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The effect of contemporaneous reserve accounting on the market for federal funds
Journal
of Banking
and
Finance
16 (1992)
1047-1056.
North-Holland
The effect of contemporaneous reserve accounting on the market for Federal funds Dennis J. Lasser* SUN Y-Binghamton,
Binghamton, NY
13902-6000,
Received April 1991, final version received
February
USA
1992
This paper evaluates the elfect of the transition from lagged to contemporaneous reserve accounting for the determination of bank reserve requirements through its impact on the market for Federal funds. The results indicate that increased target reserve uncertainty resulting from the implementation of the contemporaneous reserve accounting system (CRA) caused an initial increase in intraday Federal funds rate variance and daily interest rate differences. However, subsequent to a ‘learning’ period, intraday variance appears to be less pronounced and daily differentials appear to be narrower than under the previously used lagged reserve accounting system (LRA). These results are attributed to the lengthening of the accounting period from one to two weeks. Therefore, while not costless, the new system does not appear to have seriously disrupted the Federal funds market.
1. Introduction This paper examines the impact of the imposition of the 1984 rule change that determines bank reserve requirements. On February 1, 1984 the accounting treatment used for specifying reserve requirements changed from a lagged reserve accounting system (LRA) to a contemporaneous reserve accounting system (CRA). Under the LRA system there was a two-week lag between the average daily deposits held by the bank and the average daily reserve requirements needed to support those deposits, while under the CRA system the two periods overlap. The stated purpose of the change was to allow the Fed to conduct a more effective monetary policy. However, in order to determine the effectiveness of any regulatory action, one must consider the costs as well as the benefits of that action. In this case, such control notwithstanding, the change may have imposed a cost of increased Correspondence to: Dennis J. Lasser, Assistant Professor of Finance, School of Management, SUNY-Binghamton, Binghamton, NY 13902-6OOG. USA. *I would like to thank Doug Emery and two anonymous referees for their extremely helpful comments. Of course all remaining errors remain my own.
0378-4266/92/SO5.00
C 1992-Elsevier
Science Publishers
B.V. All rights
reserved
1048
D.J. Laser,
Ejrect of conremporaneous
reserve accounting
risk for bank liquidity managers given that reserve amounts are not fully disclosed until just prior to the end of the accounting period. The specifications of the alternative accounting standards are as follows. From September 1968, through January 1984, reserve requirements were calculated under the LRA system. Under LRA, bank reserve requirements were calculated on an average weekly basis ending each Wednesday. The requirements were a function of the average daily deposits held from Thursday through the following Wednesday, over a period that was two weeks prior to the reserve maintenance period. This created a two week lag between the time the deposits were held and the time the reserve requirement had to be met. Since February I, 1984 reserve requirements have been calculated under the CRA system. Under the current system, bank reserve requirements are calculated on an average biweekly basis ending every other Wednesday. These reserves are a function of the average daily balance of deposits held for a two-week period ending two days prior to the end of the reserve maintenance period. Therefore, the bank liquidity manager has only two days in which the amount of reserves needed are known with certainty. We examine the effect on the bank manager of the change from LRA to CRA by comparing daily interest rate patterns and intraday variances in the Federal funds market before and after February 1, 1984. Since the primary source of a bank’s reserve maintenance is the Federal funds market, any impact of the accounting rule change on bank liquidity management should be detectable by observing daily interest rate and intraday variance pattern changes in the Fed funds maket in the CRA period. The results indicate a cost to the bank manager in that there was an initial increase in the intraday volatility in the CRA period, particularly on the second Tuesday of the maintenance period. Similarly, following the change to CRA, there was an initial exaggeration of the previously existing daily interest rate pattern that existed during the LRA period. Over time, however, that exaggeration not only disappeared but seems to have become less pronounced than was prior to the rule change. The eventual smoothing would seem to result from the increased length of time of the maintenance period (from one to two weeks). Section 2 provides a brief review of the literature and describes the hypotheses to be tested. Section 3 outlines the specific testing methodologies employed and discusses the results, while section 4 provides a brief summary and conclusions. 2. Return and volatility patterns in Fed funds markets Several studies have examined daily interest rate patterns and interest rate variances in the Federal funds market. With regard rates, Barrett et al. (1988) argue that bank reserve managers tend reserves early in the reserve week in order to be assured of easily
intraday to daily to build meeting
D.J.
Lasser.
Effect
of contemporaneous
reserce
accounting
1049
their reserve requirements and thus avoiding any penalties. Therefore, they contend that Fed funds rates should be highest on Thursday and lowest on Wednesday. They find support for this argument in that the first differences of daily rates during 1970-1982 imply a significantly higher Fed funds rate on Thursday and lower rates on Tuesday and Wednesday. However, Dyl and Hoffmeister (1985) find that actual rates followed such a pattern only during 1970, when tested yearly over a period from 197&198 1. Empirical findings concerning the variance of intraday Fed funds are more consistent. Dyl and Hoffmeister (1985), using pre-1984 data, and Saunders and Urich (1988) and Spindt and Hoffmeister (1988), using post-1983 data, find a common pattern in intraday Fed funds variance. Intraday variance is lowest on Thursday and highest on Wednesday. These results appear to be a function of the regulatory constraints and, more specifically, the accounting system imposed on bank managers. Although, the effect of the accounting rule change on intraday variance has not yet been examined, Dyl and Hoffmeister hypothesize that the imposition of CRA should cause an initial increased variance, particularly on the second Tuesday and Wednesday of the accounting period, at least until managers become familiar with the new system. The change from LRA to CRA has two primary components that have potential impacts on bank reserve management. First, after the rule change, specific target reserve amounts became unknown for all but the final two days of the maintenance period. These targets were always known with certainty under the LRA system. Therefore, if bank managers build up reserves early in the accounting period as protection against uncertainty in meeting reserves as described by Barrett et al. (1988), one would expect the increased uncertainty to cause an increase in the variation of daily interest rates after February 1, 1984. Similarly, since information about the reserve target is revealed on a daily basis, the managers’ assessment of required reserves changes daily. Therefore, one would expect the reserve target uncertainty to increase intraday Fed funds volatility, especially at the end of the accounting period. The second component of the rule change consists of increasing the accounting period from one to two weeks. The effect of this component on daily Fed funds interest rates is unclear. The longer maintenance period should induce the liquidity manager to hold more excess reserves, thereby increasing early period demand. However, the impact may be less detectable since the excess demand is spread over a greater number of days, allowing the manager more latitude in meeting unexpected reserve needs. The potential impact of the longer accounting period is less confounded with respect to intraday volatility. The longer time frame should not decrease, and may well magnify, the impact of increased intraday volatility caused by the daily uncertainty of the reserve target. Furthermore, similar to the LRA
1050
D.J. Lasser, Effect
ofcontemporaneous resert‘e
accounting
system, one would expect to find lower intraday volatility early in the maintenance period. Under CRA this should be seen in lower first week intraday volatility relative to the second week of the period. Finally, we contend that a ‘learning’ period may have existed for bank liquidity managers to familiarize themselves with the new accounting system. Prior to the enactment of CRA, bank managers were not as concerned with estimating target reserves since, for reserve requirement purposes, they were always known with certainty. After CRA implementation, however, this function became an essential part of the reserve managers success in meeting reserve requirements. Therefore, one would expect managers to become more adept at estimating target reserves later in the CRA period. If such a ‘learning’ period exists, it should be reflected by higher variance immediately following implementation with a subsequent decline to lower variance later in the CRA period. 3. Test methodologies
and empirical findings
3.a. Daily return patterns
Daily Fed funds interest rates were obtained from January 1978 through December 1987 from the Federal Reserve Bank in New York. Daily interest patterns are estimated using the methodology of Gibbons and Hess (1981), as modified by Barrett et al. (1988). Specifically, the first difference of the daily interest rate is regressed on day of the week dummy variables, given as1 Diffrr= b, Mon + b,Tues + b3 Wed + b,Thur + b5 Fri + e.
(1)
If no differences in daily returns exist, the regression coefficients have an expected value of zero. The regression equation is estimated over three nonoverlapping time periods: (1) January 1978 through January 1984 (during which LRA rules were in effect), (2) February 1984 through December 1987 (under which CRA rules were in effect) and, (3) the CRA period was split into two parts in order to identify any ‘learning* by managers over time for estimating target reserves. The regression results are presented in tables 1 and 2. The results shown in table 1 for the LRA period appear to be consistent with those of Barrett et al. (1988). Fed funds interest rates are significantly higher on Thursday and significantly lower on the following Wednesday, relative to the rest of the week. Tuesday’s coefficient is also lower but not significantly different from zero, as was found by Barrett et al.
‘Similar results are obtained suggested by Allen and Saunders
when the end (1991).
of quarter
dummy
variables
are added
as is
D.J. Lasser, Effect of contemporaneous reserve accounting
Daily
return
patterns
in the Fed funds contemporaneous
Table 1 market under lagged reserve reserve accounting (CRA):’
1051
accounting
(LRA)
and
Dif,,=b,Mon+b,Tues+b,Wed+b,Thur+b,Fri (t-statistic Sample
for day of week coetlicients
Entire sampler’ (1978-87) LRA (1978-Jan.
1984)
CRA week 2 (Feb. 1984-87)
Monday
Tuesday
0.588 (0.053)’
-0.141 (- 1.456)*.’
0.079 (0.795)*
-0.118 (- 1.223)‘.’
0.792 (6.156)‘*
(- 1.268)**’ (0.501)’
-0.016 (-0.305)’
CRA week 1 (Feb. 1984-87)
in parentheses).
Friday
Thursday
0.067
-0.163
-0.179
(- 1.387)‘.’
(- 1.500)’
0.112 (2.188)”
0.054 (1.062)’
- 0.204 (-3.918)3*
0.119 (2.134)‘*
( -0.218)‘~2~’
- 0.077
0.052 (0.209)‘.2
Wednesday
2,014
-0.495 (-3.892)‘.
1,492
0.091 (1.786)’
-0.111
Cases
- 0.346 (-3.603)”
-0.092
521 501
(- 1.787)=
‘Within each sample period, a differing superscript (1, 2, or 3) represents a significant difference between days at the 95:/, level; group means with the same superscript are not signilicantly different from each other. %cludes only second week from CRA period. *Significant at 95% level.
Table 2 Daily return
patterns
in the Fed funds market
D&= b, Mon+ b,Tues+ (r-statistic Sample
Thursday
for subsamples
b, Wed+ b,Thur+
for day of week coefficients Friday
Monday 0.09 I (1.440)
1984-85 week 2
- 0.023
- 0.090
( - 0.365)
(- 1.425)
1984-85 week 1
0.188 (3.797)’
- 0.205 -4.233)‘*
0.117 (2.238)‘.**
-0.063’ -0.773)
0.134’ (1.639)
- 0.202
0.121 (1.250)’
1986-87 week 2
( - 0.095)
-0.008’
198687 week
(- 1.729)’
-0.155
I
( - 2.230)’
from CRA period:’
b, Fri
in parentheses). Tuesday 0.015 (0.239) - 0.023
( -0.468)2.3 0.094’ (1.159) -0.001
( - 0.002)’
Wednesday 0.132 (2.125)’ -0.091
Cases 266 256
(- 1.870)’ 0.047’ (0.578)
255
-0.093 (1.049)
245
(1, 2, or 3) represents a significant ‘Within each sample perioc i, a differing superscript diNerence between days at the 95% level; group means with the same superscript are not significantly diNerent from each other. ‘Signilicant at 95% level.
The results are quite different with regard to the CRA period. First of all, there does not appear to be any patterned increased demand for Fed funds early in the accounting period. While the first Monday of the period has a significantly higher Fed funds rate, the preceding Friday has a counterbalancing significantly lower rate. The lack of an identifiable early CRA period pattern may be due to the excess demand for Fed funds being spread
1052
D.J. Laser.
Effect of contemporaneous reserce accounting
out over more days as a result of the increase in the accounting period to two weeks under the CRA. Therefore, to test for the existence of an overall demand increase early in the accounting period under CRA, we compared multiday Fed fund rate levels in week one under CRA to the overall LRA rate levels. If increased excess demand for Fed funds exists, rates should be relatively higher in the first week under CRA. The following multiday perentage yield spread differentials for week 1 under CRA was compared to the levels under LRA: Yield spread differential = (Fed funds-90-day
T-bill)/90-day T-bill.
(2)
Yield spreads are employed instead of simply comparing relative rates in order to adjust for any yield curve shifts that may have occurred between the LRA and CRA periods. The yield spread differential between Fed funds and T-bill rates is found to be significantly higher at the 95% level for week 1 under CRA as compared to the LRA period. Specifically, the Fed funds rate was estimated to be 8.69% higher than the T-bill rate for week 1 under CRA, while the Fed funds rate was only 7.32% higher under LRA. This result is consistent with the notion that, although early-period excess demand for Fed funds continues to exist, it is simply spread out over more days. The results from table 1 also show that the lower return pattern previously found late in the accounting period is not apparent after the accounting rule change. Monday is the only day of the second week that is significantly different from zero and, like the estimation from week 1, has a positive coefficient. It is interesting to note that the Monday funds rate for both week 1 and week 2 are higher than other days under CRA but not under LRA. This result suggests that, under CRA, liquidity managers appear to have underestimated target reserve changes over the weekend, thus inducing the relatively higher Monday demand. Table 2 displays the results from splitting the CRA sample into two subperiods. The results are consistent with the notion that there was indeed a ‘learning’ period for liquidity managers to become more adept in forecasting target reserve amounts. The high demand existing early in the accounting period during the LRA sample is still observable to some extent in the 198485 subsample. Both the first Thursday and following Monday of the twoweek accounting period display a significantly higher daily interest rate pattern. However, a significantly higher daily interest rate is also found on the final Wednesday of the period for this sample. The latter finding implies that managers may have initially underestimated their bank’s liquidity needs under the new system. In contrast, for the 1986-87 subperiod, only the first Friday of the accounting period has a significantly lower dialy Fed funds rate. No other day displays any significantly different interest rate pattern. This result implies that liquidity managers appear to have become more
D.J. Lasser. Effect of contemporaneous reserve accounting
1053
accurate in their target reserve estimates over time. Therefore, having a two-week instead of one-week accounting period seems to have helped smooth out the interest rate pattern seen under LRA.
3.6. Intraday variance patterns
Daily high and low Fed funds and three-month T-bill interest rates (obtained from the Chicago Mercantile Exchange) were used to calculate intraday Fed fund and T-bill interest rate variances. This data set allows the use of the Parkinson (1980) extreme value method for estimating an intraday Fed fund and T-bill variances. This method has been shown to be quite efftcient in estimating variances for very short periods of time. Specifically, following Parkinson, let the variance estimate be defined as: oij=(0.361/N,)C
D,,= the Ni = the Hij= the Lij= the
ln(Hij/Lij)2,
(3)
jth observation intraday Fed funds variance for day i, number of observations for day i, highest reported yield for the jth observation for day i, lowest reported yield for the jth observation for day i,
Intraday variances are calculated over the same periods as are the daily interest rate estimates. That is, the samples are first divided into LRA and CRA periods, followed by a division of the CRA sample into subsamples of two years each. The null hypotheses tested between any two given periods for each day is Di, =Di2, where the second subscript represents the estimation period. The test statistic for the two-sided alternative hypothesis Di, #Di, is
and DizlDi, ’ F z2.nl-1,nl-1r
if42>Di1.
Finally, the intraday three-month T-bill variance is estimated to establish a benchmark for the short-term interest rate environment during each sample period. Daily intraday variance pattern comparisons between the LRX and CRA rule change periods are shown in table 3. The results show that there was a significant increase in intraday Fed funds variance during the second week of the CRA period. The second Friday, Monday, Tuesday, and Wednesday variances are significantly higher in the CRA period. The increased variance
1054
D.J. Laser.
Effect of contemporaneous reserve accounting
Table 3 Daily intraday variance patterns in the Federal funds market under the LRA and CRA systems (F-statistic comparing LRA and CRA samples in parentheses). Sample
Thursday
Friday
Monday
Tuesday
Wednesday
T-bills’
Cases
Entire sampleb (1978-98)
0.8592
1.5722
1.4776
2.0992
13.2003
0.0064
2,014
LRA (197%Jan. 1984)
1.0967
1.3956
1.3115
1.1964
12.7108
0.0115
1,492
0.1563 (7.02)*
2.0862 (1.50)8
1.9230 (1.47)*
4.6879 (3.92)8
14.6277 (1.15)
0.0022 (1.74)*
521
0.3007
0.4325
CRA week 2 (Feb. 1984-87) CRA week 1
(Feb. 1984-87)
0.1383
(5.23)*
(1.84)* (2.01)*
0.3242
0.1072
(1.03)
(10.52)’
501
‘Represents a daily variance over the designated sample period. bContains only week 2 from CRA sample. *Si Sniftcant at 98% level.
appears to be particularly pronounced on the second Tuesday, where the intraday variance increased four-fold. This result is consistent with the fact that the second Tuesday of the accounting period is the first day in which the absolute target reserve requirements are known by the liquidity manager. Furthermore, the higher second week CRA period intraday variances do not appear to be a function of the interest rate environment, since the intraday 90-day T-bill variance was significantly lower in the CRA period. Finally, intraday variances for the first week and Thursday of the second week are all significantly lower for the CRA period. This decrease may have been due to either the lengthening of the reserve maintenance period or the change in the interest rate environment. The results support those found by Spindt and Hoffmeister (1988), who argue that liquidity managers are more aggressive near the end of the accounting period. Also, the results indicate that the change to the CRA system appears to have decreased the liquidity manager’s ability to estimate deposit amounts over the last several days of the accounting period. If a ‘learning’ period existed when the new accounting rules went into effect, as was indicated from the daily return pattern results, one would expect to find a decrease in the second week intraday variances for the later (1986-87) two-year CRA period subsample, relative to the earlier (1984-85) CRA period subsample. The results of these comparisons are shown in table 4. Intraday variances are significantly smaller during the 198687 period for every day during the two week accounting period, except on Wednesday of the second week and Tuesday of the first week. Intraday 90-day T-bill variance was also slightly lower during the 1986-87 period but not significantly different relative to the 1984-85 period. This indicates that a relatively stable interest rate environment existed over the entire CRA period.
D.J. Lamer, Effect of contemporaneous reserce accounting
1055
Table 4 Daily
intraday
variance
Sample
patterns in Federal funds market for subsamples (F-statistic comparing subsamples in parentheses).
Thursday
T-bills
period
Monday
Tuesday
Wednesday
198485
week 2
0.1975
3.2750
3.1638
7.1954
13.1036
0.0023
266
198687
week 2
0.1119 (1.76)’
0.8505 (3.85)*
0.6339 (4.99)*
2.1321 (3.37);
16.2103 (1.24)
0.002 1 (0.75)
256
1984-85
week
1
0.1884
0.5198
0.6765
0.1383
0.1408
0.0022
255
1986-87
week 1
0.0913 (2.06)’
0.0816 (6.37)*
0.1942 (3.48)*
0.5032 (3.64);
0.0750 (1.877)’
0.0019 (0.85)
245
*Significant
Friday
of CRA
Cases
at 98% level.
Table 5 OLS regression
results for the CRA sample of the impact of 90-day Fed funds variability:
T-bill variability
on intraday
Dij=z,+/3,(DBILL,,)+q (r-statistics Sample
Thursday
LRA (1984-87)
1.630 (0.309)
CRA (1984-85)
- 7.352 (-0.635) 6.39 I (2.100)*
CRA (198687) *Significant
for day of week coefficients Friday
All days
N
15.050 (0.182)
- 10.548 (-0.221)
- 135.946 ( - 0.296)
1.230 (0.268)
992
- 174.233 (0.038)
- 17.303 (-0.201)
- 180.173 (-0.417)
0.809 (0.175)
493
14.339 (0.981)
- 2.237 (-0.097)
Monday
-3.701 (-0.083) 1.694 (0.016) -4.671 (-0.210)
in parentheses).
Tuesday
Wednesday
67.397 (0.061)
-7.435 (-0.129)
499
at the 95% level.
However, in order to test whether or not market conditions are a factor in the observed decrease in intraday Fed funds volatility, the following regression equation is estimated for the entire CRA period sample for each day of the week as well as for all days combined. Specifically, we estimated Dij
=
pi
+
Bi(DBfLLij)
+
Ei,
where DBILLij is defined as the Parkinson measure for jth observation T-bill intraday interest rate variability for day i. If the general interest rate environment has an impact on the intraday Fed funds variance, then the coefftcient on DBILL will be significantly different from zero. The results, given in table 5, show that 90-day T-bill variability does not appear to influence intraday movements in Fed funds rates. Thursday is the only individual day coefftcient that is significantly different from zero. This result supports the finding that the reduction in Fed funds intraday variance found for the 1986-87 subsample is primarily a function of an increase in manager
1056
D.J. Laser.
Effect of contemporaneous
reserve accounfing
familiarity with the new accounting rules. The result is also consistent with the notion that intraday Fed funds market volatility is primarily a function of day-to-day bank liquidity management and not general economic conditions, especially during the later part of the maintenance period sample. 4. Summary and conclusions This paper examines the effects of a change in reserve requirement accounting regimes on daily interest rate and intraday variance patterns in the Federal funds market. The results suggest that the uncertainty of specific target amounts imposed over four years of the CRA maintenance period caused a temporary increase in intraday volatility in the Fed funds market. There appears to have been an increase in intraday volatility during the second week of the CRA period, especially for the second Tuesday of the accounting period. Subsequent to what might be called a ‘learning’ period, however, intraday volatilities were significantly lower. The results of daily interest pattern estimations are similar. While differences existed during the first two years under the CRA system, no daily return patterns were detected during the second two years of the CRA period. Therefore, while not costless, the doubling of the accounting period from one week to two weeks appears to have aided the liquidity management process. References Allen, F. and A. Saunders, 1992, Bank window dressing: Theory and evidence, Journal of Banking and Finance 16, 585-623. Barrett, W.B., M.B. Slovin and M.E. Sushka, 1988, Reserve regulation and resource as a source of risk premia in the Federal funds market, Journal of Banking and Finance 12, 574-584. Dyl, E.A. and J.R. HolTmeister. 1985, Efftciency and volatility in the Federal funds market, Journal of Bank Research 15, 234239. Gibbons, M.R. and P.J. Hess, 1981, Day of the week effects and asset returns, Journal of Business 54, 579-596. Parkinson, M., 1980, The extreme value method for estimating the variance of the rate of return, Journal of Business 53, 61-73. Sinkey, J.F., 1988, Commercial bank financial management (Macmillan, London). Saunders, A. and T. Urich, 1988, The effects of shifts in monetary policy and reserve accounting regimes on bank reserve management behavior in the Federal funds market, Journal of Banking and Finance 1 I, 523-536. 1988, The micromechanics of the Federal funds market: Spindt, P.A. and J.R. Hoffmeister, Implications for day-of-the-week effects in funds rate variability, Journal of Financial and Quantitative Analysis 23. 401-416.
of Banking
and
Finance
16 (1992)
1047-1056.
North-Holland
The effect of contemporaneous reserve accounting on the market for Federal funds Dennis J. Lasser* SUN Y-Binghamton,
Binghamton, NY
13902-6000,
Received April 1991, final version received
February
USA
1992
This paper evaluates the elfect of the transition from lagged to contemporaneous reserve accounting for the determination of bank reserve requirements through its impact on the market for Federal funds. The results indicate that increased target reserve uncertainty resulting from the implementation of the contemporaneous reserve accounting system (CRA) caused an initial increase in intraday Federal funds rate variance and daily interest rate differences. However, subsequent to a ‘learning’ period, intraday variance appears to be less pronounced and daily differentials appear to be narrower than under the previously used lagged reserve accounting system (LRA). These results are attributed to the lengthening of the accounting period from one to two weeks. Therefore, while not costless, the new system does not appear to have seriously disrupted the Federal funds market.
1. Introduction This paper examines the impact of the imposition of the 1984 rule change that determines bank reserve requirements. On February 1, 1984 the accounting treatment used for specifying reserve requirements changed from a lagged reserve accounting system (LRA) to a contemporaneous reserve accounting system (CRA). Under the LRA system there was a two-week lag between the average daily deposits held by the bank and the average daily reserve requirements needed to support those deposits, while under the CRA system the two periods overlap. The stated purpose of the change was to allow the Fed to conduct a more effective monetary policy. However, in order to determine the effectiveness of any regulatory action, one must consider the costs as well as the benefits of that action. In this case, such control notwithstanding, the change may have imposed a cost of increased Correspondence to: Dennis J. Lasser, Assistant Professor of Finance, School of Management, SUNY-Binghamton, Binghamton, NY 13902-6OOG. USA. *I would like to thank Doug Emery and two anonymous referees for their extremely helpful comments. Of course all remaining errors remain my own.
0378-4266/92/SO5.00
C 1992-Elsevier
Science Publishers
B.V. All rights
reserved
1048
D.J. Laser,
Ejrect of conremporaneous
reserve accounting
risk for bank liquidity managers given that reserve amounts are not fully disclosed until just prior to the end of the accounting period. The specifications of the alternative accounting standards are as follows. From September 1968, through January 1984, reserve requirements were calculated under the LRA system. Under LRA, bank reserve requirements were calculated on an average weekly basis ending each Wednesday. The requirements were a function of the average daily deposits held from Thursday through the following Wednesday, over a period that was two weeks prior to the reserve maintenance period. This created a two week lag between the time the deposits were held and the time the reserve requirement had to be met. Since February I, 1984 reserve requirements have been calculated under the CRA system. Under the current system, bank reserve requirements are calculated on an average biweekly basis ending every other Wednesday. These reserves are a function of the average daily balance of deposits held for a two-week period ending two days prior to the end of the reserve maintenance period. Therefore, the bank liquidity manager has only two days in which the amount of reserves needed are known with certainty. We examine the effect on the bank manager of the change from LRA to CRA by comparing daily interest rate patterns and intraday variances in the Federal funds market before and after February 1, 1984. Since the primary source of a bank’s reserve maintenance is the Federal funds market, any impact of the accounting rule change on bank liquidity management should be detectable by observing daily interest rate and intraday variance pattern changes in the Fed funds maket in the CRA period. The results indicate a cost to the bank manager in that there was an initial increase in the intraday volatility in the CRA period, particularly on the second Tuesday of the maintenance period. Similarly, following the change to CRA, there was an initial exaggeration of the previously existing daily interest rate pattern that existed during the LRA period. Over time, however, that exaggeration not only disappeared but seems to have become less pronounced than was prior to the rule change. The eventual smoothing would seem to result from the increased length of time of the maintenance period (from one to two weeks). Section 2 provides a brief review of the literature and describes the hypotheses to be tested. Section 3 outlines the specific testing methodologies employed and discusses the results, while section 4 provides a brief summary and conclusions. 2. Return and volatility patterns in Fed funds markets Several studies have examined daily interest rate patterns and interest rate variances in the Federal funds market. With regard rates, Barrett et al. (1988) argue that bank reserve managers tend reserves early in the reserve week in order to be assured of easily
intraday to daily to build meeting
D.J.
Lasser.
Effect
of contemporaneous
reserce
accounting
1049
their reserve requirements and thus avoiding any penalties. Therefore, they contend that Fed funds rates should be highest on Thursday and lowest on Wednesday. They find support for this argument in that the first differences of daily rates during 1970-1982 imply a significantly higher Fed funds rate on Thursday and lower rates on Tuesday and Wednesday. However, Dyl and Hoffmeister (1985) find that actual rates followed such a pattern only during 1970, when tested yearly over a period from 197&198 1. Empirical findings concerning the variance of intraday Fed funds are more consistent. Dyl and Hoffmeister (1985), using pre-1984 data, and Saunders and Urich (1988) and Spindt and Hoffmeister (1988), using post-1983 data, find a common pattern in intraday Fed funds variance. Intraday variance is lowest on Thursday and highest on Wednesday. These results appear to be a function of the regulatory constraints and, more specifically, the accounting system imposed on bank managers. Although, the effect of the accounting rule change on intraday variance has not yet been examined, Dyl and Hoffmeister hypothesize that the imposition of CRA should cause an initial increased variance, particularly on the second Tuesday and Wednesday of the accounting period, at least until managers become familiar with the new system. The change from LRA to CRA has two primary components that have potential impacts on bank reserve management. First, after the rule change, specific target reserve amounts became unknown for all but the final two days of the maintenance period. These targets were always known with certainty under the LRA system. Therefore, if bank managers build up reserves early in the accounting period as protection against uncertainty in meeting reserves as described by Barrett et al. (1988), one would expect the increased uncertainty to cause an increase in the variation of daily interest rates after February 1, 1984. Similarly, since information about the reserve target is revealed on a daily basis, the managers’ assessment of required reserves changes daily. Therefore, one would expect the reserve target uncertainty to increase intraday Fed funds volatility, especially at the end of the accounting period. The second component of the rule change consists of increasing the accounting period from one to two weeks. The effect of this component on daily Fed funds interest rates is unclear. The longer maintenance period should induce the liquidity manager to hold more excess reserves, thereby increasing early period demand. However, the impact may be less detectable since the excess demand is spread over a greater number of days, allowing the manager more latitude in meeting unexpected reserve needs. The potential impact of the longer accounting period is less confounded with respect to intraday volatility. The longer time frame should not decrease, and may well magnify, the impact of increased intraday volatility caused by the daily uncertainty of the reserve target. Furthermore, similar to the LRA
1050
D.J. Lasser, Effect
ofcontemporaneous resert‘e
accounting
system, one would expect to find lower intraday volatility early in the maintenance period. Under CRA this should be seen in lower first week intraday volatility relative to the second week of the period. Finally, we contend that a ‘learning’ period may have existed for bank liquidity managers to familiarize themselves with the new accounting system. Prior to the enactment of CRA, bank managers were not as concerned with estimating target reserves since, for reserve requirement purposes, they were always known with certainty. After CRA implementation, however, this function became an essential part of the reserve managers success in meeting reserve requirements. Therefore, one would expect managers to become more adept at estimating target reserves later in the CRA period. If such a ‘learning’ period exists, it should be reflected by higher variance immediately following implementation with a subsequent decline to lower variance later in the CRA period. 3. Test methodologies
and empirical findings
3.a. Daily return patterns
Daily Fed funds interest rates were obtained from January 1978 through December 1987 from the Federal Reserve Bank in New York. Daily interest patterns are estimated using the methodology of Gibbons and Hess (1981), as modified by Barrett et al. (1988). Specifically, the first difference of the daily interest rate is regressed on day of the week dummy variables, given as1 Diffrr= b, Mon + b,Tues + b3 Wed + b,Thur + b5 Fri + e.
(1)
If no differences in daily returns exist, the regression coefficients have an expected value of zero. The regression equation is estimated over three nonoverlapping time periods: (1) January 1978 through January 1984 (during which LRA rules were in effect), (2) February 1984 through December 1987 (under which CRA rules were in effect) and, (3) the CRA period was split into two parts in order to identify any ‘learning* by managers over time for estimating target reserves. The regression results are presented in tables 1 and 2. The results shown in table 1 for the LRA period appear to be consistent with those of Barrett et al. (1988). Fed funds interest rates are significantly higher on Thursday and significantly lower on the following Wednesday, relative to the rest of the week. Tuesday’s coefficient is also lower but not significantly different from zero, as was found by Barrett et al.
‘Similar results are obtained suggested by Allen and Saunders
when the end (1991).
of quarter
dummy
variables
are added
as is
D.J. Lasser, Effect of contemporaneous reserve accounting
Daily
return
patterns
in the Fed funds contemporaneous
Table 1 market under lagged reserve reserve accounting (CRA):’
1051
accounting
(LRA)
and
Dif,,=b,Mon+b,Tues+b,Wed+b,Thur+b,Fri (t-statistic Sample
for day of week coetlicients
Entire sampler’ (1978-87) LRA (1978-Jan.
1984)
CRA week 2 (Feb. 1984-87)
Monday
Tuesday
0.588 (0.053)’
-0.141 (- 1.456)*.’
0.079 (0.795)*
-0.118 (- 1.223)‘.’
0.792 (6.156)‘*
(- 1.268)**’ (0.501)’
-0.016 (-0.305)’
CRA week 1 (Feb. 1984-87)
in parentheses).
Friday
Thursday
0.067
-0.163
-0.179
(- 1.387)‘.’
(- 1.500)’
0.112 (2.188)”
0.054 (1.062)’
- 0.204 (-3.918)3*
0.119 (2.134)‘*
( -0.218)‘~2~’
- 0.077
0.052 (0.209)‘.2
Wednesday
2,014
-0.495 (-3.892)‘.
1,492
0.091 (1.786)’
-0.111
Cases
- 0.346 (-3.603)”
-0.092
521 501
(- 1.787)=
‘Within each sample period, a differing superscript (1, 2, or 3) represents a significant difference between days at the 95:/, level; group means with the same superscript are not signilicantly different from each other. %cludes only second week from CRA period. *Significant at 95% level.
Table 2 Daily return
patterns
in the Fed funds market
D&= b, Mon+ b,Tues+ (r-statistic Sample
Thursday
for subsamples
b, Wed+ b,Thur+
for day of week coefficients Friday
Monday 0.09 I (1.440)
1984-85 week 2
- 0.023
- 0.090
( - 0.365)
(- 1.425)
1984-85 week 1
0.188 (3.797)’
- 0.205 -4.233)‘*
0.117 (2.238)‘.**
-0.063’ -0.773)
0.134’ (1.639)
- 0.202
0.121 (1.250)’
1986-87 week 2
( - 0.095)
-0.008’
198687 week
(- 1.729)’
-0.155
I
( - 2.230)’
from CRA period:’
b, Fri
in parentheses). Tuesday 0.015 (0.239) - 0.023
( -0.468)2.3 0.094’ (1.159) -0.001
( - 0.002)’
Wednesday 0.132 (2.125)’ -0.091
Cases 266 256
(- 1.870)’ 0.047’ (0.578)
255
-0.093 (1.049)
245
(1, 2, or 3) represents a significant ‘Within each sample perioc i, a differing superscript diNerence between days at the 95% level; group means with the same superscript are not significantly diNerent from each other. ‘Signilicant at 95% level.
The results are quite different with regard to the CRA period. First of all, there does not appear to be any patterned increased demand for Fed funds early in the accounting period. While the first Monday of the period has a significantly higher Fed funds rate, the preceding Friday has a counterbalancing significantly lower rate. The lack of an identifiable early CRA period pattern may be due to the excess demand for Fed funds being spread
1052
D.J. Laser.
Effect of contemporaneous reserce accounting
out over more days as a result of the increase in the accounting period to two weeks under the CRA. Therefore, to test for the existence of an overall demand increase early in the accounting period under CRA, we compared multiday Fed fund rate levels in week one under CRA to the overall LRA rate levels. If increased excess demand for Fed funds exists, rates should be relatively higher in the first week under CRA. The following multiday perentage yield spread differentials for week 1 under CRA was compared to the levels under LRA: Yield spread differential = (Fed funds-90-day
T-bill)/90-day T-bill.
(2)
Yield spreads are employed instead of simply comparing relative rates in order to adjust for any yield curve shifts that may have occurred between the LRA and CRA periods. The yield spread differential between Fed funds and T-bill rates is found to be significantly higher at the 95% level for week 1 under CRA as compared to the LRA period. Specifically, the Fed funds rate was estimated to be 8.69% higher than the T-bill rate for week 1 under CRA, while the Fed funds rate was only 7.32% higher under LRA. This result is consistent with the notion that, although early-period excess demand for Fed funds continues to exist, it is simply spread out over more days. The results from table 1 also show that the lower return pattern previously found late in the accounting period is not apparent after the accounting rule change. Monday is the only day of the second week that is significantly different from zero and, like the estimation from week 1, has a positive coefficient. It is interesting to note that the Monday funds rate for both week 1 and week 2 are higher than other days under CRA but not under LRA. This result suggests that, under CRA, liquidity managers appear to have underestimated target reserve changes over the weekend, thus inducing the relatively higher Monday demand. Table 2 displays the results from splitting the CRA sample into two subperiods. The results are consistent with the notion that there was indeed a ‘learning’ period for liquidity managers to become more adept in forecasting target reserve amounts. The high demand existing early in the accounting period during the LRA sample is still observable to some extent in the 198485 subsample. Both the first Thursday and following Monday of the twoweek accounting period display a significantly higher daily interest rate pattern. However, a significantly higher daily interest rate is also found on the final Wednesday of the period for this sample. The latter finding implies that managers may have initially underestimated their bank’s liquidity needs under the new system. In contrast, for the 1986-87 subperiod, only the first Friday of the accounting period has a significantly lower dialy Fed funds rate. No other day displays any significantly different interest rate pattern. This result implies that liquidity managers appear to have become more
D.J. Lasser. Effect of contemporaneous reserve accounting
1053
accurate in their target reserve estimates over time. Therefore, having a two-week instead of one-week accounting period seems to have helped smooth out the interest rate pattern seen under LRA.
3.6. Intraday variance patterns
Daily high and low Fed funds and three-month T-bill interest rates (obtained from the Chicago Mercantile Exchange) were used to calculate intraday Fed fund and T-bill interest rate variances. This data set allows the use of the Parkinson (1980) extreme value method for estimating an intraday Fed fund and T-bill variances. This method has been shown to be quite efftcient in estimating variances for very short periods of time. Specifically, following Parkinson, let the variance estimate be defined as: oij=(0.361/N,)C
D,,= the Ni = the Hij= the Lij= the
ln(Hij/Lij)2,
(3)
jth observation intraday Fed funds variance for day i, number of observations for day i, highest reported yield for the jth observation for day i, lowest reported yield for the jth observation for day i,
Intraday variances are calculated over the same periods as are the daily interest rate estimates. That is, the samples are first divided into LRA and CRA periods, followed by a division of the CRA sample into subsamples of two years each. The null hypotheses tested between any two given periods for each day is Di, =Di2, where the second subscript represents the estimation period. The test statistic for the two-sided alternative hypothesis Di, #Di, is
and DizlDi, ’ F z2.nl-1,nl-1r
if42>Di1.
Finally, the intraday three-month T-bill variance is estimated to establish a benchmark for the short-term interest rate environment during each sample period. Daily intraday variance pattern comparisons between the LRX and CRA rule change periods are shown in table 3. The results show that there was a significant increase in intraday Fed funds variance during the second week of the CRA period. The second Friday, Monday, Tuesday, and Wednesday variances are significantly higher in the CRA period. The increased variance
1054
D.J. Laser.
Effect of contemporaneous reserve accounting
Table 3 Daily intraday variance patterns in the Federal funds market under the LRA and CRA systems (F-statistic comparing LRA and CRA samples in parentheses). Sample
Thursday
Friday
Monday
Tuesday
Wednesday
T-bills’
Cases
Entire sampleb (1978-98)
0.8592
1.5722
1.4776
2.0992
13.2003
0.0064
2,014
LRA (197%Jan. 1984)
1.0967
1.3956
1.3115
1.1964
12.7108
0.0115
1,492
0.1563 (7.02)*
2.0862 (1.50)8
1.9230 (1.47)*
4.6879 (3.92)8
14.6277 (1.15)
0.0022 (1.74)*
521
0.3007
0.4325
CRA week 2 (Feb. 1984-87) CRA week 1
(Feb. 1984-87)
0.1383
(5.23)*
(1.84)* (2.01)*
0.3242
0.1072
(1.03)
(10.52)’
501
‘Represents a daily variance over the designated sample period. bContains only week 2 from CRA sample. *Si Sniftcant at 98% level.
appears to be particularly pronounced on the second Tuesday, where the intraday variance increased four-fold. This result is consistent with the fact that the second Tuesday of the accounting period is the first day in which the absolute target reserve requirements are known by the liquidity manager. Furthermore, the higher second week CRA period intraday variances do not appear to be a function of the interest rate environment, since the intraday 90-day T-bill variance was significantly lower in the CRA period. Finally, intraday variances for the first week and Thursday of the second week are all significantly lower for the CRA period. This decrease may have been due to either the lengthening of the reserve maintenance period or the change in the interest rate environment. The results support those found by Spindt and Hoffmeister (1988), who argue that liquidity managers are more aggressive near the end of the accounting period. Also, the results indicate that the change to the CRA system appears to have decreased the liquidity manager’s ability to estimate deposit amounts over the last several days of the accounting period. If a ‘learning’ period existed when the new accounting rules went into effect, as was indicated from the daily return pattern results, one would expect to find a decrease in the second week intraday variances for the later (1986-87) two-year CRA period subsample, relative to the earlier (1984-85) CRA period subsample. The results of these comparisons are shown in table 4. Intraday variances are significantly smaller during the 198687 period for every day during the two week accounting period, except on Wednesday of the second week and Tuesday of the first week. Intraday 90-day T-bill variance was also slightly lower during the 1986-87 period but not significantly different relative to the 1984-85 period. This indicates that a relatively stable interest rate environment existed over the entire CRA period.
D.J. Lamer, Effect of contemporaneous reserce accounting
1055
Table 4 Daily
intraday
variance
Sample
patterns in Federal funds market for subsamples (F-statistic comparing subsamples in parentheses).
Thursday
T-bills
period
Monday
Tuesday
Wednesday
198485
week 2
0.1975
3.2750
3.1638
7.1954
13.1036
0.0023
266
198687
week 2
0.1119 (1.76)’
0.8505 (3.85)*
0.6339 (4.99)*
2.1321 (3.37);
16.2103 (1.24)
0.002 1 (0.75)
256
1984-85
week
1
0.1884
0.5198
0.6765
0.1383
0.1408
0.0022
255
1986-87
week 1
0.0913 (2.06)’
0.0816 (6.37)*
0.1942 (3.48)*
0.5032 (3.64);
0.0750 (1.877)’
0.0019 (0.85)
245
*Significant
Friday
of CRA
Cases
at 98% level.
Table 5 OLS regression
results for the CRA sample of the impact of 90-day Fed funds variability:
T-bill variability
on intraday
Dij=z,+/3,(DBILL,,)+q (r-statistics Sample
Thursday
LRA (1984-87)
1.630 (0.309)
CRA (1984-85)
- 7.352 (-0.635) 6.39 I (2.100)*
CRA (198687) *Significant
for day of week coefficients Friday
All days
N
15.050 (0.182)
- 10.548 (-0.221)
- 135.946 ( - 0.296)
1.230 (0.268)
992
- 174.233 (0.038)
- 17.303 (-0.201)
- 180.173 (-0.417)
0.809 (0.175)
493
14.339 (0.981)
- 2.237 (-0.097)
Monday
-3.701 (-0.083) 1.694 (0.016) -4.671 (-0.210)
in parentheses).
Tuesday
Wednesday
67.397 (0.061)
-7.435 (-0.129)
499
at the 95% level.
However, in order to test whether or not market conditions are a factor in the observed decrease in intraday Fed funds volatility, the following regression equation is estimated for the entire CRA period sample for each day of the week as well as for all days combined. Specifically, we estimated Dij
=
pi
+
Bi(DBfLLij)
+
Ei,
where DBILLij is defined as the Parkinson measure for jth observation T-bill intraday interest rate variability for day i. If the general interest rate environment has an impact on the intraday Fed funds variance, then the coefftcient on DBILL will be significantly different from zero. The results, given in table 5, show that 90-day T-bill variability does not appear to influence intraday movements in Fed funds rates. Thursday is the only individual day coefftcient that is significantly different from zero. This result supports the finding that the reduction in Fed funds intraday variance found for the 1986-87 subsample is primarily a function of an increase in manager
1056
D.J. Laser.
Effect of contemporaneous
reserve accounfing
familiarity with the new accounting rules. The result is also consistent with the notion that intraday Fed funds market volatility is primarily a function of day-to-day bank liquidity management and not general economic conditions, especially during the later part of the maintenance period sample. 4. Summary and conclusions This paper examines the effects of a change in reserve requirement accounting regimes on daily interest rate and intraday variance patterns in the Federal funds market. The results suggest that the uncertainty of specific target amounts imposed over four years of the CRA maintenance period caused a temporary increase in intraday volatility in the Fed funds market. There appears to have been an increase in intraday volatility during the second week of the CRA period, especially for the second Tuesday of the accounting period. Subsequent to what might be called a ‘learning’ period, however, intraday volatilities were significantly lower. The results of daily interest pattern estimations are similar. While differences existed during the first two years under the CRA system, no daily return patterns were detected during the second two years of the CRA period. Therefore, while not costless, the doubling of the accounting period from one week to two weeks appears to have aided the liquidity management process. References Allen, F. and A. Saunders, 1992, Bank window dressing: Theory and evidence, Journal of Banking and Finance 16, 585-623. Barrett, W.B., M.B. Slovin and M.E. Sushka, 1988, Reserve regulation and resource as a source of risk premia in the Federal funds market, Journal of Banking and Finance 12, 574-584. Dyl, E.A. and J.R. HolTmeister. 1985, Efftciency and volatility in the Federal funds market, Journal of Bank Research 15, 234239. Gibbons, M.R. and P.J. Hess, 1981, Day of the week effects and asset returns, Journal of Business 54, 579-596. Parkinson, M., 1980, The extreme value method for estimating the variance of the rate of return, Journal of Business 53, 61-73. Sinkey, J.F., 1988, Commercial bank financial management (Macmillan, London). Saunders, A. and T. Urich, 1988, The effects of shifts in monetary policy and reserve accounting regimes on bank reserve management behavior in the Federal funds market, Journal of Banking and Finance 1 I, 523-536. 1988, The micromechanics of the Federal funds market: Spindt, P.A. and J.R. Hoffmeister, Implications for day-of-the-week effects in funds rate variability, Journal of Financial and Quantitative Analysis 23. 401-416.