The effect of substitute assets on yields in financial markets.
Stocks and bonds have long duration, which leads to uncertainty about future prices should investors wish to liquidate, while the duration of money-market instruments is short and price variation is relatively small. Hence, the link between volume and liquidity may be very different for money-market securities compared to equities. In this paper, we empirically test the link between market size/volume and liquidity for money-market instruments. We determine if a decrease in the size of the market for Bankers Acceptances (BAs) from 1984 to 2000 led to an increase in the liquidity premium for BAs, which in turn changed the relative relation between BA rates and the rates on other money-market instruments.
The ideal experimental setting to test for a direct link between low market size/volume and a high liquidity premium is one in which we can compare the returns from pairs of comparable securities with different volume. This experimental setting is difficult, if not impossible, to create in equities because of the difficulty in creating pairs of comparable securities. Money markets provide a better environment for testing the volume-liquidity conditions, because money-market securities are comparable, sharing the common characteristics of short-term maturity, low default risk, and high marketability. These common characteristics, coupled with an exogenous decline in BAs, provide an ideal experimental setting to investigate the interaction of volume and liquidity in short-term securities.
We compare the rates (yields) on bankers' acceptances to the rates on certificates of deposits (CDs), financial commercial paper (CP), and eurodollar deposits (EDs). Although all four of the money-market instruments constitute short-term borrowing, we note that the production of BAs differs from the production of CP, EDs, and CDs. Bankers' acceptances are a transaction-specific debt that is incurred when firms import and export goods. Eurodollars and Negotiable CDs constitute short-term borrowing by banks to acquire funds for general use. Financial CP is borrowing by a bank holding company for general use. However, the four instruments are homogeneous assets for investors because each has short-term maturity, low default risk, and high marketability.
In a traditional framework, a decline in BAs would lead to an inward shift in the supply curve, and with a static demand curve the result is an increase in price and lower yield. However, if the demand curves for assets with close substitutes are relatively flat (nearly horizontal), we would expect that price increases for BAs due to the decline in volume to be mitigated as investors switch to other instruments.
Our comparison of spreads between BAs and other money-market instruments covers the period from 1984 to 2000 when the supply of BAs declined by over 85%. Most of the decline occurred during the years 1991 to 2000. The decline was a supply phenomenon due to changes in the use of BAs in international trade, not a response to investor demand. In fact, the volume in the short-term security market increased over this period, particularly in the CP and CD markets.
The dynamics of the market over this period also include a narrowing of differences between rates for all of the money-market instruments. We isolate these other changes in the money markets from the changes in BAs. After controlling for day-of-the-week, calendar, term structure, credit spread, time-series, cross-equation effects, and the level of interest rates, we find market size is an important determinant of yields. We find that trading volume, using the size of the market as a proxy, has an impact on yield spreads over T-bill rates. Additionally, we find that the substitution effect is not sufficient to eliminate the impact of market size changes. However, it is strong enough to preserve the hierarchy of rates across instruments, even though rates narrowed substantially. That is, BA rates do not diverge from other money-market rates as the BA market declined, which suggests that BAs remained close substitutes for other instruments despite the large decline in BA market size.
Our results suggest that liquidity is priced (through market size/volume), but other factors (in our case, substitution across similar assets) can mitigate the price effects of changes in liquidity.
The paper is organized as follows. In Section I, we discuss the use of supply and demand models in analyzing financial markets. Section II contains a general discussion of money markets and a specific discussion of the BA environment during the sample period. In Section III we describe the data and provide descriptive statistics. Section IV presents the econometric model and our statistical results. Section V concludes.
I. Liquidity Premiums and Shifts in Supply and Demand
Although conceptually straightforward, measuring the liquidity component embodied in the price of equity is difficult. Amihud and Mendelson (1986) describe the liquidity premium as the extra return demanded by investors to hold an illiquid asset. It follows that the price of illiquid assets will contain a premium (or adjustment) for the lack of liquidity, while the price of highly liquid assets will not. For the liquidity premium to change, one or more parameters of the market for the asset must change. A decline in demand, ceteris paribus, would be a market change that would make the asset more difficult to sell, forcing the owner to lower the price to move the asset, increasing the yield to the buyer.
Roll (1984) suggests using the bid-ask spread to measure the liquidity component. However, Hasbrouck (1988) notes that the bid-ask spread is not a clean measure of liquidity in equities, because the spread contains adjustments for asymmetric information and inventory management. Recent work has used the number of securities traded as a proxy for liquidity (for example, Chordia, Roll, and Subrahmanyam, 2000, 2001; Chordia, Subrahmanyam, and Ravi, 2001; Hasbrouck and Seppi, 2001). Additionally, Elton and Green (1998) find that volume in government bonds is closely linked to liquidity. In contrast, Clyman, Allen, and Jaycobs (1997) find that low volume in the Dublin Finex exchange did not result in price differentials between it and exchanges with much greater volume of trades. The findings of Clyman et al. are unusual, since the majority of studies find a strong link between volume and liquidity. However, other preferences, such as a desire for anonymity or execution speed as discussed by Boehmer (2005), could cause the relation between volume and liquidity to differ.
Following Wurgler and Zhuravskaya (2002) and Fama (1985), we use a supply-and-demand paradigm to discuss liquidity premiums and the effect of substitute assets on these premiums. The liquidity premiums for money-market securities are typically presented as a component of the yield: yield equals the risk-free rate plus the term premium plus the default risk premium plus the liquidity premium.
We examine the BA market in which a decline in size results in a decline in the supply of BAs. Various outcomes are possible from the decline in the supply of BAs. If BAs are a unique financial asset with a downward-sloping demand curve, then there will be little or no economic pressure to shift the demand curve. The new equilibrium from the exogenous supply decrease will be a higher price and lower yield.
If other money-market securities are substitutes for BAs, demand will shift from BAs to other money-market securities, and the new price/yield combination will be determined by the degree of substitution. Since this shift does not alter the risk-free rate, the term premium, or the default risk premium, any yield change is due to a change in the liquidity premium. If other money-market securities are perfect substitutes for BAs, then supply will shift along a horizontal demand curve and settle on a new equilibrium quantity that leaves the price/yield of BAs unchanged.
A supply-and-demand analysis of the BA market provides testable hypotheses about changes in liquidity in an asset with declining market size. If BA rates fall (prices increase) and other money-market rates do not fall, then BAs have unique features that limit substitution. If BA rates increase (prices decline) and other money-market rates do not increase, then BAs require a liquidity premium to entice buyers to invest in instruments with lower liquidity compared to other money-market instruments. BA rates that do not change, or change very little, indicate that BAs, CPs, CDs, and EDs are close substitutes.
Because substitution between assets is central to our analysis, we differentiate between substitution opportunities for banks that produce the instruments and substitution opportunities for investors. Banks have limited flexibility to substitute between instruments for short-term borrowing, because the production of each instrument is unique. Conversely, investors can readily switch between instruments based on risk compared to the yield after transaction costs.
II. BAs and Money-Market Environment
If money markets were static, then investigating the effects of a change in market size for BAs would be straightforward. However, this is not the case, because in general, market rates were falling during the BA market decline.
A. The BA Environment
Most BAs are created through financing imports and exports. Much of the decline in the BA market during our sample period was due to the reduced use of BAs in foreign trade, because guaranteeing payment became cheaper when export-credit insurance became widely available (see Sie Dhian Ho and Workhorst, 1998). Export-credit insurance, which is provided through the private market and government-sponsored agencies, offers a lower cost alternative to bankers' acceptances. BAs are regulated by the Federal Reserve, and prior to 1977, were traded and held by the Federal Reserve for monetary policy purposes. The Federal Reserve currently regulates the market by indicating which BAs are eligible for discount and repurchase agreement collateral, and which are exempt from reserve requirements and can be used as collateral at the discount window. Consequently, eligible BAs have an initial maturity of 180 days or less and a lower yield than ineligible BAs. Our sample contains only eligible BAs that trade in the secondary markets in competition with CDs, CP, and EDs.
B. BAs and Other Money-Market Instruments
BAs, CP, CDs, and EDs are private-issue securities and have default risk. Their rates contain four components: (a) the risk-free rate, (b) a term premium, (c) a default-risk premium, and (d) a liquidity premium. (1)
Along with BAs, we analyze financial CP, CDs, and EDs of three-month maturities. All instruments represent bank debt except financial CP, which is issued by bank holding companies. The rate of each security contains the same risk-free rate, and, by design, each security has the same maturity. The other two factors, the risk premium and liquidity premium, are difficult to separate empirically. However, the money-market instruments we examine are all bank-related debt in various forms, and most of these instruments are created by the same set of banks. Hence, the default risk would vary little between instruments, and any relative change in spreads among negotiable CDs, EDs, financial CP, and BAs would be a function of a change in the liquidity premium, ceteris paribus.
Even though these four instruments have many similar characteristics, their rates are not identical. Each instrument serves a specific lending-borrowing purpose that differs from the others, and none have a secondary source of protection against default. Negotiable CDs are not covered by FDIC deposit insurance, so CD rates reflect the default risk of the issuing bank. CP is backed by a bank line of credit, but the bank's line of credit does not provide default protection, since all bank lines of credit have a clause that allows the bank to refuse draw requests when a materially adverse change occurs in the credit quality of the borrower. If the CP issuer is having trouble rolling over or repaying the CP, the bank can--and likely will--refuse a draw under the line of credit. EDs are dollar-based deposits in banks outside the United States, hence, they are not covered by FDIC deposit insurance. EDs may be covered by deposit insurance in the country of issue, but the typical size of an ED deposit exceeds common deposit insurance limits. For example, Canadian deposit insurance covers only deposits in Canadian dollars. Therefore, EDs are considered uninsured deposits and carry the default risk of the issuing bank.
BAs are created from a commercial transaction, but CDs, ED deposits, and financial CP all originate from the activities of financial institutions. The fact that a BA starts from a commercial transaction does not affect the default risk of the BA. Once the bank accepts the obligation and creates the BA, the payment becomes the sole obligation of the bank. Thus, these four private-issue bank-related money-market instruments have similar default risk, although we also add a variable to our regression model to capture any remaining credit risk differences.
A regulatory change occurred during our sample period that further reduced the difference between BAs and CDs and EDs. LaRoche (1993) summarizes the change and its impact on BAs:
At the end of 1990, the Board of Governors removed reserve requirements from "nonpersonal time deposits, " which include ineligible acceptances and large CDs, and from Eurocurrency liabilities. This action bodes ill for eligible acceptances since it puts CDs and Eurodollar liabilities on a more even footing with them.
The significance of the change was that banks did not have to hold reserves on EDs and CDs, a status already applicable to BAs. There are no reserve requirements for financial CP, because it is issued by bank holding companies rather than banks. Thus, the regulatory change affected only two of the four instruments, and therefore, we cannot attribute any movement common for all four rates to this change in reserve requirements.
An additional motivation for the break in 1991 may have been due to the then-forthcoming Basel regulation in 1992. Banks may have wanted to reduce their risk exposures to counterparties when accepting trade notes to create BAs. The Basel regulation induced incentives, which, starting in 1991, could have led to a decrease in BAs.
None of the four instruments have preferential tax treatment. The gains from all money-market securities are interest income and therefore are taxed as ordinary income. In addition, all the bank-related money-market instruments are corporate debt, and so receive the same federal, state, and local tax treatments. No changes occurred in the tax treatment of these instruments over our sample period.
Since the four money-market instruments have the same time to maturity, similar default risk, and no differences in taxes, we can isolate changes in the liquidity premium due to the decline in the BA market by comparing spreads among the different instruments. However, comparisons based on quoted rates are not straightforward, because some money-market instruments are discount securities and others are face-value securities with add-on interest. When both provide the same return to investors, the quoted rate on a discount instrument is less than the quoted rate on a face-value instrument.
Three of our instruments--BAs, CP, and T-bills--are discount instruments. CDs and EDs are face-value instruments with add-on interest. We adjust the quoted rates on the discount instruments to a money-market yield, which is directly comparable to the quoted rate on add-on instruments. Our formula for converting a discount yield to a money-market yield is:
Money Market Yield = (360 * discount instrument quoted rate)/ (360--[discount instrument quoted rate * days to maturity]). (1)
III. Data and Descriptive Statistics
Here, our focus is on the role of substitution in money markets when the volume of one instruments declines, in this case BAs.
We obtain our data for BAs and other money-market instruments from the Federal Reserve Board of Governors and use daily three-month rates. BA rates are the representative closing yields for acceptances of the highest-rated money center banks. We also obtain daily money-market rates for three-month negotiable CDs, three-month ED deposits, and three-month financial CP from the Fed's Board of Governors. CD rates are an average of dealer offering rates on nationally traded CDs. CP rates are an average of offer rates on CP placed by several leading dealers for firms whose bond rating is AA or the equivalent. Each of these instruments reflects the credit risk of the issuer.
Although the mix of banks that issue most of the CP might differ from the mix of banks that issue CDs or EDs, all of these banks must maintain high credit ratings to remain competitive. However, even if the banks differ in default risk across the different instruments, the relative credit quality should remain constant through time, because the Federal Reserve collects rates consistently across time periods. The Board of Governors does not provide a quality description for the ED rates.
Our sample comprises daily data from February 2, 1984 to June 30, 2000. The sample period begins on February 2, 1984 to coincide with the Federal Reserve's switch to a two-week reserve maintenance period. Selecting this time period also allows us to exclude the period of unusual volatility in short-term rates from October 1979 through October 1982, when the Fed experimented with targeting M1. Using post-switch data is also important, because some of the instruments we use are eligible for reserve-account management.
We gather monthly data from the Federal Reserve Bulletin on the quantity outstanding of BAs for the entire sample period. (2) We use the amount outstanding to define the size of the BA market. We also collect monthly data for the quantity of ED deposits, CP, and large time deposits from the Board of Governors.
The data for nonfinancial CP outstanding are available from the beginning of the sample through June of 1993. During that period, nonfinancial CP outstanding is, on average, 25.48% of total CP outstanding, with a range between 21% and 29%. We use the 25.48% average to estimate the amount of nonfinancial CP outstanding from July 1993 through June 2000. Subtracting the amount of outstanding nonfinancial CP from total outstanding CP generates the data for the size of the financial CP market. The data for outstanding negotiable CDs are not available, so we use large time deposits as our proxy for the size of the CD market.
As we note in the Introduction, volume and liquidity often are assumed to be highly positively correlated. Although we would prefer to directly test the relation between BA volume and the BA liquidity premium, we cannot do so, because BA volume and the volume of the other instruments are not available. Instead, we use market size data as our proxy for dollar volume, and use the concept of velocity to illustrate under what conditions volume would change.
We define velocity as the number of times the same inventory of instruments trades, and over time, velocity can fall, increase, or stay constant. When there is constant velocity for a security, volume must decline as the size of the market (number of securities outstanding) declines. (We note that because we examine money-market securities, we consider that the dollars outstanding is a reasonable proxy for the number of available securities, since all these securities are short-term debt securities that come in similar dollar increments.) If velocity decreases as market size declines, then volume clearly declines and using market size overstates volume. Conversely, if velocity increases as market size declines, then market size may not be a reasonable proxy for volume.
Using the data on BAs outstanding, we estimate that for volume to remain constant across the period of decline in the BA market, velocity would need to increase by over five times. At the beginning of the decline in the BA market, the size was about $52 billion outstanding. At the end of our sample period, the amount outstanding was about $10 billion. Thus, for volume to remain constant, velocity would have to increase by a factor of about 5.2, because dollar volume equals size multiplied by velocity. For volume to remain constant from the high to low point in the sample, velocity would have to increase about eight times. Accordingly, we believe that the dollar amount outstanding in the BA market provides a reasonable proxy for volume.
C. Plots and Descriptive Statistics
Panel A of Figure 1 plots the number of BAs outstanding per month. The graph shows that the dollar amount outstanding declined across the sample, with a dramatic decline beginning in the early 1990s.
[FIGURE 1 OMITTED]
Figure 1 also provides plots of financial commercial paper (Panel B), eurodollars (Panel C), and large time deposits (Panel D). A comparison shows that the size of the BA market declines across a period when the competing money markets increase in size.
LaRoche (1993) notes that a change in Federal Reserve regulations at the end of 1990 led to a structural change in the relation among BAs, negotiable CDs, and EDs. We follow LaRoche by dividing our sample at the point of this regulatory change. We also estimate a regime-switching model and find that a significant change occurs in the size of the BA market at the beginning of 1991, which is consistent with the regulatory change.
The period before the regulatory change extends from February 1984 through December 1990 and covers a time when the number of outstanding BAs was at a high and fairly stable level (starting at $74 billion outstanding and ending with $52 billion).The period after the change extends from January 1991 through June 2000 and shows a relative decline (starting at $52 billion and ending with $10 billion). We recognize that some volatility exists in the amount of BAs outstanding in the 1984-1990 period. By using the terms "fairly stable" and "declining," we mean that a trend line fitted to the early period has a slope near zero, but a trend line for the 1991-2000 period has a negative slope.
Panel A in Table I presents rate levels for the two periods, pre-decline and during the decline, in the BA market. Average rates fell significantly from the first to the second period. Across both periods, EDs have the highest average rates, followed by CDs, BAs, CP, and T-bills. EDs have the largest decline in rates (3.19 percentage points) between the two periods followed by BAs (3.031), CDs (3.021), CP (2.864) and T-bills (2.739).
If BAs are unique with no close substitute(s) and demand is static, then the decline in supply would lead to an increase in price and a decrease in BA rates. Correspondingly, the positive spreads (CD--BA and ED--BA) would increase and the negative spread (CP--BA) would also increase (become less negative or become positive). If other market instruments are close substitutes, then the higher price and lower yield for BAs would not be sustainable, because demand would shift to substitute assets with new price/yield equilibria that reflect the degree of substitution.
Panel B of Table I shows the average spreads in basis points (bp) between the competing money-market instruments and BAs (i.e., CD--BA, CP--BA, and ED--BA). BA rates are higher than CP rates, but the average spread between the two narrows from--17.71 bp to -1.04 bp across the two periods. BA rates are lower than ED rates, with the average spread declining from 17.32 bp to 1.44 bp across the two periods. While the spreads between ED-BA and CP-BA narrowed, BA rates maintained their relative position between the two instruments (CP < BA < ED). The average spread between CDs and BAs increased about one bp from the first to second period.
The declining spreads are not consistent with the existence of a unique liquidity premium for BAs that are strictly driven by relative market size. However, the declining spreads would reduce investors' inclination to switch to other instruments to achieve higher yields. For example, EDs have the highest rate in the early period and the largest spread decline (relative to T-bills) across the two periods, while CP has the lowest rate in the early period and the smallest spread decline (relative to T-bills) across the two periods. The average rates of the two instruments in the later period are only about two bp apart, reflecting that across the periods, the liquidity premium on EDs changed more than did the liquidity premium on CP. A decline from a spread of 35 bp to two bp greatly reduces the incentive to switch from CP to ED to earn higher returns. However, since the average level of interest rates declined by approximately 60% between the first and second periods, it is difficult to determine if liquidity changed across the board for all instruments or changed uniquely for each instrument.
To help disentangle these changes in liquidity, we construct relative spreads for each instrument. We calculate these spreads as the instrument yield minus the T-bill yield with this difference divided by the T-bill yield. Panel C of Table I reports relative spreads for money-market instruments. The smaller spreads are consistent with the large decline in rates from the first period to the second. (3) However, the decline in T-bill adjusted spreads rates was not consistent across instruments, reflecting idiosyncratic changes for each instrument across the two periods.
The relative spread on EDs is 11.96% in the early period and 8.47% in the latter time period. Assuming that the default risk component in the ED spread is a constant percentage of the yield, the relative liquidity premium of EDs declined across the two periods. The reverse occurred for CP with a relative spread of 7.3% in the early period and 8% in the later period. The contrasting changes indicate that ED and CP spreads over T-bills converged. The relative spread on CDs decreased across the two periods, from 9.65% to 8.46%, as did the BA relative spread over T-bills, from 9.55% to 8.12%. These lower relative spreads reflect a decline in the relative liquidity premium for both CDs and BAs.
When we use a t-test for differences in group means, we find that all of these spreads relative to T-bills are significantly different from the first to the declining period. The ED-BA spread in Panel B of Table I decreased because EDs had a larger relative decline than BAs, and the CD-BA spread increased because BAs had a larger relative decline than CDs.
The differences in relative-spread declines reflect the differing responses of these money-market instruments to changes in the economic environment. One of those changes was the contrasting changes in the market size for each instrument, BAs declined by half, CP market size tripled, CDs doubled in market size, and EDs grew slightly. However, the outcome is consistent in that spreads narrowed, both in absolute and relative terms. In our regression analysis, we control for this decline by including T-bill yields as an independent variable.
Figure 2 plots the monthly time series of spreads between BAs and the other instruments across the two sample periods. We plot monthly average spreads to reduce the noise in the plot. The noise in plots using daily spread causes the plots to be indistinguishable from each other.
[FIGURE 2 OMITTED]
Prior to 1991, the spreads between BAs and the other money-market securities show much greater variance than do the spreads in the later period. From 1992 forward, the spreads are nearly identical (spreads near zero). If an increase in the BA liquidity premium during the first period caused the spread between BAs and other money-market instruments to narrow (Figure 2), then the continual decline in BA market size/volume over the second period should have caused BA rates to increase and exceed the rates for CDs and EDs. However, Figure 2 shows that rates of all money-market instruments moved closer together while maintaining their relative hierarchy, indicating that as the volume of BAs fell dramatically in the second period of our sample, substitution helped mitigate any increase in the liquidity premium.
Figure 2 shows that the spreads between BAs and other money-market securities have narrowed. It also supports our contention that money-market instruments are close substitutes, consistent with Fama (1985).
However, we interpret univariate tests and visual evidence with caution, because other factors could offset an increase in the liquidity premium that occurs between the two periods. For example, previous research has shown that yield curve, calendar, and default risk effects can affect time-series data for market-traded instruments, and that these effects could offset an increase in the liquidity premium. Additionally, during the period of decline in the BA market, banking regulations changed dramatically. We expect regulatory changes to alter bank default risk, but again, we suggest that changes in banking regulations would have a similar impact on the representative rate of each of the bank-created money-market instruments we use in this study. We examine different controls for default risk and present one such addition in a subsequent section, but we believe that using a homogeneous group of borrowers is one of the best controls available.
D. Correlation and Cointegration of Rates Across Sample Periods
We examine the movements of rates to measure substitutability across sample periods. We do so to provide evidence of which case is more likely, that BA rates have a unique increase in liquidity premiums, or that these assets are becoming closer substitutes. During the BA market decline a unique increase in the liquidity premium for BAs should create lower comovement for BAs compared to other money-market instruments, since it would increase BA rates when other rates were falling. If BAs are less of a substitute during the decline, which would be consistent with a unique change in their liquidity premium, then correlation coefficients should be lower as well.
In Table II, Panel A shows that in every case, BA rates are more highly correlated with other rates during the decline in the BA market. Higher correlation indicates that substitutability did not decline. Moreover, all money-market rates are more highly correlated in the second period. This stronger correlation does not lead us to reject the hypothesis that BA rates have higher liquidity premiums, but coupled with the relative spreads, the correlation results support our hypothesis that during the decline, BAs did not have differentially higher liquidity premiums than did other instruments.
Panel B of Table II presents the test statistics for Phillips and Ouliaris (1990) cointegration tests across the two regimes in the BA market. If rates diverge due to a decrease in liquidity for BAs relative to the other money-market instruments, then we expect the rates to be less cointegrated in the period of decline. The test statistics are specified such that the more negative the statistic, the higher the degree of cointegration.
Two results stand out. First, BA rates are more highly cointegrated with CDs, EDs, and T-bills during the decline in the volume and size in the BA market. Second, BAs and CP are less cointegrated over the same period. The first result reflects that these asset rates converged as BA volume declined (as shown in Figure 2). Stronger cointegration indicates higher degrees of substitutability, not differing liquidity.
The second result is influenced by a large spike in CP rates that extended over several days. We examine spikes for each instrument, based on 20 of the largest spreads. We find that negative spikes are far smaller in magnitude than positive spikes. Spikes of short durations (less than three days) occur periodically in the data. The brevity of those spikes provides further support for the substitutability of BAs for CP, CD, and ED.
IV. Statistical Modeling and Results
The descriptive statistics and plots show that while the BA market was declining in size, other markets were increasing, rates were falling in general, and all rates were converging. To account for these changes, we use multivariate regressions with the addition of several independent variables. We also use additional control variables to separate these general trends from the decline in BA size.
We compare BA rates to those for CP, CDs, and EDs, and include the spread (first difference) as our dependent variable. Comparing the contribution of each instrument with the subsequent effect on rates in a single equation is appealing, but challenging, because the yields on these assets are highly correlated, collinear, and cointegrated.
There are several other factors that complicate the analysis of the decline in BA volume over the 1984-2000 period. These include 1) a fall in money-market rates between the first and second half of the period by approximately three percentage points; 2) an increase in the total size of the market for financial CP, BAs, CDs, and EDs from about $650 billion to about $1,950 billion, with most of the growth coming in the CP and CD markets; and 3) a convergence of money-market rates such that spreads between CP, BAs, CDs, and EDs were smaller on both an absolute and relative basis. If BAs were not viable substitutes for the other money-market instruments, then BA rates would diverge from the rates of CP, CDs, and EDs regardless of the changing market trends.
To isolate the effects of the fall in money-market rates, increases in the size of the market, and convergence of spreads, we model the spreads in a seemingly unrelated regression (SUR) framework to account for cross-equation correlation in the residuals. We can then determine if the liquidity premium component increases as the BA market declines in the presence of close substitutes.
We define the BA spread that we use in the regressions below as:
[BASpread.sub.t] = [MM.sub.i,t] - [BA.sub.t] (2)
where [MM.sub.i] represents ED rates, CD rates, and financial CP rates (see Knez, Litterman, and Scheinkman, 1994). We test different definitions of the BA spread, and all definitions produce results that are qualitatively similar. We report our results using the BA spread definition that provides the results that we feel are the most straightforward to interpret. We also test this definition for a unit root, and the hypothesis of a unit root is strongly rejected using an augmented Dickey--Fuller Test and a Phillips--Perron test.
A. Regression Model
We test for changes in the BA liquidity premium with the following regression model:
[BASpread.sub.t] = [[theta].sub.0] + [[theta].sub.1] RELSIZE + [[beta].sub.1] [TermSpd.sub.t] + [[beta].sub.2] [CreditSpd.sub.t] + [[beta].sub.3][TBILL.sub.t] [4.summation over (k=1)][[gamma].sub.k][D.sub.k] + [[lambda].sub.1]QTREND + [[lambda].sub.2]HOLIDAY + [[epsilon].sub.t]. (3)
[RELSIZE.sub.i] is the amount outstanding in market i divided by amount of outstanding BAs and is our test variable for changes in the liquidity premium on BAs. (4) We also estimate regressions containing dummy variables for the period of decline and find qualitatively similar results for this specification.
Table I shows that the average BA rate is in the middle of the average rates of the other securities (CP < BA < CDs < EDs). Therefore, an increase in the BA liquidity premium would move BA rates closer to CDs and EDs, but away from CP. An increase in the liquidity premium would lead to an increase in the yield and, since interest rates are falling across the sample, BA rates would fall more slowly than would rates on other money-market securities. Positive spreads would decrease and negative spreads would become more negative (which also represents a decrease). We define our test variable (RELSIZE) such that it increases as BA market size declines and the other money-market securities remain constant or rise. Thus, as the BA market declines, an increase in the BA liquidity premium would appear in our regression model (Equation 3) as a negative parameter estimate on RELSIZE for each spread, regardless of the spread used. We also note that if the liquidity premium is uniquely due to BA rates moving away from other money-market rates, then all the coefficients for each comparison instrument will be negative.
For robustness, we tried many different versions of the spread, including the spread divided by the T-bill rate, the change in spreads, the money-market rate divided by BA rates, and defining the spread as always positive by subtracting the smaller rate from the largest rate. We also used a dummy variable for the regime shift in the BA market, and we estimated the regressions using OLS, a GARCH (1,1) model, different lags, and Federal Reserve Settlement days. All empirical results are qualitatively similar regardless of the method used.
The [D.sub.k] variable in Equation (3) represents a dummy variable for each day of the week. We omit Thursday to avoid perfect collinearity, because Flannery and Protopapadakis (1988) find it to be less important than other days for three-month T-bills after accounting for clearing conventions. QTREND is a binary variable that equals one on the last trading day of the quarter, and HOLIDAY is a binary variable that equals one on the first trading day after a holiday, and zero otherwise.
We also use the level of T-bills (TBILL) as in Lamoureux and Witte (2002) as a control variable for the level of interest rates in the market. We note that T-bill rate levels are non-stationary. However, our empirical results do not change if we use lags or the change in T-bill rates, which are stationary.
An increase in the slope of the yield curve also could be positively related to a change in the rate on less-liquid securities. The rate change would occur if there were an increase in the liquidity premium as investors seeking higher yields moved into longer-term maturities. We also include the variable TermSpd in our model as our proxy for potential changes in the liquidity premium component due to steepness in the yield curve.
Griffiths and Winters (2005) find that the price of risk increases at the year-end, when investors hold cash for liquidity reasons. Thus, an increase in the credit spread is likely to be positively associated with the liquidity premium. We follow Griffiths and Winters and create a variable CreditSpd to control for changes in the price of risk associated with changes in credit spreads.
We define the term spread and the credit spread variables in Equations (4) and (5). We use a different term for the credit spread because the three-month corporate rate is CP, which is one of our money-market variables.
TermSpd = 10-Year Treasury Note Yield-three-month T-bill Yield (4)
CreditSpd = AAA l O-Year Corporate Yield--10-Year Treasury Note Yield. (5)
We estimate Equation (3) using the term and credit spreads as defined in equations 4 and 5 for each of the three spreads (ED-BA, CD-BA, and CP-BA) in a SUR framework.
B. RELSIZE Results by Subperiod
Figure 3 plots the data for the variable RELSIZE and shows that the markets for the other instruments are increasing relative to the BA market at a slow and steady pace across most of the sample period. However, the variable RELSIZE explodes near the beginning of 1998. Figure 2 showed that during the latter period rates had converged with the spreads staying near zero bp. The combination of wide spreads and slow steady growth in RELSIZE during the early part of the sample, with narrow spreads and an explosion in RELSIZE at the end of the sample period, suggests that we should not include the entire time series of data in one regression. Accordingly, we divide the sample as we did for Table I and estimate two separate SUR models. If BAs were not close substitutes, then the large increase in other money-market instruments in the second period would cause the BA liquidity premium to increase. Therefore, BA rates would rise and would diverge from other money-market rates.
[FIGURE 3 OMITTED]
Table III presents the results from estimating the SUR model separately for the two sample subperiods. Panel A provides results for the period prior to January 1991, which covers the time period during which the BA market was relatively large and stable (see, Figure 1, Panel A).
We define the spreads and RELSIZE so that a negative parameter estimate on RELSIZE for each spread is consistent with a smaller relative market size, thus increasing the BA liquidity premium compared to the other instruments. The parameter estimates on RELSIZE are significant at better than the 1% level for each spread, with positive parameter estimates on the CD and CP spread and a negative parameter estimate on the ED spread. These results are consistent with the descriptive statistics from Table I and the plots in Figure 2. However, the results are not consistent with the expected relation between market size and liquidity, indicating that in this period there were other factors that offset the traditional relation.
We note that the microstructure of this market is not easily modeled due to other exogenous factors. For example, O'Hara (1999) shows that empirical microstructure results are mixed for pricing liquidity in equity markets. We believe these factors could also affect money markets, but our focus is on whether BA rates diverge when market size declined, so we do not try to model this disconnect between size and liquidity.
Panel B of Table III provides results for the period from January 1991 to the end of our sample period, June 2000. During this period, the BA market declined in size, but the other markets grew. Again, all the parameter estimates on RELSIZE are significant at better than the 1% level, but in this period all the parameter estimates on RELSIZE are negative. The negative sign indicates that BA rates have risen on a relative basis, other rates have fallen, or both. The negative parameter is consistent with the traditional size-liquidity relation, and suggests that BA rates increased during the period of decline relative to the other rates.
Splitting the data into two subperiods provides additional insights. First, the differences in the two time periods are highlighted by the magnitude of the differences in the size of the parameter estimates on RELSIZE for each spread. The size of the parameter estimates in the early period reflects that low levels of RELSIZE are associated with large spread changes, but in the later period, high levels of RELSIZE indicate small changes in the spread. Second, the negative parameter estimates for RELSIZE in the latter period, together with the two positive parameter estimates in the prior period, indicate that rates followed the traditional relation between size and liquidity in the latter period, but not the former.
D. Control Variables
To determine if they help explain the results in the earlier period, we examine the control variables on the subperiod results in Table III. The day-of-the-week parameter estimates do not show a consistent pattern of statistical significance in Table III, indicating that the level of money-market spreads does not contain a day-of-the-week effect. We interpret the lack of a daily effect as evidence that money-market rates tend to move together, rather than as an indication of an absence of a day-of-the-week effect in money-market rates.
When we use the spread as the dependent variable, our quarter-end and holiday variables do not show a consistent pattern in Table III. Our lack of significant results indicates that although money-market rates change together at these calendar times, the differences between rates do not.
The parameter estimates on TermSpd are positive for each spread, which is consistent with the spreads becoming more positive as the yield curve increases, and with spreads widening as uncertainty about future rates increases. CreditSpdis not consistent across the spreads in the early period, but is significant and positive across all spreads in the later period. This positive relation shows that when credit risk rises in the later period, all spreads increase. TBILL is not significant in either period for the CP spread, but is significant and positive in both periods for the ED and CD spreads. This finding indicates that spreads have relative, rather than absolute, differences.
E. Additional Evidence for Rate Convergence
Thus far, our SUR model estimation shows that BA liquidity premiums increased during the period of BA market decline. However, there still may be some uncertainty about whether this increase was uniquely due to the decline in the BA market, or if all rates were converging. To provide additional evidence on rate convergence, we estimate SUR models for ED-CD, ED-CP, and CD-CP across the two time periods.
For each spread (rate X minus rate Y), we define RELSIZE as the size of market X divided by the size of market Y. In this framework, a positive parameter on RELSIZE occurs when market X increases and rate X increases, or when market Y decreases and rate Y decreases. Either of these outcomes is consistent with relatively unique markets and limited substitution. A negative parameter estimate on RELSIZE occurs when market X increases and rate X decreases, or market Y decreases and rate Y increases. Either of these outcomes is consistent with substitution across the markets and the traditional size-liquidity premium relation.
Table IV presents the results of these estimations. The estimates reveal significantly positive coefficients for RELSIZE in the first period and significantly negative signs in the latter period, which is consistent with the BA results. The consistency in results implies that the disconnect between size and liquidity in the first period was a market phenomenon and not unique to BAs. The results in the second period are consistent with both the traditional view of the relation between size and liquidity, as well as a convergence in rates through substitution across markets.
F. Robustness Checks
We perform several robustness checks to insure that our results are not a product of the SUR specification or the definition of RELSIZE. These checks include alternative definitions of RELSIZE, replacing RELSIZE with a dummy variable for the two subperiods, and estimating Equation (3) separately for each spread in a GARCH (1,1) model. All variations support the results that the liquidity premium in BA rates increased as the BA market declined, and that rates converged. All results for different definitions of the dependent variable are qualitatively similar to the results reported.
Due to the large differences in RELSIZE at the end of the period (Figure 3), we also add a dummy variable to the model equal to one after January 1998. The RELSIZE variables remain negative and significant in the period of decline in the BA market.
We also add the logarithm of the total dollar value of all the money-market instruments in our study as our proxy for total market demand. The results for RELSIZE are largely the same, negative and significant estimates that indicate reduced spreads during the period of decline.
Further, because some of the instruments are allowed for settlement without reserve requirements, we check whether Federal Reserve settlement for banks influences our results. We find no settlement effects in our data, and that including controls for settlement does not change any of our conclusions.
V. Summary and Conclusions
Although it is well understood that liquidity is an important component in the price of any asset, in practice, it is extremely difficult to observe the liquidity component in a price. This difficulty has led researchers to use trading volume or market size as a proxy for liquidity in equity markets. That is, stocks with high volume are assumed to be highly liquid, which is a very reasonable assertion. The converse of this assertion is that stocks that trade infrequently are illiquid, and this illiquidity is associated with a price adjustment, which may also be a reasonable assertion. However, it is easy to envision market structures and other financial assets where infrequent trading does not equate to an illiquidity price adjustment. We focus on a situation in which infrequent trading is the result of a decline in volume of one asset with the existence of close substitutes.
We develop an experimental design for observing the liquidity component in the prices of close substitutes that makes it possible for us to compare the prices on substitutes with different trading frequency. This design is difficult to implement in equities, because it is difficult to identify close substitutes. However, identifying substitutes is straightforward in money-market securities, because all money-market securities share the three primary characteristics of being short-term debt with low default risk and high marketability. From 1984 through 2000, the market for BAs declined by over 85%, while most other money markets increased in size, providing us with a setting of similar assets with contrasting changes in volume. We examine the link between volume and liquidity by comparing BA rates to the rates on negotiable CDs, Eurodollar deposits, and financial CP across the period when the size of the BA market declined.
If volume and liquidity are inversely related, then the liquidity premium for BAs should increase as the BA market declines. Using a variety of methods, we find evidence of an increase in the BA liquidity premium as the BA market declines, but that the premium was not sufficient to increase BA rates such that their relative position among money-market instruments changed (CP remains less than BA, which is less than CDs, which is less than EDs). This hierarchy of rates did not change because money-market rates converged. ED rates declined faster than BAs, BAs declined faster than CDs, and CP rates declined more slowly as BA market size decreased. Spreads narrowed for the other money-market instruments when BAs were removed from the analysis, thus providing additional evidence that rates converged.
Our evaluation of the role of substitute instruments in affecting money-market yields is that the substitution effect is not sufficient to eliminate the impact of size changes, since market size is an important determinant of yields. We find that trading volume, for which we use the size of the market as our proxy, has an impact on yield spreads over T-bill rates. However, the substitution effect is strong enough to preserve the hierarchy of rates across instruments, although rates did narrow substantially. Overall, the economic impact of the substitution effect is straightforward and strong. Without a strong substitution effect, rates would not have converged nor maintained their relative hierarchy in an environment in which BA market size declined, CP market size doubled, and CD market size tripled.
In addition to the importance of information in general, asymmetric information, and institutional rules for trading in the pricing and efficiency of financial markets, our work illustrates the importance of substitute assets in the equilibrium pricing process. The availability of close-substitute assets impact prices, spreads, and how market makers and dealers operate.
We note two related implications of our results. First, the influence of substitute assets is an important consideration when evaluating changes in the demand or supply of an individual asset. Our empirical results support the theoretical predictions that substitute assets create flatter demand curves, which, on average, can lead to similar yields. Second, if substitute assets exist, then the use of market characteristics, such as volume, turnover, depth of quotes, and speed of executions, are not synonymous with liquidity. The impact of a market shock, which is specific to an asset with substitutes, can differ substantially from a shock to an asset without close substitutes.
We are very appreciative of the patience and insights of the referee who guided us through several versions of this paper. We also thank George Kaufman, Bob DeYoung, Jim Moser, Eli Brewer, Doug Evanoff, Rob Bliss, and other research seminar participants at the Chicago Fed, Mark Fisher, Scott Frame, Jerry Dwyer, Larry Wall, Paula Tkac, Mark Kamstra, and other seminar participants at the Atlanta Fed, and seminar participants at the St. Louis Fed for helpful suggestions. Additional thanks to Scott Hein, Jack Cooney, Sattar Mansi, Paul Goebel, and other seminar participants at Texas Tech University along with seminar participants at the Federal Reserve Bank of Richmond. Stan Smith and Robert Van Ness also provided helpful suggestions. The views in this paper reflect the views of the authors and should not be ascribed to the Federal Reserve Bank of St. Louis nor the Federal Reserve System.
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(1) Note that other factors, such as investor taste and preference, could determine the rate. However, we view these factors as less important and empirically unobservable and, therefore, do not include them in the model.
(2) The Fed switched from monthly data to annual data beginning in 1995. However, a monotonic decline occurred for each annual observation throughout the period, therefore we expect the monthly observations to be consistent. As further evidence of the decline, as of December 2001, the Federal Reserve stopped reporting on BAs altogether.
(3) Another factor reducing the spread could be due to a decrease in information costs. Technological innovation, such as Bloomberg screens and computer networks, allowed for closer monitoring across markets, which likely increased substitutability. The decline in spreads relative to T-bills could have also occurred because of the secular increase in bank capital due to the adoption of the Basel regulations in 1992. While the convergence in spreads could be due to a reduction in information costs, the decline in money market rates with respect to T-bills may have a default risk premium motivation. The liquidity premium effect obtains over and above this "risk-free-rate effect" and the default and term premium effects. Further analysis of this decline in interest rates is beyond the scope of this article.
(4) We note that the outstanding inventory is in monthly terms for month m and the spreads are daily at time t, thus we omit the time subscript in the equation for RELSIZE.
Ken B. Cyree, James T. Lindley, and Drew B. Winters *
* Ken B. Cyree is Frank R. Day/Mississippi Bankers Chair at The University of Mississippi in University, MS, James T. Lindley is Professor at the University of Southern Mississippi in Hattiesburg, MS, and Drew B. Winters is Jerry S. Rawls Professor at Texas Tech University in Lubbock, TX and The Federal Reserve Bank of St. Louis in St. Louis, MO.
Table I. Descriptive Statistics for Bankers' Acceptances by Period This table contains rate levels and spreads across two periods. The first period from February 1984 through December 1990 is one of relative stability in BAs outstanding. The declining period is from January 1991 through June 2000. BA means bankers' acceptance, CD means certificates of deposit, CP means commercial paper, ED means Eurodollars, and T-bills are Treasury bills. All instruments have a three-month maturity. Total First Declining t-test for Sample Period Period Difference Panel A. Average Rate Levels in Percentages BA 6.3289% 8.0893% 5.0587% 73.52 CD 6.3393% 8.0939% 5.0734% 73.86 CP 6.2486% 7.9122% 5.0483% 74.11 ED 6.4098% 8.2626% 5.0730% 76.67 T-bills 5.8200% 7.4108% 4.6722% 69.64 Panel B. Average Spreads in Basis Points CD-BA 1.04 0.45 1.47 5.91 CP-BA -8.03 -17.71 -1.04 -31.87 ED-BA 8.09 17.32 1.44 54.10 CD-T-bills 51.93 68.31 40.11 27.94 CP-T-bills 42.86 50.14 37.61 13.63 ED-T-bills 58.98 85.18 40.08 42.93 BA-T-bills 50.89 67.85 38.64 28.89 Panel C. Relative Spreads compared to T-bills (BA-T-bills)/T-bills 8.72% 9.55% 8.12% 8.57 (CD-T-bills)/T-bills 8.96% 9.65% 8.46% 7.11 (CP-T-bills)/T-bills 7.71% 7.30% 8.00% -4.42 (ED-T-bills)/T-bills 9.93% 11.96% 8.47% 20.33 Table II. Correlations and Cointegration by Period for Money Market Instruments This table presents correlations and cointegration across the period of stability in the BA market compared to a period of relative decline. The period of relative stability in BAs outstanding is from February 1984 through December 1990. The declining period is from January 1991 through June 2000. BA means bankers' acceptances, CP means financial commercial paper, CD means certificates of deposit. ED = Eurodollars. T-bills = Treasury bills. All instruments have a three-month maturity. Panel A. Correlations BAs CP CD ED T-Bills First Period BA 1.0000 CP 0.9921 1.000 CD 0.9991 0.9929 1.0000 ED 0.9972 0.9873 0.9966 1.0000 T-bills 0.9670 0.9722 0.9664 0.9641 1.0000 Declining Period BA 1.0000 CP 0.9986 1.0000 CD 0.9996 0.9989 1.0000 ED 0.9990 0.9985 0.9994 1.0000 T-bills 0.9959 0.9952 0.9956 0.9945 1.0000 Panel B. Phillips-Ouliaris (1990) Cointegration Test Statistics by Period BA Rate Cointegrated with: First Period Second Period CP -24.4829 *** -10.8326 *** CD -11.5794 *** -23.3692 *** ED -19.7744 *** -21.4588 *** T-bills -4.3142 *** -6.6904 *** *** Significant at the 0.01 level. Table III. Seemingly Unrelated Regressions of BA Spreads by Period This table contains money-market spreads in basis points. In the table, BASpread is defined as MM less BA, with all instruments having a three-month maturity, MM equals either certificates of deposit (CD), commercial paper (CP), or Eurodollars (ED). BA equals bankers' acceptances. The model is: [BASpread.sub.1] = [[theta].sub.0] + [[theta].sub.1] [RELSIZE.sub.t] + [[beta].sub.t][TermSpd.sub.t] + [[beta].sub.2][CreditSpd.sub.t] + [[beta].sub.3][TBILL.sub.t] [4.summation over[k=1]] [[gamma].sub.k] [D.sub.k] + [[lambda].sub.1] QTREND + [[lambda].sub.2] HOLIDAY + [[epsilon].sub.t] where RELSIZE is the money-market size divided by the size of the bankers' acceptances market at time t. The day-of-the-week indicators ([D.sub.k]) are one on the particular day, and zero otherwise. HOLIDAY and QTREND are dummy variables that denote holidays and quarter ends. TBILL is the three-month T-bill rate in basis points. TERMSPD is the 10-year Treasury rate less the three-month T-bill rate in basis points. CREDSPD is the 10-year AAA rate less the 10-year Treasury rate in basis points. The F-test for joint significance has a null hypothesis that RELSIZE is not significant in the system of equations. CD - BA Spread CP - BA Spread Estimate t-statistic Estimate t-statistic Panel A. Period Before Decline, February 1984 through December 1990 Intercept -34.5006 *** -11.11 -42.9738 *** -4.73 RELSIZE 30.4694 *** 22.83 19.3838 *** 5.25 MON 0.3199 0.77 0.4382 0.36 TUES 1.0392 ** 2.53 0.4738 0.39 WED 0.5104 1.29 0.8196 0.70 FRI 0.5871 1.47 -0.3092 -0.26 QTREND 3.7520 *** 3.64 2.0231 0.66 HOLIDAY 0.3653 0.84 -1.4012 -1.09 TBILL 0.0078 *** 3.53 -0.0061 -0.87 TERMSPD 0.0549 *** 6.75 0.2988 *** 11.70 CREDSPD 0.0145 *** 6.76 -0.0199 *** -2.87 F-Test for Joint Significance of RELSIZE: F-statistic = 6.12 ** System Weighted [R.sup.2] = 0.4616 Panel B. Period After Decline, January 1991 through June 2000 Intercept -7.1217 *** -5.08 -5.0878 ** -2.54 RELSIZE -0.3053 *** -5.26 -0.2614 *** -3.46 MON -0.5085 ** -1.98 -0.5250 -1.44 TUES -0.0499 -0.20 -0.0272 -0.08 WED -0.2291 -0.94 -0.1204 -0.35 FRI -0.3174 -1.28 -0.7013 ** -1.99 QTREND 1.3831 ** 2.52 -3.5580 *** -4.57 HOLIDAY -0.0300 -0.11 0.4745 1.28 TBILL 0.0109 *** 6.54 -0.0028 -1.19 TERMSPD 0.0249 *** 4.75 0.0323 ** 4.26 CREDSPD 0.0097 *** 6.99 0.0160 *** 8.25 F-Test for Joint Significance of RELSIZE: F-statistic = 101.91 *** System Weighted [R.sup.2] = 0.1258 ED - BA Spread Estimate t-statistic Panel A. Period Before Decline, February 1984 through December 1990 Intercept -8.9049 -1.39 RELSIZE -86.5874 *** -6.12 MON 0.2199 0.31 TUES 1.5080 ** 2.19 WED -0.1253 -0.19 FRI 0.2961 0.44 QTREND 2.3451 1.36 HOLIDAY 0.5780 0.79 TBILL 0.0322 *** 7.82 TERMSPD 0.0921 *** 6.28 CREDSPD 0.0511 *** 15.93 F-Test for Joint Significance of RELSIZE: F-statistic = 6.12 ** System Weighted [R.sup.2] = 0.4616 Panel B. Period After Decline, January 1991 through June 2000 Intercept -22.3234 *** -11.96 RELSIZE -3.4350 *** -10.79 MON -0.8315 ** -2.44 TUES 0.0542 0.16 WED -0.1811 -0.56 FRI -0.2548 -0.78 QTREND 0.9018 1.24 HOLIDAY 0.2821 0.81 TBILL 0.0295 *** 13.28 TERMSPD 0.0686 *** 9.78 CREDSPD 0.0261 *** 14.37 F-Test for Joint Significance of RELSIZE: F-statistic = 101.91 *** System Weighted [R.sup.2] = 0.1258 *** Significant at the 0.01 level. ** Significant at the 0.05 level. Table IV. Seemingly Unrelated Regressions of other Money-Market Spreads by Period This table shows money-market spreads in basis points. Spread is as noted with all instruments having a three-month maturity for either certificates of deposit (CD), commercial paper (CP), or Eurodollars (ED). The model is: [Spread.sub.t] = [[theta].sub.0] + [[theta].sub.1] [RELSIZE.sub.t] + [[beta].sub.1] [TermSpd.sub.t] + [[beta].sub.2] [CreditSPd.sub.t] + [[beta].sub.3] [TBILL.sub.t] [4.summation over [k=1]] [[gamma].sub.k] [D.sub.k] + [[lambda].sub.1] QTREND + [[lambda].sub.2] HOLIDAY + [[epsilon].sub.t]. We define RELSIZE as money-market X size divided by the size of money market Y when we define the spread as (rate X minus rate Y). The day- of-the-week indicators ([D.sub.k]) are one on the particular day, and zero otherwise. HOLIDAY and QTREND are dummy variables that denote holidays and quarter ends. TBILL is the three-month T-bill rate in basis points. TERMSPD is the 10-year Treasury rate less the three- month T-bill rate in basis points. CREDSPD is the 10-year AAA rate less the 10-year Treasury rate in basis points. The F-test for joint significance has a null hypothesis that RELSIZE is not significant in the system of equations. ED-CD Spread ED-CP Spread Estimate t-statistic Estimate t-statistic Panel A. Period Before Decline, February 1984 through December 1990 Intercept -86.3394 *** -27.06 9.0608 1.20 RELSIZE 150.8731 *** 23.79 68.9352 *** 19.65 MON 0.3049 0.54 0.0794 0.06 TUES 0.7226 1.30 1.2796 0.94 WED -0.4320 -0.81 -0.6866 -0.52 FRI -0.0374 -0.07 0.8767 0.66 QTREND -2.0564 -1.48 0.0544 0.02 HOLIDAY -0.3125 -0.53 1.9540 1.35 TBILL 0.0563 *** 20.98 0.0110 1.50 TERMSPD 0.1534 *** 14.89 -0.2380 *** -9.05 CREDSPD 0.0559 *** 24.25 0.0339 *** 5.50 F-Test for Joint Significance of RELSIZE: F-statistic = 741.92 *** System Weighted [R.sup.2] = 0.5468 Panel B. Period After Decline, January 1991 through June 2000 Intercept -9.0408 *** -6.32 -13.0049 *** -6.07 RELSIZE -16.8841 *** -6.32 -18.3628 *** -6.30 MON -0.3446 -1.38 -0.3593 -0.91 TUES 0.0850 0.34 0.0380 0.10 WED 0.0295 0.12 -0.1043 -0.28 FRI 0.0476 0.20 0.3999 1.04 QTREND -0.3203 -0.60 4.5639 *** 5.39 HOLIDAY 0.3040 1.20 -0.2166 -0.54 TBILL 0.0152 *** 9.64 0.0317 *** 12.37 TERMSPD 0.0205 *** 4.69 0.0158 ** 2.26 CREDSPD 0.0196 *** 15.32 0.0148 *** 7.25 F-Test for Joint Significance of RELSIZE: F-statistic = 59.95 *** System Weighted [R.sup.2] = 0.1294 CD-CP Spread Estimate t-statistic Panel A. Period Before Decline, February 1984 through December 1990 Intercept 39.6081 *** 5.91 RELSIZE 7.8200 *** 7.06 MON -0.0909 -0.07 TUES 0.6075 0.51 WED -0.2194 -0.19 FRI 0.9933 0.85 QTREND 1.8880 0.63 HOLIDAY 2.0020 1.57 TBILL -0.0133 *** -1.99 TERMSPD -0.3118 *** -12.89 CREDSPD 0.0013 0.24 F-Test for Joint Significance of RELSIZE: F-statistic = 741.92 *** System Weighted [R.sup.2] = 0.5468 Panel B. Period After Decline, January 1991 through June 2000 Intercept -0.3583 -0.20 RELSIZE -4.1536 *** -6.33 MON -0.0161 -0.05 TUES -0.0483 -0.14 WED -0.1348 -0.42 FRI 0.3510 1.08 QTREND 4.8860 *** 6.80 HOLIDAY -0.5213 -1.52 TBILL 0.0167 *** 7.70 TERMSPD -0.0043 -0.74 CREDSPD -0.0046 ** -2.63 F-Test for Joint Significance of RELSIZE: F-statistic = 59.95 *** System Weighted [R.sup.2] = 0.1294 *** Significant at the 0.01 level. ** Significant at the 0.05 level.
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|Author:||Cyree, Ken B.; Lindley, James T.; Winters, Drew B.|
|Date:||Mar 22, 2007|
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