expected Loss, Gain at Disbursement, Including Option Exercise
As described in many posts on this site, and most recently here, large, sophisticated and highly rated public-sector WIFIA borrowers obviously cannot be assumed to draw on a loan commitment without regard to UST 20Y variation. In fact, it is completely predictable that such borrowers will delay or exercise their cancellation option whenever drawing on a WIFIA loan is more expensive (in PV terms, which is exactly the way such sophisticated borrowers evaluate their financing cost) than their available alternatives. They definitely have options, and they’ll definitely exercise them.
Here we’ll add the ‘non-draw’ (delay, cancel, request reset) option to our model. Note that from the borrower’s perspective, a funding loss for WIFIA is usually a gain for them, and vice-versa.
- First, consider what the borrower will do if UST 20Y rates have fallen, relative to the rate on its WIFIA loan commitment. That means that the rates of their Treasury curve correlated alternatives (short-term financing, tax-exempt bonds) will almost certainly also have fallen, and if they need a construction financing advance, they’ll go to the cheaper sources. If rates have fallen only slightly, the borrower may still draw on the WIFIA loan due to non-rate cost considerations (transaction costs, the value of other WIFIA features, diversification of debt sources, etc.). That’s the small green gain shown in the chart above. But if the fall is material, say an impact above 5% PV of loan amount, the borrower will draw from their other alternatives and WIFIA funding gains will not be realized. That’s the light grey, leftward diagonal part of the chart, the ‘out-of-the-money’ or OTM cancellation.
- Second, in contrast, consider what the borrower will do if UST 20Y rates have risen. Their short term or tax-exempt bond rates may still be the cheapest option, so they still may not draw on the WIFIA loan (an ‘in-the-money’ or ITM cancellation, light grey rightward diagonal above). But if the rise continues and is material, the WIFIA loan will quickly become their cheapest alternative. They definitely will draw, and the funding loss to WIFIA will be realized.
Overall, the pattern is now an asymmetric outcome. If predictable WIFIA borrower behavior is included in credit subsidy estimates (as it must be, per principles of FCRA law and OMB rules), expected loan funding cost losses will exceed gains. Not for every loan, every time — like credit losses, the expected loss is an average over all loans having certain characteristics over the long run.
Credit Subsidy Estimate at Loan Commitment, Disbursement Timing and Option Exercise
With the basic principles in place, we can use the model to develop more specific ways to estimate the expected funding cost for WIFIA loans. The chart above shows the estimated cost, at loan commitment, for expected funding losses incurred at the five 12-month disbursement intervals outlined in earlier sections. The Y-axis shows the estimated cost as a percentage of loan amount (e.g., like credit losses). The X-axis shows the NPV threshold at which the borrower will effectively cancel the disbursement when it’s become out-of-the-money relative to their alternatives (for simplicity, we’re leaving out ITM cancellations). A zero OTM threshold means that the borrower will cancel once the UST 20Y rate rises one basis point over the loan’s commitment rate — in effect, the maximum possible cancellation, leaving only potential losses in the estimate.
The highest credit subsidy value in our model, zero OTM threshold at a 60-month disbursement, is close to 6% of loan amount. Does this sound realistic? I think it does — imagine the variation in interest rates over five years and the impact this can have on the value of a 35-year fixed-rate bond. Mathematically, it’s pretty wide. Now consider only the loss side of equation — 6% sounds about right, and within the range of outcomes that portfolio managers typically plan for.
But more realistically, the OTM threshold is probably higher than zero. Even for ultra-efficient bond refinancings (e.g., using advance refunding when those were still available), I think the minimum threshold was about 5% PV benefit. I’d expect that large, highly rated WIFIA borrowers would apply at least that threshold, if not a little higher, leading to realistic estimates for loans to highly rated WIFIA borrowers in the 5% range for 60-month disbursements, with lower values for faster disbursements.
That’s the upper end, which I’ve outlined as a reality check. But it should be noted that credit subsidy estimates for WIFIA loans are highly customized for the specific loan — that’s true for expected funding losses as it is for expected credit losses. Some loans may be for quickly constructed projects with lower rated, financially constrained borrowers — the funding cost estimates for these may validly include very high OTM thresholds at the faster curves in the lower right of the chart, leading to estimates well below 1%. And everything in between is possible. Our model is meant to accommodate the range of currently eligible WIFIA loans, even if the vast majority of borrowers to date have been in large, sophisticated, highly rated category.
Credit Subsidy Estimate for Two Patterns of 5-Year Disbursement, Option Thresholds
The chart above illustrates the above point with specific typical loan types. The large Aa3/AA- borrower will probably use short-term financing as long as possible regardless of construction progress, delaying disbursement, and have a relatively low OTM threshold, based on bond alternatives and past history (e.g., frequent bond refinancing). That loan should be apportioned about a 5% credit subsidy estimate for funding cost — again, this is not a prediction for the specific loan, but an average cost of this type of loan over the long run (just like credit loss estimates).
In contrast, the Baa3/BBB- project financing will want to draw the WIFIA loan as quickly as possible to keep construction going. The borrower will have a very high OTM threshold, as the financing is highly idiosyncratic, the WIFIA rate works well enough and the project company has limited staff. That loan can be apportioned a credit subsidy estimate for funding cost of less than 1%.
Many other specific factors could be considered in predicting the speed and OTM threshold of WIFIA disbursement. More generally, the key is to put WIFIA loans, and predictable borrower behavior, in the correct context. WIFIA loans don’t work like student loans or small loans to unrated agricultural projects. They’re relatively big, investment-grade per statutory eligibility, and are financing projects that can only be undertaken by relatively sophisticated borrowers. In effect, WIFIA loans are institutional-quality financings that usually end up in the capital markets — and could go back there. If EPA wants to run a $25b institutional loan portfolio, they and OMB will need to step up to skills and mindset required to do it. Otherwise, federal taxpayers will be the losers. More on this in future posts.
Retrospective Test
One way to see whether a model has predictive capabilities is to ‘back-test’ it against past outcomes. That’s an involved process that I’ll undertake at some future point in this model’s development.
But we can do a rough estimate now. The vast majority of WIFIA borrowers to date fit into the highly rated, delayed disbursement, low OTM threshold category described above. Let’s assume that on average the funding cost credit subsidy that should have been apportioned for the WIFIA portfolio is about 5% on average, resulting in the utilization of about $1.3b in additional discretionary funding (assume also that Congress provided the necessary funds). Compare this to the trivial $185m that was actually apportioned for credit losses.
The portfolio disbursements through FY2025 would still of course have incurred $2.1b of funding losses. Assuming pro-rata utilization (a stretch, but for now), the $1.3b of additional discretionary funding for the purpose would have absorbed [3] all but $800m of this. Not perfect (and more losses may be on the way from the portfolio in FY2026) but much better. Total discretionary funding for the Program would have been $1.5b, with $800m of mandatory appropriations for the ‘unexpected’ funding costs. This looks like a more ‘normal’ loan program, in any case, and indicates a recognition of the actual costs incurred by the Program. A better budget signal certainly than the wholly misleading $185m actually apportioned.
As noted earlier, the 2022-2025 ‘spike’ in 60-month variation looked a bit unusual and stood out against the overall pattern. In reality, rates (both short and long term) did rise quite quickly from their Covid lows, and that would have been reflected in borrower behavior and funding cost, as the WIFIA disbursements took place in the 2022-2025 time period. Arguably, the $800m was in fact the kind of unexpected variation that mandatory appropriations were meant to cover. So, perhaps an indication that the model is working.
Impact on WIFIA Selection and Policy Implications
Overall, I think the model outlined above fulfills its purpose — to demonstrate that the expected funding cost impact of optionality in WIFIA loans to highly rated borrowers can be modelled (1) based on historical variation in relevant US Treasury rates, (2) using only simple statistical and financial analysis techniques with minimal assumptions, and (3) with a realistic understanding about how rational borrowers will behave under foreseeable circumstances in the context of institutional debt markets.
There’s no doubt that many improvements and refinements on the model can be made, and I’ll continue its development. But even at this point, I’m fairly confident that (1) the basic methodology is correct, and improved models will be using some version of it, and (2) the results, even at this stage, reflect roughly accurate (if not precise) estimates of expected average funding cost for WIFIA loans — that is, they are immediately usable in ongoing WIFIA loan apportionments. Note that an apportionment for funding cost in a WIFIA loan changes nothing from the borrower’s perspective and can be re-estimated or even completely reversed anytime if the model is revised. WIFIA’s discretionary budget authority carryover is so large (about $300m) that there won’t even be any near-term constraint on available funding. So — why not get started?
Of course, starting to apportion for expected funding cost will have an impact on WIFIA policy and operation. A few observations about that:
- Most importantly, any amount of apportionment for funding cost will recognize that this cost is an issue that must be considered in loan selection. Isn’t that the primary purpose of correct federal budgeting? Under current practice, WIFIA loans to highly rated borrowers look ‘almost free’. This misperception has led to significant misallocation of taxpayer resources and laxity in assessing material policy outcomes — in effect, the Program was apparently so cheap that no one cared what the outcomes were. Correct apportionment for the true cost will quickly change that mindset.
- More immediately, correct apportionment for funding cost will ‘level the playing field’ of loan selection between highly rated water systems using the Program for interest rate optionality and more difficult projects that really need the money but have a more meaningful policy impact. In the illustration case above, the loan to the Aa3/AA- system would likely be apportioned about 0.50% of loan amount for credit losses, making the total apportionment (including funding cost) about 5.50%. In contrast, the Baa3/BBB- project might receive a credit loss apportionment of as much as 4.50%, making the total apportionment also about 5.50%. The expected cost to taxpayers is now the same, and the Program can focus on which loan is the better deal in terms of national policy objectives.
- Finally, a feasible funding cost apportionment model should have a ‘bureaucratic’ impact that is probably more likely than anything else to prompt near-term action. As outlined in two recent posts, EPA WIFIA: Impact of Loan Options Must Be Included in Credit Subsidy Estimates, Per OMB Circular A-11 and EPA WIFIA: Program Statistical Models Predictive of Loan Outcomes, Per OMB Circular A-129, OMB policy requires that any predictable cost of a federal loan that can be identified and quantified must be modelled and included in the credit subsidy estimate at loan commitment. I don’t think there’s any doubt that funding cost in WIFIA loans can be significant — $2.1b of mandatory spending to date makes that abundantly clear. The model demonstrates that this cost is both predictable and quantifiable. At this point, continuing to make ridiculously inadequate apportionments that ignore funding cost indicates either gross negligence or intention. The Anti-Deficiency Act has something to say about both.
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Notes
[1] This is a simplified description of what I think the CSC is doing. The Treasury zero curve in the CSC is purely for the precise evaluation of a WIFIA loan’s future cash flows, net of expected credit and other losses — it’s the ‘value’ of the ‘investment’ that taxpayers are paying for in terms of taxes that don’t need to be paid because expected cash flows from the borrower provide an ‘investment return’. Like any fixed-return investment, OMB discounts these cash flows by the ‘market rate’ for a ‘price’ on the day when the money changes hands (at disbursement in a WIFIA loan) — that market rate for taxpayers appropriately comes from the Treasury curve because forgone taxes are being priced.
A WIFIA loan’s interest rate is, strictly speaking, not related to the discount rates that the CSC uses for valuation. The closeness of the loan’s interest rate based on the Treasury security most closely matching the loan’s WAL (the UST 20Y) and the CSC’s SER market rate on the commitment day (also, about the UST 20Y) is not exactly coincidental, but the values have different origins and purposes.
Future refinements of the model will incorporate these subtleties. It won’t make much difference in terms of results, but I think a full exposition will underscore a fundamental reality here — that WIFIA’s funding losses are as real as if taxpayers paid $25b for an ‘investment’ purported to be worth $24.8b but actually worth only $22.7b. More on this in a future post.
[2] Of course, the Black-Scholes model uses normal distribution assumptions in much more complex ways (e.g., lognormal focused on investment return exponents), but it has a much more ambitious purpose — the actual future price of a security. Our model is far more modest — some estimate of variation is sufficient. But the principle that markets have a ‘natural’ probability component is the same.
[3] The exact mechanics of linking the utilization of apportioned discretionary funding to re-estimates of loan funding cost will need to be determined. I think there’s a straightforward way to do it at loan commitment — OMB can use a higher discount rate to create the required amount of extra subsidy, a ‘SER-Plus’, by elevating the entire Treasury curve by a little. That’ll roughly reflect what’s likely to happen when borrowers, on average, draw on their ‘in-the-money’ commitments when rates have risen. Disbursements at funding rates higher than assumed will be naturally covered by PIA and mandatory appropriations, as was intended. But how such a SER-Plus mechanism fits into OMB budgeting procedures is another matter. More on this in future posts.
