Futures market efficiency and the federal budget deficit
Mahmoud M. Haddad
Stock index futures contract trading originated in the United States. One of the major financial innovations of the 1980s is the introduction of stock index futures in 1982. As a result of the tremendous growth in the futures index trade, many researchers focused on the relationship between futures contracts and the underlying indices, namely S&P 500. This study will investigate the impact of the federal budget deficit on futures contract prices. The sample period runs from January 1, 1984 to December 31, 1999. Monthly price quotes for stock index futures contract prices are obtained from the International Monetary Market. The prices of the nearby contract were used. This study employed the co-integration methods to test our hypothesis. An important issue in econometrics is the need to integrate short-run and long run equilibrium. Our results indicate that the cyclically adjusted federal budget deficit (fiscal policy) has exerted a statistically significant Granger-causal impact upon futures prices, at least at the 10 percent level of significance ([X.sup.2] = 2.82, [X.sup.2] = 2.21). Darat (1990 a, b) investigated spot prices and found similar conclusions. Note also that there is no Granger-causal impact in the reverse direction (DFC–>DG), since the coefficient of DFC in the DG equation is zero and over-fitting it produced was insignificant [X.sup.2] = 1.60. We also found that, there is a one-way, unidirectional Granger-causality from fiscal policy to futures prices. This may imply that futures prices are economic stabilizers and do not increase the budget deficit.
One of the major financial innovations of the 1980s is the introduction of stock index futures in 1982. By October 1987, the dollar amount value of index futures trading account for 150-200 percent of trading on the NYSE. As a result of this tremendous growth, many researchers focused on the relationship between futures contracts and the underlying indices, namely S&P 500.
Different issues concerning the relationship between futures contracts and spot prices were addressed. The first issue involves market efficiency and arbitrage. If markets are perfectly efficient, there should be no arbitrage because prices adjust fully and instantaneously to arriving new information. Accordingly, arriving new information should be reflected in both futures and spot prices. A second issue deals with information content provided by futures. It is believed that futures prices contain useful information on expected futures spot prices. A third issue deals with concern that futures markets and prices may have a destabilization influence on spot prices. There have been numerous studies investigating this last issue. For example, Harris (1989) implied that trade in index futures increases market volatility. On the other hand, Miller, Malkiel, Scholes, and Hawke, Jr. (1989), Antoniou, and Garrett (1993), Edwards (1989) and others investigated the stock market crash of 1987 and concluded that futures markets are not the culprits behind the crash.
2. LITERATURE REVIEW
It is generally agreed that a relationship exists between S&P 500 futures stock index and S&P 500 stock index. One of the models for pricing the stock index futures is the cost of carry model. This model expresses the futures price in terms of the underlying stock index, the riskless rate, and the dividend yield on the index. According to this model, the theoretical value of the stock index futures is approximated as follows:
F[C.sub.t] = [S.sub.t] [Exp.sup.[(r-d)(T-t)]]
F[C.sub.t] = the stock index futures price at time t;
[S.sub.t] = the spot stock index price at time t;
r = the riskless rate of interest over the life of the futures contract (i.e. between time T and t);
d = the stock index dividend;
T = maturity of the futures contract;
r-d = represents the net cost of carry cost.
According to this cost of carry model, if actual index futures prices exceed their perceived fair value, futures index contract is overpriced. This justifies a long arbitrage position in which the futures index contract is sold and the stock is bought. On the other hand, an under-priced futures index (i.e. if actual index futures prices below their perceived fair value) will trigger short arbitrage, and arbitrage profit can be earned by simultaneously buying futures stock index and selling the spot index. Hence, in perfectly efficient markets, spot index and stock index futures price will continuously and instantaneously adjust to new arriving information. Given this fact, it is reasonable to assume that both stock index prices and stock index futures prices will be affected by the same macrofinance variables.
A large amount of literature exists on the determination of stock prices, stock indices prices, and stock indices futures prices; however, many of these studies use daily and weekly models that require daily and weekly data resulting in excluding important variables such as budget deficit, inflation, and production output on which no daily or weekly data is available. Incorporating these macrofinance variables that the theory purported, may influence the asset price movements and enhance the usefulness of these existing models. On the other hand, excluding such important variables may lead to models that suffer from misspecification that will lead to consequences of obtaining biased results.
Several studies have utilized the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) theoretical models to explain the role of macrofinance factors in determining asset prices [see, for example, Dusak (1973), Black (1976), Ross (1976), and Darrat and Brocato (1994)].
Chen, Roll, and Ross (1986) find inflation, the industrial production index, and some measures of the term structure and risk premium important in equities pricing. Others such as Roll and Ross (1986), Grinblatt and Titman (1983), and Oldfield and Rogalski (1981) also found macrofinance factor influences to be important in stock price determination in the context of the APT approach.
Schwert (1981) found that the arrival of new information on inflation as measured by the monthly Consumer Price Index (CPI) leads to a slow adjustment of share prices. Fama and Schwert (1977) found a negative relationship between the performance of the stock market and the expected and the unexpected components.
Chang and Loo (1987) concluded that discounts on stock index futures may occur in the presence of a positive inflation risk premium priced in the stock index futures. Chang and Loo also found that stock returns and interest rates are volatile and negatively related.
A number of empirical papers have in recent years presented evidence to support the assertion that discount rate changes contain “announcements effects” relating to the future course of monetary policy, which may alter expectations about interest rates or future net cash flows accruing to institutions, and therefore, affect security prices of these institutions. Pearce and Roley (1983) found no announcement effects from discount rate changes on interest rates during the pre-October 1979 period, but a substantial effect after October-1979. Roley and Troll (1984) contend that the possibility of an announcement effect depends on the operating procedure employed by the Federal Reserve System. According to their analytical framework, no meaningful announcements are possible during the pre-October 1979 period (a period of explicit interest rate targeting). Hafer (1986) extended the analysis of Roley and Troll by adding a third sub-period, (post-October 1982 period of borrowed reserve targeting) found statistically significant responses in broad equity indexes to discount rate announcements only during the period of non-borrowed reserve targeting (October 1979 to October 1982).
Owens and Webb (2001) reported that futures market prices were unbiased predictors of target rate changes. They also found that futures contracts accurately predict the direction of target changes and are a means to enhance the prospective accuracy of market forecasts. Soderstrom (2001) found that futures-based proxies for funds rate expectations have weak predictive power for the average funds rate using daily data but are more successful in predicting the average funds rate and the funds rate target around target changes and meetings of the Federal Open Market Committee. Smirlock and Yawitz (1985) argue that announcement effects are only possible when the discount rate is changed unexpectedly (i.e. when it contains informative policy implications), while changes made solely to realign the discount rate with market interest rates (expected) would have no securities market response. Their results revealed no market response to either expected or unexpected announcements in the pre-October 1979 period and significant response for the unexpected announcements only during the post-October 1979 period. Thornton (1986) results like Smirlock and Yawitz, indicated that only unexpected changes in discount rates elicited significant response from the market interest rates. Cook and Hahn (1988) on the other hand, reported that expected discount rate changes elicited a weak response in the federal funds and T-bill market before October 1979 but no response in the subsequent period (which ran through 1985, that is, into the regime of borrowed reserve targeting), but the unexpected changes elicited changes in federal funds and T-bill rates over both periods.
3. METHODOLOGIES AND PROCEDURE
Researchers have used arbitrage pricing theory (APT) to explain the role of macrofinance variables such as: federal budget deficit, industrial production index, consumer price index, monetary base, term structure, and risk premium on stock price determination.
Darrat and Brocato (1994) [hereinafter D&B] examine the efficiency of the U.S. stock market as it pertains to a number of major macrofinance factors. Specifically (D&B) looked at the link between stock returns and seven macrofinance factors: federal budget deficit, industrial production index, inflation, monetary base, interest rate, term structure of interest rates, and risk premium. The authors found that current stock prices fully reflect all available information on the industrial production index, the inflation rate and monetary base. The federal budget deficit exerted significant lagged impact on current U.S. stock returns. Neither the term structure nor the risk premium variables showed any significant impact. Their tests suggested that while direct information on a particular factor may be used efficiently in equity valuation, the intermediate information generated by such a factor may or may not be fully utilized in pricing decisions. One of the major findings of their direct test is the systematic importance of the term structure and risk premium as conduits variables through which information on other factors influencing stock returns.
D&B believe that the variation in the deficit factor could have a high “information quotient” for the rational investor. Knowledge of an increased deficit might lead to: 1) an increase in expected taxes to cover the spending shortfalls; 2) an increase in expected inflation due to expected debt monetization; 3) an expected increase in the interest rate as a result of an expected increase in government borrowing; and/or 4) an increase in various risk premium associated with deficit-induced financial market uncertainty.
The valuation models of securities markets suggest that interest rates are essential to stock price movements. The standard economic argument revolves around the discount rate used in computing the present value of expected future cash flows. Simirlock and Yawitz (1985) found that through interest rates movements, long-term bonds compete with stocks for investors’ dollars. Accordingly, an increase in long-term interest rates would negatively impact stock prices. On the other hand, an increase in interest rates may negatively impact future corporate profitability either by causing a recession or by raising financing costs, which will lead to a negative impact on share prices.
Changes in the money supply may affect the stock index futures contracts prices through changes in stock prices caused by inflationary expectations or through portfolio substitution. Homa and Jaffee (1971) and Hamburger and Kochin (1972) supported the view that past increases in money led to increases in equity prices. The implication of their work was that investors could earn above normal profits by using a trading strategy based on the observed behavior of the money stock. On the other hand, Rozeff (1974) as well as Davidson and Froyen (1982) have shown that past money changes do not contain predictive information on stock prices. Other studies, including Pearce and Roley, found that stock prices respond only to the unanticipated change in money supply. In either case, money seems to play an important factor in the determination of stock price and on stock index futures contracts prices and thus, we conclude that stock index futures contracts prices will change as well due to changes in money supply.
Previous research showed that economic activities will impact corporate profitability and thus, influence stock prices because a change in output will have an impact on cash flow (positive if output increases, negative if output decreases). The index for Industrial Production is used as a surrogate measure of GNP because GNP is not available on monthly basis and thus, it would be the appropriate variable to use. The relationship between the federal budget deficit and stock prices has been investigated in the literature of various authors. Roley and Schall (1988) concluded by saying that a growing budget deficit will tend to depress stock prices because of increases in market interest rates and discount rates used by investors futures cash flows. On the other hand, if the economy is not operating at full capacity the effect may be offset by an increase in the output level due to fiscal stimulus.
In addition, the relationship between the federal budget deficit and several other variables has been thoroughly researched in the literature. For example, Darrat (1990b), and Darrat and Brocato (1994) examined the budget deficit/stock prices link; Evans (1987), Cebula (1988), and Darrat (1990a) examined the budget deficit/interest rates link; Modigliani (1983), Protopapadakis and Siegel (1987), and Barnhart and Darrat (1988) examined the budget deficit/inflation link; Hutchison and Pigott (1984) and Deravi, Gregorowics, and Hegji (1992) examined the budget deficit/exchange rate link; and Darrat (1988), and Bachman (1992) examined the budget deficit/trade deficit link.
Despite this apparent voluminous research on the impact of the federal budget deficit on many economic and financial variables, the potential impact of the federal budget deficit on the futures market remains an unexplored issue. This study will explore, utilize and modify relevant models developed in previous studies by incorporating the above relevant macrofinance variables that may influence price movements of stock index futures contracts. To distill the empirical results, recent advances in the econometrics of co-integrated systems in conjunction with a multivariate vector auto-regression (VAR) modeling technique will be used. Using a multivariate VAR model is aimed at avoiding the “omission of variable” bias plaguing most previous studies in this area.
Given the findings of D&B concerning the impact of macrofinance factors on spot asset prices, we expect that futures investors will similarly react to changes in these variables–federal budget deficit, industrial production index, consumer price index, monetary base, term structure, and risk premium on stock price future index determination. If futures market participants have symmetrical information as do spot market participants, and if they process this information efficiently, then these macrofinance variables should cause the same effect on both markets (i.e. spot and futures) net present values. On the other hand, if futures market participants are more sensitive to changes in the macrofinance factors than do spot market participants, and react accordingly, then stock index futures prices will react faster than spot prices.
In this section we start by first giving a general background on the methodology used in this research, that is co-integration. An important issue in econometrics is the need to integrate short-run and long run equilibrium. The traditional approach to the modeling of short-run is the partial adjustment disequilibrium in the partial adjustment model. An extension of this is the ECM (error correction model). The theory of co-integration developed by Granger (1981) and elaborated by Engle and Granger (1987) addresses this issue of integrating short-run dynamics with long-run equilibrium.
A time series [y.sub.t] is said to be integrated of order 1 or I(1) if [DELTA][y.sub.t] is a stationary time series. A stationary time series is said to be I(0). A random walk is a special case of I(1) series, because, if [y.sub.t] is a random walk, [DELTA][y.sub.t] is a random series or white noise. A white noise is a special case of a stationary series. A time series [y.sub.t] is said to be integrated of order 2 or I(2) if [DELTA] [y.sub.t] is I(1) and so on. If [y.sub.t] ~ I(1) and [u.sub.t] ~ I(0), then their sum [Z.sub.t] = [y.sub.t] + [u.sub.t] ~ I(1).
Suppose that [y.sub.t] ~ I(1). Then [y.sub.t] and [x.sub.t] are said to be co-integrated if there exists a [beta] such that [y.sub.t] – [beta] [x.sub.t] is I(0). This is denoted by saying [y.sub.t] and [x.sub.t] are CI(1,1) (More generally, if [y.sub.t] ~ I(d) and [x.sub.t] ~ I(d), then [y.sub.t] and [x.sub.t] ~ CI(d,b) if [y.sub.t] – [beta][x.sub.t] ~ I(d,b) with b > 0). What this means is that the regression equation [y.sub.t] = [beta][x.sub.t] + [u.sub.t] makes sense because [y.sub.t] and [x.sub.t] do not drift far apart from each other over time. Thus, there is a long-run equilibrium relationship between them. If [y.sub.t] and [x.sub.t] are not co-integrated, that is [y.sub.t] – [beta][x.sub.t] = [u.sub.t] is also I(1), they can drift apart from each other more and more as time goes on. Thus, there is no log-run relationship between them. In this case, the relationship between [y.sub.t] and [x.sub.t] that we obtained by regressing [y.sub.t] on [x.sub.t] is “spurious”.
If [x.sub.t] and [y.sub.t], are co-integrated, there is a long-run relationship between them. Furthermore, the error correction model (ECM) can describe the short run dynamics. This is known as the Granger representation theorem.
If [x.sub.t] ~ I(1), [y.sub.t] i(1), and [z.sub.t] = [y.sub.t] – [beta] [x.sub.t] is I(0), then x and y are said to be co-integrated, The Granger representation theorem says that in this case [x.sub.t] and [y.sub.t] to be considered by ECMs of the form
[DELTA] [x.sub.t] = [p.sub.1][z.sub.t-1] + lagged ([DELTA][x.sub.t], [DELTA] [y.sub.t]) + [e.sub.1t]
[DELTA][y.sub.t] = [p.sub.2][z.sub.t-1] + lagged [DELTA] ([x.sub.t], [DELTA] [y.sub.t]) + [e.sub.2t]
where at least one of [p.sub.1] and [p.sub.2] is nonzero and [e.sub.1t] and [e.sub.2t] are white noise.
Granger and Lee suggest a further generalization of the concept of co-integration. Define [w.sub.t] = [[SIGMA].sup.t.sub.j-0][z.sub.t-j]. that is, [w.sub.t] is an accumulated sum of [z.sub.t] or [DELTA][w.sub.t] = [z.sub.t]. Since [z.sub.t] ~ I(0), [w.sub.t] will be I(1). Then [x.sub.t] and [y.sub.t] are said to be multico-integrated if [x.sub.t] and [w.sub.t] are co-integrated. In this case, [y.sub.t] and [w.sub.t] will also be co-integrated. It follows that [u.sub.t] = [w.sub.t] – [alpha][x.sub.t] ~ I(0), where [alpha] is the co-integration constant. If [x.sub.t] and [y.sub.t] are multico-integrated, Granger and Lee show that they have the following (generalization) ECM representation:
[DELTA][x.sub.t] = [p.sub.1][z.sub.t-1] + [[sigma].sub.1][u.sub.t-1] + lagged ([DELTA][x.sub.t], [DELTA][y.sub.t]) + [e.sub.1t]
[DELTA][y.sub.t] = [p.sub.2][z.sub.t-1] + [[sigma].sub.2][u.sub.t-1] + lagged ([DELTA][x.sub.t], [DELTA] [y.sub.t]) + [e.sub.2t]
It is important in the analysis of co-integrated systems to test for co-integration. We first apply unit root tests to check that x and y are both I(1). If x and y are co-integrated, u = y – [beta] x is I(0). On the other hand, if they are not co-integrated, u will be I(1). Engle and Granger (1987) suggest several co-integration tests but suggest that using the ADF to test for unit roots is the best.
The sample period runs from January 1, 1984 to December 31, 1999. Monthly price quotes for stock index futures contract prices are obtained from the International Monetary Market. The prices of the nearby contract were used. Contracts were rolled forward into the next contract maturity last day of the nearby contract month. Necessary data on the various macrofinance variables are available from the Citibase data tape. These variables include: Industrial Production Index (X) to measure the business cycle; the Consumer Price Index (NF) to measure the inflation rate; the monthly average of the monetary base adjusted for reserve requirements (B) to represent monetary policy moves; the yield on long-term government bonds (LGB) and the three-month Treasury Bill rate (TB) from which to measure term structure (TS); the corporate bond yield on BAA-rated bonds (BAA) and (LGB) to distill a measure of risk premium (RP). The federal budget deficit (G) is obtained from the various issues of Federal Reserve Bulletin.
The variables used in the VAR model are defined as follows (L) is the lag operator, whereby (1 – L) [x.sub.t] = [x.sub.t] – [x.sub.t-1]:
D[G.sub.t] = (1 – L)[G.sub.t], where G is the cyclically-adjusted federal budget deficit.
D[X.sub.t] = (1 – L)log [X.sub.t], where X is the Industrial Production Index.
DN[F.sub.t] = (1 – L)log N[F.sub.t], where NF is the Consumer Price Index (urban, all items).
D[B.sub.t] = (1 – L)log [B.sub.t] where B is the monthly average of the monetary base adjusted for reserve requirements.
T[S.sub.t] = (1 – L)(LG[B.sub.t] – T[B.sub.t-1]) where LGB is the yield on long-term government bonds, and TB is the three-month Treasury Bill rate.
DR[P.sub.t] = (1 – L)(BA[A.sub.t] – LG[B.sub.t]), where BAA is the corporate bond yield on BAA-rated bonds.
F[C.sub.t] = [(1 – L).sup.2]log F[C.sub.t], where F[C.sub.t] is the stock index futures price at time t.
Each of the seven variables are tested for the presence of unit roots (nonstationarity) using the Augmented Dickey-Fuller (ADF) test with and without a deterministic time trend. The test is of the form (Z is any variable):
[DELTA][Z.sub.t] = [alpha] + [beta]t + T[Z.sub.t] + [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Where t is a time trend. If the t-statistic on T is significant, we reject the null hypothesis that Z in levels contains a unit root (that is, Z is then considered stationary in levels). Otherwise, we go to the second stage where we test whether Z in first-difference is instead stationary. Note that the lag length K is determined using Akaike’s FPE procedure. The results are given in Table 1.
These results in Table 1 indicate that all variables (except for the inflation variable NF) are stationary if expressed in first-difference. The NF variable appears stationary in all levels. Therefore, inflation cannot be co-integrated with the remaining variables in the system since it is ~ I(0) whereas the other variables are ~ I (1). However, the remaining six variables are all integrated of the same order (degree one) and thus they may be co-integrated if they share a common unit root. If they are co-integrated, then they possess a long-run (equilibrium) relationship which must be introduced into the VAR model if we want to avoid misspecification.
To check for possible co-integration, we used Engle-Granger’s (1987) two-step procedure. In the first stage, we perform an optimal co-integrating regression using the level (non-stationary) forms of the variable. The optimal regression is the one, which uses the conditioning variable with the highest [R.sub.2]. In the second stage, we recover the estimated residuals from the optimal co-integrating equation and test them for nonstationarity using a similar ADF test applied on these residuals. The null hypothesis is nonstationarity (nonco-integratedness). If the null is rejected, then the variables are said to be co-integrated.
Using the optimal conditioning variable [beta] with [R.sup.2] = .0981, the test statistics are -3.42 and -3.26 with and without a time trend. The critical values (5%) from Davidson and Mackinam (1993) are -4.71 and -4.98 respectively. Thus, we could not reject the null hypothesis of the existence of co-integration among the seven macrofinance variables. We also check the robustness of the results using another conditioning variable which has the second highest [R.sub.2] = 0.961; namely FC. The associated test statistics are also none significant (-3.87 and -3.86 respectively).
Therefore, we can argue that there appears to be no co-integration (long-run) relationships among the variables and we can thus proceed by specifying a regular (standard) VAR model. The third step is the specification of individual equations, one for each of the seven variables. We used the FPE to determine the lag lengths in each equation (see Darrat and Brocato 1994 for details). We impose a prior; a maximum of 12 monthly lags, though we allow it to extend beyond that if the proper was obtained at 12.
Where the superscripts in the lag polynomials indicate the appropriate lag profiles based on the FPE criterion.
In the under-fitting tests, we ask the question: Does the system improve if we delete 2 lags from each non-zero test? We performed 9 such tests on the system. [total system estimations for the over and under-fitting test are: 49+9=58]. The results are given in Table 3.
The results of Table 3 indicate that all over-fitting checks produced insignificant statistics implying no need to over fit the model. In addition, majority of the under-fitting checks indicated that omitting lags from the non-zero cells would worsen the fit of the model. Thus, these diagnostic tests suggest that the basic VAR model fit the monthly data quite remarkably. Another evidence for the appropriateness of the model is that no structural instability was found in any of the seven equations according to the Chow test. We used two alternative breaking dates: the midpoint, and the October 1987 (details are available upon request). Further, the Breusch-Godfrey test of autocorrelation (of up to sixth-degree) suggested absence of significant autocorrelation. The Ramsey’s test of misspecification suggested a proper specification. All in all, then, the VAR model presented above is statistically adequate and empirically reliable.
Having specified our seven equations, we obtain the 7×7 VAR model reported in Table 2 (note that each variable is entered in its stationary form determined in stage 1 above). This above VAR model is only tentative because the specification as given above is determined for the variables on equation-by-equation basis. Of course, this structure may change once the equations are pooled together to form a system of seven equations. Thus, we need to check for any changes in the system’s structure by means of a series of over and under-fitting diagnostic checks. In the over-fitting tests, we add (say, 2 additional) lags to every cell in the system whether zero or non-zero elements. For example, we make the first cell [a.sup.3.sub.11](L) instead of [a.sup.1.sub.11](L) and estimate the whole new system by Zellner’s SUR method. From the results, we get the lag likelihood ratio and examine whether the additional 2 lags are in fact required to improve the system. We do this for every cell in the model (that is, 49 separate estimations and consequent tests).
The final stage is to distill the Granger-causality inferences from the VAR model. To do that, we test for the joint significance of the non-diagonal elements in the model. Observe first that there are two types of Granger-causality:
(a) a variable X causes another Y in the weak sense:
This occurs if the variable X survived the FPE procedure and appears with a non-zero element in the Y equation.
(b) a variable X causes another Y in the strong sense:
This occurs if, in addition to (a), the coefficients on X as a group proved statistically significant (at least at the 10 percent level).
Thus, for example, the variable DB has a zero cell in the DFC equation. This means that DB does not Granger-cause DFC even in the weak sense. However, the variable DG appears with a non-zero cell in the DFC equation. This means that the variable DG (budget deficit) Granger-causes DFC (futures prices) at least in the weak sense. Whether this Granger-causality from DG –> DFC is also of the strong sense, we need to test whether the coefficient [a.sup.1.sub.12](L) is statistically significant. Table 4 reports the test results on all non-zero cells (a large value indicates statistical significance, i.e., Granger-causality of the strong type).
These results indicate that the cyclically adjusted federal budget deficit (fiscal policy) has exerted a statistically significant Granger-causal impact upon futures prices, at least at the 10 percent level of significance ([X.sup.2] = 2.82, [X.sup.2] 2.21). Darat (1990 a, b) investigated spot prices and found similar conclusions. Note also that there is no Granger-causal impact in the reverse direction (DFC–>DG), since the coefficient of DFC in the DG equation is zero and over-fitting it produced was insignificant [X.sup.2] = 1.60. Thus, there is a one-way, unidirectional Granger-causality from fiscal policy to futures prices. This may imply that futures prices are economic stabilizers and do not increase the budget deficit. Note further that the lag in effect of budget deficit on futures prices is rather short (one month) according to the Akaike FPE procedure. Thus, the effect of budget deficits on futures prices is strong but quick, evaporating within a month of the initial change. We have also noticed that, except for the budget deficit, none of the other variables seem to exert a Granger-causality effect upon future index prices as seen by the zero cells on all these variables in the DFC equation. These finding are not surprising in view of the fact that an efficient futures index was investigated. Similar studies are desirable on individual security contracts. Such study will explore the impact of said macrofinance factors on interest rate sensitive (bonds) futures contracts. This will also highlight the effects, if any, that diversification may have in diminishing the impact of macrofinance factors on futures contacts indices.
ADF TEST RESULTS
Variable (Z). [T.sub.u]. [K.sub.w]. [T.sub.w]. [K.sub.w]
(A) In Levels
Deficit (G) -1.29 11 -1.30 11
Index(X) -1.49 3 -0.06 3
Inflation Rate (NF) -5.58 ** 1 -5.61 ** 1
Monetary Base (B) 0.34 1 0.72 1
Term Structure of
(TS) -1.99 3 -1.73 3
Risk Premium (RP) -2.69 * 10 -2.10 10
Futures Prices (FC) -3.59 ** 1 -1.18 1
B. In First-
DG -7.75 ** 10 -7.80 ** 10
DX -4.59 ** 2 -4.59 ** 2
DNF -7.83 ** 5 -7.87 ** 5
DB -5.94 ** 1 -5.93 ** 1
DTS -5.36 ** 2 -5.72 ** 2
DRP -3.52 ** 9 -3.47 ** 9
DFC -4.32 ** 1 -4.24 ** 1
Note: An ** indicates a 5% rejection of the null hypothesis that the
variable contains a unit root. [T.sub.u] and [T.sub.w] are the test
statistics on T with and without a time trend respectively. [K.sub.u]
and [K.sub.w] are the proper (FPE-based) lag lengths on the lagged
dependent variable with and without a time trend.
DFC [a.sup.1.sub.11(L) [a.sup.1.sub.12(L) 0
0 DFC [b.sub.1]
DG 0 [a.sup.11.sub.22(L) 0
0 DF [b.sub.2]
DB 0 0 [a.sup.1.sub.33(L)
0 DB [b.sub.3]
DX = 0 0 0
0 DX + [b.sub.4]
NF 0 0 0
0 NF [b.sub.5]
DRP [a.sup.3.sub.61(L) 0 [a.sup.7.sub.63(L)
0 DPR [b.sub.6]
DTS 0 [a.sup.1.sub.72(L) [a.sup.1.sub.73(L)
[a.sup.3.sub.77(L) DTS [b.sub.7]
DX = [a.sup.1.sub.44(L)
DFC 0 0
DG 0 0
DB [a.sup.1.sub.35(L) [a.sup.4.sub.36(L)
DX = [a.sup.6.sub.45(L) [a.sup.3.sub.46(L)
NF [a.sup.1.sub.55(L) [a.sup.4.sub.56(L)
DRP 0 [a.sup.10.sub.66(L)
DTS 0 [a.sup.7.sub.76(L)
Table 3: LOG LIKELIHOOD RATIO TESTS OF MODEL SPECIFICATIONS
Log Likelihood Ratio
Null Hypotheses ([X.sub.2]) Statistics D.F.
Over-fitting Tests[a.sup.1.sub.11](L) 1.02 2[a.sup.3.sub.12](L) 0.40 2[a.sup.2.sub.13](L) 0.45 2[a.sup.2.sub.14](L) 1.19 2[a.sup.2.sub.15](L) 0.07 2[a.sup.2.sub.16](L) 1.00 2[a.sup.2.sub.17](L) 0.57 2[a.sup.2.sub.21](L) 1.60 2[a.sup.21.sub.13](L) 1.33 2[a.sup.2.sub.23](L) 2.37 2[a.sup.2.sub.24](L) 0.05 2[a.sup.2.sub.25](L) 1.12 2[a.sup.2.sub.26](L) 0.45 2[a.sup.2.sub.27](L) 1.70 2[a.sup.2.sub.31](L) 1.41 2[a.sup.2.sub.32](L) 3.36 2[a.sup.3.sub.37](L) 0.64 2[a.sup.2.sub.34](L) 2.16 2[a.sup.3.sub.35](L) 1.37 2[a.sup.6.sub.36](L) 1.77 2[a.sup.2.sub.37](L) 1.82 2[a.sup.2.sub.41](L) 2.41 2[a.sup.2.sub.42](L) 0.53 2[a.sup.2.sub.43](L) 0.21 2[a.sup.3.sub.44](L) 1.41 2[a.sup.3.sub.45](L) 1.51 2[a.sup.3.sub.46](L) 2.38 2[a.sup.2.sub.47](L) 1.85 2[a.sup.2.sub.51](L) 1.89 2[a.sup.2.sub.52](L) 2.18 2[a.sup.2.sub.53](L) 2.59 2[a.sup.4.sub.54](L) 0.60 2[a.sup.3.sub.55](L) 1.99 2[a.sup.6.sub.56](L) 1.51 2[a.sup.2.sub.15](L) 2.73 2[a.sup.5.sub.61](L) 2.31 2[a.sup.2.sub.62](L) 0.28 2[a.sup.2.sub.63](L) 3.68 2[a.sup.2.sub.64](L) 2.92 2[a.sup.2.sub.65](L) 1.44 2[a.sup.2.sub.66](L) 0.11 2[a.sup.2.sub.67](L) 1.38 2[a.sup.2.sub.71](L) 0.22 2[a.sup.3.sub.72](L) 1.03 2[a.sup.3.sub.73](L) 0.07 2[a.sup.5.sub.74](L) 2.76 2[a.sup.2.sub.75](L) 0.13 2[a.sup.9.sub.76](L) 1.82 2[a.sup.5.sub.77](L) 0.39 2
Under-Fitting Tests[a.sup.9.sub.22](L) 72.75 ** 2[a.sup.2.sub.36](L) 10.17 ** 2[a.sup.4.sub.45](L) 10.26 ** 2[a.sup.1.sub.46](L) 16.69 ** 2[a.sup.2.sub.56](L) 17.99 ** 2[a.sup.1.sub.61](L) 3.53 2[a.sup.5.sub.63](L) 9.02 ** 2[a.sup.8.sub.66](L) 14.01 ** 2[a.sup.1.sub.74](L) 6.08 ** 2[a.sup.5.sub.76](L) 10.61 2[a.sup.1.sub.77](L) 2.89 2
Table 4: GRANGER-CAUSALITY TEST STATISTICS
Null Hypotheses. [X.sup.2] Statistics. D.F.[a.sup.1.sub.11](L) = 0 0.06 1[a.sup.1.sub.12](L) = 0 2.82 * 1[a.sup.11.sub.22](L) = 0 277.02 ** 11[a.sup.1.sub.33](L) = 0 5.10 ** 1[a.sup.1.sub.35](L) = 0 5.32 ** 1[a.sup.4.sub.36](L) = 0 10.05 ** 4[a.sup.1.sub.44](L) = 0 0.18 1[a.sup.6.sub.1](L) = 0 15.23 ** 6[a.sup.3.sub.46](L) = 0 19.94 ** 3[a.sup.2.sub.54](L) = 0 9.5 ** 2[a.sup.1.sub.55](L) = 0 37.77 ** 1[a.sup.4.sub.56](L) = 0 15.42 ** 4[a.sup.3.sub.61](L) = 0 12.05 ** 3[a.sup.7.sub.63](L) = 0 21.15 ** 7[a.sup.10.sub.66](L) = 0 44.21 ** 10[a.sup.1.sub.72](L) = 0 8.59 ** 1[a.sup.1.sub.73](L) = 0 4.98 ** 1[a.sup.3.sub.74](L) = 0 7.49 ** 3[a.sup.7.sub.76](L) = 0 20.40 ** 7[a.sup.3.sub.77](L) = 0 14.75 ** 3
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Dr. Mahmoud M. Haddad, Ph.D. Dr. Haddad is a professor of Finance at the School of Business Administration, The University of Tennessee at Martin. Dr. Haddad has published in corporate finance, portfolio management, risk measurement and management, international finance and futures and options. His papers have been published in leading refereed journals. He has broad consultation, managerial and practical experience.
Dr. Omer Benkato, Ph.D. Dr. Benkato is a professor of Finance at the School of Business Administration, Ball state University at Muncie, Indiana. Dr. Benkato has published in corporate finance, portfolio management, risk measurement and management, international finance and futures and options. His papers have been published in leading refereed journals. He has broad consultation, managerial and practical experience.
Dr. Amin M. Haddad, DBA, Governor, Palestinian Monetary Authority. Dr. Haddad has published numerous articles in corporate finance, and accounting. His papers have been published in leading refereed journals. He has broad consultation, managerial, Governmental and practical experience.
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