Understanding the Behavior

of COFI

Office of Thrift Supervision

Risk Management Division

_________________________

Anthony G. Cornyn, CFA

Director

Donald Edwards

Radu Filimon, Ph.D.

Eberhard Irmler

Robert Kazdin

Elizabeth Mays, Ph.D.

_________________________

Office of Thrift Supervision

1700 G Street, N.W.

Washington, D.C. 20552

The Eleventh District Cost-ofFunds Index (COFI) is a proxy

for the actual cost of funding for

mortgage loans in the Eleventh

District of the Federal Home

Loan Bank System.1 The index is

used to price adjustable-rate

mortgages, borrowings, and

swaps. Thus, a good understanding of the behavior of the

COFI is a key to sound asset/liability management of depository

institutions, particularly for

California institutions. 

The stability of the index reflects

the composition of existing liabilities of the 11th District, a significant percentage of which

have fixed interest rates. There

is, however, another factor at

work here—the strong re t a i l

nature of the index. This adds

special characteristics to the

COFI’s behavior because of the

sluggish way in which re t a i l

interest rates adjust to changes in

market rates.

COFI and Market

Interest Rates

The relation between market

interest rates and COFI is complex. In general, COFI follows

Treasury rates over the interest

rate cycle but with a lag ( s e e

Figure 1 on page 2). During the

December 31, 1988 to June 30,

1995 period, market rates went

through an almost complete rate

cycle with a peak of 9.6% (in

M a rch 1989) and a trough of

3.1% (in September 1992). Over

the same period, COFI followed

a narrower rate band with a peak

of 8.9% (in July 1989) and a

trough of 3.6% (in April 1994).

The 1989-95 period is interesting

in two respects. First, COFI

peaked four months after the

Treasury rates peaked but it bottomed-out 19 months after market rates did. Second, COFI

volatility, measured by the peakto-trough spread, was 530 basis

points, while the market rates

volatility was 650 basis points.

Based on the 1989-95 cycle, it

appears that COFI adjusts faster

to declines than to increases in

Risk Management Series

By Radu Filimon, Ph.D., Senior Financial Economist

(202)906-5733

1 The Eleventh District includes the states of Arizona, California, and Nevada. The

index is calculated based on the monthly interest expenses, the average monthly

balance of liabilities, and an adjustment factor (which annualizes the index based

on a 365-day year). Interest paid on deposits, FHLB advances, and other borrowings (e.g., repos, subordinated debt, and so on), represents most of the interest

expense used in the COFI calculation. Additionally, the COFI includes net cashflows from off-balance sheet contracts that are accounted for as hedges for liabilities (e.g., net income paid and accrued, amortization of deferred losses or gains,

and net origination fees). For more details see, Passmore, The 11-th District Cost

of Funds Index, Federal Home Loan Bank of San Francisco, 1989.
Office of Thrift Supervision

page 2

Figure 1. COFI Lags Changes in Market Rates

12-Month

Treasury Rate

COFI

9.6

8.9

3.1 3.6

1989 1990 1991 1992 1993 1994 1995

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

2 The NMCOF represents the cost-of-funds for all OTS-regulated, SAIF-insured thrift institutions; it is calculated following the

same methodology as that used to calculate the COFI.

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

Figure 2. COFI and the National COF Display Similar

Trends

1989 1990 1991 1992 1993 1994 1995

NMCOF

COFI

market rates and the adjustment

is incomplete.

The way COFI adjusts to

changes in market rates does not

appear to be determined by

COFI’s regional nature. Over the

same rate cycle, COFI and the

National Median Cost-of-Funds

(NMCOF) exhibited similar

trends (see Figure 2, on page 3).

Though the levels of two indexes

were different at times (especially during the 1989-91 period},

they adjusted to changes in

Treasury rates with a substantial

lag.2

One should not read too much

into the behavior of the COFI

based on a single rate cycle,

however. Several factors, specific

to the 1989-95 cycle, may have

produced the observed patterns

in the rate cycles. In particular,

COFI’s incomplete adjustment to

changes in market rates may be

just the side-effect of the index’s

adjustment lag. That is, if retail

rates indeed adjust with a lag to

market rates, then it would be

rational for institutions to forgo

raising deposit rates to match

past increases in market rates,

when a new, downward, trend in

rates is widely expected.

The COFI’s adjustment to market rates reflects the interplay of

two factors. First, COFI represents the cost of existing liabilities (and off - b a l a n c e - s h e e t

positions), some of which have

long remaining maturities. For

example, during a period of

declining rates an institution’s

cost-of-funds can be expected to

decline slowly as the existing

fixed-rate liabilities gradually
Table 1. Remaining Maturity Structure of 11th District

Liabilities*

(Balances as a percentage of total liabilities)

1989 1990 1991 1992 1993 1994 1995

Non-Maturity Liabilities

Demand Deposits & Escrows 13.44 16.21 21.15 25.90 27.21 28.20 21.70

Other Liabilities 2.10 1.81 1.50 1.38 1.69 1.60 1.62

Total 15.53 18.03 22.65 27.28 28.90 29.80 23.33

Variable Rate Liabilities NA NA NA NA 7.73 8.52 10.50

Liabilities Maturing in 3 Months or Less

Certificates of Deposits 18.26 22.64 25.78 21.94 16.22 14.87 14.61

Borrowings 19.33 14.62 10.35 9.64 7.25 6.08 10.62

Total 37.59 37.26 36.13 31.59 23.47 20.96 25.23

Liabilities Maturing in 4 to 36 Months

Certificates of Deposits 32.29 31.74 30.28 30.77 28.70 31.33 34.19

Borrowings 7.41 6.86 6.09 4.36 3.79 4.08 3.70

Total 39.70 38.61 36.37 35.12 32.48 35.42 37.88

Liabilities Maturing in 36 Months or More

Certificates of Deposits 2.58 2.22 1.86 3.45 5.00 3.54 2.01

Borrowings 4.59 3.88 2.99 2.56 2.42 1.72 1.04

Total 7.17 6.11 4.85 6.01 7.42 5.26 3.06

* Data as of the end of June quarter.

Risk Management Series

page 3

m a t u re and are replaced with

new lower-rate funds. 

Second, a large proportion of the

COFI liabilities are retail funds

which, even if they have stated

maturities that are short term

(e.g., demand deposits and

short-term (CDs), have offered

rates that adjust incompletely

and with a lag to changes in market rates3. This stickiness of retail

rates acts to lengthen COFI’s

adjustment lag beyond the

length implied by their remaining maturities. Since retail funds

reprice to current market rates

with a lag, it might take a prolonged period of rate stability

before retail rates catch up with

past changes in market rates.4

Average Maturity of

COFI Liabilities

The weighted-average re m a i ning maturity of COFI liabilities is

rather short. In June 1995, about

59% of COFI liabilities consisted

of demand deposits, variablerate liabilities, and liabilities

with remaining maturity of three

months or less (see Table 1, below).

Only about 3% of the COFI liabilities had remaining maturities

of 36 months or longer.

The remaining maturity of COFI

liabilities shortened over the

1989 to 1995 period. Short-maturity liabilities (i.e., the non-matur i t y, the variable-rate, and the

short remaining maturity liabilities) increased somewhat over

the period, from 53% of total liabilities in 1989 to 59% in 1995.

Over the same period, liabilities

maturing in more than 36

months declined from 7% to 3%

of total liabilities.

Based on the data in Table 1, the

weighted-average re m a i n i n g

maturity of COFI liabilities

(excluding non-maturity and

variable-rate liabilities), appears

to be about 12 months. This suggests that it would take about 12

months for COFI to fully adjust

to a one-time change in market

rates. This estimate, however,

ignores the effect of put and call

options that are embedded in

these liabilities. In general, a liability’s remaining maturity is

shortened by the options. For

example, CDs may be withdrawn early when interest rates

rise and callable debt may be

retired when rates decline. This

effect, however, is moderated by

the fact that options on retail

funds are not usually exercised

rationally. That is, a high percentage of CDs and demand

deposits are rolled over when it

would make sense to withdraw

the funds and invest them elsewhere at higher rates.

3 The reasons for the stickiness exhibited by retail rates are unclear. See, O’Brien, Orphanides, and Small, Estimating the Interest

Rate Sensitivity of Liquid Retail Deposit Values, Conference on Bank Structure and Competition, Federal Reserve Bank of

Chicago, May 1994.

4 An econometric analysis of the relation between COFI and market rates confirms these conclusions. For details, see Filimon,

Proposed COFI Equation, OTS internal memorandum, 1995.
volatility measure for the

demand deposit rate was only

370 basis points (this is also

lower than COFI’s volatility of

510 basis points).

The lagged adjustment to

changes in market rates is eviOffice of Thrift Supervision

page 4

Figure 3).

5 Over the period March

1989 to June 1995, the amplitude

of the market rate cycle was

m o re than 600 basis points

(equal to the difference between

the highest and the lowest rates,

over the period). Over the same

period, the corre s p o n d i n g

Most of the COFI

Liabilities are Retail

Funds

Retail funds have a diff e re n t

repricing behavior than market

funds. First, depositors often fail

to exercise their option to withdraw their deposits when market rates are more attractive.

Second, institutions seem able to

attract new retail funds at rates

that are lower than market rates.

The combination of these factors,

which applies to both demand

deposits and CDs, makes the

remaining maturity calculation

above rather imprecise .

The retail component of 11 t h

District liabilities is large. In

1995, almost all the deposits,

consisted of non-bro k e re d

deposits (see Table 2). And more

than half the liabilities are

deposits with balances of less

than $80,000. 

Over the 1989 to 1995 period,

retail deposits in the 11th District

increased. First, the size of the

deposit base increased from 67%

of liabilities in 1989, to over 73%

in 1995. Second, brokered funds

declined from 8.9% of liabilities

in 1989, to 1.1% in 1995. Third,

deposits with balances of less

than $80,000 increased from 43%

to 52% of liabilities, over the

same period. 

The Behavior of

Demand Deposit

Rates and Balances

Demand deposit rates are less

volatile than Treasury rates (see

Table 2. Structure of 11th District Deposits*

(Balances as a percentage of total liabilities)

1989 1990 1991 1992 1993 1994 1995

Source of Funds

Retail Funds 57.67 65.69 74.89 79.02 74.34 76.95 72.35

Brokered Funds 8.90 6.87 3.79 2.61 2.65 1.17 1.09

Balance Size

Less than $80,000 42.76 48.48 54.65 59.50 55.80 56.64 51.77

Between $80,000 and $100,000 9.45 10.77 11.45 11.22 11.26 11.15 10.47

Greater than $100,000 14.36 13.32 12.57 10.91 9.92 10.34 11.20

Total Deposits 66.57 72.57 78.68 81.63 76.99 78.12 73.43

* Data as of the end of June quarter.

5 The demand deposit rate is calculated as the weighted-average rate of all the demand deposit and escrow account rates.

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

Figure 3. Demand Deposit Rates Are Less Volatile

Than Market Rates

1989 1990 1991 1992 1993 1994 1995

3-Month Treasury

COFI

Demand Deposits

Rate

8.8 8.9

5.6

2.7

3.7

1.9
Risk Management Series

page 5

dent in the trough dates of the

rate cycles. The 3-month

Treasury rate reached its trough

in September 1992, but demand

deposit rates did not stop declining until 18 months later. A s

F i g u re 3 indicates, the most

recent peak in demand deposit

rates (July 1989) was much closer

to the peak in market rates

( M a rch 1989). Comparing the

peaks of the various rate cycles,

however, does not yield as clear

cut conclusions as the comparison of their troughs. This suggests that deposit rates may

adjust faster to declines than to

increases in market rates. 

Demand deposit balances do not

appear to be very sensitive to the

absolute level of interest rates

(see Figure 4). Deposit balances

increased from about $26 billion

in 1989 to almost $48 billion in

March 1994, while deposit rates

declined slightly, reaching their

minimum level of 1.9% in March

1994. 

Demand deposit balances, however, seem to be sensitive to the

s p read between deposit and

market rates. Over the sample

period, deposit balances first

i n c reased while the spre a d

between market and deposit

rates narrowed (during the 1989

to 1991 period), then increased

slightly over the next two years

(during 1992 and 1993). Finally,

during 1994 and 1995, balances

declined rather dramatically as

the spread between market and

deposit rates increased. 

The decline in nominal deposit

balances over the last 18 months

of the sample period is a fairly

s t rong sign of the corre l a t i o n

between balances and deposit

rate spreads. Typically, aggregate

Figure 4. Demand Deposit Balances Adjust to the

Spread Between Demand Deposit and

3-month Treasury Rates

1989 1990 1991 1992 1993 1994 1995

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

0

50

100

150

200

250

300

350

400

Spread DD Balance

deposit balances increase over

time as a result of inflation, population growth, and GDP

growth.

CD Rates are more reliable but

they still lag and have incomplete adjustments.

The Behavior of CD

Rates and Balances

CDs’ balances and rates also

exhibit low sensitivity to

changes in market rates, though

their sluggish adjustment to

market rates is less pronounced

than that of demand deposits’.

Because CDs re p resent more

than one-fifth of total COFI liabilities, the behavior of CD rates

and balances is an important

determinant of COFI’s behavior.

Three-month CD rates track fairly closely Treasury rates of similar maturity (see Figure 5 on page

6). There is a slight lag during

the downward trend in rates

over the period 1989 to 1992. The

lag during the upward trend in

market rates, however, seems to

be substantial. 

The volatility of CD rates, as

m e a s u red by the diff e re n c e

between the maximum and minimum levels over the sample

period, is slightly lower than that

of market rates. This would

imply that CD rates adjust

almost completely to changes in

market rates.
Office of Thrift Supervision

page 6

Conclusions

The COFI has a lagged and

dampened response to changes

in market rates. Its low volatility,

however, is only partially due to

the fact that some of the liabilities underlying the index have

fixed rates and maturities.

Retail funds—which represent a

large percentage of the COFI liabilities—contribute heavily to

the COFI’s special behavior

because the rates on these funds

adjust only slowly and incompletely to changes in market

rates. The strong retail nature of

the 11th District liabilities also

adds a special pattern to the

COFI’s behavior: the index

adjustment to increases in market rates seems to be slower than

its adjustment to declines in rates

■

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

Figure 5. CD Rates Have Low Sensitivity to Changes

in Market Rates

1989 1990 1991 1992 1993 1994 1995

3-Month Treasury Rate

COFI

3-Month CD Rate