Nigeria: Selected Issues
Author: International Monetary Fund. African Dept.
Publication Date:
07 Mar 2018
eISBN:
9781484345481
Language:
English
Keywords:
ISCR; CR; income; yield; Nigeria; revenue; yield-macro Nelson-Siegel models; Only NSM; par yield curves; yield macro NSM impulse response function; coupon market yield rate; Inflation; Oil prices
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Selected Issues

Abstract

Selected Issues

Factors that Determine the Nigerian Term Structure of Interest Rates1

This chapter examines factors that determine the Nigerian term structure of interest rates by applying the yield and the yield-macro Nelson-Siegel models—the latter incorporating macroeconomic factors—for the period 2012 to 2017 Q2. Results suggest that the models fit the term structure for the period analyzed and indicate presence of a relationship between the chosen macroeconomic variables and the short-end of the yield curve. For maturities of less than a year, the slope and curvature of the yield curve are particularly sensitive to macroeconomic shocks.

A. Introduction

1. Nigeria’s yield curve (and term structure of interest rates) has taken different shapes and levels over the past few years (Figure 1).2 During the period examined (2012 to 2017Q2), the term structure declined (2012 to 2013), increased (2014 to 2015), and changed shape becoming slightly inverted (2016–17).

Figure 1.
Figure 1.

Federal Government Domestic Yield Curves

(Yield rates, percent)

Citation: IMF Staff Country Reports 2018, 064; 10.5089/9781484345481.002.A005

Source: Fund staff estimate

2. Economic and market developments explain some of the yield curve dynamics. These include:

  • A sharp decline in oil prices that began in late 2014, carried into 2015 before stabilizing in 2016. Highly dependent on oil revenue, as oil price collapsed and production fell (due to infrastructure sabotage), one would have expected yields in Nigeria to increase during this period on the expectation that Nigeria’s financing needs would increasingly be met through domestic bond issuance;

  • Capital flight following the delisting of the Nigeria government bond from the JP Morgan index in October 2015, should have contributed to higher yields observed that year; and

  • Large swings in inflation, from double digits in 2012 to single digits in 2013, and reverting to double digits in 2016, would have increased the yield curve movements.

3. However, a deeper look at the behavior of Nigeria’s yield curve against some of these developments may suggest some counter-intuitive movements. For example,

  • Higher revenue (from elevated oil prices) and lower expenditure, say in 2012 relative to one for 2015, would imply less reliance on borrowing to meet the budget remit, and hence reduced pressure on the yield curve. Still, despite the small difference in the volume of domestic financing, and favorable market sentiment in 2012 when oil price was at its peak, the yield curve in 2012 was above the 2015 one, even though macroeconomic conditions would have implied lower premium for investors holding government securities.3

  • The announcement by JP Morgan in September 2015 to de-list the Nigerian government securities from its index would normally trigger a sell-off as both JP Morgan index investors and index trackers divest their holdings, thus putting upward pressure on yields. Nevertheless, the yield curve shifted down in 2016 compared to 2015; and

  • With respect to inflation, the yield curve movement between 2012 and 2013 was in line with expectation. The decline in inflation lowered the premium at the long-end of the yield curve in 2013. However, the yield curve dynamics was less pronounced between 2015 and 2017, when inflation doubled. Between these periods, though the yield curve shifted upwards, the level of increase was only important at the short end of the curve.

4. Consequently, a further examination into the relationship between the relevant macroeconomic variables and the yield curve is warranted. Investigating the relationship between oil price, liquidity and inflation, and the yield curve, may help to identify underpinning factors that influence the evolution of the yield curve, and hence the government’s borrowing cost.4 This chapter attempts to examine the interaction between the yield curve and macroeconomic factors, by utilizing term structure models. It is structured as follows: it first describes the model, theory and data utilized, then discusses model performance and concludes with policy implications.

B. Models, Theory, and Data

Models

5. The term structure models used in this chapter are those based on Nelson-Siegel models (NSMs). Two types of term structure models are widely discussed in the academic literature, the Nelson-Siegel and the Affine-Term Structure models.5 Fund staff have developed a software that allows modeling the term structure based on either of these models. Readers interested in the details of these models are referred to Gasha et al (2010). For the purpose of this chapter, the Nelson-Siegel models were selected since they capture macroeconomic factors. A brief description of the NSMs can be found in Appendix A.

6. Shifts and changes of the yield curve can be explained by the level, slope (steepness) and curvature (humpness). The factors’ sensitivities to shocks are described by the loading factors. The loading factor of the level is equal to one, meaning it affects yields across maturities equally. For instance, an increase in this factor, “the level”, is symbolized by an upward parallel shift of the yield curve. The slope of the yield curve, is the spread between the long and short maturity yields, as a result the loading factor decays as maturity increase. A shock to the slope would make the yield less steep, as it affects the short-term rates more than long maturities. Hence, a contractionary (accommodative) monetary policy reduces (amplifies) the slope of the curve. The curvature of the yield curve is the sum of spreads between long and medium-term maturity yields and the medium and short-term maturity yields. The loading factor is maximized at medium maturities and is zero at the shortest and longest maturities. An increase in this factor would increase the humpness of the curve.

Theory

7. The slope, and the short end-of the yield curve, is closely associated with monetary policy. The degree of influence would depend on the effectiveness, soundness and credibility of the monetary policy framework (see chapter 6). Policy makers may use monetary policy instruments to anchor inflation, manage liquidity and/or stabilize money market conditions.

8. The curvature is mainly affected by interest rate volatility. Studies based on the US Treasury yield curve, have found the curvature to be influenced by short-term interest rate volatility (Christiansen et al, 2002).

9. The level, and yield rates at the longer maturities are influenced by macroeconomic factors. These tend to be long-run macroeconomic variables, including business cycle drivers and government policies (monetary, fiscal, structural) that may impact the supply of government securities, whereas investors’ demand is motivated by:

  • Inflation risk premia – the more volatile inflation is, the higher the premium to account for inflation uncertainty in the future;

  • Credit risk premia – investors may demand higher compensation as sovereign risk heightens;

  • Term premia – investors may require compensation for tying up their money for longer maturities as opposed to reinvesting in short-term securities;

  • Illiquidity premia – investors prefer instruments that can be easily traded in any size without influencing the market price; the less liquid an asset, the higher the yield.

  • Preferred habitat – some investors demand bonds of a certain maturity for exogenous reasons, for example, pension funds and insurers have preference for securities with longer tenors to match their long-term liabilities.

Data

10. Term structure models utilize zero-coupon yield curves. Observed market yield curves exhibit the relationship between yield to maturity rates (gross redemption yields) against time to maturity. Zero coupon market yield rates are not readily available, apart from those securities at the short end of the yield curve (with maturities less than a year). For this reason, coupon bonds are often used to derive zero coupon bonds.

11. In this analysis, zero coupon yield curves were constructed from par yield curves.6 Par yield curves based on rates from primary bond auctions were used because: (a) the absence of sufficient secondary market data and the possibility of liquidity segmentation in parts of the yield curve meant the use of observed market yield curves was not ideal nor an option, and (b) they directly capture the government’s cost of borrowing, as opposed to secondary market rates which often trade away from issuance rates, reflecting other factors such as market conditions and liquidity. That said, primary auction rates are not free of influence—in particular, the issuer can influence rates by rejecting and accepting certain offers. However, in the case of Nigeria, such practice is not common, issuances are transparent and predictable. The few times where issuances have differed from plan, the actions were taken to exclude outlier bids as opposed to the issuer acting opportunistically.

12. Monthly data covering the period 2012 to 2017 Q2 were used. The period provides for 66-time series observations, across 7 maturities, 3-months (3M), 6-months (6M), 1-year (1Y), 3-year (3Y), 5-year (5Y), 7-year (7Y) and 10-year (10Y).

13. Macroeconomic factors that are common in influencing the yield curve and real economic activity were chosen. These comprise: monetary policy rate (MPR), inflation rate, liquidity (using Broad Money as a proxy) and oil price.7

C. Findings: Performance of the Yield-Only NSM

14. The NSM yield-only model fits the term structure of Nigerian yields (Appendix Figure 1).8 The mean and standard deviation of the residuals of the measurement equations are negligible across maturities, and the goodness of fit test measured by Chi-square test statistic indicate the zero-coupon yield curve and the estimated term structure differ by a small amount (Table 1).

Table 1.

Nigeria: Yield-Only NSM, Yield Curve Fitting Residuals, 2012–17

article image
Source: Fund staff estimates

15. The average yield curve has been relatively flat. The estimated average yield curve is only slightly upward sloping at the short end of the curve but displays a flat shape for longer maturities (Figure 2). This characteristic prevails through time (Appendix Figure 2).9 Of the three factors that depicts the yield curve, the level of the estimated term structure is the most stable, showing minor variation relative to its mean, whereas the curvature is highly volatile (Figure 3).10

Figure 2.
Figure 2.

Observed Yields and Estimated Average Yield Curve

(Percent)

Citation: IMF Staff Country Reports 2018, 064; 10.5089/9781484345481.002.A005

Source: Fund staff estimate
Figure 3.
Figure 3.

Estimates of the Yield Curve Loading Factors and Yield Factors

Citation: IMF Staff Country Reports 2018, 064; 10.5089/9781484345481.002.A005

Source: Fund staff estimates

D. Findings: Performance of the Yield-Macro NSM

16. The relationship between macroeconomic variables and the yield curve is captured through the yield-macro model. The yield macro model exhibits fitness to the yield curve; the estimated means and standard deviations of the residuals of measurement equations are small for all maturities, and the chi-square statistics result confirm goodness of fit (Table 2).

Table 2.

Nigeria: Yield-Macro NSM Yield Curve Fitting Residuals, 2012–17

article image
Source: Fund staff estimates

17. The dynamics of the yield curve factors (level, slope and curvature) do not exhibit similar behavior to the macroeconomic variables. There are tenuous similarities between the level and the curvature with that of MPR and liquidity, respectively, (Figure 4). The trend of inflation and oil prices correspond to the curvature of the yield curve over 2016–17.

Figure 4.
Figure 4.

Estimates of Factors from Yield-Macro NSM

(Percent)

Citation: IMF Staff Country Reports 2018, 064; 10.5089/9781484345481.002.A005

Source: Fund staff estimate

18. The findings can be summarized as follows:

  • Short-term rates react significantly and quickly to macroeconomic variables, whereas long-term rates are explained by non-macroeconomic variables. Indeed, for maturities of less and equal than one year, around 50 percent of the variance of the yield curve is explained by macroeconomic factors (mostly inflation and oil price fluctuations), whereas they explain 30 percent of the variance at longer maturities (Table 3). The impulse response functions indicate that the slope and curvature react to macroeconomic shocks; the level on the other hand, appears to be unresponsive, apart from liquidity shock which affects it in the short-term but dissipates through time (Figure 5).

  • The dynamics of the yield curve are driven by the level factor, which is closely associated with long-term rates. The level explains 30 percent (at 3-year maturity) to 60 percent (at 10-year maturity) of the variance in the yield curve (Table 3).

Table 3.

Nigeria: Yield-Macro NSM Variance Decomposition for 60 Months Period

article image
Source: Fund staff estimates
Figure 5.
Figure 5.

Results of Yield Macro NSM Impulse Response Functions

Citation: IMF Staff Country Reports 2018, 064; 10.5089/9781484345481.002.A005

19. The analysis presented offers partial explanations to the counterintuitive movements of the yield curve. Oil price, liquidity and inflation were discussed as factors with potential links to the yield curve, though the movement of the yield was counterintuitive to recent movements in oil prices and liquidity. These observations resonated with the findings of the analysis which demonstrated non-macroeconomic factors to be the main drivers for the dynamics of the yield curve. Of the three, inflation was found to be the most relevant, in line with the ex-ante observation, accounting for up to 28 and 10 percent of the yield’s variance at shorter and longer maturities, respectively (Table 3 and Figure 5).

20. There could be a stronger link between other macroeconomic variables and the yield curve. For example, growth rates and primary balances may offer stronger linkages, particularly with the level of the yield curve. Such macroeconomic variables could not be included in this chapter as high frequency data was not available.11

E. Policy Implications

21. The results of the analysis suggest that short-term rates are prone to shocks; reducing government’s exposure to them may reduce costs and risks over the long-term. To manage the risks imposed by short-term securities, the Debt Management Office (DMO) has publicly announced its intention to gradually reduce the size of T-bills, which it began to do from December 2017 onwards. The strategy is to issue Eurobonds (worth $3bn) and use their proceeds to retire T-bills as they mature. In addition, the DMO could skew its issuance program towards medium to -long tenor securities, but deepening liquidity along the curve would be important before doing so.12

Appendix I. The Nelson-Siegel Models1

Term structure models capture the change in the level and shape of the term structure over time. They describe the shape of the yield of the curve across maturity, as well its dynamics over time.

Nelson and Siegel (1987) proposed to fit the forward curve using a flexible, smooth parametric function given by:

(1)f(τ)=β1+β2e(−λτ)+β3e(−λτ)(λτ)

Where given the forward rate of this form they show that a static yield curve is:

(2)y(τ)=β1+β2[1−e(−λτ)(λτ)]+β3[1−e(−λτ)(λτ)−e(−λτ)]

A dynamic version of this model was introduced by Diebold and Li (2006) who proposed that the coefficients β1, β2 and β3 should be treated as time-varying structure factors, namely: level, slope and curvature factors, respectively. The dynamic version with time-varying coefficients is given by:

(3)yt(τ)=β1,t+β2,t[1−e(−λτ)(λτ)]+β3,t[1−e(−λτ)(λτ)−e(−λτ)]

Here, t is the time period, τ is time to maturity and λ is the decay parameter. β1,t, β2,t and β3,t are time-varying term structure factors. Their coefficients are usually referred to as factor loadings. β1,t is related to the level because its factor loading is 1 and therefore its effect is the same for all maturities. The loading of β2,t is 1 for an instantaneous maturity and decays to zero at an exponential rate as maturity increase, and conceptually captures the slope of the yield curve, which also decreases with maturity; the rate of decay is determined by the parameter λ. The loading on β3,t starts at zero, increases for medium maturities and then decays to zero, thereby creating a hump-shape and linking it to the curvature of the yield curve; the decay parameter λ determines at which maturity this component reaches its maximum.

In the context of state space representation, Equation 3, can be specified as:

(4)βt=μ+Φβt−1+νt

Equation 4, called the transition equation, governs the dynamics of the state vector, which is given by the unobservable vector, βt = [β1,t, β2,t, β3,t]

As in Diebold and Li (2006), it is assumed that these time-varying factors follow a vector autoregressive of order one, VAR(1), where the mean state vector µ is a 3 X 1 vector of coefficients.

The transition matrix Φ is a 3 X 3 matrix of coefficients, and νt is a white noise transition disturbance with a 3 X 3 non-diagonal covariance matrix Q.

(5)Yt=Xβt+ϵt

Equation 5, referred to as the measurement equation, is the specification of the yield curve itself, and relates N observable yields to three unobservable factors. The vector of yields Yt, contains N different maturities Yt = [y1 (τ1) ... y (τN)]’. The measurement matrix X is a N X 3 matrix whose columns are the loadings associated with the respective factors, and εt is the white noise measurement disturbance with N X N diagonal covariance matrix H. The system can be written as follows:

6)[β1,tβ2,tβ3,t]=[μ1μ2μ3]+[φ11φ12φ13φ21φ22φ23φ31φ32φ33][β1,t−1β2,t−1β3,t−1]+[ν1,tν2,tν3,t]
(7)[y1(τ1)⋮yt(τN)]=[11−e−λτ1λτ11−e−λτ1λτ1e−λτ1⋮⋮⋮11−e−λτNλτN1−e−λτNλτNe−λτN][β1,tβ2,tβ3,t]+[ε1,t⋮εN,t]
(8)(νtϵt)=N[(00),(Q00H)]
(9)E(β0⋅νt′)=0E(β0⋅ϵt′)=0

In order to facilitate estimation, it is assumed that both disturbances are orthogonal to each other and to the initial state β0.

In the Nelson-Siegel yield-macro model, the state-space model is expanded to include macroeconomic variables. Diebold, Rudebusch and Auroba (2006) expanded the state vector to include monetary policy, inflation and manufacturing capacity utilization. The inclusion of macroeconomic variables does not change the state space specifications Equation 4 and 5, but ˙t is redefined to include the new variables, so for example, βt = [β1,t β2,t β3,t α1,t α2,t, α3,t], where αj,t., represent macroeconomic variables.

Appendix II. Performance Evaluation of Nelson-Siegel Models

Appendix Figure 1.
Appendix Figure 1.

Performance Evaluation of the Yield Only NSM, 2012–17

(Percent)

Citation: IMF Staff Country Reports 2018, 064; 10.5089/9781484345481.002.A005

Source: Fund staff estimates
Appendix Figure 2.
Appendix Figure 2.

Term Structure of Interest Rates, 2012–17

(Percent)

Citation: IMF Staff Country Reports 2018, 064; 10.5089/9781484345481.002.A005

Source: Fund staff estimates

References

  • Alfonso, A., and M. Martins, 2010, “Level, Slope, Curvature of the Sovereign Yield Curve and Fiscal Behaviour,” Working Paper 1276, December (Frankfurt, Germany, the European Central Bank).

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  • Ang, A., and M. Piazzesi, 2003, “A no-arbitrage vector autoregression of term structure of dynamics with macroeconomic and latent variables,” Journal of Monetary Economics, 746–787.

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  • Basel for International Settlements, 2005. “Zero-coupon yield curves: technical documentation”, No 25, October (Basel, Switzerland: Basel for International Settlements).

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  • Diebold, F. X., and C. Li, 2006, “Forecasting the Term Structure of Government Bond Yields,” Journal of Econometrics, 130, 337–64.

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  • Diebold, F, G. Rudebusch, and B. Aruoba, 2005, “The Macroeconomy and the Yield Curve: a Dynamic Latent Factor Approach,” Journal of Econometrics, 310–338.

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  • Gasha, G., Y. He, C. Medeiros, M. Rodriguez, J. Salvati, and J. Yi, 2010, “On the Estimation of Term Structure Models and An Application to the United States,” Working Paper 10/258, November (Washington DC: International Monetary Fund).

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  • Christiansen, C., and J. Lund, 2002, “Revisiting the Shape of the Yield Curve: the Effect of Interest Rate Volatility”, Social Science Research Network.

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  • Litterman, R., and J. Scheinkman, 1991, “Common Factors Affecting Bond Returns”, Goldman Sachs Publications.

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  • Nelson, C. and A. Siegel, 1987, “Parsimonious Modeling of the Yield Curves”, The Journal of Business, 473–489, October.

1

Prepared by Miriam Tamene and Marwa Ibrahim, who provided excellent input with chart preparation.

2

The term structure of interest rates is the zero-coupon yield curve, which can be derived from gross redemption yield curve or par yield curve (¶10 – ¶11).

3

External financing was higher by $570 million in 2015 relative to 2012.

4

Liquidity captures the exit of foreign investors as local investors step-in to purchase their government bond holdings, thus keeping yields stable.

5

While such models are widely used (BIS 2005), most published analytical work use US Treasuries (bonds and bills).

6

Par yield rates were obtained from the Nigerian Debt Management Office for various maturities. These were used to construct par yield curves, by applying straight line interpolation between maturities. The choice for straight line interpolation was made after testing a sample data for 2012 that utilized the best polynomial fit. Because of small observation points the benefit between polynomial fit and straight-line interpolation was negligible. From the par yield curve, the discount factor for each maturity period was derived which were then used to derive the zero-coupon yield curves.

7

Analysis using money market rates, instead of monetary policy rate, found similar result. In fact, the contribution of money market (call) rates to the variance composition was less than MPR.

8

Appendix Figure 1 illustrates the performance of the model for each maturity.

9

Appendix Figure 2 shows the term structure of interest rates through time, from 2012 to 2017. It is worth noting that the consistent display of relatively flat yield curve is unusual, often the term structure of interest rates exhibits an upward sloping curve.

10

Please note that the slope of term structure is actually -β2,t that is, the software estimates it as the negative of the slope.

11

In addition, the Nigerian government securities market is relatively nascent compared to countries that employ these types of models to analyze the yield curve; Nigeria’s 10 years versus 30 years or more in many cases (the first Nigerian ten-year bond was issued in 2007). As a result, the period analyzed (and available data) could be relatively short to establish a strong link with macroeconomic factors.

12

FGN bonds’ liquidity is relatively poor, a rule of thumb liquidity indicator used by debt management practitioners suggest the ratio of turnover to outstanding amount should be in the range of 10X, versus, 1.17X for FGN bonds (and 16X for T-bills).

1

This section is mainly an extract from an internal Fund technical paper prepared by Ying He, Richard Munclinger and Jiangbo Yi. The paper describes the term structure models available in the Fund staff developed software. Seven models are available, of which five are based on Nelson -Siegel (which include versions that incorporate macroeconomic variables). In this chapter, the three factor Nelson-Siegel Model was applied, along with its yield-macro version.

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Cover IMF Staff Country Reports
Nigeria: Selected Issues
Author: International Monetary Fund. African Dept.
Volume/Issue:
Volume 2018: Issue 064
Publisher:
International Monetary Fund
ISBN:
9781484345481
ISSN:
1934-7685
Pages:
92
DOI:
https://doi.org/10.5089/9781484345481.002

Federal Government Domestic Yield Curves

(Yield rates, percent)

Observed Yields and Estimated Average Yield Curve

(Percent)

Estimates of the Yield Curve Loading Factors and Yield Factors

Estimates of Factors from Yield-Macro NSM

(Percent)

Results of Yield Macro NSM Impulse Response Functions

Performance Evaluation of the Yield Only NSM, 2012–17

(Percent)

Term Structure of Interest Rates, 2012–17

(Percent)