USC FBE FINANCE SEMINAR presented by Darrell Duffie FRIDAY, November 10, 2006 10:30 am – 12:00 pm, Room: JKP-202

Systemic Dynamics in the Federal Funds Market

Adam Ashcraft and Darrell Duffie New York Federal Reserve Bank and Stanford University

Preliminary work, October, 2006 Acknowledgements: Data from The Federal Reserve Bank of New York, conversations with James McAndrews, and interviews with anonymous traders.

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Federal Funds • Banks are monitored for minimum balances, averaged over two week periods. • Banks do not receive interest for overnight balances. • Federal funds is a common interbank medium for settlement, for example of securities and currency trades. • Intra-day overdrafts are limited and penalized. • Over-the-counter trading is bilaterally negotiated, largely by telephone.

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Figure 1: An over-the-counter market is completely connected, but not transparent. Search and negotiation are crucial.

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Figure 2: If search costs are the only market friction, the most efficient market structure is hub-and-spoke, for example an electronic limit-order book, or a single broker.

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9.72

9

9.67

8.95

9.62

8.9

9.57 Low λ High λ

8.85 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

9.52 2

Low λ High λ

0.12 Instantaneous Return

1.8

Price, high λ

Price, low λ

9.05

0.08

0.04

0

0

0.2

0.4

0.6

0.8

1 1.2 Calendar Time

1.4

Figure 3:

1.6

1.8

2

Liquidity shock at time 0.4. Low search intensity λ = 125; high search intensity λ = 625. Source: Duffie, Gˆ arleanu, and Pedersen (2005).

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Figure 4: Because of size differences, the “effective” market structure of over-the-counter markets is a hybrid.

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Figure 5: The cross-sectional distribution of fed-funds senders by total volume in December 2005 is more skewed than log-normal.

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siz 1 e

Figure 6: Stylized “fuzzy” hub-and-spoke market structure.

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Table 1: Average Behavior of Sends in the Fed Funds Market during December 2005. “Big” means top-ten by volume.

Sender

Receiver

Median number of receivers

Median monthly volume ($ millions)

Small

Big

3.1

14.4

Small

Small

1.4

2.4

Big

Small

2006.4

645,796

Big

Big

7.0

1,487,043

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B

100

A

100

100

C

Figure 10: How can A, B, and C all send 100 with no initial inventory? One cannot ignore the dynamics.

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50 B

100

100

0

150 A

100

C

Figure 11: These trades can be implemented in one round, starting with the circled inventories.

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0 B

100

100

0

1 A

100

C

Figure 12: The same trades can also be implemented in many trades from much smaller inventories.

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1 B

99

100

0

0 A

100

C

Figure 13: After the first of many trades.

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0 B

99

99

1

0 A

100

C

Figure 14: After the second of many trades.

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0 B

99

99

0

1 A

99

C

Figure 15: After the third of 300 trades.

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CHIPS DTC Depository Institutions Foreign Banks Foreign Central Banks GSEs Special Situations

Figure 16: Breakdown of largest-by-volume 100 master account types, by number of accounts.

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.06 .04 .02 0 -.02 -.04

Reserve Balance Relative to Monthly Send

1710

1720

1730

1740 1750 time of day

1800

1810

1820

1830

Figure 17: Targeting balances during the crucial 30 minute period: 17:30 to 18:00.

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400 0

Number of Sends by Top 100 accounts 100 200 300 1700

1710

1720

1730 1740 time of day

1750

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1800

1810

1820

8 6 4 2 0

Lent by Top 100 accounts (billions $)

1700

1710

1720

1730 1740 1750 time of day

1800

1810

1820

1830

Figure 18: Distribution across lenders of volume of loans, within top 100 accounts. Stanford University, 2006

Probabilistic model of transactions • Over 225 million observations in 2005, top 100 master accounts. • Logit estimator of the probability that i sends (or lends) to j in minute t:   Bi (t) Bj (t) pij (t) = L Vi , Vj , , , Rij , σ(t), 1{t ∈ [ 17:30 , 18:30 ]} , Vi Vj where – Vi is log of monthly volume of bank i during 17:00 to 18:30. – Bi (t) is the balance of bank i at the beginning of minute t minus median-over-days balance of i at t. – Rij is lagged-month (i, j) trades as a fraction of all trades to j, plus lagged-month (i, j) trades as a fraction of all trades from i. – σ(t) is the trailing 30-minute rate volatility. Stanford University, 2006

Basic Results • Transactions show precautionary targeting of balances. • Loans are far more sensitive to balances than are other transactions. • Balance targeting is more active when rate volatility is higher. • Doubling the size of bank i increases the likelihood of a send to bank j by over 50%. • Controlling for prior relationship, size of a counterparty is more predictive of a loan than of a non-loan transaction. • The 17:30 to 18:30 period is the most critical for balance targeting.

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Special Effects • September 2001: lower sensitivity to balances after 9-11. • On 9-11, drop in dependence on largest banks (BONY?). • Quarter end: increased sensitivity to balances. • Notorious 15th-day-of-month effect (due to corporate taxes and GSE interest payments) is not obvious in the data. • Maintenance effects not apparent. End-of-day balance targeting behavior does not vary markedly within the two-week settlement cycle. From interviews: This may reflect the impact of “sweeps.”

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Gridlock? • Precautionary gridlock: With a low balance, bank i waits for a send from j before processing a send to k. Supply shocks could mean that j is meanwhile waiting for a send from m, who is waiting for a send from n, who is . . . • According to interviews: A systemic gridlock was a significant risk on 9/11, when BONY was incapacitated. A concerted effort to provide liquidity by the Federal Reserve and top banks averted an even greater protential problem. See Lacker (2003), McAndrews and Potter (2002).

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0.1200%

5-530pm

Lend probability

0.1000%

530-630pm

0.0800%

0.0600%

0.0400%

0.0200%

0.0000% m-3sd

m-2sd

m-1sd

mean

m+1sd

m+2sd

m+3sd

Normalized reserve balance

Figure 19: Probability of lend is more sensitive to balances in the last hour.

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0.0800% 0.0700%

5-530pm

Borrow probability

0.0600%

530-630pm

0.0500% 0.0400% 0.0300% 0.0200% 0.0100% 0.0000% m-3sd

m-2sd

m-1sd

mean

m+1sd

m+2sd

m+3sd

Normalized reserve balacne

Figure 20: Probability of borrow is more sensitive to balances in the last hour.

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0.0400%

0.4000% Pr(lend)

0.0350%

0.3950% Pr(send) 0.0300% 0.3900%

0.3850%

0.0200%

Pr(Send)

Pr(Lend)

0.0250%

0.0150% 0.3800% 0.0100% 0.3750% 0.0050% 0.0000%

0.3700% m-3sd

m-2sd

m-1sd

mean

m+1sd

m+2sd

m+3sd

Normalized reserve balance

Figure 21: Loans are 81 times more sensitive to balances than are non-loan sends.

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Table 2: The interest rate negotiated depends on the excess balances of the borrower and the lender banks. Here is the mean negotiated rate less the average rate in the market at this minute, for banks with low (10%-ile) and high (90%-ile) excess balances.

Low Borrower

High Borrower

Low-Balance Lender

1.8 basis points

0.2 basis points

High-Balance Lender

1.1 basis points

−2.6 basis points

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Rate impact (basis points)

2

0

-2

-4 0

50

100

150

200

Pair excess balance measure

Figure 22: The rate negotiated, relative to the mean market rate at that minute, depending on the sum of the excess-balances percentiles of the borrower and the lender banks. Stanford University, 2006

6000

5000

Number of loans

4000

3000

2000

1000

0 1

2

3

4

5

6

7

8

9

10

Lender's decile, by relative excess balance

Figure 23: For loans to borrowers most in need of federal funds (the lowest decile by relative excess balances), the number of loans made by each decile of lenders, sorted by the lender’s relative excess balances. Stanford University, 2006

Negotiating a rate late in the day R(k, t) − r(t) = c − 2.5 q(k, t) + 6.7 s(k, t) + ǫ(k, t) (4.7)

(7.7)

• R(k, t) is the rate negotiated by pair k at minute t. • r(t) is the mean rate negotiated in the market at minute t, in basis points. • q(k, t) is the sum of the cross-sectional quantile ranks of lender and borrower, in forecasted relative balances. • s(k, t) is the difference of the cross-sectional quantile ranks of lender and borrower, in size. Stanford University, 2006

.002 .0015 0

.0005

Volatility .001 1700

1710

1720

1730 1740 1750 time of day

1800

1810

1820

1830

Figure 24: Trailing 30-minute fed funds rate volatility, across 251 business days.

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0.0800%

0.0700%

0 vol

0.0600%

1sd vol

Pr(Lend)

0.0500%

0.0400%

0.0300%

0.0200%

0.0100%

0.0000% m-3sd

m-2sd

m-1sd

mean

m+1sd

m+2sd

m+3sd

Normalized reserve balance

Figure 25: Lend sensitivity to balances increases with volatility.

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