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Authorized for public release by the FOMC Secretariat on 1/12/2024
September 7, 2018
An analysis of the recent dynamics in the federal funds market
Gara Afonso (FRB New York), Roc Armenter and Benjamin Lester (FRB Philadelphia) 1
Rising rates in the repurchase (repo) market have been often cited as the driving factor behind
the increase in rates and drop in volume in the fed funds market during the first half of the year.2
As the Effective Federal Funds Rate (EFFR) came within 5 basis points (bps) of the top of the
target range, a “small technical adjustment” was implemented on June 14, 2018, reducing the
Interest On Reserves (IOR) to 5 bps below the top of the target range. Since then, the EFFR
has settled at 1.91%, 9 bps below the top of the target range, with only a modest drop in fed
funds volume.3 Figure 1 plots the the IOR, the EFFR, and a measure of repo rates—the Secured
Overnight Finance Rate (SOFR)—relative to the top of the target range, from the start of the year
to the end of July, along with the evolution of trading volume in the fed funds market.4
Going forward, repo rates and other factors could exert additional upward pressure on fed funds
rates, possibly requiring an additional technical adjustment to IOR. In this note, we analyze the
recent changes in the fed funds market (up through July) through the lens of a structural model
that captures the pass-through effects of repo rates. Using reasonable parameter values, the model
reproduces closely the observed dynamics in the fed funds market, and hence provides an attractive
framework for quantitative analysis.
We find that the effects of higher repo rates on the fed funds market were driven by the Federal
Home Loan Banks (FHLBs) shifting their balances toward repo markets, and obtaining better rates
from banks on those funds remaining in the fed funds market. Our analysis also illustrates how
the lockstep movement in repo rates with the IOR was crucial to the success of the June technical
adjustment. According to the model, further technical adjustments to the IOR would ensure that
fed funds rates trade well within the target range even if repo rates soar, but interest-rate control
may come at the cost of seriously inhibiting the fed funds trading.
The memo is organized as follows. In the first section, we highlight the key features of the
model, with a more detailed description provided in the Appendix. In Section 2, we use the model
to analyze the effects of the rising repo rates and the June technical adjustment. Section 3 discusses
interest rate control going forward, with a focus on the effects of further technical adjustments in
response to renewed pressure from repo rates. Section 4 concludes.
1
We thank Ryan Bush, James Clouse, Elizabeth Klee, Jane Ihrig, Antoine Martin, Ed Nosal, Sam Schulhofer-Wohl,
Julie Remache, William Riordan, Joseph Wang, and Jacqueline Yen for their continued help and feedback.
2
Market participants often cited the large increase in Treasury bill supply as the main driver of the higher repo
rates. See also the May Tealbook box “Recent Pressures in Money Markets” for additional discussion.
3
The adjustment “has had exactly the intended effect on money market conditions,” according to Potter (2018).
4
All market rates are as reported by FRB New York and exclude month end dates. The Tri-Party General
Collateral Rate (TGCR) showed similar dynamics, though it typically trades about 3 bps lower than the SOFR.
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Figure 1: Key dynamics in the fed funds market in 2018
(a) Selected rates
(b) Fed funds volume
Basis points
$ billions
120
10
5
0
100
−5
−10
80
−15
−20
60
−25
SOFR
EFFR
IOR
−30
Feb
Mar
Apr
May
Jun
Jul
Feb
Mar
Apr
May
Jun
Jul
Source: Federal Reserve Bank of New York
1
Brief description of the model
Our starting point is the structural model developed in Armenter and Lester (2017), designed to
analyze fed funds trades between depository institutions that qualify for IOR (or “banks,” for short)
and FHLBs.5 Banks are heterogeneous: Some have a net balance-sheet benefit from borrowing
funds from a FHLB, perhaps due to Liquidity Coverage Ratio (LCR) considerations; while others
face a net cost from borrowing due to, e.g., FDIC assessment fees. More precisely, the net return
from borrowing fed funds for bank i at rate ρi is
πib = IOR + xi − ρi
where xi is the balance-sheet net benefit, which can be positive or negative, and varies across banks
according to a parametric distribution that we calibrate to match the observed dispersion in fed
funds rates. We introduce search frictions to capture the over-the-counter nature of trades, and
to generate several salient features of the fed funds market, including incomplete arbitrage, rate
dispersion, and limited participation by banks.
We take repo rates to be exogenous, as conditions in the fed funds market do not seem to
currently influence repo rates directly.6 Focusing on the FHLBs’ options and decisions, we assume
that the transmission of repo rates into the fed funds market occurs through two channels:
• Supply channel. FHLBs split their balances between the fed funds and repo markets
5
For further details on the model, data, and calibration see the Appendix. This is not the only structural model
of the fed funds market post-2008; see Bech and Klee (2011), Chen et al. (2016), Schulhofer-Wohl and Clouse (2018),
Kim et al. (2017), and Afonso et al. (2018), among others.
6
Of course, there are common determinants of fed funds and repo rates—most importantly, the IOR, which we
assume has full pass-through with repo rates in our model exercises. It is also likely that, as reserves become scarce,
there will be additional linkages between the fed funds and repo markets, perhaps through the banks’ liquidity
decisions.
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according to a linear function of the spread between the EFFR and SOFR,
λ = λ∗ + ε (EFFR − SOFR) ,
where λ is the share of the FHLBs’ balances allotted for lending in the fed funds market, λ∗
is an intercept term, and ε > 0 captures the sensitivity of the FHLBs’ liquidity portfolio to
the spread.7 This channel operates primarily through the supply of funds, but will also elicit
a response in rates. For example, FHLBs will divert liquidity away from the fed funds market
in response to higher repo rates, which in turn will lead banks to compete for the scarcer
balances by bidding up fed funds rates.
• Outside-option channel. When seeking a counterparty in the fed funds market, FHLBs
have an outside option for their balances, given by a weighted average of the repo rate and
the prevailing rate at the Overnight Reverse Repurchase Agreement Facility (ONRRP),
r = (1 − α)ONRRP + α max {SOFR, ONRRP} ,
where α ∈ [0, 1] determines the sensitivity of the outside option to repo rates.8 FHLBs will
never accept a fed funds trade that offers a lower rate of return than this outside option, r.
Hence, if α > 0 and SOF R > ON RRP , an increase in the repo rate improves the outside
option for FHLBs, who then demand better rates from banks in the fed funds market.
The “arbitrage surplus,” defined as the spread between the IOR and the FHLBs’ outside option
S = IOR − r, is the key determinant of fed funds rates and volume in the model. For any given
pair of counterparties, the gains from trade will be the sum of the arbitrage surplus and some
idiosyncratic factors, like the FHLBs’ preference for early return of funds and the bank’s balancesheet considerations. Whenever there is a change in arbitrage surplus, all bilateral trades in the
market must adjust—and some may actually become unprofitable.
2
The fed funds market in 2018
For calibration and exposition purposes, we focus on the current year until July and split the data
into three distinct episodes reported in Table 1, delimited by the evolution of repo rates and the
technical adjustment to the IOR. We use the moniker “low repo” to denote the first period, from
January 1 – March 9, 2018, when repo rates were relatively low. The second period, from April 23
7
The FHLBs’ liquidity requirements may imply a lower bound on the supply of fed funds, λ ≥ λ̄. We found
no evidence in our calibration that fed funds lent by FHLBs are at a lower bound for the time being, and thus we
have chosen to omit it. See Tikonoff and Wang (2017) for further discussion. Another possible concern with our
specification is that FHLBs raise some of the funds lent through Discount Notes (DN), perhaps $10 bn. or more.
This suggests that the spread between DN rates and the EFFR may be a relevant determinant of the FHLBs supply
and its omission may lead us to overstate the FHLBs response to repo rates.
8
The case α = 1 corresponds to the specification in Schulhofer-Wohl and Clouse (2018). A possible structural
interpretation of α < 1 is that FHLBs have less bargaining power in the repo market late in the day.
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– June 13, 2018, is labeled “high repo” for the obvious reasons. Finally, the “technical adjustment”
period starts on June 14, 2018, when the IOR was reduced by 5 bps, and ends with the month of
July.9 Since the model does not encompass bank-to-bank trades, we focus on fed funds volume lent
by FHLBs.10
Table 1: Key changes in spreads and fed funds volume
Low repo period
Jan. 1 - Mar. 9
(I)
IOR
ONRRP rate
SOFR
EFFR
FF Volumea
Total
By FHLBs
High repo period
Apr. 23 - Jun. 13
(II)
(II)-(I)
Tech adjustment period
Jun. 14 - Jul. 31
(III)
(III) - (II)
0
-25
-15
-8
0
-25
-3
-5
0
0
+12
+3
-5
-25
-8
-9
-5
0
-5
-4
98
96.8
83.3
81.2
-14.7
-15.6
76.6
74.7
-6.7
-6.5
All spreads in basis points relative to top of the FOMC’s target range.
Source: Federal Reserve Bank of New York and FR2420.
a
Volume is reported in $ bn.
In the Appendix, we show that the model can be calibrated to fit the data remarkably well:
we match the EFFR and most of the distribution of fed funds rates within half a basis point in all
three periods. The model also reproduces the changes in fed funds volume, though it is not capable
of fully explaining the drop in volume since mid-June.11 Importantly, the model’s parameter values
appear reasonable and close to alternative estimates, whenever they are available. Given the model’s
quantitative fit, we next deploy it to better understand the transmission of repo rates to the fed
funds market, along with the effects of the technical adjustment to the IOR.
2.1
The effects of repo rates on the fed funds market
Our first exercise is to analyze the effects of the run-up in repo rates observed in the first half of
the year.12 We set the IOR and the ONRRP rate at 175 and 150 bps, respectively, matching the
FOMC’s target range between the March and June FOMC meetings. In the low repo period, we
9
We discard the period March 10 to April 22 as one of transition. See the Appendix for futher discussion. The
analysis does not include the recent uptick in the EFFR and drop in the fed funds volume.
10
Ignoring bank-to-bank trades appears innocuous in the current environment, as Table 1 shows the vast majority
of trades do involve a FHLB. Potter (2018) also shows that the share of trades above the IOR has remained low
(Figure 9). However, the inter-bank segment of the market may regain traction over the medium term. See Afonso
et al. (2018) for a model capable of generating such dynamics, as well as “Normalization scenarios in a structural
model of the federal funds market,” FOMC memo distributed June 1, 2017.
11
One potential factor, that is not modeled here, is that there may have been a decrease in aggregate liquidity by
FHLBs due to seasonal factors. See “Developments in the Federal Funds Market Following the Technical Adjustment
to IOR,” memo distributed on July 20, 2018.
12
While market participants often cited the large increase in Treasury bill supply as the main driver of the higher
repo rates, Baer et al. (2018) suggests other factors may have contributed to the increase in money market rates.
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set the repo rate 15 bps below the IOR—the same spread observed for the first two months of the
year. In the high repo period, we set the repo rate equal to the average SOFR recorded between
the end of April and the June FOMC meeting, just 3 bps below the IOR. We solve the model for
each scenario and report the predicted EFFR and volume in the last two columns of Table 2.13
Table 2: The effects of high repo rates
Exogenous
Low repo period
High repo period
Overall Change
Model results
IOR
Repo rate
EFFR
Volume ($bn.)
175
175
160a
172b
167.4
170.4
96.8
81.2
0
+12
+3
-15.6
+0.7
+2.6
-0.3
-10.8
-7.7
+2.9
Decomposition:
Supply
Outside option
Interaction
All rates are in basis points. The ONRRP rate is constant at 150 bps.
Based on 1/1/2018-3/9/2018 data for the SOFR rate.
b
Based on 4/23/2018-6/13/2018 data for the SOFR rate.
a
In response to rising repo rates, FHLBs allocate fewer funds to the fed funds market and, with
those funds remaining in the fed funds market, they negotiate better rates. To isolate the effect
of the former—the supply channel—we calculate the model-implied fed funds rates and volume
allowing the FHLBs’ portfolios to change but holding constant the outside option, r. Similarly, to
quantify the outside option channel, we fix FHLBs’ portfolios and calculate the changes in rates and
volume resulting only from the change in the outside option r. The contribution of each channel
to rates and volume is reported in the lower right portion of Table 2, along with the interaction
between the two channels.
Both channels are found to have an important quantitative role. The supply channel naturally
has a large effect on volume. In addition, as FHLBs shift their portfolio away from the fed funds
market, banks are forced to compete for scarcer funds, eliciting a mild increase in fed funds rates.
The outside-option channel has a larger effect on rates, explaining most of the change in the
EFFR by itself. Our calibration implies that the 12 bps increase in the repo rate improved the
FHLBs’ outside option by 9 bps—a large effect. More surprisingly, the rise in the outside option
also has a substantial effect on fed funds volume. The reason is that the increase in the repo rate
reduces the arbitrage surplus between FHLBs and banks. As FHLBs demand (and obtain) higher
rates, banks with sufficiently large balance-sheet costs choose not to participate in the fed funds
market, which reduces the overall transaction volume. Finally, the interaction effect reflects the
endogenous response of the FHLBs’ supply to the higher fed funds rates caused by the increase in
13
In other words, the low-repo and high-repo scenarios correspond to columns (I) and (II), respectively, in Table
1. Indeed, the model predictions track closely the observed averages between April 23 and June 13, 2018.
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the outside option; restoring some of the fed funds volume and nudging rates downward.
Finally, we have observed some renewed upward pressure on fed funds rates in the last weeks
of August, with the EFFR increasing by 1 bp and volume dropping by close to $ 10 bn. While this
latest episode is too short—and the changes in rates too small—for us to re-evaluate our model at
this time, the drop in fed funds rates appear roughly in line with the model’s predicted response
to a 3 − 4 increase in repo rates. Fed funds volume would also be reduced in the model, though
likely by a smaller amount than we observed.
2.2
The effects of the technical adjustment to the IOR
Next, we use our model to analyze the technical adjustment approved by the FOMC in mid June,
whereby the IOR was set to 5 bps below the top of the target range. As Table 1 illustrates, this
adjustment was effective in pushing down the EFFR, which settled at 1.91—only 4 bps below the
IOR, but now safely away from the top of the target range of 2%.
A key observation is that repo rates moved in lockstep with the IOR, as shown in Figure 1. Using
the model, we decompose the impact of the technical adjustment into the direct effect resulting
from the decline in the IOR—keeping the repo rate constant—and the indirect effect following the
subsequent drop in the repo rate.
Table 3 reports the results. The “no adjustment” scenario sets the IOR at 200 bps and the repo
rate at 197 bps, based on the values observed in the month or so prior to the FOMC June meeting.
The “adjustment” scenario sets the IOR and repo rates at 195 and 192 bps, respectively, and fits
the data observed since the implementation of the technical adjustment quite well.14
Table 3: The effects of the technical adjustment
Exogenous rates
Model results
IOR
Repo rate
EFFR
Volume ($bn.)
No adjustment
Adjustment
200
195
195a
192b
195.4
190.8
81.2
79.6
Overall Change
-5
-5
-4.6
-1.6
-3.2
-1.4
-12.6
+11.0
Decomposition:
Direct
Indirect
All rates are in basis points. The ONRRP rate is constant at 175 bps.
Based on 4/23/2018-6/13/2018 data for the SOFR rate.
b
Based on 6/14/2018-7/31/2018 data for the SOFR rate.
a
We find that the lockstep movement of the repo rate and IOR is crucial to the overall success
of the technical adjustment. As Table 3 illustrates, the direct effect of reducing IOR has a large
impact on the EFFR—falling more than 3 bps—but also leads to a sharp reduction in fed funds
14
In both scenarios the ONRRP rate is set at 175 bps. The model does overstate the fed funds volume after the
technical adjustment, so the drop in volume in Table 3 is smaller than observed in the data.
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volume. A cut in the IOR reduces the arbitrage surplus one for one and, as the pie shrinks, less
guests show up at the party: FHLBs respond to the lower fed funds rates by diverting balances
to the repo market, and banks with high balance sheet costs can no longer post a competitive
rate. The combined effect is a large pass-through from the IOR to the EFFR, accompanied with a
precipitous drop in volume.
The subsequent drop in repo rates—the indirect effect—pushes the EFFR further down but
almost fully reverses the drop in fed funds volume. This is a consequence of both the supply and
outside-option channels discussed earlier. First, the drop in the repo rate reduces FHLBs appetite
for the repo market, causing balances to flow back to the fed funds market. Second, it reduces the
FHLBs outside option and thus restores a large fraction of the arbitrage surplus that was lost by
the drop in the IOR. Reversing the comparative statics discussed in the last section, the increase in
the arbitrage surplus sustains trading and allows banks to remain active in the fed funds market.
3
Interest-rate control going forward
3.1
Higher repo rates and additional technical adjustments
We now use our model to explore the scope for further technical adjustments to IOR in response
to renewed pressure from higher repo rates. Figure 2 reports the model-generated EFFR and fed
funds volume for a range of repo rates given the current level of the IOR (teal line) and when it is
set 5 bps lower (coral line). Under the current regime, fed funds rates are remarkably resilient, with
the EFFR remaining more than 5 bps below the top of the target range for all repo rates below
2%. The relationship between the EFFR and the repo rate is nearly linear, with a pass-through
of about 30%.15 The effect on trading activity is more pronounced, as fed funds volume is cut
in half when repo rates reach 2%, and drops even faster as repo rates rise further. According to
the model, this sharp decline occurs because both FHLBs and banks retreat from the fed funds
market as the arbitrage surplus shrinks, with the combined effect becoming stronger as the market
becomes increasingly thinner.
Figure 2 also displays the EFFR and volume across repo rates when IOR is set to 190 bps.16 The
lines (in coral) are noticeably steeper. The pass-through from repo to fed funds rate is substantially
higher and volume drops precipitously to less than $20 bn for repo rates above 2%. This exercise
illustrates that, as the arbitrage surplus shrinks, conditions in the fed funds market become more
sensitive. Intuitively, a change of 1 bps in the repo rate is proportionally larger the narrower the
margins are in the market in the first place.
This lesson could be particularly relevant if policymakers implement further reductions in the
IOR; we find that, even though additional technical adjustments may be effective in ensuring
interest-rate control in response to rising repo rates, they run the risk of thinning the fed funds
15
That is, the EFFR increases by 3 bps for every 10 bps increase in the repo rate. This is essentially the same
pass-through value as in Schulhofer-Wohl and Clouse (2018).
16
Note that the values reported in Figure 2 do not reflect the overall effects of a technical adjustment, because in
practice the repo rate moves in lockstep with the IOR.
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Figure 2: Fed funds rates and volumes
Effective Federal Funds Rate
Fed funds volume (FHBLs only)
●
195
●
● IOR = 190 bps
● IOR = 195 bps
193
●
Basis points
192
191
190
189
●
●
●
●
●
●
●
●
●
●
●
●
60
●
●
50
● ●
● ●
● ●
●
● ●
●
● ●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
40
●
187
185
●
70
●
●
●
●
●
●
●
188
186
●
●
●
80
●
●
$ Billions
194
90
● ●
●
30
●
●
●
●
20
●
●
10
190
195
200
Repurchase rate (basis points)
205
●
185
190
195
200
Repurchase rate (basis points)
205
market to the point of irrelevance. Table 4 reports the model’s predictions for the EFFR and fed
funds volume to various shocks to the repo rate under three different values of the IOR: when the
IOR remains at its current level (195 bps), when it is reduced 5 bps below its current level, and
when it is reduced 10 bps below its current level. For each calculation, we assume that repo rates
move in lockstep with the IOR so that, after the technical adjustment to the IOR, the net change
in the repo rate is less than the initial shock.17
Our results suggest that the EFFR would remain within the target range even if the repo rate
increased by 15 bps, relative to its current level.18 However, keeping a significant buffer between
the EFFR and the top of the target range might require additional technical adjustments. In some
cases a reduction in the IOR of 10 bps would be needed to restore the EFFR to the midpoint of
the target range, but this would come at a steep cost, nearly wiping out all volume in the fed
funds market in the worst case. As discussed earlier, the direct and indirect effects of a drop in
IOR roughly cancel each other. However, in all but one scenario the net effect on the repo rate is
positive, that is, the drop in IOR may have been sufficient to restore interest-rate control in the
fed funds market but repo rates were left higher than before.
It is possible that our model overstates the drop in fed funds volume for some of the scenarios
in Table 4. There are indeed good reasons to believe that FHLBs would not completely flee the
fed funds market. For example, FHLBs need a minumum of early return liquidity between $30
and $40 bns., which is not available in tri-party repo transactions.19 We explored this possibility
17
Recall both the IOR and the repo rate are exogenous in our model, so the degree of pass-through from IOR to
the repo rate is a premise of the scenario rather than a result.
18
A sustained period with repo rates above 2% could incentivize banks to lend their excess reserves holdings in the
repo market—perhaps even borrowing in the fed funds market for this purpose. This consideration is not present in
our model, but could be an important force in driving up fed funds rates while possibly also reigning in repo rates.
19
Delivery-Versus-Payments (DVP) repos do offer early return liquidity, but FHLBs appear limited in their capacity
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Table 4: Upward repo pressure and IOR adjustments
Repo rate +10 bps
Repo rate +8 bps
Exogenous rates
IOR
Repo rate
195
200
190
195
185
190
Model results
EFFR
Volumea
193.2
61.5
188.8
56.0
184.5
50.3
Exogenous rates
IOR
Repo rate
195
202
190
197
185
192
Repo rate +12 bps
Exogenous rates
IOR
Repo rate
195
204
190
199
185
194
Model results
EFFR
Volumea
194
53.8
189.6
48.4
185.4
40.1
Repo rate +15 bps
Model results
EFFR
Volumea
194.9
45.0
190.6
38.7
186.6
28.2
Exogenous rates
IOR
Repo rate
195
207
190
202
185
197
Model results
EFFR
Volumea
196.3
30.8
192.4
21.0
188.7
12.9
The ONRRP rate is set at 175 bps and the baseline repo rate at 192 bps. All rates in basis points.
In $ bn.
a
by imposing a lower bound on the FHLBs’ fed funds holdings of $40 bn. in our specification
for the supply channel. According to the model, a FHLBs’ constraint mutes the negative effects
from higher repo rates, with fed funds rates further away from the top of the target range and, of
course, higher fed funds volume. Indeed, as the FHLBs’ constraint effectively removes an important
transmission channel, the pass-through from repo to fed funds rates is lower, albeit not zero since
the outside-option channel remains active.
3.2
The effects of changes to the FDIC assessment fee
The removal of the large-institution surcharge, scheduled to take place before the end of this year,
is often cited as an additional factor that may drive up fed funds rates. According to our model,
a reduction in balance-sheet costs would increase fed funds rates and volume, but the magnitude
of the effect depends on (i) the extent to which currently active banks benefit from the reduction,
and (ii) whether currently inactive banks are encouraged to return to the fed funds market.20 We
compute an upper bound on the effect of removing the large-institution surcharge by reducing all
banks’ balance-sheet costs by 4.5 bps. According to the model, this leads the EFFR to increase by
slightly less than 3 bps—a relatively modest amount that would not derail interest-rate control—
while boosting fed funds volume. However, the surcharge removal leaves the fed funds market more
to expand their DVP repo activity past their current levels of about $10-15 bn per day. Of course, it is also possible
that a large spread between repo and fed funds rate leads FHLBs to invest in their DVP repo capacity overall, bringing
in a permanent shift in their liquidity portfolio. In addition, the Federal Housing Finance Authority (FHFA) may
revise its liquidity regulations for the FHLBs, likely increasing the overall requirements but allowing the FHLBs more
flexibility in their portfolio composition.
20
Since our calibration is based on observed rates, there is considerable uncertainty around the distribution of
balance-sheet costs for those banks that are currently inactive.
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vulnerable to increases in repo rates: We find that repo rates at or above 2.10% would then push
the EFFR above the top of the target range, absent any further adjustment to the IOR.
3.3
The effects of changes in FHLBs liquidity management
The FHFA has recently issued a revision to its liquidity regulations for FHLBs, to be phased in
over the next year. The new regulations aim to increase the liquidity pools of FHLBs and broaden
the pool of eligible assets to include, among other asset classes, Treasury securities.21 While the
overall effects of the new liquidity regulation are quite uncertain, it is possible that the net effect
of the new regulations is to decrease the FHLBs’ fed funds investment, perhaps sharply.
As a first pass to assess the possible impact of the new FHFA regulations, we conduct a simple
counterfactual exercise in the model: Keeping rates at those observed in the technical adjustment
period, we introduce a negative shock to the FHLBs’ supply that drives their fed funds lending down
to $40 and $30 bn. The result is an increase in the EFFR of 3 and 4 bps, respectively. Similarly to
the effects of the removal of FDIC assessment fee, the regulations are not, by themselves, likely to
threaten interest-rate control but do increase the risk associated with further repo increases.
4
Concluding remarks
Despite a number of simplifying assumptions, our model is able to match the recent dynamics in
the fed funds market quite well. In particular, we have assumed that the transmission between
the repo market and the fed funds market is a one-way street: Repo rates influence conditions in
the fed funds market, but not vice versa. If this is, indeed, the case, then there may be cause
for concern. The IOR would be essentially the sole policy lever, perhaps with the ONRRP rate
providing minimal assistance, and the fed funds market would be no more than the proverbial
canary in the coal mine—a warning system of changes in overall financing conditions, but a cog no
more in the implementation of monetary policy. Such a situation could have serious drawbacks.
Were the EFFR to drift out of the target range for reasons idiosyncratic to the fed funds market—
perhaps due to a change in the liquidity management strategies of FHLBs—an adjustment to the
IOR would effectively and, arguably, unduly influence a broad spectrum of money market rates.
Finally, we conducted our analysis within the strict confines of abundant reserves. As the
normalization process unfolds and reserves become scarce, the inter-bank segment of the fed funds
market may revive and drive the EFFR above the IOR.22 The EFFR may also become more closely
tied to the financing cost of banks, improving the resilience of the fed funds market and perhaps
restoring some two-way linkages with other money markets. However, whether scarce reserves are
a desirable goal remains unknown.
21
More precisely, the FHFA determined to exclude Treasury securities when measuring the FHLB core mission
achievement. For more details, see the FHFA advisory bulletin AB 2018-07, “Federal Home Loan Bank Liquidity
Guidance,” issued August 23, 2018.
22
What exactly constitutes “scarce” reserves, and how scarcity will manifest, are open questions. See (Afonso et
al., 2018) for an analysis of the transition from abundant to scarce reserves.
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Appendices
A
Model
A.1
Description
There are two agent types in the model: FHLBs, which lend their balances in either the fed funds
or repo markets; and banks, which can borrow from the FHLBs in the fed funds market. The
Fed sets the rate banks earn on their reserves as well as the offering rate at the ON RRP facility,
denoted R and ONRRP, respectively. FHLBs do not qualify to earn interest on reserves, so their
idle balances, if any, earn a zero net return. The prevailing rate in the repo market, p, is exogenous
and taken as given by all agents.
Banks. Each bank i decides whether to be active in the fed funds market and, if so, it sets
an interest rate, denoted ρi , that it will pay to borrow a fixed amount from a FHLB. If the bank
obtains funds, it deposits them at the Fed and earns interest on reserves R overnight. Banks may
also have have additional considerations associated with a fed funds transaction, denoted xi , to be
interpreted as the net balance sheet benefit. Balance-sheet considerations may include costs, like
the FDIC fee on total assets, and benefits, like a favorable LCR treatment for borrowing funds
from FHLBs.23 The payoff from borrowing fed funds for bank i is then
πib = R + xi − ρi .
(1)
The distribution of xi across banks is given by c.d.f. G over support X ⊂ <—including both
positive and negative values. If a bank is not active or does not match, it earns zero payoff.
FHLBs. FHLBs split their balances between the fed funds market and the repo market. There
are many considerations that go into this decision, including regulatory requirements, timing of the
day, and, of course, prevailing rates. We assume that FHLBs allocate a share of their balances for
lending at the fed funds according to
λ = λ∗ + ε (ρ̂ − p)
(2)
where ρ̂ denotes the EFFR, λ is the share of aggregate balances to be lent in the fed funds market,
and λ∗ , ε > 0 govern the level and elasticity of the supply of funds, respectively. This “supply”
specification can be derived as an approximation to a simple model where fed funds and repo
transactions are imperfect substitute instruments for the FHLBs’ liquidity needs.
We assume balances lent in the repo market are simply expected to earn the net interest rate p.
To lend in the fed funds market, though, FHLBs need to match with a bank.24 To do so, FHLBs
23
For further details on balance-sheet considerations see Wang and Bush (2018).
A more accurate specification for (2) would then include both the expected rate if matched and the probability
of matching—ideally, in both fed funds and repo markets. We have computed a version of the model with the
expectation specification for the fed funds market and results are very similar.
24
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seek to lend their balances at a particular rate ρ among those posted by the banks. If successfully
matched, the FHLB obtains payoff
π l (ρ) = ρ + τ
(3)
where τ captures possible advantages that are specific of fed funds transactions for FHLBs, like
early return of funds.25 If unmatched in the fed funds market, FHLBs earn outside option r. We
model the latter as a weighted average between the ON RRP rate and the repo,
r = (1 − α)ONRRP + αp,
(4)
where α ∈ [0, 1]. One can interpret parameter α as the bargaining power of a FHLB late in the day
in the repo market, or perhaps simply as the probability of finding a suitable counterparty then.26
Either way, the parameter governs the pass-through coefficient of repo rates into the expected
outside option in the fed funds market.
Matching frictions. We capture the over-the-counter nature of trading in the fed funds with
search frictions. In particular, we use a “directed search” model, which assumes that there is
enough transparency for FHLBs to target a particular rate, but not enough to guarantee that they
would obtain it. For any given posted rate ρi , we define a queue qj as the ratio of FHLB’s balances
seeking the rate to the measure of banks posting it. The matching function µ(q) then determines
the probability a bank is matched, with ν(q) ≡ µ(q)/q pinning down the probability that a FHLBs
matches in the submarket for rate ρj .
A.2
Model solution
We briefly document how the model is solved.27 The key decisions in the fed funds market occur
in three different stages. First, banks have to decide whether or not to enter the fed funds market
given their balance sheet considerations, xi . Second, those banks that enter have to choose an
interest rate, ρi . Finally, given the interest rates that have been posted, FHLBs have to choose
which one to approach. In order to describe optimal behavior at each stage, we work backwards.
Search by FHLBs. Once interest rates have been posted, each FHLB seeks the rate that offers
the maximum expected payoff, taking into account both the actual interest rate being offered and
the probability of being matched. In particular, the expected payoff from a lender choosing a
segment or submarket with interest rate ρi and queue length qi is
Πl (ρi , qi ) = ν(qi ) (ρi + τ ) + (1 − ν(qi ))r.
(5)
The first term captures the probability that the FHLB is matched, in which case it obtains the
25
For a throughout discussion of the FHLBs liquidity needs and constraints, as well as timing considerations, see
LeSeur (2014).
26
See Schulhofer-Wohl and Clouse (2018) for a structural model where the repo rate determines the outside option
of the fed funds market.
27
See Armenter and Lester (2017) for a complete discussion of the model equilibrium and solution.
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payoff (3), while the second term captures the probability that the FHLB fails to match, earning
instead the outside option.
Let Π̄l denote the maximum expected payoff that a FHLB can obtain in the fed funds, or
“market utility.” In equilibrium, then, any submarket with a positive queue qi > 0 must satisfy
Πl (ρi , qi ) = Π̄l .
(6)
That is, in equilibrium, any bank that is able to attract FHLBs must deliver an expected payoff
equal to the market utility: For example, if a bank posts a relatively low interest rate, FHLBs must
be compensated with a high probability of being matched (i.e., a short queue length), and vice
versa. Using (5) to solve (6) yields a relationship between rates and queues:
ρi = r − τ +
Π¯l − r
.
ν(qi )
(7)
Note that the search frictions allow different rates to co-exist in equilibrium.
Interest rate posting by banks. The FHLBs’ indifference condition in equation (7) lays bare the
trade-off facing banks: They can post a low interest rate and match with low probability but earn a
large margin if they do so, or they can attract more GSEs by posting a higher interest rate, in which
case they will match with higher probability but earn a narrower spread. Taking this trade-off as
given, a bank with balance sheet consideration xi solves the following profit maximization problem:
µ(q)(R + xi − ρ)
Π¯l − r
subject to ρ = r − τ +
,
ν(q)
maxρ,q
where the market utility Π¯l is taken as given. From the objective function, it’s clear that a bank’s
expected profits are equal to the product of the probability of being matched, µ(qi ), and the revenue
from accepting a deposit, R + xi − ρi . The necessary and sufficient first-order condition associated
with the problem is
µ0 (qi ) =
Π¯l − r
.
R + xi + τ − r
(8)
Together with the indifference condition (7), we obtain the optimal queue and rate as a function
of the balance-sheet considerations, q(xi ), and ρ(xi ). Thus search frictions endow the banks with
some market power, while rates remain responsive to aggregate conditions.
Bank entry decision. A bank enters the fed funds market if, and only if, its expected profits
from doing so are nonnegative. One can easily show that a bank’s profits are increasing in xi , so
that the optimal entry decision is determined by a cutoff rule: There exists a unique x̄ > 0 such
that profits are nonnegative if, and only if, xi ≥ x̄. From (1) is quite immediate that if bank i posts
ρi = R + xi it then obtains zero profits. Optimality (8) also requires that the bank cannot obtain
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positive profits by varying the rate. Together with (7), this implies
x̄ = Π¯l − τ − R.
(9)
Fed funds market aggregate consistency. The fed funds market must “clear,” in the sense that
the queues qi must be consistent with the FHLB’s supply of aggregate balances:
Z
∞
q(xi )dG(xi ) = λ.
(10)
x̄
Conditions (9) and (10) are used to pin down the threshold and market utility in equilibrium. We
can then compute the volume in the fed funds market as the number of matches realized,
Z
∞
µ(q(xi ))dG(xi )
V =
x̄
and the volume-weighted distribution over traded rates is given by p.d.f.
f (ρi ) =
µ(q(xi ))dG(xi )
V
if qi > 0, zero otherwise. We can then readily compute the EFFR ρ̂—as well as any moment of
interest of the volume-weighted distribution of fed funds rates.28
Equilibrium. To close the model, the supply of funds λ must be consistent with (2). More
formally, an equilibrium consists of a supply of funds λ, a threshold x̄, and a joint distribution of
queues and rates q(xi ), ρ(xi ) such that equations (2) to (10) are satisfied.
B
Calibration
B.1
Data and time periods
We work with public and confidential data for the present year to date. The model is not suited
to day-to-day variation, so we split the data into three data episodes and work with the average
values over the period, after removing the last business day of each calendar month.29 The data
episodes are:
1. January 1st to March 9th, when the EFFR stayed constant at 8 basis points below IOR, repo
rates were generally well below the EFFR, and volume in the fed funds market averaged close
to $100 bn.
2. April 23th to June 13th, when the EFFR traded just 5 basis points below interest on reserves,
repo rates were systematically above the EFFR, and fed funds volume dropped to $80 bn.
28
Because of the search frictions, fed funds volume is always less than the total balances supplied by the FHLBs:
We assume that the difference is lent in the repo market, later in the day.
29
Non quarter-end month-end movements have become minimal in the second quarter of 2018, but for comparison
purposes we remove them for the whole time sample. For more detail see Tikonoff and Wang (2018).
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3. June 14th to July 31st, from the time the technical adjustment to the IOR was effective to
the latest date of our analysis.
We discard the time period between March 10th to April 22nd as one of transition. Dates were
chosen such that policy rates—interest on reserves and ONRRP rate, as well as the target range
by the FOMC—were constant within each data episode.
We use public data for the fed funds rate distribution as released by the Federal Reserve Bank
of New York. We equate the repo rate to the SOFR, relying again on public data from the Federal
Reserve Bank of New York.30 For volume data, we use fed funds transactions by FHLB.31 Table
5 reports the summary statistics for the variables of interest. For each time episode we work with
the average over the period, though we keep an eye on the median as well to avoid any particular
value to be driven by outliers.
Payoffs and quantities in the model are scale free, so we choose to normalize the measure of
banks to one, express volume in billions of dollars, and rates in basis points. The data also follow
this choice of units.
B.2
Specifications
For the distribution of balance-sheet considerations we use a fine grid over support [−15, 10] and
approximate G(x) with a Gamma distribution with two parameters, shape and scale.32 For exposition purposes, we use the (unconditional) mean µx and standard deviation σx , which can be
expressed in basis points.
The matching function is given by µ(q) = 1 − exp (−q), which is commonly used in direct
search models for its tractability. In any case, we do not have data to fine tune a more flexible
specification.
B.3
Parameter choices
The model parameters to calibrate are six: λ∗ , ε from the supply function (2); µx , σx for the
distribution of balance-sheet considerations; τ , the FHLBs’ special valuation of fed funds; and the
weight α from the outside option (4). All these parameters are kept constant across data episodes.
Policy and repo rates are set to their observed values in each data episode, as reported in Table 5.
We target the fed funds volume due to FHLBs and EFFR in each data episode, as well as the
25th and 75th percentiles in the dollar-weighted distribution of fed funds rates. We ignore the
FFR 99th Percentile, which is typically set by a bank-to-bank funds transaction that the model is
not set to capture. The fed funds volume in the first data episode is matched exactly by choice of
30
Using the TGCR requires a slight re-calibration of the model, since the TGCR is typically below the SOFR. The
main results, though, are essentially unchanged.
31
We thank Joseph Wang for his help. Results are very similar if we use instead total fed funds volume.
32
The choice of parametric distribution is mainly for convenience, remaining parsimonious while being quite flexible.
The support was chosen such that results were invariant to the particular bounds.
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Table 5: Summary Data
1/1/2018 - 3/9/2018
Mean
Median
Max.
Min.
Effective FFR
FFR 1st Percentile
FFR 25th Percentile
FFR 75th Percentile
FFR 99th Percentile
142
139.4
141.8
143
152
142
140
142
143
150
142
140
142
144
165
142
130
141
142
148
Fed funds volume (total)
Fed funds volume (by FHLB)
98
96.8
97
96.2
115
114
84
81.9
SOFR
134.9
134
145
128
Memo: IOR = 150 bps, ONRRP rate = 125 bps.
4/23/2018 - 6/13/2018
Mean
Median
Max.
Min.
Effective FFR
FFR 1st Percentile
FFR 25th Percentile
FFR 75th Percentile
FFR 99th Percentile
170
165.8
169.1
171.2
181.5
170
166
169
171
181
170
166
170
172
187
170
165
169
170
180
Volume
VolumeFHLB
83.3
81.2
83
81.1
94
91.3
63
60.8
SOFR
172.4
172
181
165
Memo: IOR = 175 bps, ONRRP rate = 150 bps.
6/14/2018 - 7/31/2018
Mean
Median
Max.
Min.
Effective FFR
FFR 1st Percentile
FFR 25th Percentile
FFR 75th Percentile
FFR 99th Percentile
191
189.2
190.5
191.8
205.4
191
190
191
192
206
192
190
191
194
206
190
188
189
191
200
Volume
VolumeFHLB
76.6
74.7
78
75.7
88
85.3
59
56.7
SOFR
191.6
190
204
187
Memo: IOR = 195 bps, ONRRP rate = 175 bps.
All rates in basis points. Volume in $ billions. Month ends excluded.
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units. We are hence left with 11 targeted moments and 6 free parameters, so arguably the system
is over-identified.
Table 6 reports the model fit. All targeted rates are matched within half a basis point—a
rounding error for all purposes. In addition, the model matches the 1st percentile of the fed funds
rate distribution for two out of three episodes, the exception being the period 4/23-7/18 when some
fed funds rates were agreed 4 basis points below the EFFR. In the model as well as in the data,
more than 80% of total traded volume is within plus/minus one basis point of the EFFR. Fed funds
volume in the model is very close to the data, though it overstates somewhat the volume in the
more recent episode—perhaps due to a decrease in aggregate liquidity by FHLBs.33
Table 6: Model fit
1/1 - 3/9
Effective FFR
FFR Percentile 1st
FFR Percentile 25th
FFR Percentile 75th
FFR Percentile 99th
Fed funds Volumea
Data
142
139.4
141.8
143
152
96.8
Model
142.4
139.9
141.6
143.2
145.2
96.8
4/23 - 6/13
Data
170
165.8
169.1
171.2
181.5
81.2
Model
170.4
168.6
169.5
171.1
172.5
81.2
6/14 - 7/31
Data
191
189.2
190.5
191.8
205.4
74.7
Model
190.8
189.1
190.2
191.4
192.7
79.6
All rates in basis points. Data are period means, excluding month ends.
Volume in $ bn., excluding bank-to-bank transactions.
a
The parameter values are reported in Table 7. The elasticity of the supply function is quite low,
with an increase in the spread between the EFFR and the repo rate of one basis points shifting $1.6
bn—less than 2% of the FHLBs average liquidity—into the fed funds market. The level is within
estimates of total liquidity balances by FHLBs.34 The distribution of balance sheet considerations
is quite disperse and points to balance sheet costs as retaining an important role in the market—
yet the calibration points to smaller costs than the estimates of the marginal cost of the FDIC fee
by Banegas and Tase (2016).35 Banks with zero or positive balance sheet considerations play an
important role in our results. These banks post moderately higher rates and constitute a growing
fraction of the market according to the model—up to a fourth of all active banks, and an even
larger fraction of fed funds trade.36
We are not aware of any current study to contrast our last two parameter values, the value of
early return money for FHLBs and the repo-rate pass-through to the outside option.37 We instead
33
We did find that total FHLBs’ overnight loans decreased in the last month or so. See also “Developments in the
Federal Funds Market Following the Technical Adjustment to IOR,” memo distributed on July 20, 2018.
34
The FHLB’s office of finance reports a total liquidity portfolio of $133 bn. in April 2018 (www.fhlb-of.com).
The estimate, though, includes cash balances with commercial banks as pass-through reserves. See also Tikonoff and
Wang (2017).
35
Since we are basing our calibration on traded rates, the model is actually silent about the balance-sheet considerations of banks that stayed inactive thorough the sample period.
36
These facts line up with banks that were termed “non-IOER arbitrage borrowers” in Wang and Bush (2018).
37
That said, 3 basis points appears a reasonable estimate for the marginal value of early return money for FHLBs.
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Supply function
Level λ∗
Elasticity ε
119 $bn.
1.6 $bn./bp
Distribution G(x)
Mean µx
Std.Desv. σx
−3 bps
4 bps
FHLBs preferences
Early funds return τ
3 bps
Outside option
Repo pass-through α
.75
Table 7: Parameter values
briefly discuss how the calibration pins down the parameters τ and α. A key feature of the model
is that no agreed-upon rate can be valued below the outside option of the FHLBs. By either giving
an additional value for fed funds—a higher τ —or by weighing down the repo rate—a lower value of
α—the calibration can reconcile the large fraction of trades with rates below the repo rate in the
last two episodes. Parameter α also effectively governs the strength of the outside-option channel
for repo rates: If α = 0, repo rates would impact the fed funds market only through the supply
channel.
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References
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Yesterday, Today, and Tomorrow,” February 2018. Federal Reserve Bank of Philadelphia WP
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Baer, Tony, Ari Morse, and Tony Rodrigues, “Quantifying Stock and Flow Effects of
Treasury-Bill Issuance on Money Market Rates ,” MarketSource, Federal Reserve Bank of New
York August 2018.
Banegas, Ayelen and Manjola Tase, “Reserve Balances, the Federal Funds Market and Arbitrage in the New Regulatory Framework,” Finance and Economics Discussion Series 2016-079,
Board of Governors of the Federal Reserve System (U.S.) September 2016.
Bech, Morten L. and Elizabeth Klee, “The Mechanics of a Graceful Exit: Interest on Reserves
and Segmentation in the Federal Funds Market,” Journal of Monetary Economics, 2011, 58 (5),
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Chen, Han, Jim Clouse, Jane Ihrig, and Elizabeth Klee, “The Federal Reserve’s Tools for
Policy Normalization in a Preferred Habitat Model of Financial Markets,” Journal of Money,
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Kim, Kyungmin, Antoine Martin, and Ed Nosal, “Can the US interbank market be revived?,” June 2017. Federal Reserve Bank of Chicago.
LeSeur, Eric, “Primer: FHLB Liquidity Management and its Impact on the Fed Funds Market,”
MarketSource, Federal Reserve Bank of New York October 2014.
Potter, Simon, “Confidence in the Implementation of U.S. Monetary Policy Normalization,”
August 2018. Speech, Remarks at the 23rd EMEAP Governors’ Meeting, Manila, Philippines.
Schulhofer-Wohl, Sam and James A. Clouse, “A Sequential Bargaining Model of the Fed
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of Chicago 2018.
Tikonoff, Anna and Joseph Wang, “Money Markets: Fed Funds Volumes Trended Higher in
First Half of 2017 as FHLBs Increased Debt Issuance,” MarketSource, Federal Reserve Bank of
New York July 2017.
and
, “Why do Overnight Unsecured Funding Rates Decline on Non Quarter-end Month-
ends?,” MarketSource, Federal Reserve Bank of New York July 2018.
Wang, Joseph and Ryan Bush, “Fed Funds: Beyond IOER Arbitrage,” MarketSource, Federal
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@FedFRASER