An Empirical Study of the Treasury Bill Market in Malaysia: Part 1 Using Treasury Bills as a Predictor of Inflation

Transcription

1 Pertanika 10(3), (1987) An Empirical Study of the Treasury Bill Market in Malaysia: Part 1 Using Treasury Bills as a Predictor of Inflation ANNUAR MD. NASIR*, SHAMSHER MOHAMAD* and ZAINAL AB1DJN MOHAMED! ^Department of Management Studies, Faculty of Economics and Management, Universiti Pertanian Malaysia, Serdang, Selangor Darul Ehsan, Malaysia. Key words: Treasury bill; efficient market; interest rates; expected inflation; nominal return; real return. ABSTRAK Objektif utama kajian adalah untuk menguji teori Fama mengenai penggunaan kadar faedah jangka pendek sebagai peramal inflasi. Kajian ini telah mendapati bahawa pasaran 91-hari bil perbendaharaan Malaysia tidak cekap. Kami dapat merumus bahawa tiada asas untuk menggunakan faedah jangka pendek sebagai proksi terhadap inflasi terjangka. ABSTRACT The main objective of this study is to test Fama s theory of short term interest rates as predictors of inflation. The study found that, using 3 months treasury bill discount rates to approximate monthly nominal return, the Malaysian 91-days treasury bill market was not efficient. We found that there is no basis to use short term interest as proxy for expected inflation. THEORETICAL BACKGROUND This paper attempts to test Fama's (1975) theory of short term interest rates as predictors of inflation in the Malaysian Treasury Bill Market. This will serve as a first phase in a series of study of the Treasury Bill Market in Malaysia. A treasury bill pays no interest and any return would come from the fact that the bills are issued and sold in the market at a discount, that is at prices below their maturity value of $1000. Prior to August 1973, treasury bills were made available "on tap" that is they were issued as and when an investor wanted to buy them and the rates of discount were pre-determined by the government on the recommendation of the Central Bank. On August 20, 1973, treasury bills were sold by regular weekly tenders. Since the tender system was introduced, 91-days bills have been offered every week, 182-day bills every fortnight and 364-day bills every four weeks \ This study focusses on the efficiency of the 3 months treasury bill, that is bills that have 3 months before payment of the promised $1000. Irving Fisher (1930) hypothesized that the nominal interest rate should fully reflect all available relevant information concerning the possible future values of the rate of inflation. He stated that the nominal interest rate would approimately equal to the sum of the epected real return and expected rate of inflation. He suggested that the real return is determined by real factors and is independent of the inflation rate. Earlier studies suggest that there is a positive relationship between the nominal interest and the level of commodity prices (well known in economics as the Gibson paradox) rather than the relationship between the interest For more information, please refer to Money and Banking in Malaysia, Bank Negara Malaysia 1979, pp *Dept. of Agricultural Economics, UPM.

2 ANNUAR MD. NASIR, SHAMSHER MOHAMAD AND ZAINAL ABIDIN MOHAMED rate and the rate of change in prices as hypothesized by Fisher. Most of these studies were summarized by Roll (1972). Fama (1975) provides some empirical evidence as to the reliability of the Fisher relationship or Fisher effect using U.S. data. His dual tests of market efficiency and the hypothesis that the expected real return on the Treasury bills is constant confirms the Fisher relationship. His results suggest that variation in nominal interest rates fully reflect inflation expectation and that the nominal interest rates can be used as proxies for expected inflation. Holvoet (1979) and Lenora (1980) also confirmed this effect using Belgium and U.K. data respectively. Roll (1970) showed that the prices in the treasury bill market in the U.S. obey a fair game model which is an indication of market efficiency. On the other hand, other studies have provided contrary empirical evidence regarding the Fisher hypothesis. Nelson and Schwert (1977) and Roll (1972) show that there is no statistically reliable relationship between interest rates observed in the market at any point in time and the rate of inflation subsequently observed. A similar conclusion was arrived at by Mansor (1981) using the Malaysia data. Such results suggest an inefficient market, in a sense that, relevant available information is not fully utilised in setting interest rates. Inflation and Efficiency in the Treasury Bill Market: Theoretical Background For bills with one month to maturity, the function of the market at time t-1 is to determine an equilibrium nominal price V t. In analyzing the efficiency of the market, focus will be on the question of how does the market correctly use available information about inflation in setting V i.e. whether the price of V tfully reflects available information on inflation. Efficiency in the bill market means that in setting the treasury bill price at t-1; the market correctly uses all available information to assess the distribution of expected inflation from M to t. Then the nominal return of a treasury bill set at t-1 can be written as: v t - v, (1) where R = nominal return from t-1 to t V = treasury bill price at maturity = $1000. R can be interpreted as the period interest rate set by the market at t-1 and realized at t. If P is the price level of consumption good at t, then the real return on a treasury bill from t-1 to t can be expressed as Equation (2) can be rewritten as V P (3) P Defining: thc-wrte of inflation, A t as the rate of change in commodity price level where A t = P - p. (4) t-i Thereby equation (3) can be expressed in term of nominal return and inflation rate as follows 2 ; r = 1 + R - 1 (5) Breaking the terms and rearranging, Equation 5 can be rewritten as R t = r, + i t + r t^ t (6) Normally the cross-product r t A is generally small and no harm is done if equation (6) is reduced to (6a) where R = r + A (6a) The above equation is the well known Fisher relationship which states that the real return is the difference between the nominal return and inflation rate over the same period of time. Efficiency in the treasury bill market implies See appendix A. 350 PERTANIKA VOL. 10 NO. 3, 1987

3 AN EMPIRICAL STUDY OF THE TREASURY BILL MARKET IN MALAYSIA that if <p t _ i is the set of information available at t 1 and if 0 ( m i is the set of information used by the market to assess the distribution of A at t-l,then <^ti = ^-^ Given this, the following relationship can be stated (Fama, 1976). f m ( v where f ( and E ( <(>:-,) = f ( A/ *._,) (8) (9) ) denotes probability density function ) means expectation notation METHODOLOGY Since a test of market efficiency is also simultaneously a test of market equilibrium model, we now specify a model of market equilibrium. Given these market efficiency conditions specified in (7), (8) and (9) the following can be stated: E ( r / * t_!» R t^ = E ( r ) ( 10 ) The bill price implied in R t set by the market at any time is based on the expectation that the real return is constant. Although the assumption might be unrealistic, nevertheless it is a useful approximation if it leads to a testable implication of market efficiency. Given the relationship between nominal return, inflation and real return in equation (6) & (6a), coupled with the expected real return to be constant (E (r) in (10)) then the market's expectation of the inflation rate is given by the following equation. If the market is efficient then Consequently (12) (13) In sum, if the market is efficient and if the equilibrium expected real return is constant through time, then all variation through time on the nominal return R, represents the best estimated value of expected inflation rate. Hence R the nominal rate observed at t 1 is the best possible predictor of the rate of inflation from t- 1 to t. The Model From equation (13) and given R set at t - 1 then the true expected value of A tgiven <f> t-1and R ( can be expressed as follows: E(A/* l _ I.R t ) = R 1 ~E(r) (14) For estimation purposes, equation (14) is written as: A t = a + b(r t ) +fo If the equilibrium expected return is constant through time and market is efficient, then, the coefficient of the regression becomes H o :a = -E(r)andb a 1.0 Otherwise H is rejected When H is true, it follows that all available o information about the expected value of A is summarized in the value of R ( and there is no way to use any information available at t - 1 to correctly assess a nonzero expected value of the disturbance term e (. In other words if H is true then o * 0 and also t-test = coefficient of autocorrelation/standard error of autocorrelation coefficient. wheres.e. (coeff.) = 1/n-r andt = no. of lag The following regression equations will be estimated to investigate the above hypothesis = a + = a + H o b b : a b c (R ) < R,'> = i = 0 + c( A,) + + c(r ( ',) + E(r) e, (i) e, (ii) To test that the expected real return is constant, the following regression will be estimated. r t =a b(r t ) + e t where r t = R A (vi) PERTANIKA VOL. 10 NO. 3,

4 ANNUAR MD. NASIR, SHAMSHER MOHAMAD AND ZAINAL ABIDIN MOHAMED t= a t b(r t + c(r tl ) H : a = E(r) b = 0 c = 0 (v) (vi) (vii) Data The discount rate on the 3-months treasury bills will be taken to approximate the monthly nominal return. Data were obtained from the Quarterly Economic Bulletin published by the Central Bank of Malaysia. The period of study was from January 1975 to December The monthly CPI index published in the Quarterly Economic Bulletin will be used as a proxy for the inflation rate where At = CPI - CPI X 100 CPI RESULTS Autocorrelation Behaviour To test the market efficiency of treasury bill markets by assuming expected real return is cortstant means that the autocorrelation behaviour of the expected real return, r t should be equal to zero for all lags. The results (not shown) suggest that the treasury bill market in Malaysia is in a sense weakly inefficient due to significant autocorrelation (ac.) of lag 6, 13, 22 during the 1975 to 1984 period. Results for subperiods also support the conclusion that our treasury bill market seems to be inefficient, (ac. between /0.0 and 0.3/ for all lags). The Behaviour of A Assuming A t = E( A (/ $ t-l) + e that is, A can be decomposed into two terms, its expected value at t-1 ajid the deviation of the observed value at t from this expected value. What is relevant here to analyse is the right hand side of the above equation, which is basically a white noise with mean of zero and uncorrelated through time. The results show that e is correlated through time (ac. between [0.03 and 0.22 I) for some lags and equivalent to zero for other lags. In summary we cannot accept the hypothesis that C'has mean zero and uncorrelated through time. Hence there is a possibility that the time series of past values of A t mav be of help in predicting the future value of A t which is the inflation proxy. Hence the future value of inflation can be or may be predicted by using past value of inflation. In other words, the market might not be using all available information or that the information is not fully utilized. The A utocorrelation Behaviour of First Difference R - R (} The sample autocorrelation of monthly treasury bills normally is close to 1.0 for earlier lags and gradually dies off slowly. The autocorrelation of treasury bills like CPI (consumer price index) indicates that there is much persistence through time in the level of R and that past series value of 91 -days treasury bills have subtantial information about future values. This also means that the most recent observed value of one month nominal rate of return of treasury bills is the best information on the rate to be observed one months hence or consistent as a martingale where R, +, = R, + e t Analysis of Regression Results Table 1 summarizes regression statistic to test the hypothesis that b, is equal to 1 and that the autocorrelation of disturbance term e t should equal to zero. Basically we can conclude that the results do not support the hypothesis stating that all available information about the expected value of is summarized in the value of R. In fact for all the periods and subperiods under study the R 2 for the regression A = a + b(r ) + eis very low (0% -9%). The coefficient of regression is quite close to 1.0 but the magnitude is negative. A similar conclusion could be drawn by glancing through the sub-period results. Tables 2 and 3 summarize further the results of regression analysis incorporating lag factors of A tand R. Apart from a low t-statistic value, there were no improvement in the coefficient of determination. F-statistics indicate the hypothesis that b ] = b 2 = = 0 cannot be rejected at 5% level of significance. Tables 4, 5 and 6 summarize the regression estimates to test that the expected real return is 352 PERTANIKA VOL. 10 NO. 3, 1987

5 AN EMPIRICAL STUDY OF THE TREASURY BILL MARKET IN MALAYSIA TABLE 1 A ( = a + br ( a b S.E.(a) S.E.(b) Adj. R 1 F-value : F-value : (2.243)c (1.817)d (-1.268) , F-value : (.2.367) TABLE 2 = a + b R + b A It 2 " t S.E. (a) S.E. (b^ S.E. (b 2 ) Adj. R 2 F-value : F-value : F-value : (1.917)d (-1.088) (1.226) (1.812)d (-1.214) ( ) (1.66) (1.302) (4.384) c significant at 5% d significant at 10% TABLE 3 A t = a + bj R t S.E. (a) S.E. (b,) S.E. (b g ) Adj. R (2.17)c (-0.48) (0.145) F-value : (1.729)d (-0.598) (0.174) F-value : (2.5)c (-1.0) 8.8 (0.73) F-value : 1.95 PERTANIKA VOL. 10 NO. 3,

6 ANNUAR MD. NASIR, SHAMSHER MOHAMAD AND ZAINAL ABIDIN MOHAMED TABLE 4 r t = a + br t a b S.E. (a) S.E. (b) Adj. R 2 F-value : c (-2.23)c (2.27)c F-value : (-2.37)c (2.36)c F-value : 5.6 TABLJ: a b ) b 2 S.E. (a) S.E. (b } ) S.E. (b g ) Adj. R 2 F-value : 2, (-2.17)c (0.765) (-0.145) (-1.73)d (0.85) (-0.17) F-value : ) (-2.47)c (L079) (-0.73) F-value : 3.0 c significant at 5% d significant at 10% TABLE a b^ b 2 S.E. (a) S.E. (b^ S.E. (b g Adj. R 2 F-value : c (-1.92)d (2.9)c (-1.23) (-1.8)d (1.9)d (0.26) F-value : (-1.66) (l-.79)d (1.38) F-value : PERTANIKA VOL. 10 NO. 3, 1987

7 AN EMPIRICAL STUDY OF THE TREASURY BILL MARKET IN MALAYSIA constant. In summary we can conclude that there is no relationship between the expected real return and the nominal return suggesting that the hypothesis of expected real return being constant might not be valid. Similarly, autocorrelation for expected real return, shows some sign of market inefficiency. Further conclusions couid not be drawn looking at the generalized regression results. CONCLUSION The major conclusion that can be derived from this study is that our 3 months treasury bill market is inefficient. From theory, we know that a test of efficiency means a joint hypothesis that the market is efficient and that the model assumed to test efficiency is correct. In this case the model of constant expected real return is not valid and inefficiency in the treasury bills market might also be an indication of information market inefficiency. Nevertheless, here we found that there is no basis to use short term interest rates as proxies for expected inflation. REFERENCES FAME, E. (1970): "Efficient Capital Market: A Review of Theory and Empirical Work." / Finance 25(2): (1975): "Short Term Interest Rates as Predictors of Inflation." Amer. Econ. Rev. 65(2): (1976): Foundation of Finance, Basic Book, New York. FISHER, IRVING. (1930): The Theory of Interest. Reprint New York: Augustus M. Kelley. HOLVOET, P. (1973): Inflation and Stock Returns, MBA thesis, Katholieke Universiteit Leuven, 83pg. LENORA, M.C. (1980): Market Efficiency and Fisher Effect: A British Extension, MBA thesis, Kathoiieke Universiteit Leuven, 4 tpg. MANSOR MD. ISA. (1981): Stocks, Bonds and Bills as Inflation Hedge: The Malaysian Experience, MBA thesis, Katholieke Universiteit Leuven 1981, 112pg. NELSON C.R. and G.W. SCHWERT. (1977): Short Term Interest Rates As Predictors of Inflation; On Testing the Hypothesis that the Real Rate of Interest is constant/' Amer. Econ. Rev. 67(2): ROLL, R. (1970): The Behavior of Interest Rates. New York: Basic Books. (1972): Interest Rates on Monetary Assets and Commodity Price Index Changes," /. Finance. 27(2): Received 7 November 1986 APPENDIX A Those familiar with Fama (1975, 1976) will notice differences in the expression for arriving at equation (5). The difference lies in defining the rate of inflation (expression (4)), Fama defines inflation as rate of change in purchasing power, that is where A,= tr = 1/P (A) and P is the commodity price level at time t. We expresses rate of inflation as the rate of change in price level where P - P (A) can be further simplified as follows: (B) Notice that the numerator of both (A) and (B) are the same in magnitude but different in signs and furthermore the denominator in (B) is smaller than that of (A). However, the difference is generally small between prices for short intervals. PERTANIKA VOL. 10 NO. 3,