Eco. 512 Online Quiz and Discussion (Determination of Interest Rates and Yield Curve Analysis in Financial Markets)
The Yield Curve is a graphical representation of the interest rates on debt for a range of maturities. It shows the yield an investor is expecting to earn if he lends his money for a given period of time. In view of the above assertion, you have been invited to present a paper at the Centre for African Economies, Abuja on the theme “Determination of Interest Rates and Yield Curve Analysis in Financial Markets”. What will tell your audience?
Ukaigwe, Ugochukwu Francis
Pg/CBN/MSC/21/0005
512.2
uukaigwe@gmail.com
Question
The yeild curve is a graphical representation of the interest rate for debt for a rate of maturities. It shows the yeild an investor is expecting to earn if he lends his money for a given period of time. In view f the above assertions, you have been invited to present a paper at the center for African Economics in Abuja on the theme “ determination of interest rate and yeild curve analysis in financial markets” what will you tell the audience?
Answer
After salutations and introductions, I would introduce myself to the audience after observing due protocols I would further introduce the theme “determination of interest rate and yeild curve analysis in financial markets” I would further sharpen their minds just as emphasized by the classical school of taught in Economics I would expatriate on the term interest rate as a payment made by a borrower to the lender of monies borrowed and expressed in percentages or verities as payments are due for goods and services as desired furthermore I will give an instance where this capital can be retained by the owner to use for production and additional products generation of more capital so we can say interest rate goes to the owner of the capital.
I will continue to mention major the various schools of taught regarding interest rates starting with the Keynes who believed interests rates are purely a monetary phenomenon and as such a payment for the use of money John Stuart Mill believed interest rate is a remuneration and for abstinence and the Classical school of taught mentions interest rates as postponing consumption so capital can be created they believe that to abstain from consumption is painful and the lender is paid a reward called the interest rate the Neo-classical pronounced interest rates as the price for the use of loan-able funds to mention a few. I would further enlighten the audience of the GROSS AND PURE INTRESTS which is the payment which the borrower makes to the lender less the principal so it is composite item lading to a number of payments such as Pure/net interests simply said is the payment for the use of capital or money alone the reward for management which implies the lender incurring expenditure to keep proper records of the borrowers by buying accounts and maintaining staff, this entails he has to remind the borrower and file suits when such need arises the reward for inconvenience can be interpreted when the loaned money is forgone for the duration of the loan so such funds cannot be used for more profitable purposes as more funds must be searched from other sources the reward for risk taking which exposes one to risk when seeking funds and just as a major law in economics we would examine the demand and supply sides of interest rates
The demand side consists of continuous demands for capital driven towards productivity and consumable purposes as desired by the investor subject to laws of verifiable proportions so additional use of capital would not be as productive as the initial stage my instance would assume an investor invests N10,000 in a factory and looks forward to 20% yeild over a period of time, so if another installment of an equivalent sum would not be productive as the initial which can be say 15% and the third 10% . here the higher the interest rate demand for capital will reduce and high at a low rate of interest other factors of demand for capital includes growth in population, technological progress, rationalization standards of living in the community among-est other progress parameters. On the supply side the supplied capital would depend on savings and implying that savings would be at a savings capacity according to their locations taking particular note of those who save irrespective of the interest rate meaning this group save no matter the conditional outlook so they cannot be induced to save as saving is like a culture to induce interest rate to increase supplying more funds at the instance to yeild cure moves upwards to the right.
In determining the interest rate yeild curve an analysis is given at a level of income is determined by the interest rate due to interactions in the demand and supply curve of a given capital as illustrated below.
yield curve
Yield curve depicting the positive relationship between the time to maturity(term) and the interest rate (yield) of a debt instrument.
Quantity of Capital
The graph above explains the determination of interest rate yeild analysis as demand and supply curve interacts at E1 and that is the equilibrium point. more so, OQ quantity of capital are demanded and supplied at Ox interest rate when eve it rises above Ox or OR1 the demand for investment fund falls as supply for funds rises. I would illustrate that supply of capital is more than demand thus, (R1s>Rd1) interest rate would reduce to the equilibrium level and the reverse will be the case when interest rate fall to OR2.
On the demand for capital, it is usually greater than supply (R2d>R1S1)are the interests rates rises to OR it is sometimes called the ultimate situation where one of the equality between investment and savings resulting to an equilibrium or a national state, say savings are more than OQ2 of the interest rate would fall downwards below OR as the demand for capital remains stable to encouraging less interests rate and by so doing demands for funds will rise to further rise interests rate to its equilibrium level.
In conclusion, I would examine different classical school of taught as propounded by Marshal and Pigon of the classical model which Keynes disagreed with and stated that the monetary factors are neglected as the classical believe money is a medium of Exchange over goods and services and fails to take into account that money is a store of value Keynes went on to explain that the determinants of interest rate is monetary phenomenon other criticisms includes the unrealistic assumptions of full employment where the classical base the arguments on full employment where interests are rewards for savings is important for the well being as postulated by Keynes rule where resources are unemployed again income is not consistent but a variable and classical argue income as a given rate which equlibrates to a mechanism of demands of invisible funds by savings and Keynes maintains income as a variable and not a constant so equality distinguishes savings and investment as a result of changes in income and not the variations of interests rate. These neglesting effects of investment on the level of income comes in such a way that a rise in the interest rate will warrant a fall in investment and make it less profitable and results in a decline in output. Income levels and employment levels will fall reducing savings contrary to the classical assertions that savings is a direct function of interest rate further more, low interest rate encourages investments, employment and income and savings but Keynes does not believe investment depends on interest rate but on marginal efficiency of capital.
Finally, some criticisms or school of taught would be savings and investment schedules are not dependent implying that the two are determinants of yeild therefore the demand and sup[ply curves of savings are assumed to be independent of each other furthermore the change in demand and demand curve can shift up or below D0 curve without affecting the supply curve Keynes went on to maintain a position which explains that the two curves are not independent of one another an illustration is an intervention change demand curve to rise upwards leading to higher savings to shift the supply curve so when supply shifts demand changes. At this point I would entertain questions thank you.
Reference
Applied Principles of Economics-Nwaimo C.O
Macroeconomics for universitie-Wilie J.Okowa
Advanced Economics Theory-M.L.Jhingan
NAME: CHIDERA IKENNA UGWU
REGISTRATION NUMBER:PG/ CBN/MSC/21/0010
COURSE: FINANCIAL INSTITUTION AND MARKET (ECO 512)
A yield is the return which an investor gets for holding or investing in a bond. So, a yield curve is a graph that plots the returns or interest rates of bonds with the same credit quality but different maturity periods/time. The slope of a yield curve shows the possible rate of changes in the future interest rate or economic activity; it also depicts the cumulative expectations of the lenders in relation to the borrower. There are 3 types of yield curve – they are:
Normal Yield curve
Inverted Yield curve
Flat Yield curve
A normal yield curve is the type of yield curve where the yields on the bond increases as maturity date lengthens. Here bonds with longer maturity date gives a higher yield than bonds with a shorter maturity time. This is due to risks associated with time.
A normal yield curve
Inverted yield curve is the type of yield curve where yields with short term duration are higher to the yields from a longer tem duration
Inverted yield curve
Flat yield curve is the type of yield curve where yields on longer term bond and yields on shorter term bonds are close to each other. it predicts an economic transition.
The interaction of yield curve, interest rate and financial market analysis
Investors uses the yield curve to make predictions on the future economic outlook, this helps to guide their investment decisions. normal yield curve depicts an economic expansion and economic stability. The slope is a positive slope showing that the investors expects the economy to grow in the future in response to economic expansion and associated with this growth is the expectation that inflation rate will rise in the future. The expectation of rise in inflation rate makes the investors to expect a tightening of the monetary policy by the monetary authority which will imply an increase in the future interest rate so as to slow economic growth and reduce the inflationary tendencies. This creates uncertainty about the future rate of inflation and poses a risk on the future cash flows. Thus, the investors incorporate these risks into the yield curve by demanding higher yields (interest rate) for bonds with maturities further into the future. A normal yield curve starts with low yields (lower interest rates) for short term bonds and then increases (the interest rate increases) for long term bonds. Thus, it is an upward sloping curve
An inverted yield curve points to an economic recession. It is a downward slope curve which shows that bonds with short term duration has higher interest rate in comparison to bonds with long term duration which has lower interest rate. So investors expects yields from long term bonds to decline further in the future as a result of deterioration in the economic activities. The downwad or negative slope of the yield curve indicates that investors believe that there will be an economic recession and that the monetary authority will respond by reducing the interest. In the period of economic downturn, investors tend to purchase bonds with long duration over bonds of short duration as they seek for safe investments. Thus, bidding up the price of long duration bonds, driving their yield down.
A flat yield curve is one that gives similar yields for all bonds,notwithstanding whether they are short term or longterm bond. The flat nature of the curve shows an uncertain economic situation, where difference between the yields of short term and long term bonds are just little. in such period when uncertainty is high investors demand similar yields(interest rates) for all bonds, whether with long or short term maturity. It may come at the end of a high economic growth period that is leading to inflation and fears of a slowdown. It might appear at times when the central bank is expected to increase interest rates.
Finally, investors uses the yield curve to predict where the economy is heading to and thus, guide them in making investment decisions. If the yield curve depicts an economic expansion the investors will demand high interest rate and will be willing to invest in bonds with high interest rate. If the yield curve points to an economic recessson, investors might move their money into secured assets such as staple goods that do well in economic recession. Interest rates and bond prices are inversely related. The bond price will reduce when interest rate increase and with a decrease in the interest rate, the prices of bond will increase.
Reference
Hayes, A. (2022). Yield curves explained and how to use them in investing. Retrieved from https://www.investopedia.com/terms/y/yieldcurve.asp
Saylor acadaemy. (2022). Principle of finance. Retrived from www. Saylor academy .org
INTRODUCTION
Interest rate plays a central role in the formulation of monetary policies of any economy, this largely stems from the role interest rate plays in determining the deployment of surplus investable fund to deficit sectors of any given economy. in essence, the extent to which credit is extended to productive sectors is intricately bound to interest rate developments, which in turn determine the affordability of funds (Nyarota et al 2015). interest rate developments also determine the flow of capital across international frontiers, as cross-border investors search for favorable returns on their investment (RBZ, 2014). furthermore, the competitiveness of a country’s products both in the domestic and export markets is contingent upon the evolution of interest rates in that economy.
Interest rate as earlier pointed is the cost of capital or price paid for inducing economic agents with surplus to save rather than spend and invest in long term assets rather than hold cash. this rate reflects the interaction between the demand for and the supply of money, the varying degree of risk associated as well as the maturity of any financial asset. this lends a hand as to why there exist a multiplicity of interest rates each reflecting a particular economic variable
high interest rate is a disincentive to borrowing but an incentive to savings thereby slowing down the economy. Conversely low interest rate encourages borrowing and economic growth in that, the lower the interest rate, the higher the profit expectation (other things being equal) as businesses are expected to pay small portion of their income as interest for fund borrowed (CBN 2016) It is obvious that the process of determination of interest rates will differ significantly under alternative degrees of openness of the economy. For example, in the case of a fully open capital account some form of interest arbitrage will hold, with domestic interest rates depending on world interest rates, expected devaluation, and perhaps some risk factors. In contrast, in countries with a completely closed economy, open economy factors will obviously play no role, and the nominal interest rate will be determined by conditions prevailing in the domestic money market and by expected inflation. Most developing countries, however, do not fall in either of these two extreme categories, so that interest rates will in general depend on domestic money market conditions, as well as on the expected rate of devaluation and world interest rates. From a policy perspective it is important to determine the way in which these different factors actually affect interest rates.
Against this background, this paper seeks to examine how interest rate is determined in an economy, it probes further and analyze the yield curve which happens to be the graphical representation of interest rate on debt for a range of maturities, showing the yield an investor is expecting to earn if he lends his money for a given period of time.
INTEREST RATE DETERMINATION
Economic agents (market participants) make financing and investing decisions in a dynamic financial environment. They must understand the economy, the role of the government in the economy, and the financial markets and financial intermediaries that operate in the financial system. This section of this paper looks at two economic theories about the determinants of the level of interest rates and then, because there is not one interest rate in an economy but a structure of interest rates, we describe the factors that affect the structure of interest rates and finally examine the relationship between interest rates and the maturity of debt instruments (yield curve)
Theories of Interest Rate Determination
The two economic theories of interest rate determination discussed in this work are;
Loanable funds theory
Liquidity preference theory
I. Loanable Funds Theory
The neo-classical theory of interest (loanable fund theory of interest) owe its origin to Knut Wicksell, a Swedish Economist. Economists like Ohlin, Myrdal, Robertson, Lindahl and J. Viner have also made contributions to this theory. the main proposition of this theory is that the rate of interest is determined by the demand for and the supply of loanable funds
I.I. Demand for Loanable Funds
According to the loanable fund theory of interest, demand for loanable funds arises for the following three purposes:
Investment
hoarding and
Dissaving
Investment: investment constitutes a greater part of the demand for loanable funds. It refers to the expenditure for the purchase of making of new capital goods including inventories. The price of obtaining such funds for the purpose of these investments depends on the rate of interest. A rational economic agent will compare the expected return from an investment with the cost of borrowing to finance the investment (rate of interest). A lower interest rate compared with expected return and other things being equal will translate to high demand for loanable funds and vice versa. The above interaction between loanable fund and the rate of interest connotes an inverse relationship between the rate of interest and loanable fund.
Hoarding: another constituent of the demand for loanable funds is hoarding. Hoarding here insinuates holding above the amount required as idle cash balances to satisfy the desire for liquidity. In contrast with investment demand for loanable fund, the demand for loanable funds for hoarding purpose is a decreasing function of the rate of interest. An interplay which suggests that at low rate of interest, demand for loanable funds for hoarding will be more and vice-versa.
Dissaving: Dissaving’s is the reverse of savings. This demand comes from the economic agents when they want to spend beyond their current income. Like hoarding it is also a decreasing function of interest rate.
I.II. Supply of Loanable Funds
The supply of loanable funds is made up of four basic components which include;
Savings
Dishoarding
disinvestment and
bank credit.
Savings: Savings constitute the most important source of the supply of loanable funds. Savings is that part of disposable income not consumed, the difference between the income and expenditure. Since, income is assumed to be stable, the amount of savings varies with the rate of interest. Individuals as well as business firms will save more at a higher rate of interest and vice-versa.
Dishoarding: Generally, individuals may dishoard money from the past hoardings at a higher rate of interest. Thus, at a higher interest rate, idle cash balances of the past become the active balances at present and become available for investment. If the rate of interest is low dishoarding would be negligible.
Disinvestment: Disinvestment occurs when the existing stock of capital is allowed to wear out without being replaced by new capital equipment. Disinvestment will be high when the present interest rate provides better returns in comparison to present earnings. Thus, high rate of interest leads to higher disinvestment and so on.
Bank Money: Banking system constitutes another source of the supply of loanable funds. The banks advance loans to the businessmen through the process of credit creation. The money created by the banks adds to the supply of loanable funds.
I.III Loanable Funds Theory Determination of Interest Rate.
According to loanable funds theory, equilibrium rate of interest is that which brings equality between the demand for and supply of loanable funds. In other words, equilibrium interest rate is determined at a point where the demand for loanable funds curve intersects the supply curve of loanable funds.
Where DI = Dissaving’s, H= Hoarding, I= Investment, DI= Disinvestment, DH= Dishoarding and S=Savings.
From Figure 1. The rate of interest is determined at the point of intersection of the two curves, the supply of loanable funds curve (SL) and the demand for loanable funds curve, DL. Fig. 1 shows that the equilibrium rate of interest is EM; at this rate, the demand for loanable funds is equal to the supply of loanable funds i.e. OM.
In an economy, households, business, and governments supply loanable funds (i.e., credit) in the capital market. The higher the level of interest rates, the more such entities are willing to supply loan funds; the lower the level of interest, the less they are willing to supply. These same entities demand loanable funds, demanding more when the level of interest rates is low and less when interest rates are higher. According to the loanable funds theory, formulated by the Swedish economist Knut Wicksell in the 1900s, the level of interest rates is determined by the supply and demand of loanable funds available in an economy’s credit market (i.e., the sector of the capital markets for long-term debt instruments) More specifically, this theory suggests that investment and savings in the economy determine the level of long-term interest rates. Short-term interest rates, however, are determined by an economy’s financial and monetary conditions.
Given the importance of loanable funds and that the major suppliers of loanable funds are commercial banks, the key role of this financial intermediary in the determination of interest rates should be clear. It is via monetary policy, as implemented by the Federal Reserve (informally, the Fed), that the supply of loanable funds from commercial banks can be altered and thereby change the level of interest rates. That is, the Federal Reserve, through the tools that it has available, can increase (decrease) the supply of credit available from commercial banks and thereby decrease (increase) the level of interest rates.
II. Liquidity Preference Theory of Interest (Rate Determination)
As oppose to the classical model where the determinants of the equilibrium interest rate are the “real‟ factors of the supply of saving and the demand for investment, in the Keynesian analysis, determinants of the interest rate are the “monetary‟ factors alone. Keynes’ analysis concentrates on the demand for and supply of money as the determinants of interest rate. According to Keynes, the rate of interest is purely a monetary phenomenon. Interest is the price paid for borrowed funds. People like to keep cash with them rather than investing cash in assets. Thus, there is a preference for liquid cash. People, out of their income, intend to save a part. How much of their resources will be held in the form of cash and how much will be spent depend upon what Keynes calls liquidity preference, Cash being the most liquid asset, people prefer cash. And interest is the reward for parting with liquidity. However, the rate of interest in the Keynesian theory is determined by the demand for money and supply of money. Since money is not consumed, the demand for money is a demand to hold an asset. Keynes outline three motives for holding money, they are:
Transaction motive
Precautionary motive
Speculative motive
Transaction Demand for Money: this is the demand for money to meet day-to-day transactions. As there is a gap between the receipt of income and spending, money is demanded. Incomes are earned usually at the end of each month or fortnight or week but individuals spend their incomes to meet day-to-day transactions. Since payments or spending are made throughout a period and receipts or incomes are received after a period of time, an individual needs active balance in the form of cash to finance his transactions. Transaction demand for money is an increasing function of money income. Symbolically, Tdm = f (Y)
Where, Tdm stands for transaction demand for money and Y stands for money income
Precautionary Demand for Money: this is the demand for money to meet unplanned expenditures like sickness, unemployment etc. The amount of money held under this motive also depends on the level of money income of an individual. People with higher incomes can afford to keep more liquid money to meet such emergencies. This means that this kind of demand for money is also an increasing function of money income. The relationship between precautionary demand for money (Pdm) and the volume of income is normally a direct one. Thus, Pdm = f (Y)
Speculative Demand for Money: This is also called Keynes’ contribution. The speculative motive refers to the desire to hold one’s assets in liquid form to take advantages of market movements. The cash held under this motive is used to make speculative gains by dealing in bonds and securities whose prices and rate of interest fluctuate inversely. Speculative demand for money (Sdm) varies inversely with the rate of interest. Thus, Sdm = f (r)
Where, Y is the rate of interest.
II.I Total Demand for Money
The total demand for money (DM) is the sum of all three types of demand for money. That is, Dm = Tdm + Pdm + Sdm. The demand for money is negatively sloped because of the inverse relationship between the speculative demand for money and the rate of interest. However, the negative sloping liquidity preference curve becomes perfectly elastic at a low rate of interest. According to Keynes, there is a floor interest rate below which the rate of interest cannot fall. This minimum rate of interest indicates absolute liquidity preference.
II.II Money Supply
The supply of money in a particular period depends upon the policy of the central bank of a country. Money supply curve is perfectly inelastic as it is institutionally given.
II.III Liquidity Preference Theory Determination of Interest Rate
In Keynes Liquidity Preference Theory, the rate of interest is determined by the demand for money and the supply of money.
OM is the total amount of money supplied by the central bank. At point E, demand for money becomes equal to the supply of money. Thus, the equilibrium interest rate is determined at oi. Now, suppose that the rate of interest is greater than oi. In such a situation, supply of money will exceed the demand for money. People will purchase more securities. Consequently, its price will rise and interest rate will fall until demand for money becomes equal to the supply of money. On the other hand, if the rate of interest is less than oi, demand for money will exceed supply of money, people will sell their securities. Price of securities will tumble and rate of interest will rise until we reach point i. Rajib(2019).
YIELD CURVE ANALYSIS
The Yield Curve is a graphical representation of the interest rates on debt for a range of maturities. It shows the yield return an investor is expecting to earn if he lends his money for a given period of time. The yield curve graph displays a bond’s or equity yield on the vertical axis and the time to maturity across the horizontal axis. The curve may take different shapes at different points in the economic cycle, but it is typically upward sloping.
Factors Influencing the Yield Curve
Inflation
The Central Bank of any country tend to respond to a rise in expected inflation with an increase in interest rates. A rise in inflation leads to a decrease in purchasing power and, therefore, investors expect an increase in the short-term interest rate.
Economic Growth
An economic growth may be associated with an increase in inflation due to a rise in aggregate demand. Economic growth also translates to a strong competition for capital, with more options to invest available for investors. Thus, strong economic growth leads to an increase in yields and a steeper curve.
Interest Rate
If Interest rate on Treasuries raised, this increase will result in higher demand for treasuries and, thus, eventually lead to a decrease in interest rates.
Various Shapes of The Yield Curve As Influenced By These Factors
Normal Shape
The positively sloped yield curve is called normal because a rational market will generally want more compensation for greater risk. Thus, as long-term securities are exposed to greater risk, the yield on such securities will be greater than that offered for lower-risk short-term securities.
Inverted Shape Yield Curve
An inverted curve appears when long-term yields fall below short-term yields. An inverted yield curve occurs due to the perception of long-term investors that interest rates will decline in the future. This can happen for a number of reasons, but one of the main reasons is the expectation of a decline in inflation.
When the yield curve starts to shift toward an inverted shape, it is perceived as a leading indicator of an economic downturn. Such interest rate changes have historically reflected the market sentiment and expectations of the economy.
Steep shape yield curve
A steep curve indicates that long-term yields are rising at a faster rate than short-term yields. Steep yield curves have historically indicated the start of an expansionary economic period. Both the normal and steep curves are based on the same general market conditions. The only difference is that a steeper curve reflects a larger difference between short-term and long-term return expectations.
iv. Flat shape yield curve
A flat curve happens when all maturities have similar yields. This means that the yield of a 10-year bond is essentially the same as that of a 30-year bond. A flattening of the yield curve usually occurs when there is a transition between the normal yield curve and the inverted yield curve.
vi. Humped shape yield curve
A humped yield curve occurs when medium-term yields are greater than both short-term yields and long-term yields. A humped curve is rare and typically indicates a slowing of economic growth.
Importance of The Yield Curve
1. Forecasting Interest Rates
The shape of the curve helps investors get a sense of the likely future course of interest rates. A normal upward sloping curve means that long-term securities have a higher yield, whereas an inverted curve shows short-term securities have a higher yield.
2. Financial Intermediary
Banks and other financial intermediaries borrow most of their funds by selling short-term deposits and lend by using long-term loans. The steeper the upward sloping curve is, the wider the difference between lending and borrowing rates, and the higher is their profit. A flat or downward sloping curve, on the other hand, typically translates to a decrease in the profits of financial intermediaries.
3. The Tradeoff between Maturity and Yield
The yield curve helps indicate the tradeoff between maturity and yield. If the yield curve is upward sloping, then to increase his yield, the investor must invest in longer-term securities, which will mean more risk.
4. Overpriced or Underpriced Securities
The curve can indicate for investors whether a security is temporarily overpriced or underpriced. If a security’s rate of return lies above the yield curve, this indicates that the security is underpriced; if the rate of return lies below the yield curve, then it means that the security is overpriced. CFI(2022)
REFERENCES
Corporate Finance Institute (2022). Yield curve. Corporate finance institute https://corporatefinanceinstitute.com/resources/fixed-income/yieldcurve.
Rajib, K S.(2019). Liquidity Preference Theory of Interest (Rate Determination) of JM Keynes. Research gate publication https://www.researchgate.net/publication/335881211.
RBZ (2014). Monetary Policy Statement: January 2014, Harare: Reserve Bank of Zimbabwe
Research Department (2016). Interest rate. Education in Economics series CBN/EES/Series/03/2016
S. Nyarota, W. Nakunyada , N. Mupunga & K. Kupeta(2015). interest rate determination under a multiple currency environment: the case of Zimbabwe. RBZ working paper series N0 3: 2015
FINANCIAL MARKETS AND INSTITUTIONS ASSIGNMENT .
OLUYOLE BUKOLA GRACE.
PG/CBN/MSC/21/0015
What is the Yield Curve?
A yield curve is a line that plots yields (interest rates) of bonds having equal credit quality but differing maturity dates. The slope of the yield curve gives an idea of future interest rate changes and economic activity.
The Yield Curve is also a graphical representation of the interest rates on debt for a range of maturities. It shows the yield an investor is expecting to earn if he lends his money for a given period of time. The graph displays a bond’s yield on the vertical axis and the time to maturity across the horizontal axis. The curve may take different shapes at different points in the economic cycle, but it is typically upward sloping. A graph of yields over time
A fixed income Analyst may use the yield curve as a leading economic indicator, especially when it shifts to an inverted shape, which signals an economic downturn, as long-term returns are lower than short-term returns.
• Yield curves plot interest rates of bonds of equal credit and different maturities.
• The three key types of yield curves include normal, inverted, and flat. Upward sloping (also known as normal yield curves) is where longer-term bonds have higher yields than short-term ones.
• While normal curves point to economic expansion, downward sloping (inverted) curves point to economic recession.
How a Yield Curve Works
A yield curve is used as a benchmark for other debt in the market, such as mortgage rates or bank lending rates, and it is used to predict changes in economic output and growth. The most frequently reported yield curve compares the three-month, two-year, five-year, 10-year, and 30-year Treasury debt.
A normal yield curve is one in which longer maturity bonds have a higher yield compared to shorter-term bonds due to the risks associated with time. An inverted yield curve is one in which the shorter-term yields are higher than the longer-term yields, which can be a sign of an upcoming recession. In a flat or humped yield curve, the shorter- and longer-term yields are very close to each other, which is also a predictor of an economic transition.
Types of Yield Curves
1) Normal Yield Curve
This is the most common shape for the curve and, therefore, is referred to as the normal curve. The normal yield curve reflects higher interest rates for 30-year bonds as opposed to 10-year bonds. If you think about it intuitively, if you are lending your money for a longer period of time, you expect to earn a higher compensation for that.
The positively sloped yield curve is called normal because a rational market will generally want more compensation for greater risk. Thus, as long-term securities are exposed to greater risk, the yield on such securities will be greater than that offered for lower-risk short-term securities.
A longer period of time increases the probability of unexpected negative events taking place. Therefore, a long-term maturity will typically offer higher interest rates and have higher volatility.
A normal or up-sloped yield curve indicates yields on longer-term bonds may continue to rise, responding to periods of economic expansion. A normal yield curve thus starts with low yields for shorter-maturity bonds and then increases for bonds with longer maturity, sloping upwards. This is the most common type of yield curve as longer-maturity bonds usually have a higher yield to maturity than shorter-term bonds.
For example, assume a two-year bond offers a yield of 1%, a five-year bond offers a yield of 1.8%, a 10-year bond offers a yield of 2.5%, a 15-year bond offers a yield of 3.0%, and a 20-year bond offers a yield of 3.5%. When these points are connected on a graph, they exhibit a shape of a normal yield curve.
A normal yield curve implies stable economic conditions and should prevail throughout a normal economic cycle. A steep yield curve implies strong economic growth in the future—conditions that are often accompanied by higher inflation, which can result in higher interest rates.
2) Inverted Yield Curve
An inverted curve appears when long-term yields fall below short-term yields. An inverted yield curve occurs due to the perception of long-term investors that interest rates will decline in the future. This can happen for a number of reasons, but one of the main reasons is the expectation of a decline in inflation.
When the yield curve starts to shift toward an inverted shape, it is perceived as a leading indicator of an economic downturn. Such interest rate changes have historically reflected the market sentiment and expectations of the economy.An inverted yield curve instead slopes downward and means that short-term interest rates exceed long-term rates. Such a yield curve corresponds to periods of economic recession, where investors expect yields on longer-maturity bonds to become even lower in the future.1 Moreover, in an economic downturn, investors seeking safe investments tend to purchase these longer-dated bonds over short-dated bonds, bidding up the price of longer bonds driving down their yield.
An inverted yield curve is rare but is strongly suggestive of a severe economic slowdown. Historically, the impact of an inverted yield curve has been to warn that a recession is coming.
3. Steep Yield Curve
A steep curve indicates that long-term yields are rising at a faster rate than short-term yields. Steep yield curves have historically indicated the start of an expansionary economic period. Both the normal and steep curves are based on the same general market conditions. The only difference is that a steeper curve reflects a larger difference between short-term and long-term return expectations.
4. Humped Yield Curve
A humped yield curve occurs when medium-term yields are greater than both short-term yields and long-term yields. A humped curve is rare and typically indicates a slowing of economic growth.
5. Flat Yield Curve
A flat curve happens when all maturities have similar yields. This means that the yield of a 10-year bond is essentially the same as that of a 30-year bond. A flattening of the yield curve usually occurs when there is a transition between the normal yield curve and the inverted yield curve.
A flat yield curve is defined by similar yields across all maturities. A few intermediate maturities may have slightly higher yields, which causes a slight hump to appear along the flat curve. These humps are usually for the mid-term maturities, six months to two years.
As the word flat suggests, there is little difference in yield to maturity among shorter and longer-term bonds. A two-year bond could offer a yield of 6%, a five-year bond 6.1%, a 10-year bond 6%, and a 20-year bond 6.05%.
Such a flat or humped yield curve implies an uncertain economic situation. It may come at the end of a high economic growth period that is leading to inflation and fears of a slowdown. It might appear at times when the central bank is expected to increase interest rates.
In times of high uncertainty, investors demand similar yields across all maturities.
What Is Yield Curve Risk?
Yield curve risk refers to the risk investors of fixed-income instruments (such as bonds) experience from an adverse shift in interest rates. Yield curve risk stems from the fact that bond prices and interest rates have an inverse relationship to one another. For example, the price of bonds will decrease when market interest rates increase. Conversely, when interest rates (or yields) decrease, bond prices increase.
How Can Investors Use the Yield Curve?
Investors can use the yield curve to make predictions on where the economy might be headed and use this information to make their investment decisions. If the bond yield curve indicates an economic slowdown might be on the horizon, investors might move their money into defensive assets that traditionally do well during recessionary times, such as consumer staples. If the yield curve becomes steep, this might be a sign of future inflation. In this scenario, investors might avoid long-term bonds with a yield that will erode against increased prices.
Yield Curve: A Front and Back View
Because the yield curve charts the cost of money starting from one month in the future all the way to 30 years out, those time periods are broken down in chunks, known as the front end, belly, and back end of the yield curve. Different rates over time are good for tracking what kind of yield you can expect if you invest, or what interest rate you’ll pay if you borrow. For instance, if you’re borrowing money for a car or a mortgage, it’s important to check rates that go out a lot farther than one month, because your loan will be lengthy. But if you’re opening a one-year CD, the front end of the yield curve will determine the rate you receive (in most cases, a lot lower than the one you’ll pay for your mortgage, unfortunately).
Sometimes you’ll hear the front end and back end of the yield curve called the “short” and “long” ends:
• The front end refers to short-term securities that will mature in the near term, usually in one year or less. They’re the most sensitive to interest rate moves. Banks use short-end rates to set deposit amounts for checking accounts and savings deposits. A high interest rate on a deposit account is one way for banks to encourage you to open an account.
• The “belly” of the curve is what it sounds like, the middle of the curve. It reflects rates anywhere from two years out to a decade. Longer-term CDs, such as three- and five-year ones, may be based on rates in the shorter end of the belly.
• The back end refers to longer-dated bonds with maturity dates of 10 years or more. Mortgages and long-dated corporate bonds are based on back-end interest rates.
The yield curve moves in two ways: up and down.
A normal yield curve slopes upward, meaning the interest rate on shorter-dated bonds is lower than the rate on longer-dated bonds. This compensates the holder of long-term bonds for the time value of money and for any potential risk that the bond issuer might default.
A curve with higher back-end rates is sometimes called a steepening yield curve, because yields rise over time. When plotted on a chart, the line moves from the lower left to the upper right, showing the higher progression
What Is a Flat or Inverted Yield Curve?
If the yield curve starts to flatten, looking more like a pancake than a rising ski slope, bond market participants begin to worry. Their concern is that the shape of the curve will invert, with longer-term yields falling below short-term yields. A flattening yield curve can happen when short-term rates rise or long-term rates fall.
Why does this matter? Because it can signal a recession. Rising short-term rates indicate fears that people might lose jobs or businesses might close, making debt harder to repay and short-term loans more risky. In this environment, investors demand higher compensation in return for rising short-term risk.
Short-term yields also can rise versus longer ones if the Fed is in a rate-hike cycle, trying to slow down the economy by making money harder to borrow. Rate hikes have their biggest impact on the front end of the yield curve, typically causing those rates to rise more than longer-term rates.
`investors start looking for other places to put their money, perhaps because they don’t expect a good return in the stock market. This makes them gravitate toward higher yields offered by long-term bonds. The stronger demand causes those back-end bond prices to rise, lowering their yields (yields move inversely to the underlying bond price).
It’s not something that happens often, but an inverse yield curve—in which the back-end yield falls below the front-end yield—should raise eyebrows.
Influencing Factors
1. Inflation
Central banks tend to respond to a rise in expected inflation with an increase in interest rates. A rise in inflation leads to a decrease in purchasing power and, therefore, investors expect an increase in the short-term interest rate.
2. Economic Growth
Strong economic growth may lead to an increase in inflation due to a rise in aggregate demand. Strong economic growth also means that there is a competition for capital, with more options to invest available for investors. Thus, strong economic growth leads to an increase in yields and a steeper curve.
3. Interest Rates
If the central bank raises the interest rate on Treasuries, this increase will result in higher demand for treasuries and, thus, eventually lead to a decrease in interest rates.
Importance of the Yield Curve
1. Forecasting Interest Rates
The shape of the curve helps investors get a sense of the likely future course of interest rates. A normal upward sloping curve means that long-term securities have a higher yield, whereas an inverted curve shows short-term securities have a higher yield.
2. Financial Intermediary
Banks and other financial intermediaries borrow most of their funds by selling short-term deposits and lend by using long-term loans. The steeper the upward sloping curve is, the wider the difference between lending and borrowing rates, and the higher is their profit. A flat or downward sloping curve, on the other hand, typically translates to a decrease in the profits of financial intermediaries.
3. The Tradeoff between Maturity and Yield
The yield curve helps indicate the tradeoff between maturity and yield. If the yield curve is upward sloping, then to increase his yield, the investor must invest in longer-term securities, which will mean more risk.
4. Overpriced or Underpriced Securities
The curve can indicate for investors whether a security is temporarily overpriced or underpriced. If a security’s rate of return lies above the yield curve, this indicates that the security is underpriced; if the rate of return lies below the yield curve, then it means that the security is overpriced.
Yield Curve Theories
1. Pure Expectation Theory
This theory assumes that the various maturities are substitutes and the shape of the yield curve depends on the market’s expectation of future interest rates. According to this theory, yields tend to change over time, but the theory fails to define the details of yield curve shapes. This theory ignores interest rate risk and reinvestment risk.
2. Liquidity Preference Theory
This theory is an extension of the Pure Expectation Theory. It adds a premium called liquidity premium or term premium. This theory considers the greater risk involved in holding long-term debts over short-term debts.
3. Segmented Market Theory
The segmented market theory is based on the separate demand and supply relationship between short-term securities and long-term securities. It is based on the fact that different maturities of securities cannot be substituted for one another.
Since investors will generally prefer short-term maturity securities over long-term maturity securities because the former offers lower risk, then the price of short-term securities will be higher, and thus, the yield will be correspondingly lower.
4. Preference Habitat Theory
This is an extension of the Market Segmentation Theory. According to this theory, investors prefer a certain investment horizon. To invest outside this horizon, they will require some premium. This theory explains the reason behind long-term yields being greater than short-term yields.
Asuzu Chinwendu Emmanuella.
2021/241941.
Economics.
Question 1.
Using sturge rule= 1+3•3LogN
= 1+3•3Log33 = 6•0
So we have 6 class interval.
1. Class interval= 17-18, 19-20, 21-22, 23-24, 25-26, 27-28.
2. Midpoint X = 17•5, 19•5, 21•5, 23•5, 25•5, 27•5.
3. Frequency = 5, 6, 8, 7, 4, 3.
4. Cumulative frequency= 5, 11, 19, 26, 30, 33.
5. Relative frequency= 15•15, 18•18, 24•24, 21•21, 12•12, 9•09.
Relative cumulative frequency= 15•15, 33•33, 57•57, 78•78, 90•90, 100.
Question 2.
1. SAMPLE.
A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.
2. POPULATION.
A population is the whole set of individuals in a group, whether that group is a country or a collection of people who share a certain trait.
Population Definition in Statistics and How to Measure It
A population is the group of people from which a statistical sample is taken in statistics. Therefore, a population is any collection of people who have something in common. A statistically substantial subset of a population, rather than the complete population, may be referred to as an example or sample. In addition to this, a statistical analysis of a sample needs to provide an estimate of the standard deviation, or the standard error, of its findings from the total population. Only a whole or complete population analysis would have zero standard error.
3. CONTINUOUS VARIABLE.
A continuous variable can be defined as a numerical variable whose value is attained by measuring. These variables can take any type of numeric value and can be divided into further relevant smaller increments such as fractional and decimal values. A continuous variable is a kind of quantitative variable that is frequently used in machine learning and statistical modeling to describe data that is measurable in some way. Continuous variables are measured on scales such as height, temperature, weight, etc.
4. DISCRETE VARIABLE.
A discrete variable is a kind of statistics variable that can only take on discrete specific values. The variable is not continuous, which means there are infinitely many values between the maximum and minimum that just cannot be attained, no matter what.
5. STATISTICS.
Statistics for economics concerns itself with the collection, processing, and analysis of specific economic data. It helps us understand and analyze economic theories and denote correlations between variables such as demand, supply, price, output etc. Let us understand this in some detail.
6. DATA.
Data are facts or figures to be processed; evidence, records, statistics, etc. from which conclusions can be inferred; information.Data can be defined as a representation of facts, concepts, or instructions in a formalized manner, which should be suitable for communication, interpretation, or processing by human or electronic machine.
ECO 512: INTRODUCTION TO FINANCIAL MARKETS ASSIGNMENT
MOSES OJONUGWA ODUMU PG/CBN/MSC/21/0020
Question
The Yield Curve is a graphical representation of the interest rates on debt for a range of maturities. It shows the yield an investor is expecting to earn if he lends his money for a given period of time. In view of the above assertion, you have been invited to present a paper at the Centre for African Economies, Abuja on the theme “Determination of Interest Rates and Yield Curve Analysis in Financial Markets”. What will tell your audience?
Answer:
Yield Curve
A yield curve is a line that plots yields (interest rates) of bonds having equal credit quality but differing maturity dates. The slope of the yield curve gives an idea of future interest rate changes and economic activity.
A yield curve is used as a benchmark for other debt in the market, such as mortgage rates or bank lending rates, and it is used to predict changes in economic output and growth. The most frequently reported yield curve compares the three-month, two-year, five-year, 10-year, and 30-year U.S. Treasury debt.
Types of Yield Curves
There are three main shapes of yield curve shapes:
i. Normal (upward sloping curve),
ii. Inverted (downward sloping curve), and
iii. Steep
iv. Flat.
v. Humped
Normal Yield Curve
A normal or up-sloped yield curve indicates yields on longer-term bonds may continue to rise, responding to periods of economic expansion. A normal yield curve thus starts with low yields for shorter-maturity bonds and then increases for bonds with longer maturity, sloping upwards. This is the most common type of yield curve as longer-maturity bonds usually have a higher yield to maturity than shorter-term bonds.
Inverted Yield Curve
An inverted yield curve instead slopes downward and means that short-term interest rates exceed long-term rates. Such a yield curve corresponds to periods of economic recession, where investors expect yields on longer-maturity bonds to become even lower in the future. Moreover, in an economic downturn, investors seeking safe investments tend to purchase these longer-dated bonds over short-dated bonds, bidding up the price of longer bonds driving down their yield.
Steep
A steep curve indicates that long-term yields are rising at a faster rate than short-term yields. Steep yield curves have historically indicated the start of an expansionary economic period. Both the normal and steep curves are based on the same general market conditions. The only difference is that a steeper curve reflects a larger difference between short-term and long-term return expectations.
Flat Yield Curve
A flat yield curve is defined by similar yields across all maturities. A few intermediate maturities may have slightly higher yields, which causes a slight hump to appear along the flat curve. These humps are usually for the mid-term maturities, six months to two years.
Humped
A humped yield curve occurs when medium-term yields are greater than both short-term yields and long-term yields. A humped curve is rare and typically indicates a slowing of economic growth.
Yield Curve Risk
Yield curve risk refers to the risk investors of fixed-income instruments (such as bonds) experience from an adverse shift in interest rates. Yield curve risk stems from the fact that bond prices and interest rates have an inverse relationship to one another. For example, the price of bonds will decrease when market interest rates increase. Conversely, when interest rates (or yields) decrease, bond prices increase.
How Investors Can Use the Yield Curve
Investors can use the yield curve to make predictions on where the economy might be headed and use this information to make their investment decisions. If the bond yield curve indicates an economic slowdown might be on the horizon, investors might move their money into defensive assets that traditionally do well during recessionary times, such as consumer staples. If the yield curve becomes steep, this might be a sign of future inflation. In this scenario, investors might avoid long-term bonds with a yield that will erode against increased prices.
Influencing Factors
1. Inflation
Central banks tend to respond to a rise in expected inflation with an increase in interest rates. A rise in inflation leads to a decrease in purchasing power and, therefore, investors expect an increase in the short-term interest rate.
2. Economic Growth
Strong economic growth may lead to an increase in inflation due to a rise in aggregate demand. Strong economic growth also means that there is a competition for capital, with more options to invest available for investors. Thus, strong economic growth leads to an increase in yields and a steeper curve.
3. Interest Rates
If the central bank raises the interest rate on Treasuries, this increase will result in higher demand for treasuries and, thus, eventually lead to a decrease in interest rates.
Importance of the Yield Curve
i. Forecasting Interest Rates
The shape of the curve helps investors get a sense of the likely future course of interest rates. A normal upward sloping curve means that long-term securities have a higher yield, whereas an inverted curve shows short-term securities have a higher yield.
ii. Financial Intermediary
Banks and other financial intermediaries borrow most of their funds by selling short-term deposits and lend by using long-term loans. The steeper the upward sloping curve is, the wider the difference between lending and borrowing rates, and the higher is their profit. A flat or downward sloping curve, on the other hand, typically translates to a decrease in the profits of financial intermediaries.
iii. The Tradeoff between Maturity and Yield
The yield curve helps indicate the tradeoff between maturity and yield. If the yield curve is upward sloping, then to increase his yield, the investor must invest in longer-term securities, which will mean more risk.
iv. Overpriced or Underpriced Securities
The curve can indicate for investors whether a security is temporarily overpriced or underpriced. If a security’s rate of return lies above the yield curve, this indicates that the security is underpriced; if the rate of return lies below the yield curve, then it means that the security is overpriced.
Yield Curve Theories
i. Pure Expectation Theory
This theory assumes that the various maturities are substitutes and the shape of the yield curve depends on the market’s expectation of future interest rates. According to this theory, yields tend to change over time, but the theory fails to define the details of yield curve shapes. This theory ignores interest rate risk and reinvestment risk.
ii. Liquidity Preference Theory
This theory is an extension of the Pure Expectation Theory. It adds a premium called liquidity premium or term premium. This theory considers the greater risk involved in holding long-term debts over short-term debts.
iii. Segmented Market Theory
The segmented market theory is based on the separate demand and supply relationship between short-term securities and long-term securities. It is based on the fact that different maturities of securities cannot be substituted for one another. Since investors will generally prefer short-term maturity securities over long-term maturity securities because the former offers lower risk, then the price of short-term securities will be higher, and thus, the yield will be correspondingly lower.
iv. Preference Habitat Theory
This is an extension of the Market Segmentation Theory. According to this theory, investors prefer a certain investment horizon. To invest outside this horizon, they will require some premium. This theory explains the reason behind long-term yields being greater than short-term yields.
References
Corporate Finance Institute (2023). Yield Curve – Definition, Diagrams, Types of Yield Curves (corporatefinanceinstitute.com). https://corporatefinanceinstitute.com/resources/fixed-income/yield-curve/
https://www.chicagofed.org/publications/chicago-fed-letter/2018/404
Investopedia (2023). Yield Curves Explained and How to Use Them in Investing (investopedia.com). https://www.investopedia.com/terms/y/yieldcurve.asp