Okorafor U ^{1*}, Abe JB, Amusa SO, Alakija TO, Ajibola AS
^{1} Department of Statistics, Yaba College of Technology, Yaba, Lagos, Nigeria.
*Corresponding Author: Okorafor, U., Department of Statistics, Yaba College of Technology, Yaba, Lagos, Nigeria, Tel: +2348150750279; Fax: +2348150750279; Email: okoraforuneke@gmail.com
Citation: AS Okorafor U, Abe JB, Amusa SO, Alakija TO, Ajibola AS, et al. (2023) NonParametric Analysis of Nigeria Treasury Bills: Kruskal Wallis Analysis Approach. Arch Mol Med & Gen 3: 118.
Received: March 29, 2023; Accepted: April 8, 2023; Published: April 12, 2023.
Copyright: © 2023 Okorafor U, et al. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
This study examined Nonparametric analysis of Nigeria Treasury bill maturity rates from 1990 to 2014 employing Normality Test, Homogeneity Test, Kruskal Wallis Test and Nemenyi Post Hoc Test methods. The data is secondary in nature and the statistical package used was SPSS version 20. The results shows that there is no significant mean difference between the Treasury bill maturities over the years (p > 0.05). Further tests also revealed that none of the variables is statistically (significantly) higher than the other. Investment was not affected by the Treasury bill rates over the period studied. We recommend that the regulatory authorities should make Treasury bill rates attractive to deposit money banks in order to ensure that they subscribe to a significant percentage of the Treasury bill issued by the Central Bank.
Non – Parametric, Kruskal Wallis, Nemenyi Post Hoc Test, Homogeneity test.
A sound, dynamic, and competitive financial sector is essential to promote growth and reduce poverty by mobilizing savings and allocating resources efficiently. Banks and other financial institutions have tremendous effects on the economy, especially in underdeveloped economies where the financial markets are weak and, in most cases, nonexistent (Mishkin, 2004). Banks are the most dominant players in the Nigerian financial system holding 93 percent, 98 percent, and 92 percent of the total assets, deposits, and loans of the financial sector respectively in the year 2010 while microfinance companies hold 4 percent of assets, 2 of deposits, and 8 percent of loans, insurance companies hold only 3 percent of total assets (1). The Nigerian banking sector is underdeveloped. However, it has been changing speeds over the years due to developments in global and domestic financial markets. One of the major sources of shortterm funding for the government is generated through treasury bills. They account for 7.8% of the total asset of the Nigerian banking sector. The Nigerian financial market is not a sophisticated market and still in the early stage of development. Due to rapid change taking place in the banking environment in Nigeria, a continued analysis of bank portfolio behavior has become essential. Conventional banking theory suggests that at any point in time, the quantity of a given asset held by banks is a function of the total amount of assets available, relative yields, and liquidity considerations (2). However, the use of total assets in any other case and relative yields in the Nigerian case would not be strong in explaining the portfolio behavior of a given asset. Nigerian Treasury bills are short term government debt securities issued by the CBN on behalf of the Federal Republic of Nigeria to finance government expenditure. They are also primary market instruments for regulating money supply via Open Market Operation (OMO).
Statement of the Problem: A study of this nature is always necessitated by the existence of certain problems. The major problem that triggered off this study is the reoccurrence of general price instability and persistent inflationary pressures in the economy, despite the plethora of monetary policy tools adopted and applied over the years. There is also this problem of general feeling that a continuous annual rate of money increase will adversely increase the rate of price level which will directly lead to inflation, thus requiring a policy response.
Objectives of the Study: The objectives of this study are to
Scope and Limitation of the Study: This study is confined only to use the best statistical tools for the amount of Treasury bill rates in Nigeria from 19902014. The limitations to this study are inadequate time, resource constraint and lack of accessibility to some valuable information among others.
Significance of the Study: The findings from this study will provide insight on the trend of Nigeria Treasury Bill maturities as a shortterm asset for Deposit Money Bank (DMBs}.
Empirical Studies: In the banking industry, assets and liabilities are managed to overcome volatilities or uncertainties arising from business activities. In other words, banks need to manage their cash flows, cost of funds and return on investments while maintaining liquidity all the time. Kosmidous, Pasiouras & Floropoulos (3) examine the impact of asset and liability composition on earnings on a sample of 80 UK banks using data from 1996–2002. The authors used 457 observations during that time period arranged as unbalanced pooled data to regress operating profit of banks by their assets and liabilities. Their results show that high profit banks earn lower returns on assets than the low profit banks in general but the loss is more than covered because of the lower cost associated with their liabilities compared to their low profit competitors. These findings indicate that it is a lower cost of liabilities than the higher return on assets that contributes to the higher profit among the competing banks. In the case of liabilities, their analysis estimates that customer deposit and short term funding were the most costly source of funds for both domestic and foreign banks. Kosmidous, Pasiouras & Fotopoulos (3) were of the opinion of their study that liability management contributes more to creating the profitability differences among banks. Chu, Pittman, and Chen (4), in their work on the possible effect of CPI on Inflation or disinflation looking into maturing US Treasury InflationProtected Securities say that time series behavior of CPI forecasts can provide timely feedback to the Federal Reserve Open Market Committee. This means that CPI is a very strong tool to indicate possible inflation and disinflation in United State of America. In the quest to know how availability of inflation protected bonds might affect asset allocation decision of investors, Fama (5) found out that, the real (inflationadjusted) returns on indexed bonds are less volatile than the returns on similar conventional bonds. Also, the correlation with stock returns is much lower for the indexed bonds. An examination of asset allocation among stocks, indexed bonds, conventional Treasuries, and a riskless asset suggests that substantial weights should be given to indexed bonds in an efficient portfolio. Mark and Aris (6) studied whether macroeconomic factors do affect aggregate Stock Returns with GARCHmodel of daily equity returns and used nominal variables like; Consumers Price Index, Producers Price Index and used real factors; balance of payment, employment reports and Housing Starts. They found out that all these variables are related to lower return volatility except Real Gross National Product which is statistically significant at 1%. Treasury bill returns and common stock returns were examined in Turkey, and it was observed that its equity premium was different from that of developed countries (7). Such research has not been carried out in Nigeria. In a bid to explain the reason for bond premium, they introduced inflation risk and default risk to an existing setpricing model by Mehra and Presscott (8) to them, inflation risk is not sufficient to bring about such alarming equity premium. Akinbobola, (9), CPI overstated changes in the cost of living which they measured with budget share of food. They used Engel Curves to Estimate Bias in the Canadian CPI as a CostofLiving Index.
Data Source: The results presented here were derived from data obtained from secondary sources. The data consists of the yearly time series of Nigeria’s Treasury Bill Interest Rates. The data on three months, six months and twelve months Treasury bill maturities in Nigeria were obtained from the Central Bank of Nigeria Statistical Bulletin.
Method of Data Analysis: The method of analysis used was Kruskal Wallis Analysis of variance test to test for differences among several means. Data entry and analysis were carried out using SP SS version 20.
KruskalWallis OneWay Analysis of Variance (Using Ranks): KruskalWallis test provides the alternative nonparametric procedure where more than two (k) independent samples are to be compared against one continuous dependent variable and where the data is on the ordinal scale.
Procedure: The data from the groups are ranked jointly from low to high or high to low as though he constituted the same row sample then letting it be the sums of the rank assign to ni observations in the ith sample. The Kruskal Wallis test is then based on a statistic:
Decision Rule: If the H0 is true and each sample is at least 5 observations, a sampling distribution of H can be approximately close with a X2 distribution with (k1) df.
Consequently, we reject H0 against the alternative that these µ’s are not all equal at the level of significant α.
Nemenyipost Hoc Test
First, we need to calculate the standard error (where k is the number of samples being compared and n is the total number of recorded observations).
and then we need to calculate the minimum significant difference which is simply:
MSD = SE * q (where q will = 3.31 for 3 samples, 3.63 for 4, 3.86 for 5, 4.03 for 6, 4.29 for 8 & 4.47 for 10
Results
Table 1: Money Market Interest Rate (per cent).
Years 
3 months treasury bills 
6 months treasury bills 
12 months treasury bill 
1990 
19.60  20.50  22.10 
1991 
15.71  17.09  22.10 
1992 
20.80  22.30  22.10 
1993 
23.60  23.26  23.99 
1994 
15.00  15.00  15.00 
1995 
13.62  13.65  13.96 
1996 
12.94  13.21  13.43 
1997 
7.04  7.49  7.46 
1998 
10.20  10.50  9.98 
1999 
12.68  12.75  12.59 
2000 
10.60  10.27  10.67 
2001 
10.20  10.50  9.98 
2002 
16.31  16.99  16.50 
2003 
14.31  13.07  13.04 
2004 
13.69  12.47  13.32 
2005 
10.53  10.38  10.82 
2006 
9.75  9.33  8.35 
2007 
10.29  9.74  8.10 
2008 
11.95  11.85  11.84 
2009 
12.96  13.03  12.85 
2010 
6.52  6.28  5.67 
2011 
5.69  4.90  4.70 
2012 
8.40  7.85  7.18 
2013 
7.94  7.47  5.54 
2014 
20.80  28.29  92.80 
Source: CBN Statistical Bulleting
Figure 1: Time Plot for the 3 months treasury bills.
The graph for the 6 months treasury bills indicates that investment in treasury bills were in their lowest position in 1981, 1997 and 2011 though it was declining from 1994 to 1997. The holding of treasury bills exhibited a tremendous increase in 2014. The two major factors that may be responsible for such a big jump in the investment of treasury bills in Nigeria banking sectors are major decline in loan disbursement and a surge in the holding of excess reserves.
Figure 2: Time plot for the 6 months treasury bills.
Figure 3: Time plot for the 12 months treasury bills.
The graph for the 12 months treasury bills indicates that investment in treasury bills were in their lowest position in 1981, 1997 and 2011 though it was declining from 1994 to 1997. The holding of treasury bills exhibited a tremendous increase in 2014. The two major factors that may be responsible for such a big jump in the investment of treasury bills in Nigeria banking sectors are major decline in loan disbursement and a surge in the holding of excess reserves.
Table 2: Kruskal Wallis test for the mean difference in the Treasury bill maturity rates

Groups 
N 
Mean Rank 
Treasury bill maturity rates 
3 months 
34 
51.56 
6 months 
34 
51.29  
12 months 
34 
51.65  
Total 
102 

Table 3: Test Statistics^{a,b}

Treasury bill maturity rates 
ChiSquare 
.022 
df 
2 
.989 
a. Kruskal Wallis Test
b. Grouping Variable: Groups
The test statistic (H) is shown to be 0.022, P = 0.05, critical value (from Chi tables) = 5.991
0.022 < 5.991. Therefore, as our 'H' value is less than the critical value, our result is not significant at the 5% level as the output above shows. Since the calculated is less than the X2 tab (i.e 0.022 < 5.991), we accept H0 and conclude that there are no significant mean differences between the Treasury bill maturity rates for the period under study. For detailed analysis, we need to conduct a post hoc test.
Nemenyi Post Hoc Test
First, we need to calculate the standard error....
(Where k is the number of samples being compared and n is the total number or recorded observations). and then we need to calculate the minimum significant difference which is simply:
MSD = SE * q(where q will = 3.31 for 3 samples, 3.63 for 4, 3.86 for 5, 4.03 for 6, 4.29 for 8 & 4.47 for 10).
So: SE = sq root of (3* (75+1)) ÷ 12, 228÷12 = 19.00
so, MSD = 4.3589*3.31 = 14.428
We now need to construct a simple cross tabulation to see where any differences in means exceed this MSD value.
The following findings emanate directly from the study.
i The graph of the Nigeria treasury bills shows that investment in treasury bills were in their lowest position in 1981, 1997 and 2011 and in their highest position in 2014.
ii. From the Kruskal Wallis test, it was found out that there is no significant mean difference between the Treasury bill maturity rates.
iii. The results of the Nemenyi Posthoc test show that none of the variables are statistically (significantly) higher than the other.
The following are the conclusion:
i. Investment in treasury bills were in their lowest position in 1981, 1997 and 2011 and in their highest position in 2014.
ii. There is no significant mean difference between the Treasury bill maturity rates for the period studied.
Consequent upon the findings of this study, as follows are the requisite recommendations.
i. The regulatory authorities should make Treasury bill rate attractive to deposit money banks in order to ensure that they subscribe a significant percentage of the Treasury bill issued by the Central Bank.
ii. The banks should ensure more effective management of their loan portfolio.
iii Deposit Money Banks and other investors can invest in any of the three types of treasury bills as there is no significant difference in their values or returns.
1. Batini N (2004) ‘Achieving and maintaining price stability in Nigeria’. IMF Working Paper WP/04/97, June.
2. Mishkin FS (2004) The Economics of Money, Banking, and Financial Markets. Boston: Pearson Addison Wesley.
3. Kosmidou K, Pasiouras F, Fotopoulos J (2004) Linking profits to assetliability management of domestic and foreign Banks in the UK. Applied Financial Economics 14: 13191324.
4. Chu, Pittman, Chen (2007) “Macroeconomic factors and the UK stock market.”Journal of Business and Accounting 18: 619–636.
5. Fama EF (1981) “Stock returns, real activity, inflation, and money.” American Economic Review 71: 545–565.
6. Mark J Flannery, Aris A Protopapadakis (2002) Macroeconomic Factors Do Influence Aggregate Stock Returns, The Review of Financial Studies 15: 751782.
7. Aydemir O, Demirhan E (2009) “The relationship between stock prices and exchange rates: Evidence from Turkey.” International Research Journal of Finance and Economics, Issue 23: 207–215.
8. Mehra R, Presscott EC (1985) "The Equity Premium: A Puzzle." Journal of MonetaryEconomics 15: 145161.
9. Akinbobola, TO (2012) The dynamics of money supply, exchange rate and inflation in Nigeria. J. Applied Fin. Bank 2: 117141.
10. CBN (2008) Central Bank of Nigeria (CBN), Monetary Policy Department Series 1, CBN/MPD/Series/01/2008. www.cbn.
11. Melnik (1999) CommercialBank Portfolio Behavior: An Empirical Analysis. The Journal of Finance.