Market Mutual Funds and Market Efficiency:
Implications for Individual Investors
by William L. Seyfried
James H. Packer
William L. Seyfried firstname.lastname@example.org is a professor in the Department of Accounting, Finance and Economics at Winthrop University. James H. Packer is a professor in the Department of Economics and Finance at the University of Central Arkansas.
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Examined in this article is whether from 1990 to 1996 money market mutual fund managers anticipated and/or reacted to changes in short-term interest rates in terms of adjusting the average maturity of their asset holdings. Using cointegration analysis and Granger-causality, the authors found that money fund managers both anticipate and react to changes in short-term interest rates. This finding has significant implications for those concerned with and affected by interest rate changes.
The US securities markets, especially the equities market, are commonly characterized as informationally efficient. This important notion of market efficiency is labeled the Efficient Market Hypothesis (EMH). (See Levy, Ch. 12, 1995.) This hypothesis has several important implications for the individual investor. One is that under-priced stocks are difficult to identify. The most often cited evidence that this is true is that professional money managers usually fail to achieve risk-adjusted returns equal to that of index funds. The most obvious implication for investors who, with reason, agree with the EMH is that they should follow a passive investment strategy that focuses on minimization of time, taxes and transaction costs. For those that don't agree, there is usually some degree of doubt about the extra expenses resulting from an active investment strategy.
The market efficiency concept should also apply to interest-rate-sensitive instruments, such as bonds and money market instruments. If the market for these instruments is informationally efficient, all existing information should already be accounted for in the price and yields of the assets, and market participants should be unable to anticipate any changes in interest rates on a predictable basis. But, contrary to the massive scrutiny afforded the capital markets by investors and academics in an attempt to support/refute the EMH, the one market that has received scant attention is the money market. For the typical individual investor, participation in the money market is epitomized by money market mutual funds (MMMFs). From an origin as recent as the early 70's, MMMFs now comprise a market of 1200 taxable and nontaxable funds that had assets of more than $1.1 trillion as of early 1998.
One of the central tenets of the EMH is competition. Yield data on MMMFs is readily available for all the world to see and may easily influence investors' selection of particular funds. MMMF managers can attempt to differentiate their yields by changing risk classes via shifting funds into usually higher yield certificates of deposit (CDs) and, especially, commercial paper (CP) and away from lower yield Treasury securities. This choice is largely guided by each fund's investment policy. However, the greatest opportunity for money fund managers to differentiate their funds' returns from others in the same risk class is to forecast short-term interest rates and alter fund maturity in response to the forecast. [Stigum, 1978]
The rationale is that MMMF managers, in the aggregate, can alter the average maturity of MMMF assets to benefit from impending interest rate changes. If rates are expected to increase, then the average maturity will be shortened so that funds' yields will increase quicker. If rates are headed down, then an increased maturity will slow the yield decline.
Investors should be curious about whether or not the MMMF average maturity index (AMI), and changes in that average maturity provide useful information in terms of impending short-term interest rate changes. Simultaneously, an analysis of the relationship between average maturity and short-term interest rates should provide additional evidence that supports or contradicts the concept of market efficiency as it applies to MMMFs.
This study examines joint questions of the usefulness of aggregate maturity MMMF data and the concept of market efficiency. Similar to Domian (1992), we utilize Granger-causality to determine if a short-term relationship exists between the AMI of the MMMF market (measured in days) and short-term interest rates (proxied by 3-month T-bill rates). In addition, cointegration analysis is used to test for a possible long-term relationship between the same variables. It is not the authors' intention to determine specifically how MMMF managers forecast the movement of interest rates, just that they may be successful in doing so. Study results would have obvious practical implications from several different aspects.
First, the analysis examines the EMH by focusing on professional money managers. Intuitively, MMMF managers are expected to outperform the market and may exhibit superior timing ability. Investors want to know if professional money managers are indeed successful in anticipating changes in short-term interest rates and are, therefore, worthy of attention. Just what is the future short-term direction of interest rates?
Second, borrowers want the same kind of guidance from the opposite perspective. Should needed loans be negotiated now, or should such an action be postponed in anticipation of declining rates? The third aspect is from the standpoint of policymakers/regulators. A primary component of current interest rates is expected inflation. Scrutiny of a changing AMI may provide evidence of interest rate expectations (including expected inflation) from a policy point of view. And, finally, financial institutions, such as banks, brokerage firms, and even MMMF managers, want to see what others are thinking. These differing perspectives comprise the clientele for the present study.
Section II below delineates previous research. Section III describes the data, hypotheses and methodology. Section IV presents the empirical results and Section V provides a summary and conclusions.
II. Previous Research
The original MMMF kingpin is William E. Donoghue, who created, flourished with, and, later, sold the Money Fund Report to IBC. In his Complete Money Market Guide (with Thomas Tilling, 1981), Donoghue contends his MMMF average maturity is useful in signaling the future direction of short-term interest rates for investors. This book includes unsupported contentions about using changes in the average maturity index to determine "what the professionals in the field think interest rates will be in the near future." [1981 119]
Fund managers select, maintain and/or alter their fund's average maturity based primarily on their expectations of interest-rate changes. Decisions about maturity have an obvious effect on eventual returns. In general, a fund's average maturity is shortened if rates are expected to rise and lengthened if a decline in rates is anticipated. A small AMI change (+/- 1 to 2 days) indicates that interest rates will be more-or-less stable. The more pronounced the AMI change (especially changes of +/- 3 or more days, and, especially, such movements in the same direction 3 weeks in a row), the more pronounced the change in interest rates. [Donoghue, 1981] These contentions are expressed, with some variation, both in the book and in related articles quoting or expressing Donoghue's views. [Donoghue 1981; Jasen and Herman 1989; Willis 1988]
Despite the magnitude and widespread use of money funds, little research has been published to date on the subject of fund managers' ability to forecast changes in short-term interest rates. Ferri and Oberhelman (1981) analyze fund managers' aggregate ability to shorten maturity before increases in CD rates and lengthen maturity before rate decreases. They examine changes in the overall average maturity index (provided by Donoghue's newsletter) and subsequent changes in one-month and two-month CD rates during the period November 1975 to July 1980. Their statistical analysis consists primarily of t-tests and classical, one-way analysis of variance.
All average maturity changes examined exhibit the expected signs. Negative AMI changes are followed, on average, by positive CD rate changes. Positive AMI changes tend to be followed, on average, by negative CD rate changes. Most of the results indicating that managers reduce AMI prior to increases in interest rate were statistically significant but, in many cases, significance was not found for increases in AMI being followed by lower interest rates. Ferri and Oberhelman's overall conclusion is that MMMF managers "have a fairly consistent" and "commendable record" of success. [1981 29]
A study by Packer and Pencek (1990), essentially, replicates the Ferri-Oberhelman procedure using a newer, longer sample period, 1982-1989. Their results are generally less consistent and less statistically robust overall than those of the previous study. They find statistically significant results in a few cases for positive changes in 3-month CD rates following negative AMI changes, but not for negative changes in CD rates following positive AMI changes. Questions are also raised concerning some elements of the Ferri and Oberhelman procedure. Their overall conclusion is that "the usefulness of changes in AMI appears to be greatly lessened in the 1980's." [1990 16]
A more recent study by Domian (1992) uses Granger-causality to examine the relationship between fund maturity and interest rates over the period 1982-1990. The author concludes that funds' average maturity is altered to fit the pattern present in rate changes and not the other way around. Fund managers appear to be reacting to rate changes, rather than being proactive by taking action prior to rate changes. This result implies that changes in maturity by money market funds do not provide useful information.
Donoghue has not provided any empirical evidence to support his contentions other than illustrative examples. The conclusions provided by the Ferri-Oberhelman and Domian studies are clearly contradictory, while the Packer-Pencek findings are more indeterminate, though generally unsupportive of Ferri-Oberhelman. Ferri-Oberhelman conclude changes in the AMI are useful in predicting the future course of interest rates. Packer-Pencek conclude their results are much less consistent and are not statistically robust. Domian's results indicate MMMF managers are merely reactive and do not anticipate changes in rates.
Are the different results due to the examination of different periods? Ferri-Oberhelman considered the mid- to late-1970s, while the other authors studied the 1980s. In addition, new statistical techniques have been developed since the previous studies were completed – in particular, it is recognized that one should test for cointegration (a long-term relationship) prior to employing Granger-causality (a test for a short-term relationship). The present study attempts to resolve the conflicting results from these earlier studies relative to Donoghue's contentions about the general usefulness of MMMF average maturity.
III. Data Analysis
In our study we sought to detect both the short- and long-run relationships between AMI and short-term interest rates. To detect a long-run relation, cointegration is employed. Granger-causality is used to examine the short-run relationship in both directions. A finding that short-term interest rates Granger cause AMI would imply that MMMF managers react to changes in interest rates by adjusting their average maturity index. However, if AMI is found to Granger cause short-term interest rates, it would suggest that MMMF managers are able to anticipate changes in interest rates, raising questions about market efficiency.
This analysis of MMMFs uses weekly data from January 1990 to December 1996 for the Average Maturity Index and 3-month Treasury bill rates to determine the forecasting abilities of the fund managers. As pointed out by Domian (1992), "a constant portfolio maturity can be maintained if newly purchased securities have about twice the maturity of the overall fund average." Since the AMI during the period studied ranged from 35 to 66 days (See Table 1 below.) securities with two- to four-month maturities would be typical for new MMMF investments. Because the three-month Treasury bill is the most actively traded security in this class, we chose to use its interest rate in this study. The AMI is compiled by IBC Donoghue's Money Fund Report published in Barron's. This money fund report creates a weighted average of the maturity of 1200 taxable money market mutual funds. Treasury bill data were downloaded from the Federal Reserve Bank's FRED database. The database was compiled using secondary market information collected each Friday by the Federal Reserve. Contrary to the multitude of information and data sources available for the capital markets, one dominant information source exists for MMMFs. IBC's Money Fund Report provides weekly data on MMMFs, including fund asset size, annualized yields and dollar-weighted average maturities of individual MMMFs. IBC also reports a dollar-weighted average maturity for the aggregate MMMF market as a whole, which we have labeled the average maturity index or AMI.
Average Maturity Index
3-month Treasury Bill Rate
The Augmented Dickey-Fuller (ADF) test is used to test for the presence of unit roots and stationarity. Testing for stationarity is essential prior to running any regression as lack of stationarity makes traditional inference invalid by giving rise to misleading values of R2 and t-statistics (Kennedy, 1998; p263). Among other problems caused by lack of stationarity is that the variable in question lacks a fixed, stationary mean. The ADF test is conducted from the OLS estimation of equation (1) below. Results of the unit root and stationarity tests for both levels and first differences are reported in Table 1.
(1) D X = r 0 + r 1Xt-1 + S r iD X t-i + e t
where X is the variable being tested for stationarity. The null hypothesis is that r 1=0 while the latter term (S r iD X t-i) is designed to remove any serial correlation. If the results indicate that one should reject the null hypothesis, then X is said to be stationary.
While Domian rigorously employed Granger-causality in examining his study variables, he did not test for cointegration. Failure to acknowledge cointegration when it exists can lead to spurious regression results and possible incorrect inferences. If two time series are cointegrated, then some linear combination(s) between the variables may exist. Some linear combinations may be stationary even though the variables may not be (the individual variables can move away from each other). They could be linked together as if on a tether. On the other hand, if variables display a lack of cointegration, then no longer-term link seems to exist and "they can wander arbitrarily far away from each other" according to Dickey, Jansen, and Thornton (1991).
A popular test for cointegration between two variables was developed by Engle and Granger (1987). The first step in the procedure is to determine the order of integration of the variables. A time series is integrated of order d if it achieves stationary after being differenced d times. If the time series does contain a unit root, then first-differencing is necessary for stationarity. The variable is then said to be first-order integrated, I(1). A variable stationary in level form is I(0). If the two variables are integrated of different orders, then no cointegration exists. However, if the two variables are integrated of the same order, d, and if the residual from regressing one variable on the other is integrated of an order less than d, then the variables are cointegrated. Thus, cointegration exists if two variables, X and Y, are I(1) and the residuals from the regression of Y on X is I(0).
Like Domian, we employ Granger-causality in this paper to analyze the possible short-term relationship between MMMF aggregate maturity and interest rates over the first seven years of the 1990's. A time series, X, is said to Granger-cause another time series, Y, if using past values of X improves the prediction of current values of Y. In other words, if changes in X precede changes in Y, X is said to "Granger cause" changes in Y. This can be tested by running a regression of Y on past values of Y and X. The F-test of the joint significance of the X terms offers insights into the short-run relationship. However, if the two series are cointegrated, then a linear combination between the two variables exists and it is then necessary to estimate an Error-Correction Model (ECM). This is necessary in part to distinguish short-run from long-run effects. The ECM takes into account the linkage between two cointegrated time series by incorporating the lagged residual from the cointegrating equation into the Granger-causality model as shown in equation (2):
(2) D Y = B0 +S Ai D Y t-i + S Bi D X t-i + Ket-1 + e
where Y is the dependent variable, X is the independent variable and et-1 is the lagged residual from the cointegrating equation. (Note: in the absence of cointegration, the lagged residual is excluded from the equation.) The change in Y (D Y) and change in X are used since, in our study, both variables are stationary in first differences. The null hypothesis is B1=0, B2=0, . . . , Bn=0 with the alternative hypothesis being at least one Bi is not equal to zero (i.e., some relationship exists between previous values of D X and D Y).
IV. Empirical Results
The correlation coefficient between the AMI and the interest rate on the three-month treasury bill during the period was -0.69. Summary data on the variables can be seen in Table 1 (above). In Figure 1 (below) the AMI and interest rates are plotted on the three-month treasury bill for the period studied. As is clear from visual inspection, a negative relationship between the two variables is apparent.
The results of the ADF test (See Table 2 below.) indicate that both variables are I(1) and, thus, both are first difference stationary, therefore, the cointegration technique is appropriate. (Akaike's Information Criterion (AIC) was used to determine the appropriate lag lengths.)
ADF Test for Unit Roots
*significant at the 1% level (MacKinnon Critical Values)
Next cointegration analysis is employed. The Engle-Granger test involves regressing AMI as a function of the interest rate and a constant and then examining the residuals for stationarity using the ADF test as in (1). The null hypothesis, no cointegration, is accepted as the ADF statistic of -2.08 is insignificant. To confirm this result, the process is repeated regressing interest rates as a function of AMI and a constant and examining the residuals. Once again, an insignificant ADF statistic of -1.87 (See Table 3 below.) resulted, confirming that the variables are not cointegrated.
Engle-Granger Test for Cointegration
Residuals from AMI = f (interest)
Residuals from interest = f (AMI)
Table 4 (below) presents the Granger-causality test results for interest rates and average maturity. The F-statistic of 3.22 suggests that one should reject the null hypothesis that changes in AMI do not cause changes in interest rates with a 1% level of significance. This indicates that changes in the AMI Granger-cause changes in short-term interest rates and thus implies that MMMF managers anticipate changes in short-term interest rates with a nine-week lag. The second F-statistic of 3.65 suggests that one should reject the null hypothesis that changes in interest rates do not cause changes in maturity with a 10% level of significance. This result indicates that money market mutual fund managers do react to changes in short-term interest rates with a one-week lag. These results indicate that dual causality does exist and that money managers are both proactive and reactive with regard to changes in short-term interest rates.
D AMI does not cause D IR
D IR does not cause D AMI
1/7/90 - 12/30/96
*indicates a 1% level of significance; **indicates a 10% level of significance
Note: AIC was used to determine the appropriate lag lengths (included in parentheses).
V. Concluding Remarks
This paper is focused on the relationship between money market mutual fund managers’ average maturity index and short-term interest rates. In it we provide empirical evidence using cointegration techniques and Granger-causality modeling to analyze the direction of this relationship. Since cointegration was not found to exist between the variables, a long-run relationship was not detected. This lends support to the idea that the market is efficient in the long run. However, the results indicate that, at least for the sample period studied, managers appear to anticipate changes in short-term interest rates approximately nine weeks in advance, while reacting to changes the following week. This raises questions about the efficiency of the market in the short run.
The ability of managers to anticipate changes in short-term interest rates is consistent with the earlier studies by Ferri and Oberhelman (1981) and Donoghue and Tilling (1981), in which they found that MMMF managers modify their AMI to benefit from anticipated changes in short-term interest rates. However, in line with Domian (1992), MMMF managers were found to react to changes in interest rates (Domian did not find evidence for managers anticipating changes in short-term interest rates). Differences between the results of this study and that by Domian may be due to changes in Fed policy in that they attempt to send signals prior to actual changing the federal funds rate.
Given the results of this study, the activities of professional money managers may be worth scrutinizing by investors to gain insight as to the short-term direction of interest rates. Borrowers may also benefit by considering whether to negotiate for necessary loans now or postpone action based on the expected change in interest rates. Since expected inflation is a primary component of interest rates, policymakers may benefit as well from examining changes in AMI to attain evidence about inflationary expectations. Thus, it appears to be useful for investors and others to consider changes in AMI as signals for future changes in short-term interest rates when making their decisions.
1. In short, security prices do not long depart from justified economic prices determined by investor expectations about future returns and risks. Markets are considered infomationally efficient when prices reflect both historical and current information and all that can be inferred about the future.
2. AIC is determined by minimizing in (SSE/T) + 2K/T where T is the sample size, K, is the number of regressors and SSE is the error sum of squares. [Kennedy, 1998 103]
3 It should be noted that, as modern econometrics packages provide specific levels of significance, the specific level of significance was 6% (the critical value as 5% level of significance is 3.84 and 10% level of significance is 2.71. while the calculated value in this case was 3.65.
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