During the recent financial crisis, the interest rates and the yield curves have been frequently changing. The Bank of England offers access to the most recent yield curves as well as to the archived data on interest rates in the past.

By using the relevant data, theoretical concepts and models, answer the following three questions:

Question 1. What is the term structure of interest rates? Construct the yield curves in the UK for the end of each quarter in the last five years. You can use the surface chart type in Excel, or a similar 3D representation. Describe financial instruments used for your yield curves. How is the interest rate on those financial instruments calculated?

The term structure of interest rates refers to the relationship between interest rates and maturities which is better known as the yield curve. It also plays a key role in an economy of a country. (Gurkaynak, R., J. Wright, 2012) .It also used by banks to evaluate bonds. Apart from the aforementioned functions, economists all over the world use yield curves to predict fore coming inflation rates, have a better grasp of financial markets and to also predict tomorrows interest rates. During the recent financial crisis, the interest rates and the yields have been frequently changing with time. The Bank of England offers access to the most recent yield curves as well as to volumes of archived data on interest rates in the past. For instance, the yield curves in the United Kingdom for the end of each quarter in the last five years include the following:

(a) UK instantaneous commercial bank liability forward curve

The curve on the day of the previous MPC meeting is provided as reference point

(b) UK instantaneous nominal forward curve (gilts)

The curve is used as a reference point usually during the day of a previous MPC meeting.

(c) UK instantaneous nominal forward curve (OIS)

* The curve on the day of the previous MPC meeting is provided as reference point

(d) UK instantaneous implied real forward curve (gilts)

The curve on the day of the previous MPC meeting is provided as reference point

(e) UK instantaneous implied inflation forward curve (gilts)

The curve on the day of the previous MPC meeting is provided as reference point

These yield curves tend to use three different financial instruments as written in the context below:

Gilt edge securities (gilts); Gilt edge securities is an financial instrument whereby the bank of England was involved in many agreements where the government guaranteed to pay the holders of the gilts fixed cash payments twice a year until its maturity date. (Greenwood, R., D. Vayanos ,2010) It is at maturity date that then the holders received their final coupon payment and their principal. This financial instrument protects the value of the investment from erosion by inflation. This is usually done by adjusting coupon and principal payments to account of accrued inflations due to gilt issues. This is seen in the above curve (b), curve (d) and curve (e).

Forward rate agreement; this type of financial instrument is clearly seen in curve (a) where two different counterparties are seen to agree to the difference between an agreed interest rate and yet an unknown LIBOR rate of specified maturity that prevails at an agreed date in the future. Nevertheless, this payments are calculated against an initial agreed notional principal and at the same time gives room for institutions to look into future interbank borrowing. Not only does it allow the banks to look into future interbank borrowing but also helps them to have a look at the recent or by that time lending rates. There are also bilateral agreements. This bilateral agreements allow for no secondary market.

Overnight index swaps; overnight index swaps is seen in curve (c).This are contracts that involve the exchange at the maturity date of payment linked to a predefined interest rate. One of them is linked to the compounded overnight interest rates that prevail over the life of the contract. This is usually calculated by the Wholesale Market Brokers Association. (Greenwood, R., D. Vayanos ,2010) Swap; swap involves an agreement between two counterparties. In this agreement, the two counterparties agree to exchange fixed interest rate payments for floating interest rates payments. The interest rates are usually based on a pre-determined notional principal which is at the start of each number of successive periods.

There are different ways in which interests on these financial; statements are calculated. First off, different approaches are taken to come to a conclusion. This involves using a variety of measures that will assist in calculating the interest rate. This measures include, income, market and asset approaches. In the income approach, certain cash inflows and outflows are put into consideration. The present and future cash inflow and outflows are put into consideration.The present is used to calculate and predict the future. However, many assumptions are used when calculating the interest rates. This assumptions requires one to have a well-grown knowledge of the marketplace on hand. This involves knowing the creditworthiness of the enterprise.

Question 2. Based on the theories of the term structure, explain the shapes and changes in the yield curve you observe. What can you say about the behavior of the liquidity premium in this period?

There are several theories that are employed in term structure:

a)Expectation theory

b)Segmentation theory

c)Normal yield curve theory

d)Inverted yield curve theory

In expectation theory, the people in the market expectations about the future interest will determine the shape of the yield curve. For example, people borrow loans expecting the interest rates to go down at a certain point.

Segmentation theory states that, the shape of the curve in this case the yield curve is determined by people participating in the market. This is mainly affected by market prices and the capability of the people involved in the market.

Normal yield curve theory

This a normal yield curve. Its shape is usually up-sloping. This means that the yield of long-term securities is higher than the yield of short-term securities. The curve becomes steeper if the yield between the long-term securities and the short-term securities is bigger

Inverted yield curve theory

It occurs when the yield for long term securities is lower than the yield for short term securities. The curve is still in the up-sloping shape. This theory is the direct opposite of normal yield curve theory. It also referred to as a negative yield curve. This type of yield curve is very rare and occurs when people have no expectation or any confidence in the future interest rates and economy.

The following explains these theories in relation to the Bank of England.

The type of yield curves employed for the future periods include the nominal forward rates. In these types of yield curves, the interest rates for the future periods are simply incorporated with the present days spot interest rates for loans of different maturities. For instance, suppose todays interest rates for borrowing and lending money for 6 months is 6% per annum and that the rate for borrowing and lending for 12 months is 7%. Taken together the two interest rate contain an implicit forward interest rates for borrowing for a six months period starting in six month time. (Campbell, J. Y., Lo, A. W. C., & MacKinlay, A. C., 1997).

Secondly, there is the use of the real spot forward rates. Real spot forward rates involve a return on nominal bond that is in two categories. The first category stated is being a real rate of return and a compensation for the erosion of purchasing power arising from inflation. For example, a conventional government nominal zero coupon bonds, the nominal return is certain due to maturity but real return is not because of inflation uncertainty. (Bernanke, B. S., & Gertler, M., 1995).

Lastly, it has used the implied inflation rates that comprise the nominal rates covering the real interest rates as well as a compensation for the erosion of the purchasing power of this investment by inflation. The Bank of England used this decomposition and the real and nominal yield curves. These types of curves were used to calculate the implied inflation rates factored in to nominal interest rates. This is often interpreted as a measure of inflation expectations. (Weber, A., 2008).

In summary, the behavior of the liquidity premium is determined by the expectations theory. Liquidity refers to the degree in which an item can be bought and sold in any without influencing the actual or initial price of the item. Liquidity premiums are usually affected by time, that is, they can be affected by a certain period of the year or a certain time of the month. However, pricing is usually distributed differently at different periods and hence this should be taken into consideration .Also, trends in the market can actually affect liquidity premium of a certain item, for example, new trends in cars affects the old or other models available. In the expectation theory, in the curves plotted, a rising short term interest rates create the positive yield curves. (Obstfeld, M., Rogoff, K. S., & Wren-Lewis, S., 1996).

Question 3. Calculate the coefficient of correlation between yields on the instruments with the shortest and the longest maturity in your sample. Would you expect it to be lower or higher than that between assets with the medium-term and the longest maturity? Why?

For a continuous compounding, an amount A invested for n years at a rate r grows at Ae gilts. The expectations in this are meant to be high. This is because of the type of yield curves formed. The yield curves in this scenario will be positive due to a rising short term interest rates. Hence, this makes them higher than that between assets with the medium-term and the longest maturity. Following the segmented market hypothesis that states, different investor confine themselves to certain maturity segments making the yield curve a reflection of prevailing investment policies, there is reasonable answer to why coefficient of correlation between yields on the instruments with the shortest and the longest maturity will be positive hence making it high. (Frankel, J. A., 1995).

References

Frankel, J. A. (1995). Financial markets and monetary policy. MIT Press.

Weber, A. (2008). Financial markets and monetary policy. BIS Review, 116, 2008.

Bernanke, B. S., & Gertler, M. (1995). Inside the black box: the credit channel of monetary policy transmission (No. w5146). National bureau of economic research.

Campbell, J. Y., Lo, A. W. C., & MacKinlay, A. C. (1997). The econometrics of financial markets (Vol. 2, pp. 149-180). Princeton, NJ: princeton University press.

Campbell, J. Y., Lo, A. W. C., & MacKinlay, A. C. (1997). The econometrics of financial markets (Vol. 2, pp. 149-180). Princeton, NJ: princeton University press.

Obstfeld, M., Rogoff, K. S., & Wren-lewis, S. (1996). Foundations of international macroeconomics (Vol. 30). Cambridge, MA: MIT press.

Greenwood, R., D. Vayanos (2010) "Price Pressure in the Government Bond Market," The American Economic Review, 100, Papers and Proceedings, pp. 585-590

Gurkaynak, R., J. Wright (2012) "Macroeconomics and the Term Structure," Journal of Economic Literature, 50, pp. 331-367

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