Yield Curve Shapes

YIELD CURVE SHAPES: A CASE STUDY IN KENYA

A MANAGEMENT RESEARCH PROJECT SUBMITTED IN PARTIAL

FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF THE

BACHELOR OF COMMERCE DEGREE, KENYATTA UNIVERSITY.

2015

DECLARATION

This research project report is our own original work and has never been presented for the award

of degree in a University.

This project report has been submitted with my approval as the University supervisor.

Sign:…………………………………………………Date: ……………………………

MR.

DEPARTMENT OF APPLIED SCIENCE

SCHOOL OF ECONOMICS

KENYATTA UNIVERSITY

DEDICATION

To our beloved parents.

ACKNOWLEDGEMENT

First we thank our almighty God who gave us strength to work, good health and for His continued

blessings and guidance in accomplishing this work.

Secondly, we are deeply indebted to our family and classmates for the moral and intellectual

support they offered us in one way or the other throughout our study period. Without their support,

encouragement and value for education, we could not have succeeded in our research study.

We also acknowledge the people whose assistance directly or indirectly facilitated the completion

of this proposal. We wish to extend special thanks to our supervisor: for his constructive guidance

during the preparation and completion of this thesis. He was of great importance and mentorship

and his insightful and constructive comments, ideas, points helped in clarifying the focus and

direction of our work. Without his encouragement, patience, support and strictness when needed,

we would never have completed this work.

Our appreciation also goes to the World Bankfor providing us with the data we needed for the

study of this project. Plus all those who in one way or the other offered their invaluable time and

ideas but we could not mention here because of space. We say thank you for the unlimited and

kindly support during our study and life.

TABLE OF CONTENTS

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

LIST OF TABLES viii

LIST OF FIGURES ix

LIST OF ABBREVIATIONS 1

ABSTRACT xi

CHAPTER ONE: INTRODUCTION 1

1.1 Background 1

1.2 Movement of Yield Curve 2

1.2.1 The Kenyan Scenario 4

1.3 Overview of Yield Curve Shapes 5

1.4 Patterns of Yield Curves and their Implications 6

1.4.1 Flat 7

1.4.2 Upward Sloping/Normal 8

1.4.3 Downward Sloping/Inverted 9

1.5 Problem Statement 11

1.6 Objectives of the Study 11

1.7 Significance of the Study 12

CHAPTER TWO: LITERATURE REVIEW 14

2.1 Introduction to Theoretical Review 14

2.2 Theories of the Term Structure of Interest Rates 14

2.2.1 Expectations Hypothesis 14

2.2.2 The Segmented Market Theory 17

2.2.3 The Liquidity Premium Theory 18

2.3 Theoretical Behavior of the Term Structure and Economic Activity 19

2.4 Empirical Review 20

2.5 Conclusion 23

CHAPTER THREE: RESEARCH METHODOLOGY 24

3.1 Introduction 24

3.2 Research Design 24

3.3 Target Population 24

3.4 Data Collection 25

3.5Data Analysis 25

CHAPTER FOUR: DATA ANALYSIS 29

4.1 Introduction 29

4.2 Descriptive Analysis 29

4.2.1 Descriptive Statistics 29

4.2.2 Yield Curve 31

4.2.3 Comparison Yield Curve and Real GDP Growth Rate 32

4.3 Reliability Test 33

4.4 Correlation Analysis 33

4.5 Regression Analysis 34

4.5 Discussion of the Findings 34

CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATIONS 39

5.1 Introduction 39

5.2 Summary and Discussions of the Study 39

5.3 Conclusion 40

5.4 Recommendation 41

5.5 Implications of the Study 41

5.6 Limitation of the Study 42

5.7 Suggestion for Further Research 42

APPENDICES 48

Appendix One: Data 48

LIST OF TABLES

Table 4.1: Data Description 29

Table 4.2: Descriptive Statistics 30

Table 4.3: Reliability Statistics 33

Table 4.4: Correlation Analysis 33

Table 4.5: Model Summary 34

Table 4.6: ANOVA 35

Table 4.7: Coefficients of the Regression Model 36

LIST OF FIGURES

Figure 1: Flat Yield Curve, (David, 2013) 7

Figure 2: Upward-sloping/Normal Yield Curve, (David, 2013) 9

Figure 3: Downward-sloping/Inverted Yield Curve (David, 2013) 10

Figure 4.4: Lagged and Un-lagged Yield Curve 31

Figure 4.5: Real GDP Growth Rate 32

LIST OF ABBREVIATIONS

ANOVA – Analysis of variance.

CBK – Central bank of Kenya.

CBR - Central bank rate.

GDP - Gross domestic product.

REHTS - Rational expectation hypothesis of term structure.

SPSS - Statistical package for social sciences.

T.BILL - Treasury bill.

U.S. - United states.

ABSTRACT

The idea of interest rates (yields) is the defining indicator of the global debt capital market and an

understanding of it is vital to the smooth running of an economy as a whole. All participants in the

market be it the issuers of capital, borrowers, investors or bank intermediaries will have a need to

estimate, interpret and understand interest rate yields phenomenon. Yield curve explains the

difference between short term and long term interest rates. Normally because short term rates are

lower than longer term ones such that a graph plotting interest rates as a function of maturity

distinct rises as maturity lengthens. Factors that play a role in causing long term yields to move up

and down include inflation, economic growth, supply and demand factors and investor attitude

toward risk. The focus of this research was on the phenomenon of the term spread in forecasting

economic activity (recession/boom) in Kenya. It looked at two objectives which were to establish

the various patterns of the yield curve over time in Kenya and to determine the ability of yield

curve to predict economic growth and recessions. Causal research design was adopted for this

study. The study targeted real GDP growth rate and yield spread for 8 years ranging 2006 to 2013.

Secondary data was used for the purpose of this study. Data was collected from World Bank data

base. Descriptive statistics such as mean and standard deviation was used to describe the variables.

Regression analysis was used to describe the relationship between variables and determine the

ability of yield curve to predict economic growth and recessions. The study found that the shape

of yield curve indicates the cumulative priorities of all lenders relative to a particular borrower.

Lenders usually are concerned about a potential default so they offer long term loans for higher

interest rates than they offer for short term loans. It found that Lagged Yield Spread was seen

having a weak positive association (0.097) with Real GDP growth rate which means that lagged

yield spread cannot effectively predict real GDP growth rate for the next period. It found that real

GDP growth has a significant relationship with Lagged Yield Spread. The study recommends that

the government should take the findings of the study more seriously so as to minimize the impacts

of recessions through policy decisions. It finally recommended that studies be done on other

models based on Nelson & Siegel.

CHAPTER ONE: INTRODUCTION

1.1 Background

The idea of interest rates (yields) is the defining indicator of the global debt capital market and an

understanding of it is vital to the smooth running of an economy as a whole. All participants in the

market be it the issuers of capital, borrowers, investors or bank intermediaries will have a need to

estimate, interpret and understand interest rate yields phenomenon. Fund managers that accurately

predict the shape, nature and directions of yields will consistently outperform those that do not.

Mishkin (2010) defined yield curve as a plot of yields on bonds with differing terms to maturity

but the same risk, liquidity and the tax consideration. The term yield refers to the annualized

percentage increase in the value of a debt instrument in the context of debt market (Yield Curve,

2011, June 12). The Kenya government securities yield curve is derived from the relation between

interest rates of treasury bill/bonds and the time to maturity of bonds of different tenors.

Yield curve explains the difference between short term and long term interest rates. Normally

because short term rates are lower than longer term ones such that a graph plotting interest rates

as a function of maturity distinct rises as maturity lengthens. But now and then, the difference

begins to flatten and eventually, short term rates will rise above long term rates at which point the

yield curve is said to be inverted (Hulbert, 2014). The Kenyan yield curve is currently the flattest

it’s been since 2009 when it was emerging from a recession in the same year (Hulbert, 2014). A

flattening yield curve doesn’t appear to be that worrisome from a macroeconomic point of view,

but it will undoubtedly have a bigger impact on certain industries like in financial sector where

flattening yield curve signals disappointing net interest incomes and bank margins.

The shape of yield curve indicates the cumulative priorities of all lenders relative to a particular

borrower (Rjwilmsi, 2002). Lenders usually are concerned about a potential default so they offer

long term loans for higher interest rates than they offer for short term loans. Occasionally when

lenders are seeking long term debt contracts more aggressively than short term debt contract, yield

curve inverts with interest rates (yields) being lower for the longer periods of repayment so that

lenders can attract long term borrowing. This would be the case in the event that the suppliers of

funds expected that future rates would be even lower. In that case, offering low rates for the long

term bonds is seen as a way of cashing out and securing better rates now than is expected in the

long term.

Yield curves are usually upward sloping asymptotically (Rjwilmsi, 2002). Two common

explanations for upward sloping yield curve are; markets are anticipating a rise in interest rates.

Investors who are willing to lock their money in now need to be compensated for the anticipated

rise in the rate thus the higher interest rate on long term investments. Another explanation is that

longer maturities entail greater risk for the lender. A risk premium is needed by the market since

at longer durations there is more uncertainty and a greater chance of catastrophic events that impact

the investment (Rjwilmsi, 2002). Explanations depend on the notion that economy faces more

uncertainties in the distant future than in the near term. If the market expects more volatility in the

future even if interest rates are anticipated to decline, the increase in the risk premium can influence

the spread and cause an increasing yield.

1.2 Movement of Yield Curve

Factors that play a role in causing long term yields to move up and down include inflation,

economic growth, supply and demand factors and investor attitude toward risk. Generally, slower

growth, low inflation and depressed risk attitude will help the performance of shorter term bonds

and cause yields to fall and vice versa (Thomas, 2007).Changes in investor expectation can also

change the slope of yield curve. Signals provided by yield curves maybe very sensitive to changes

in financial market conditions. The precise effect of these changes on yield curve will depend on

whether they stem from technical factors or economic fundamentals. For example because

different maturities of fixed income securities appeal to different clientele, a permanent shift in the

relative importance of clientele could produce permanent shifts in the slope of yield curve (Arturo

et al, 2006).

Yield curves help describe the relationship among short term, medium and long term rates at a

given point in time because it is the starting point for pricing fixed income securities and other

financial assets. The normal yield curve depicts a line that ascends from lower interest rates on

shorter term bonds to higher interest rates on longer term bonds. Researchers have studied the yield

curve statistically and have found that shift or changes in the shape of yield curve are attributable

to a few unobservable factors (Dal et al, 2000).

Wu (2001) examined the relationship between Federal Reserve monetary policy surprises and the

movement of the slope factor of the yield curve in the U.S. after 1982. He found that the Fed

Reserve monetary policy actions exert a strong but short lived influence on the slope factor. They

explain 80%-90% of the movement of slope factor but such influence usually dissipates in one-

two months. Again monetary policy surprises don’t induce significant changes in the level factor

implying that during this period the Fed Reserve affected the yield curve primarily through

changing its slope.

Ang et al (2001) examines the influence of inflation and real economic activity on the yield curve

in an asset pricing framework, in their model bond yield are determined not only by the three

unobservable factors, level, slope and curvature but also by an inflation measure and a real activity

measure. They find that incorporating inflation and real activity into the model is useful in

forecasting the yield curve movement. Inflation and real activity help explain the most or short

term bond yield and medium term bond yield up to maturity of one year but most of long term

bond yield are still accounted for by the unobservable factors. Therefore they conclude that

macroeconomic variables can’t substantially shift the level of yield curve.

A monetary policy tightening generates high nominal short term interest rates initially but because

of its anti-inflationary effects these rates quickly fall back since long term rates embed expectation

of this behavior of short term rates they increase by only a small amount. As a result, the slope of

yield curve declines when contractionary monetary policy shocks occur. After all it is difficult to

believe that the structure of macroeconomic has little effect on long term interest rates or on the

level of the yield curve since long term nominal interest rates are the sum of expected long run

inflation and long term real interest rates (David, 2013).

1.2.1 The Kenyan Scenario

Kenya government securities yield curve is derived from the relation between interest rates of

treasury bills/bonds and the time to maturity of bonds of different tenors. Interest rates of Treasury

bills are the prevailing weighted averages rates for 91 day, 182 day and 364 day papers while

interest rates for Treasury bond are the average prevailing secondary market yield for bonds based

on years to maturity. CBK has attributed the recent sharp fall in Kenya shilling to speculative

activity. However, our opinion is that the recent moves on both the interest rates front and the

currency are reflective of the monetary policy followed by the CBK specifically of keeping interest

rates too low for too long. The reason for the CBK’s cautious stance is to promote economic growth

as well as to guard against any macroeconomic instability (Irungu, 2014, July 8).

Whereas, market interest rates (T-bill and bond yields) have now corrected to the right levels, the

policy rates (CBR) remain too low at 6.25%. The last time inflation was at these levels in early

2009 when the CBR was at 8.25%, 200 basis points higher than the current levels. The only interest

rate directly linked to the CBR was the rate at which commercial banks borrow from the CBK on

overnight basis. Since overnight borrowing rates have been rising on account of this, the CBK de-

linked the overnight borrowing rate of commercial banks from the CBR on 29

June 2011 and set

a rate of 8% for the overnight window. It led to a temporary cap on the exchange rate of the shilling

but more importantly limited the usefulness of the CBR.

1.3 Overview of Yield Curve Shapes

The term structure of interest rates refers to the relationship between the yields of bonds with

different terms to maturity. When interest rates of such bonds are plotted against their terms, it

represents the yield curve. The yield curve is also defined as the plot of yields on bonds with

different terms to maturity with the same risk profile, liquidity and tax considerations and it

describes the term structure of interest rates for particular types of bonds, such as long-term

government bonds of 10 years and over (Mishkin, 2010). Economists and investors believe that

the shape of the yield curve reflects the market’s future expectation for interest rates and conditions

for monetary policy. The yield curve can be classified as upward sloping, flat or downward sloping

(Mishkin, 2010).

When the yield curve is upward-sloping, the short-term interest rates, such as 91-day Treasury bill

rate, are below the long-term rates, such as long-term government bond 10 years and over. When

yield curves are flat, the short-term interest rates and long-term interest rates are the same. When

the yield curves are downward-sloping, the long-term rates are below the short-term rates. Mishkin

(2010) states that, besides explaining different shapes of the yield curves, a good theory of the term

structure of interest rates must explain the following three important empirical facts:

i. Interest rates on bonds of different maturities move together over time.

ii. When short-term interest rates are low, yield curves are more likely to have an upward

slope; when short-term interest rates are high, yield curves are likely to slope forward and

be inverted.

iii. Yield curves usually slope upward.

Economists including Hicks (1946) and Mishkin (1999) have developed theories to explain the

empirical observations about the shape of the yield curve; the three main theories being the

expectations hypothesis, the segmented market theory and the liquidity premium theory. The

fourth theory, the preferred habitat theory, is closely linked to the segmented market theory. These

theories are explained further in chapter two.

1.4 Patterns of Yield Curves and their Implications

Markin et al (1986) argued that the persistence of change in the federal funds rate engineered by

the Federal Reserve helps explain why the yield curve from 3-6 months has had negligible

forecasting power. It is crucial that only bonds carrying the same risk are plotted on the same yield

curve. The most commonly used are treasury securities due to their risk-free nature and are as such

a benchmark for working out yield on other types of debt.

1.4.1 Flat

The flat yield curve is observed when all maturities have similar yields and sends signal of

uncertainty in the economy. To become inverted yield curves must pass through a period where

long term yields are the same as short term rates and when that happens, the shape will appear to

be flat or more commonly a little raised in the middle (smartmoney.com). It could also imply that

interest rates are expected to remain constant and gives a consensus that future yields will remain

the same as current yields. Thus there is no difference between short-term and long-term yield

rates.

Figure 1: Flat Yield Curve, (David, 2013)

A flat yield curve is a sign that investors are not sure about the economic growth and inflation in

future.

1.4.2 Upward Sloping/Normal

The normal yield curve depicts a curve whereby the yield rises as maturity lengthens and reflects

investor expectation for the economy to grow in the future and importantly for the growth to be

associated with a greater expectation that inflation will rise in the future rather than fall (Hulbert,

2014). This expectation that inflation will rise makes the CBK tighten monetary policy by raising

short term interest rates in future to slow economic growth and dampen inflationary pressure. It

also creates a risk premium associated with the uncertainty about the future rate of inflation and

the risk this possesses to the future value of cash flows. Since the rate of inflation is expected to

increase the risk on the value of money becomes such that a shilling today may be worth much

less tomorrow. Lenders price these risks into the yield curve by demanding higher yields for

maturities further into the future while borrowers profit from passage of time since yields decrease

as bonds get closer to maturity.

Ordinarily, short term bonds carry lower yields to reflect the fact that investor money is under less

risk. The longer you tie up your cash the theory goes, the more you should be rewarded for the risk

you are taking (Hulbert, 2014). Normal yield curve therefore slopes gently upwards as maturities

lengthen and yields rise from time to time. However the curve twists itself into a few recognizable

shapes each of which signals a crucial but different turning point in the economy. When those

shapes appear it’s often time to alter your assumptions about economic activity by using yield

curves. Investors who risk their money for longer expect to get a bigger reward in form of higher

interest than those who risk their money for shorter time periods and therefore as maturities

lengthen, interest rates get progressively higher and curve goes up.

According to Shapiro (2005), a normal yield curve implies that forward rate is higher than current

spot rate. Generally, an upward sloping yield curve is an indicator that investors expect firm future

economic growth accompanied by high inflation and therefore high interest rates

Figure 2: Upward-sloping/Normal Yield Curve, (David, 2013)

1.4.3 Downward Sloping/Inverted

The inverted yield curve occurs when long term yields fall below short term yields and under

unusual circumstances, long term investors will settle for lower yields now if they think the

economy will slow/decline in the future. Campbell (1986) showed that an inverted yield curve

accurately forecast U.S. recession. New York Federal Reserve regards it as a valuable forecasting

tool in predicting recession two to six quarters ahead (Joseph et al, 1996). It also implies that the

market believes inflation will remain lower than current levels because even if there is a recession,

a low bond yield will still be offset by low inflation.

It is like a paradox because why would long-term investors settle for lower yields while short term

investors take so much less risk? The reason to this is because long term investors will settle for

lower yields now if they think rates and the economy are going even lower in the future. They are

rare to occur and if they occur they are followed by economic slowdown or recession and lower

interest rates.

This curve implies that interest rates are expected to fall. Shapiro (2005) noted that a downward

sloping yield curve could also signal that forward rates are lower than current spot rates. This

downward sloping yield curve is a fairly accurate indicator of an expectation of slow future

economic growth by investors which is accompanied by low inflation rates and therefore low

interest rates.

Figure 3: Downward-sloping/Inverted Yield Curve (David, 2013)

1.5 Problem Statement

Predicative capabilities are valued skills in any financial market. The yield curve, as represented

by the spread between long-term and short-term interest rates has gained prominence in recent

years as a useful tool for forecasting future economic activity and the likelihood of recession or

boom (Joseph, 2006). Several studies like Moolman (2002) and Khomo et al (2007) have

demonstrated that the slope of the yield curve or the term spread, as represented by the difference

between yields on long-term and short-term treasury securities, is a useful indicator for future

economic activity and thus a good leading economic indicator. The inversion of the yield curve,

where short-term interest rates rise above long-term interest rates, has in the past provided a

positive statistical relationship with the odds of a recession ahead and is thus widely regarded as a

harbinger for an economic downturn. Such evidence is extensively documented in the United

States and other developed countries. Inverted curves have been among the most reliable predictor

of recessions in the modern economic era (Arturo et al, 1996).

Unlike the South African scenario where Moolman (2002) and Khomo et al (2007) had

foundations for their research laid down by the pioneer Nel (1996), there is a considerably distinct

lack of similar research for the Kenyan scenario. Our paper aims to fill that crucial gap. Less

attention has been paid to the theoretical reasons explaining the yield curve’s predictive power.

The focus of this research was on the phenomenon of the term spread in forecasting economic

activity (recession/boom) in Kenya.

1.6 Objectives of the Study

i. To establish the various patterns of the yield curve over time in Kenya.

ii. To determine the ability of yield curve to predict economic growth and recessions.

1.7 Significance of the Study

This research will help indicate the current tradeoff between maturity and yield confronting the

investor. If investor wishes to alter the maturity of a portfolio, the yield curve indicate what gain

or loss in rate of return maybe expected for each change in portfolio average maturity. With an

upward sloping curve, investor may be able to increase a bond portfolio expected annual yield by

extending the portfolio average maturity. However the prices of long term bond are more volatile

creating greater risk of capital loss. Moreover long term instruments tend to be less liquid and less

marketable and therefore investors must weigh the gain in yield from extending its maturity against

added price, liquidity and risk.

The study will also help show if a security’s rate of return lies above or below the yield curve. The

former indicates to investors that a particular security is temporarily underpriced relative to other

securities of the same maturity. This is a buy signal which investors will take advantage of hence

driving the price of the purchased security upward and its yield back down toward the yield curve.

If rate of return is below the yield curve, this indicates an overpriced security and investors will

sell it, pushing its price down and its yield back up toward the curve.

To banks, this study will help indicate what the shapes of yield curve reflect to these financial

intermediaries. A rising curve is generally favorable for the institution because they borrow most

of their funds by selling short term deposits and lend a major portion of these funds long term. The

more steeply the curve slopes upward the wider the spread between borrowing and lending rates

the greater the potential profit for financial intermediary earnings.

However if the curve starts to flatten out or slope downward, this should serve as a warning signal

to portfolio managers of these institutions because it squeezes the earnings of banks. If upward

sloping yield curve start to flatten out, managers try to lock in relatively cheap sources of funds by

getting long term commitment from depositors and other funds supplying customers.

CHAPTER TWO: LITERATURE REVIEW

2.1 Introduction to Theoretical Review

The aim of this chapter is to provide an explanation of the theories underpinning the term structure

of interest rates. By offering a complete schedule of interest rates across time, the term structure

embodies the market’s anticipation of future events. An explanation of term structure gives us a

way to extract this information and to predict how changes in the underlying variables affect the

yield curve. This chapter also addresses the empirical findings of the previous literature on the

term structure with regard to its predictive ability of economic activities. This is important since

such a review provides the background information about the topic, potential problems that may

arise in the calculation of the yield curve, and how the yield curve can be used to determine the

economy’s future direction.

2.2 Theories of the Term Structure of Interest Rates

2.2.1 Expectations Hypothesis

The expectations hypothesis of the term structure states that the interest rate on a long-term bond

will equal an average of the short-term interest rates that is expected to occur over the life of the

long-term bond (Mishkin, 1999). For example, if people expect that short-term interest rates will

be 10% on average over the coming five years, the prediction is that the interest rate on bonds with

five years yield to maturity will also be 10%. The key assumptions behind this hypothesis are that

short-term and long-term securities can be treated as perfect substitutes, investors are risk neutral

and the shape of the yield curve is determined by investors’ expectations of future interest rates

and future inflation (Michaelsen, 1965).

To see how the assumption that securities with different maturities are perfect substitutes leads to

the expectations hypothesis, the following two investment strategies are considered: buy a one-

year bond, hold it for one year, and reinvest the proceeds in another one-year bond, one year from

now. The alternative would be to buy a two year bond and hold it for two years. According to the

expectations hypothesis, both strategies should yield exactly the same result, since investors are

indifferent to bonds of different maturities, and bonds are perfect substitutes. The interest rate on

the two-year bond must equal the average of the two one-year interest rates. For example, assume

the current interest rate on the one-year bond is 7% and an investor’s expectation is that the interest

rate on the one-year bond next year will be 10%. If the investor pursues the strategy of buying the

two one-year bonds, the expected return over the two years will equal 8.5%, which is (7%+10%)/2.

The investor will be willing to hold the two-year bond only if the expected return per year of the

two-year bond is equal to or greater than 8.5%. In other words, the interest rate on the two-year

bond must equal 8.5%, the average interest on the two one-year bonds.

It is evident that the rising trend in expected short-term interest rates produces an upward-sloping

yield curve (positive yield curve) along which interest rates rise as maturity lengthens. It is also

clear from the numerical example that when the yield curve is upward-sloping, the short-term

interest rates are expected to rise in the future. In the event that long-term rates are currently above

the short-term rates, the average of future short-term rates is expected to rise.

When the yield curve slopes downward, the average of future short-term interest rates is expected

to be below the current short-term rates, implying that short-term interest rates are expected to fall,

on average, in the future (Mishkin, 1999). Only when the yield curve is flat does the expectations

theory suggest that short-term interest rates are not expected to change, on average, in the future

(Howells et al, 2002).

The expectations hypothesis explains why interest rates of different maturities tend to move

together over time. Historically, an immediate increase in short-term interest rates tends to be

higher in the future. As such, a rise in short-term interest rates will raise people’s expectations of

future short-term rates. In this theory, long-term rates are the average of expected future short-term

rates; therefore a rise in short-term rates will also raise long-term rates, causing short-term rates

and long-term rates to move together over time (Howells et al, 2002). The expectations theory also

explains why, when interest rates are low, yield curves are usually upward sloping, and when

interest rates are high, yield curves are usually downward sloping. When short-term interest rates

are low, economists and market participants generally expect them to rise to some normal level in

the future. The average of future expected short-term rates will be above current short-term rates,

and as such the yield curve would have a positive slope. On the other hand, if the short-term interest

rates are high, the expectation will be that they will come down. Therefore long-term rates would

drop below short-term rates. This is because the average of expected future short-term rates would

be below current short-term rates and the yield curve would slope downward and become inverted.

The expectations hypothesis explains another important fact about the relationship between the

short-term and long-term interest rates: interest rates are mean-reverting. They tend to return to

their normal levels if they are unusually high or low, and hover around that normal level (Howells

et al, 2002).

This implies that short-term interest rates will have more volatility than long-term rates: short-term

rates represent an average of future short-term rates (Mishkin, 1999). The shortcoming of the

expectations hypothesis is that it cannot explain why long-term yields are normally higher than

short-term yields, in other words, why the yield curve is usually upward sloping. If the short-term

rates are low now, they are expected to go up in the future. In that case the yield curve will be

upward sloping. On the other hand, if the short rates are high now, they are expected to go down

and in that case the yield curve will be downward sloping. Now, at a given point in time, short-

term yields are as likely to be high as they are to be low. Therefore, they are as likely to go up as

they are to go down in the future. That means that the expectations theory predicts that the yield

curves are as likely to be upward sloping as they are to be downward sloping.

The critique of the expectations is that it cannot explain why the yield curve is usually upward

sloping. The key assumptions behind this hypothesis are that short-term and long-term securities

can be treated as perfect substitutes do not hold in all situations. The theory neglects the risks

inherent in investing in bonds.

2.2.2 The Segmented Market Theory

Howells et al, (1998) assert that individuals have strong maturity preferences and those bonds of

different maturities trade in separate and distinct markets. The demand and supply of bonds of a

particular maturity are supposedly minimally affected by bond prices of neighboring maturities. It

is clear that there is now a limit to how far one can go in maintaining that bonds of close maturities

will not be close substitutes. This theory holds that investors have specific investment preferences

that are ultimately dictated by the nature of their liabilities (Howells et al, 1998).

For example, commercial banks, whose liabilities are mainly short-term ones, tend to invest in

short-term securities, not to expose to the risk of interest increase, with a consequent fall in the

market value of the bonds when liabilities are due. By contrast, life insurance companies issue

many long-term contracts, and also tend to hold longer-term bonds. Thus, spot rates for any

maturity should exclusively depend on the relative demand for and supply of securities with that

particular maturity. (Irturk, 2006)

This segmented market theory suggests that the segmented market behavior of lenders and

borrowers basically determine the shape of the yield curve. A market segmentation theory implies

that the rate of interest for a particular maturity is determined solely by demand and supply factors

for that maturity, with no reference to conditions for other maturities. Borrowers and lenders have

rigid maturity preferences and do not deviate from those preferences no matter how attractive the

yields are for other maturities. The inverted yield curve would signify a greater demand and smaller

supply for short-term securities or a greater supply of long-term debt and lesser demand for long-

term securities (Irturk, 2006). It does not, however, explain why interest rates tend to move

together over time. It also does not offer any insights into why yield curves typically slope upward

when interest rates are very low and slope downward when interest rates are very high.

The segmentation theory has been criticized on the following grounds; it assumes that there is no

substitutability between markets i.e. it assumes that markets operate independently. This is not true

because the “market walls” are porous and participants can move freely.

2.2.3 The Liquidity Premium Theory

The Liquidity Premium theory advanced by Hicks (1946), states that the interest rate on a long-

term bond will equal an average of short-term interest rates expected to occur over the life of the

long-term bond, plus a term premium increasing with maturity. It concurs with expectations theory

in that it gives the same importance to the expected future spot rates but places more emphasis on

the effects of the risk preference of market participants. It asserts that risk aversion will cause long

term rates to be systematically greater than short-term rates. This amount is usually stated as an

amount increasing with maturity. It can be said that longer term interest rates are not only reflective

of lenders future assumptions for the interest rates, but also include a premium for holding these

longer term bonds. The concept of compensation of investors for the added risk of having their

money tied up for a longer period is introduced (Irturk, 2006). That is, investors must be paid an

extra return in the form of an interest rate premium to encourage them to invest in long-term

securities and compensate them for the increased risk (Van Zyl et al 2003)

An increase in the riskiness of bonds reduces the demand for bonds. As a result, the bond prices

go down and the interest rates go up. Alternatively, according to the liquidity preference

framework, an increase in the riskiness of bonds raises the demand for money, resulting in an

increase in the interest rate (Wei, 2014). The liquidity premium theory’s main assumption is that

bonds of different maturities are substitutes, but not perfect substitutes, which means that the

expected return on one bond does influence the expected return on a bond of a different maturity.

The theory cannot explain flat and inverted yield curves and is only capable of explaining the

normal yield curve i.e. upward sloping yield curve. It cannot explain that yields of different terms

move together, because the supply and demand of the two markets are independent. In this theory,

term premiums do not need to be positive and an increasing function to maturity. (Irturk, 2006)

2.3 Theoretical Behavior of the Term Structure and Economic Activity

Interest rates are strongly affected by changes in the business cycle and often move in the same

direction that the business cycle is moving. According to Rose (2003), market interest rates tend

to rise when the economy is expanding toward its peak or highest point, and fall when the economy

is contracting toward the trough of a recession or its lowest point. Therefore an upward-sloping

yield curve suggests that short-term interest rates are expected to rise. An inverted yield curve

would imply short-term interest rates are expected to fall and a flat yield curve suggests that the

short-term and long-term interest rates are the same. This means that rates are not expected to

change in the future. If the term structure of interest rates reflects in part the collective inflation

expectations or recession, it is intuitive to believe that it must also reflect market participants’

assessments of future real economic activity (Estrella et al, 1991).

In the US since the 1960s, yield curve inversions (as measured by the difference between the ten-

year and three-month Treasury rates) have preceded every recession on record (Estrella, 2005).

Since the interest rate cycles precede the business cycles, it is assumed that a positively sloped

yield curve is associated with economic expansion, hence growth in real economic activity.

2.4 Empirical Review

According to Joseph et al (1996), in reference to the Rational Expectation Hypothesis of the Term

Structure (REHTS), long term rates should reflect market expectation for the average level of

future short term rates. As such, the rates spreads that form the basis of forward rates should predict

future changes in the spot rate. In the purest interpretation of REHTS, there are no term premiums

in forward rates. Changes in the slope of yield curve are equivalent to what the market expects

interest rates to be at a particular point in the future. This term premium is the different between

the forward rate and the corresponding expected spot rate. Unfortunately, neither expected interest

rates changes nor term premiums are directly observable in the market.

The standard test of expectation theory uses a long term rate with a maturity equal to twice that of

the short rate. Studies by Shiller et al (1983) reported coefficients for the forward rate premium

that were not significantly different from zero indicating (using standard regression method) that

the yield curve from 3-6 month has had negligible power to forecast changes in 3 month rate. Two

concepts central to the test of expectation theory reviewed below are the forward and term

premium rates. For example an investor can purchase a 6month T-bill now or purchase a 3 month

bill now and reinvest his funds 3 month from now in another 3 month bill. The forward rate is the

hypothetical rate on the 3 month bill 3 month in the future that equalizes the rate of return from

the two options given the current 3-6 month rates.

By using Campbell’s (1986) model, the slope of the term structure correctly predicted the five

cyclical turnings points over the last 40 years. It has to be said that many more expensive

econometric models cannot predict these turning points. This model is described in Campbell’s

(1989) dissertation. Basically, this interest rate based model is very simple. It has only two

components: slope of the term structure (the long term – short term yield spread) and measure of

the average propensity to hedge in the economy.

Much closer to home, Khomo et al (2007) have done a study on similar properties of the yield

curve as a predictive tool. They sought to utilize Estrella et al’s (1991) probit and modified probit

models to assess the yield curve’s ability to predict recession in South Africa. The study also

sought to establish the source of the yield curve’s forecasting abilities. Their results confirmed its

ability to act as a simple tool for forecasting economic conditions of recession by policymakers

and investors in the South African market. It has left open the possibility of testing for the same in

the Kenyan market to assess whether or not the yield curve can be manipulated in the same way

to act as a predictor for both booms and recessions.

Similarly, Moolman (2002) used a probit model to evaluate the term structure or yield spread as a

predictor of turning points in the South African business cycle. The yield spread was defined as

the difference between the yield on 10-year government bonds and 3-month bankers’ acceptances.

The results indicated that the term structure or yield spread successfully predicts turning points of

business cycle two quarters ahead. The negative empirical relationship between the term structure

of interest rates and the business cycle conforms to economic theory. If the yield on 10-year

government bonds is currently 4% or more below the yield on 3-month bankers’ acceptances, the

probability that the economy will be in a recession two quarters ahead is 99%. On the other hand,

if the yield on 10-year government bonds is currently 4% above the yield on 3-month bankers’

acceptances, the probability that the economy will be in a recession two quarters ahead is 15.4%.

A yield spread greater than 1.5694% predicts that the economy is more likely to be in a recession

than in an expansion two quarters ahead.

First of all, we need to learn the link between the term structure and economic growth to especially

understand how to predict business cycle turning points with the term structure. Basically, if we

consider the basic intuition of the model, we can see that interest rates are ex ante measures and

represents expected future payoffs. Besides, if market rates are set, we can assume that

expectations of future economic growth influence this process.

This basic intuition is described using an example in the paper. If we assume that investors want

to insure their economic well being, thus most of the investors would prefer a reasonably stable

level of income rather than very high income in one stage of the business cycle and very low

income in another stage. Besides the investors side, assume that the economy is currently in a

growth stage and the general agreement is for a slowdown or recession during the next year.Here,

this desire to hedge will lead consumers to purchase a financial instrument which will deliver

payoffs in the slowdown, such as a one year discount bond. At this point, if many consumers buy

the one-year bond, then the price of the security will increase and the yield to maturity will

decrease. Besides, the consumers may sell their shorter term assets to finance the purchase of the

one year bonds. Thus, this selling pressure will drive down the price of the short term instrument,

besides raise its yield. (Irturk, 2006)

After understanding the assumptions, if a recession is expected under these circumstances, we will

see long rates decrease and short rates will increase. Thus, the yield curve or term structure will

become flat or inverted. As a result, we can say that the shape of the term structure of interest rates

provides a forecast of future economic growth.

2.5 Conclusion

Employing the term structure of interest rates is, indeed, useful for implementing monetary

policies. The Central Bank should also keep an eye on supply and demand for Treasury Bonds,

such as evenly distributed maturity in their issuance and government funds portfolios as the risk

premiums due to the continued imbalance of supply and demand increase the volatility of interest

rates. This in turn constraints the effectiveness of monetary policies (Lim, 2005).

Caution must be exercised as Fernandez et al (2011), point out that “no standard theoretical

approach exists to relate the yield curve to forecasts of future economic activity….and the curve’s

close association with subsequent changes in production, consumption, investment and other

components of real GDP remains purely empirical”. The ability of the yield curve to predict

recession is not necessarily policy invariant and there is no guarantee its performance will continue

unaffected in the current global economic phase and the near future.

CHAPTER THREE: RESEARCH METHODOLOGY

3.1 Introduction

This chapter identifies the procedure and techniques that will be used in the collection, processing

and analysis of data. Specifically the following subsections are included; Research design, target

population, sample design, data collection instruments, data collection procedures and finally data

analysis.

3.2 Research Design

Research design refers to the plan structure and strategy of investigation concerned so as to obtain

answers to research questions and control variance (Mugenda, 2003). Causal research design was

adopted for this study, since it seeks to establish the relationship between real GDP growth and

lagged yield spread. It explores the effect of one variable on another, measuring what impact a

specific change had on existing norms hence is useful in hypothesis testing (Kotler et al., 2006).

The design was preferred because it accommodates correlational studies that seek to investigate

the relationship between the research variables.

3.3 Target Population

According to Cooper and Schindler,(2003) a population element is the amount of quantitative data

on which measurements are being taken. The target population of this study is the interest rates of

the Central Bank of Kenya. The study targeted real GDP growth rate and yield spread for 8 years

ranging 2006 to 2013.The study period was chosen because it contained the latest data that will

show how lagged yield spread determines real GDP growth rate today. The lagging was done in

order to determine the yield from the previous period. Data was lagged one year period ahead.

3.4 Data Collection

Secondary data was used for the purpose of this study. Data was collected from World Bank data

base. Annual data obtained was from 2006 to 2013 which was the study period. Specifically, real

GDP figures were collected from the Kenya National Bureau of Statistics. This was to be used as

the dependent variable for our study. Interest rates were obtained from the CBKs annual reports

and were to be used in the calculation of the yield spreads.

3.5 Data Analysis

The collected data from World Bank was entered into the Statistical Package for Social Sciences

(SPSS) version 20 for analysis. Descriptive statistics such as mean and standard deviation was

used to describe the variables.Regression analysis was used to describe the relationship between

variables and determine the ability of yield curve to predict economic growth and recessions.

Regression analysis was done using the analytical model below;

Yi=𝛽

𝑜

+ 𝛽

𝑋

+ ε

Where;

Y = Real GDP growth

= Lagged Yield Spread

constant term of the model

Co-efficient of the model

є = error term.

Yi = Real GDP growth. GDP is the standardmeasure of aggregate economic activity. GDP Growth-

is the percentage change between the GDP amounts of two periods. A positive amount indicate an

economic growth while a negative amount indicate economic decline.Our research model is

designed to predictreal GDP growth into the futurebased on the current yield spread. We achieve

this by running a series of regressions using real GDPgrowth and the lagged interest rate spread.

We regressreal GDP growth against the index of leadingeconomic indicators like bond and

mortgage interest rates, stock futures markets and the yield curve. Thisenables us to make a

comparison with other simple forecasting techniques.

= Lagged Yield Spread one year ahead. It is the difference between the quoted rates of return

on two different investments usually of different credit quality. There are several measures of yield

spread like the z-spread and option –adjusted spread but the former is mostly preferred since it

uses the entire yield curve to value individual cash flows of bonds and therefore provide a more

realistic valuation than an interpolated yield curve which is based on a single point of

curve.Increasing yield spreads are a leading indicator for expansions and decreasingyield spreads

are a leading indicator for recessions. According to the expectationshypothesis the yield spread is

equal to the expected future short rate and aterm premium. Falling yield spreads before recessions

are caused by both factors (fall in aggregate demand of products and services and rise in interest

rates), where the decreasing expectation to future short rates is more important (Hamilton et al,

2002). Yield spreads predict future recessions based upon monetary policy. Tight monetary policy

is usedto stabilize output growth and causes the yield spread to decrease. The powerof the yield

spread as a leading indicator depends on the monetary authority’s behavior (Estrella, 2005).

0 =

constant term of the model.

1 =

Co-efficient of the model. It measures the effect of the lagged yield spread on the real GDP

growth rate. It also allows us to answer the research question "is the predictor X

related to the

response Yi?" If the confidence interval for β

contains 0, then we conclude that there is no

evidence of a relationship between the predictorX

and the response Yi in the population. On the

other hand, if the confidence interval for β

does not contain 0, then we conclude that there is

evidence of a relationship between the predictor X

and the response Yi in the population.

є = error term. It is the amount at which the equation may differ during empirical analysis.The

error term is also known as the residual or the remainder term. When the actual GDP differs from

the GDP in the model during an empirical test, then the error term will not be equal to 0, which

means there are other factors that influence it.

We chose to conduct a reliability test so as to measure reliability of our data by administering the

same test twice over a period of time to each data set. The scores were then correlated in order to

evaluate the test for stability over time.Cronbach's alpha is a measure of internal consistency, that

is, how closely related a set of data is as a group. It is considered to be a measure of scale reliability.

A "high" value for alpha does not imply that the measure is uni-dimensional. The Cronbach's alpha

is therefore a coefficient of reliability or consistency

Correlation analysis contributed to our understanding of economic behavior by aiding in locating

the critically important variables on which others depend. The effect of correlation is to reduce the

range of uncertainty. The prediction based on correlation analysis is likely to be more variable and

near to reality.

Once sure that the two variables of real GDP growth and yield spread were closely related, we

estimated the value of one variable given the value of another using regression analysis.The

primary result of a regression analysis is a set of estimates of the regression coefficients.The study

used Ordinary Least Squares (OLS) regression model. This model was used to describe the

relationship between variables and determine the ability of yield curve to predict economic growth

and recessions.

We used OLS-regression as the method of choice since most international studies (Estrella and

Hardouvelis, 1991; Shiller et al, 1983; and Campbell’s, 1986) have used it, and thus making

comparisons between Kenyan and international results quite straightforward. The real change in

GDP tries to answer the question of how much we can expect the economy grow on a yearly basis

over the next, say, one or two years given the contemporaneous lagged yield spread.

Lagged yield spread was used over the un-lagged yield spread because it showed data for the

previous period as compared to current period.

CHAPTER FOUR: DATA ANALYSIS

4.1 Introduction

This chapter covers data analysis, interpretation and discussion of the research findings. The data

was analyzed using a regression analysis and presented in form of tables, graphs and regression

model. The chapter is organized in six sections; descriptive statistics, reliability test, correlation

analysis, yield curve and discussion of findings.

4.2 Descriptive Analysis

This section sought to determine a description of the data that was used to establish the various

patterns of the yield curve over time in Kenya and to determine the ability of yield curve to predict

economic growth and recessions.

4.2.1 Descriptive Statistics

Table 4.2 presents descriptive statistics

Table 4.1: Data Description

Years

Real GDP growth rate

(%)

Interest Rate Spread

(%)

Lagged Interest rate

Spread

2006

6.33

5.43

7.61

2007

6.99

7.31

5.43

2008

1.53

0.71

7.31

2009

2.74

4.62

0.71

2010

5.80

11.86

4.62

2011

4.42

1.33

11.86

2012

4.55

12.08

1.33

2013

4.69

10.06

12.08

Source: World Bank, 2014

GDP is the sum of consumer spending, Investment made by industry, Excess of Exports over

Imports and Government Spending. Due to inflation GDP increases and does not actually reflect

the true growth in economy. That is why inflation rate must be subtracted from the GDP to get the

real growth percentage called the real GDP. Real Gross Domestic Product (real GDP) is a

macroeconomic measure of the value of economic output adjusted for price changes. This

adjustment transforms the money-value measure, nominal GDP, into an index for quantity of total

output.Real GDP is calculated by nominal GDP divided by the deflator, or R = N/D. The deflator

is a measurement of inflation since a designated base year.

Moolman (2002) used a probit model to evaluate the term structure or yield spread as a predictor

of turning points in the South African business cycle. The yield spread was defined as the

difference between the yield on 10-year government bonds and 3-month bankers’ acceptances. For

this study, yield spread is the difference between the yield of 10 year government bonds and 3-

month bankers’ acceptances.

Table 4.2: Descriptive Statistics

Mean

Std. Deviation

Real GDP growth rate (%)

4.6313

1.8152

Lagged Yield Spread one year

ahead

6.3687

4.25187

Source: Research Data, 2014

From the findings, a period of 8 years (2006 – 2013) was used in this study. Real GDP growth rate

had a mean score of 4.6313 and standard deviation of 1.8152 while Lagged Yield Spread had a

mean score of 6.3687 and a standard deviation of 4.2519. The findings indicate that over the period

under study, real GDP growth rate was 4.63% while lagged yield spread was 6.37%.

4.2.2 Yield Curve

The yield curve is estimated with the adjusted dataset. Figure 4.4 shows the results for the adjusted

dataset.

Yield Spread was lagged in order to determine the yield for the next period. In this study, yield

spread for 2006 was lagged to show the yield for the year 2007 until the year 2013. Figure 4.4

presents the findings for lagged and un-lagged spread sheets.

Figure 4.4: Lagged and Un-lagged Yield Curve

Source: Research Data, 2014

From the figure above, yield curve had no stable rate but keeps on changing period over period.

There were low yields reported in the year 2002008 while the highest was in years 2010 and 2012.

The spread had an increase from the year 2008 to 2010 but decreased in the year 2011 but increased

again in the year 2012.

4.2.3 Comparison Yield Curve and Real GDP Growth Rate

The study sought a comparison between yield curve and real GDP growth rate. Figure 4.2 presents

the findings.

Figure 4.5: Real GDP Growth Rate

Source: Research Data, 2014

From the figure above, real GDP growth rate showed an upward curve from the year 2006 to 2007

but decreased from 6.99% in the year 2007 to 1.53 in the year 2008. Growth rate increased in year

2010 to 5.8%. From 2011, real GDP growth has shown an upward flow from 4.42% to 4.69% in

the year 2013.

4.3 Reliability Test

Table 4.3: Reliability Statistics

Cronbach's Alpha

N of Items

.731

Source: Research Data, 2014

4.4 Correlation Analysis

The Pearson product-moment correlation coefficient (or Pearson correlation coefficient for short)

is a measure of the strength of a linear association between two variables and is denoted by r.

Basically, a Pearson product-moment correlation attempts to draw a line of best fit through the

data of two variables. Pearson correlation coefficient was conducted to examine the relationship

between variables.

Table 4.4: Correlation Analysis

Real GDP

growth

Lagged Yield

Spread

Pearson Correlation

Real GDP growth

0.097

Lagged Yield

Spread

0.097

Source: Research Data, 2014

The Pearson correlation coefficient, r, can take a range of values from +1 to -1. A value of 0

indicates that there is no association between the two variables. As cited in Wong &Hiew (2005)

the correlation coefficient value (r) range from 0.10 to 0.29 is considered weak, from 0.30 to 0.49

is considered medium and from 0.50 to 1.0 is considered strong. However, according to Field

(2005), correlation coefficient should not go beyond 0.8 to avoid multicollinearity. Since the

correlation coefficient is (0.097), which is less than 0.8, there is no multicollinearity problem in

this research.

From table 4.4, the findings indicate that real GDP growth rate and lagged yield spread were shown

to have a positive association between them but the association was weak which means that lagged

yield spread cannot effectively predict real GDP growth rate for the next period.

4.5 Regression Analysis

In addition, the group conducted a multiple regression analysis so as to test relationship between

Lagged Yield Spread (independent) on GDP (dependent). We used SPSS, a data analysis and

statistical software, to code, enter and compute the measurements of the multiple regressions for

the study. Researchers assumed 95% confidence interval. Table 4.4 presents regression model

summary

Table 4.5: Model Summary

Model

R Square

Adjusted R Square

Std. Error of the

Estimate

.097

.009

-.156

1.95147

Source: Research Data, 2014

Analysis in table 4.5 above shows that the coefficient of determination (the percentage variation

in the dependent variable being explained by the changes in the independent variables) R-squared

equals 0.009 that is, Lagged Yield Spread explains0.9 percent of real GDP growth rate.

The P-Value of 0.046 (Less than 0.05) implies that the model at the 5 percent was significant as

shown in table 4.5.

Table 4.6: ANOVA

Model

Sum of Squares

Mean Square

Sig.

Regression

.215

.057

0.046

Residual

22.849

3.808

Total

23.065

a. Dependent Variable: GDP growth rate (annual %)

b. Predictors: (Constant), Lagged Interest rate Spread (%)

Source: Research Data, 2014

ANOVA findings (P- value of 0.046) in table 4.6 show that there is a weak correlation between

the predictor’s variables (Lagged Yield Spread) and response variable (Real GDP growth). An F

ratio is calculated which represents the variance between the groups, divided by the variance within

the groups. A large F ratio indicates that there is more variability between the groups (caused by

the independent variable) than there is within variables, referred to as the error term. The P value

is 0.046 which is less than 0.005 significance level.

Coefficient of determination explains the extent to which changes in the dependent variable can

be explained by the change in the independent variables or the percentage of variation in the

dependent variable (real GDP growth) that is explained by the independent variable (Lagged Yield

Spread). Table 4.6 presents the coefficients of the regression model.

Table 4.7: Coefficients of the Regression Model

Model

Unstandardized

Coefficients

Standardized

Coefficients

Sig.

Std. Error

Beta

(Constant)

4.369

1.303

3.354

.015

Lagged Interest rate

Spread (%)

.041

.173

.097

.238

.042

a. Dependent Variable: GDP growth rate (annual %)

Source: Research Data, 2014

From the coefficient of determination, the study model or equation:

Yi=𝛽

𝑜

+ 𝛽

𝑋

+ ε

𝛽

𝑋

+ 𝜀

𝑖

Where;

Y = Real GDP growth

= Lagged Yield Spread

constant term of the model

Co-efficient of the model

є = error term.

The study equation becomes:

Y=4.369 + 0.041X

According to the model, when Lagged Yield Spread is at zero, the dependent variable (real GDP

growth) will be 4.37%.

The determinant for Lagged Yield Spreadwas0.041.The findings show that Lagged Yield Spread

predicts 4.1% only of the change in real GDP growth rate.

4.6 Discussion of the Findings

The study found that yield curve is capable to predict economic growth and recessions but cannot

do it accurately because of a weak association it has with real GDP growth rate. Studies by Shiller

et al (1983) reported coefficients for the forward rate premium that were not significantly different

from zero indicating (using standard regression method) that the yield curve from 3-6 month has

had negligible power to forecast changes in 3 month rate. Studies by Shiller et al (1983) reported

coefficients for the forward rate premium that were not significantly different from zero indicating

(using standard regression method) that the yield curve from 3-6 month has had negligible power

to forecast changes in 3 month rate. Much closer to home, Khomo et al (2007) have done a study

on similar properties of the yield curve as a predictive tool. Their results confirmed its ability to

act as a simple tool for forecasting economic conditions of recession by policymakers and investors

in the South African market.

Khomo et al (2007) have done a study on similar properties of the yield curve as a predictive tool.

Their results confirmed its ability to act as a simple tool for forecasting economic conditions of

recession by policymakers and investors in the South African market. According to Joseph et al

(1996), in reference to the Rational Expectation Hypothesis of the Term Structure (REHTS), long

term rates should reflect market expectation for the average level of future short term rates. The

results form a study done by Moolman (2002) indicated that the term structure or yield spread

successfully predicts turning points of business cycle two quarters ahead. The negative empirical

relationship between the term structure of interest rates and the business cycle conforms to

economic theory.

Campbell’s (1986) model, the slope of the term structure correctly predicted the five cyclical

turnings points over the last 40 years. Moolman (2002) used a probit model to evaluate the term

structure or yield spread as a predictor of turning points in the South African business cycle. The

findings showed that the term structure or yield spread successfully predicts turning points of

business cycle two quarters ahead.

CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATIONS

5.1 Introduction

This chapter presents the summary of the findings presented in chapter four in accordance to the

study objective. The study aimed at establishing the various patterns of the yield curve over time

in Kenya and to determine the ability of yield curve to predict economic growth and recessions. It

also presents conclusions and the recommendations to the study.

5.2 Summary and Discussions of the Study

The study found that the shape of yield curve indicates the cumulative priorities of all lenders

relative to a particular borrower. Lenders usually are concerned about a potential default so they

offer long term loans for higher interest rates than they offer for short term loans. Yield curves are

usually upward sloping asymptotically but this study found a varied trend in the yield curve. The

study found that the two common explanations for upward sloping yield curve are; markets are

anticipating a rise in interest rates and that longer maturities entail greater risk for the lender. The

study found that the factors that play a role in causing long term yields to move up and down

include inflation, economic growth, supply and demand factors and investor attitude toward risk.

Generally, slower growth, low inflation and depressed risk attitude will help the performance of

shorter term bonds and cause yields to fall and vice versa.

From the study findings, Lagged Yield Spread was seen having a weak positive association(0.097)

with Real GDP growth rate which means that lagged yield spread cannot effectively predict real

GDP growth rate for the next period. The study found that the coefficient of determination (the

percentage variation in the dependent variable being explained by the changes in the independent

variables) R-squared equals 0.009 that is, Lagged Yield Spread explains 0.9 percent of real GDP

growth. The study found that when Lagged Yield Spread is at zero, the dependent variable (real

GDP growth rate) will be 4.37%. It found that real GDP growth has a significant relationship with

Lagged Yield Spread.

The study found that yield curve is capable to predict economic growth and recessions but cannot

do it accurately because of a weak association it has with real GDP growth rate. Studies by Shiller

et al (1983) reported coefficients for the forward rate premium that were not significantly different

from zero indicating (using standard regression method) that the yield curve from 3-6 month has

had negligible power to forecast changes in 3 month rate. Much closer to home, Khomo et al

(2007) have done a study on similar properties of the yield curve as a predictive tool. Their results

confirmed its ability to act as a simple tool for forecasting economic conditions of recession by

policymakers and investors in the South African market.

The results form a study done by Moolman (2002) indicated that the term structure or yield spread

successfully predicts turning points of business cycle two quarters ahead. The negative empirical

relationship between the term structure of interest rates and the business cycle conforms to

economic theory. Campbell’s (1986) model, the slope of the term structure correctly predicted the

five cyclical turnings points over the last 40 years.

5.3 Conclusion

The study concludes that Lagged Yield Spread has a weak positive association with Real GDP

growth. It concludes that the coefficient of determination (the percentage variation in the

dependent variable being explained by the changes in the independent variables) R-squared equals

0.009 that is, Lagged Yield Spread explains 0.9 percent of real GDP growth. The study concludes

that when Lagged Yield Spread is at zero, the dependent variable (real GDP growthrate) will be

4.37%. It concludes that real GDP growth has a significant relationship with Lagged Yield Spread.

The results of this study lend encouraging support for the ability of the yield curve to predict

changes in real GDP in Kenya. Including more explanatory variables, or more lagged values of

the GDP growth rate, to the regressions remains a subject for further research. The regressions of

this thesis also made use only of the spread between a long and a short yield, whereas more

information from the yield curve could be extracted by using more differences along the maturity

spectrum.

5.4 Recommendation

If the government can take the findings of the study more seriously, we can minimize the impacts

of recessions through policy decisions.

This research only tests commonly used models. It would be interesting to see a more extensive

review of available models and their performance against each other. It therefore recommends that

studies be done on other models based on Nelson & Siegel. The study also recommends to change

the data selection criteria from the one used in this study.

5.5 Implications of the Study

The study found that Lagged Yield Spread does not accurately predict real GDP growth rate. The

implication of this is that if a country depends on Lagged Yield Spread to predict the future real

GDP growth rate, policy makers can be misguided and formulate policies that will not be support

actual real GDP growth rate.

5.6 Limitation of the Study

The estimation of the model proposed by Estrella (2005) might prove difficult in the case of

Finland, due to the use of annual data, which leads to the problem of a relatively small sample.

However, it serves an explicit theoretical justification for investigating the predictive power of the

Kenyan yield curve to subsequent GDP.

5.7 Suggestion for Further Research

The coefficient of determination (the percentage variation in the dependent variable being

explained by the changes in the independent variables) R-squared equals 0.796 that is, Lagged

Yield Spread explains 79.6 percent of real GDP growth. It means there is 20.4 percent unexplained.

The study therefore suggests that other study be done to explain the 20.4 percent.

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APPENDICES

Appendix One: Data

Years

Real GDP growth rate

(%)

Interest Rate Spread

(%)

Lagged Interest rate

Spread

2006

6.33

5.43

7.61

2007

6.99

7.31

5.43

2008

1.53

0.71

7.31

2009

2.74

4.62

0.71

2010

5.80

11.86

4.62

2011

4.42

1.33

11.86

2012

4.55

12.08

1.33

2013

4.69

10.06

12.08

Source for real interest rate is International Monetary Fund, International Financial Statistics and

data files using World Bank data on the GDP deflator. Real interest rate is the lending interest rate

adjusted for inflation as measured by the GDP deflator.

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