Interest Rate Risk

In: Other Topics

Submitted By akshaya12345
Words 6633
Pages 27
Interest Rate Risk
Dr HK Pradhan XLRI Jamshedpur

Hull Ch 7 Fabozzi chapters on duration & Convexity, Ch-7, Convexity Stochastic Process notes

Session Objectives j
 Valuation of fixed income securities  Risks in fixed income securities
 Traditional measures of risk
– (we know PVBP, duration and convexity, M-Square) M Square)

 VaR based risk measures  Interest rate volatility calculations  Portfolio risk & Cash flows mapping issues  Var for Interest Rate Derivatives  Interest rate risk and Bond portfolio management

Profile of Interest Rate Markets, Instruments & Institutions

Bond Price
P

1  y 

C1

1



1  y 

C2

2



1  y 
Ct

C3

3



1  y n

Cn

price

Sum of the present values of each cashflows p

P



n

t 1

1  y 

t



M

1  y n

yield
 price < par (discount bond)  price = par (par bond)  price > par (premium bond)

Concept of Accrued Interest p
 When you buy a bond between coupon dates, you pay the seller: Clean Price plus the Accrued Interest
– pro-rated share of the fi coupon: i d h f h first interest d does not compound b d between coupon payment dates.

LD
Days Accrued Interest  Total

T from last Coupon between Coupon Date Dates Days

ND
(Coupon)

Dirty

Price  Clean price  Accrued

Interest

Accrued Interest  Face *

C T  LD * 2 ND  LD

Bond Valuation
Value of a bond is the present value of future cashflows, so the pricing equation of the bond is:

tP 

1  y  n C1

v



1  y 
Ct

C2

1 v



1  y 


C3

2v

 M

1  y n1v

Cn

tP  t 1

1  y  1  y  v t 1

1  y v 1  y n1

When v= 1, what happens?

This gives the dirty price (also known as the full price) The dirty price is the fair value or market value of the bond You…...

Similar Documents

Interest Rates

...INTEREST RATE RISK MANAGEMENT: DEVELOPMENTS IN INTEREST RATE TERM STRUCTURE MODELING FOR RISK MANAGEMENT AND VALUATION OF INTEREST-RATE-DEPENDENT CASH FLOWS Andrew Ang* and Michael Sherris† ABSTRACT This paper surveys the main concepts and techniques of recent developments in the modeling of the term structure of interest rates that are used in the risk management and valuation of interest-rate-dependent cash flows. These developments extend the concepts of immunization and matching to a stochastic interest rate environment. Such cash flows include the cash flows on assets such as bonds and mortgage-backed securities as well as those for annuity products, life insurance products with interest-rate-sensitive withdrawals, accrued liabilities for definedbenefit pension funds, and property and casualty liability cash flows. 1. INTRODUCTION The aim of this paper is to discuss recent developments in interest rate term structure modeling and the application of these models to the interest rate risk management and valuation of cash flows that are dependent on future interest rates. Traditional approaches to risk management and valuation are based on the concepts of immunization and matching of cash flows. These ideas were pioneered in the actuarial profession by the British actuary Frank Redington (1952). Interest rates have long been recognized as important to the risk management of insurance liabilities. Recent developments have incorporated a stochastic approach to modeling......

Words: 18994 - Pages: 76

Interest Rates

...Interest Rates, Income Distribution, and Monetary Policy Dominance: Post Keynesians and the "Fair Rate" of Interest Author(s): Louis-Philippe Rochon and Mark Setterfield Source: Journal of Post Keynesian Economics, Vol. 30, No. 1 (Fall, 2007), pp. 13-42 Published by: M.E. Sharpe, Inc. Stable URL: http://www.jstor.org/stable/27746784 . Accessed: 28/08/2013 13:51 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . M.E. Sharpe, Inc. is collaborating with JSTOR to digitize, preserve and extend access to Journal of Post Keynesian Economics. http://www.jstor.org This content downloaded from 140.159.34.46 on Wed, 28 Aug 2013 13:51:45 PM All use subject to JSTOR Terms and Conditions LOUIS-PHILIPPE ROCHON AND MARK SETTERFIELD Interest rates, income distribution, and monetary policy dominance: Post Keynesians and the "fair rate" of interest Abstract: paper In light of the growing interest in "new consensus" models, Post Keynesian alternatives to the Taylor rule. It......

Words: 7910 - Pages: 32

An Analysis of Exchange Rate and Interest Rate

...AN ANALYSIS OF THE EFFECTS OF INTEREST RATE AND EXCHANGE RATE CHANGES ON STOCK MARKET RETURNS: EMPIRICAL EVIDENCE OF GHANA STOCK EXCHANGE A thesis submitted to the Institute of Distance Learning, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the degree of COMMONWEALTH EXECUTIVE MASTERS OF BUSINESS ADMINISTRATION Institute of Distance Learning, KNUST JUNE, 2011 DECLARATION I hereby declare that this submission is my own work toward the Commonwealth Executive Master of Business Administration and that, to the best of my knowledge, it contains no material previously published by another person nor material which has been accepted for the award of any other degree of the University except where due acknowledgement has been made in the text. RANSFORD CHARLES ENYAAH (STUDENT ID No: 20103521) …………………… Signature …………………. Date Certified by: EDWARD ACHEAMPONG (SUPERVISOR) …………………… Signature …………………. Date Certified by: ……………………………… Head of IDL …………………… Signature …………………. Date i DEDICATION I dedicate this project work to the Lord Almighty and all my loved ones. ii ACKNOWLEDGEMENT First of all, I thank the almighty God for fulfilling his promises to my life and for granting me the strength, wisdom and knowledge to complete this work My profound gratitude goes to my Supervisor, Mr. Edward Acheampong (Lecturer, Methodist University College, Ghana) for his unflinching......

Words: 13267 - Pages: 54

Whether the Interest Rate Pushes Equity Risk Premium Rate Up?

...Introduction: We know the fact that low interest rate affects stock market price. Low interest rate decreases the cost of capital and increases the confidence of investors. The equity risk premium is the "extra return" that investors collectively demand for investing their money in stocks instead of holding it in a risk less or close to risk less investment. As a consequence, equity risk premium reflects both investor hopes and fears about stocks, rising as the fear factor increases. As a measure the equity risk premium can be an individual stock or the overall stock market provides over a risk-free rate. And the size of the premium will be a standard to compensate with a higher premium in the stock market. Thus, a portfolio manager when the equity risk premium increases in the future, the investors will sell out stock market because the stocks are over priced. So the legislators and pension administrators decide how much to set aside to meet future pension obligations, based upon assessments of equity risk premiums. However the history data of ERP (Equity Risk Premium) from Federal Reserve System shows it keeps low and stable state but increases suddenly since 2006. At the same time the Federal Funds Effective Rate goes down and keeps low state. We know that interest rate is a way to control inflation. Inflation is a factor causes too much money chasing too few goods. “Changes in the federal funds rate affect the behavior of consumers and......

Words: 3534 - Pages: 15

Interest Rates

...industry began to fail, the US Treasury increased the interest rate on Treasury bills as a way to bring more money back to the government. As you can see from the graph, in 2009 a 1 year Treasury bill had an average interest rate of 0.55%. Throughout the short recession, the interest rate remained above 0.20% because Treasury bills were not in high demand. People had their own financial troubles, so very few could afford to send money to the government. In the first few quarters of 20122, you can see a drop in the interest rate. This was a result of the recession coming to an end. More people were able to buy Treasury bills, lowering the interest rate. In early 2012, the interest rate rose slightly, then dropped off to 0.12%, where it has remained steady since. Taking a look at the four week, three month, and six month Treasury bills, you can see the same trends. In the first quarter of 2011, the four week bill dropped substantially, from 0.10% to 0.02% and remained there until the economy began to pick back up. Notice the steady rise during 2012, and then another drop off during the second quarter of 2013. This means more people were buying Treasury bills. The three and six month Treasury bills were very similar during the recession. At the beginning of 2009, those bills were relatively high in interest rates. As there was a larger demand, the interest rates began to drop off, until 2012, when demand eased up and the interest rates began to rise again. During 2013, both......

Words: 667 - Pages: 3

Interest Rate

... | Achievements / Awards |VAT—And Reservation for Under Developed States, Published By : Academic Research Journals (ndia)  | |Frequency : Bi-Annual | |ISSN : 2319-443X  | | | Hobbies / Interests |Painting | |Designing | |Drawing | |Cinema and theater-going | Personal Details |Father’s Name: Dr. Asit Kumar Pal ...

Words: 361 - Pages: 2

Interest Rate

...With HACK's bank recent cut on interest rate 12 months earlier, loan base has grown, however profit has not, this is due to the fact that lowering interest rate does not necessary mean a rise in profit as consumers may refuse to hold the bank's money and present it to a rival bank, thus does not return to the Hack bank, subsequently causing a fall in security investments and deposits as well as a loss in an interest earning asset. In other words, the non banking public does not want to hold funds with HACK bank possibly due to competitive interest rates for deposits or stability. Although it would seem logical for the bank to lower credit standards or reduce interest rate in order to advance credit and increase profit. It is not necessarily the right thing to do, as the non banking public seek to hold the bank's deposits in a hostile free bank, with minimal risk. Consequently the non banking public will turn away from institution who offer a lower credit standard or lower interest rate due the possibility of non repayment thus consequently could impact the non banking publics asset, this is one of the many reasons why the non banking public refuse to hold funds with a bank that lowers their standards. Instead of lowering rates, HACK bank should be paying competitive rates, to indicate to the market that they can keep up and is stable enough to hold funds. Although HACK bank's loan base has increased, its cut on interest rate, has not benefited in the liquidity side of......

Words: 478 - Pages: 2

Interest Rate

...Assignment #3 Intrest rates are considered to be the price of holding money and the opportunity cost of any investment. After analysing intrests rates in our course do you think that interest rate in Egypt reflect the real opportunity cost of holding money? why or why not? Please support your answer with all the references you have searched. The opportunity cost of holding money is the cost that could be realized if money were invested instead of held. In other words, it is the interest rate that money is earning in a chosen investment. Typically, it is the interest rate that is set on a bond, particularly a government bond. Given the other investment choices that could be made, this cost could be very different from one person or entity to another. To determine the true opportunity cost of holding money, it is necessary to first determine what the investment vehicle would have been. After that, the next step is to research what the interest rate would be on that investment strategy. If the annual percentage rate is a single percent, then one percent annually would be the opportunity cost of holding onto the money. Assigning a definite value would require first knowing how much money was being held, and how long it would be held for. In economics, investing and holding money are known as mutually exclusive choices. This means that both cannot be done at the same time with the same money. If the money is being invested, it cannot be held. It may be possible for an......

Words: 510 - Pages: 3

Risk Free Interest Rate

...CHAPTER 12: COST OF CAPITAL A. OVERVIEW Definition: Cost of capital refers to the rate of return • a firm must earn on its investment projects to increase the market value of its common shares • required by market suppliers of capital to attract funds to the firm Notes: • If project rate of return > cost of capital ( value of firm increases • If project rate of return < cost of capital ( value of firm decreases • Goal: minimize cost of capital Assumptions: 1. Business risk (not able to cover operating costs) is unchanged 2. Financial risk (not able to cover financial obligations) is unchanged 3. Cost of capital is measured on an after-tax basis Basic equation: Ways to evaluate the basic equation: 1. Time-series: historic cost of capital 2. Compare with other firms (cross-section) Example 1 (Time-series) Firm A had a cost of long-term debt 2 years ago of 8%. Risk-free cost of long-term debt is 4%. Business risk premium is 2%, and financial risk premium is 2%. What is the cost of long-term capital of the firm when the current risk-free cost of long-term debt is 6%? Example 2 (Cross-section comparison) Firm B is in the same business and with a financial premium of 4%. The cost of capital of firm B is higher than that of firm A by 2 %. Definition: Target capital structure refers to the desired optimal mix of debt and equity financing that most firms attempt to achieve and maintain. B. COST OF LONG-TERM......

Words: 1094 - Pages: 5

Interest Rates

...Exam 2 Study Guide Chapter 6: Interest Rates 1. Using the yield curve to predict interest rates (section 6-6) 2. Determinants of market interest rates (section 6-3) Be sure you know how to calculate any given components with given supporting information. 3. What determines the shape of a yield curve (section 6-5) Practice problems: 6-2, 6-3, 6-4, 6-5, 6-7, 6-9, 6-11, 6-14 Chapter 7: Bond Valuation 1. Key characteristics of bonds (7-2) 2. Bond valuation (7-3) 3. Bonds with semi-annual coupons (7-6) 4. Assessing a bond’s risk (7-7) 5. Bond yields (7-7) Practice problems: 7-1, 7-2, 7-3, 7-4, 7-5, 7-8, 7-9, 7-16 Chapter 8: Risk & rates of Return 1. Stand-Alone risk (8-2) 2. Risk in a portfolio context (8-3) 3. Relationship between risk and rate of return (8-4) 4. Implications for corporate managers & investors (8-6) Practice problems: 8-1, 8-3, 8-4, 8-6, 8-7, 8-11, 8-12, 8-14 *In addition please review the Cengage assignments & Team application activities that apply to the above chapters. Important note: Please note that this is only a study guide and should not be taken as the actual content of your second exam. In other words, reading the sections above and attempting the problems recommended should put you in a comfortable position to handle majority of questions in the exam. It is therefore prudent to expand your preparation beyond this guide....

Words: 265 - Pages: 2

Interest Rates

...Jeniffer Kim Theory of Interest Professor Chiacchiere How Interest is Effecting the U.S. Markets Today In 5000 BC, the lending of “food” money was commonplace in Middle East civilizations. Early loans and interest were based on agricultural produce. Because the acquired seeds and livestock could be replenished and reproduce themselves, the people could easily repay loans with interest using these goods. Throughout history, the practice of having interest charged on loans developed over the years. Today, people pay interest using various foreign currencies. It has been legal and regulated by different states, but it also has been restricted in different countries because of religious reasons. In the past, some cultures have regarded charging any interest for loans as sinful. Charging interest was known as ursury and Christians, Muslims and even Buddhists condemned those who practiced it. Although some disapproved of charging interest, there is no doubt that it has played a large role in moving the markets and impacting our society today. In the U.S., changes in interest rates can have both a positive and negative effect on the economy, inflation and recessions, and the stock and bond markets. Many may ask why people use interest in their everyday lives and how it makes a direct impact on the economy. When an individual takes out a loan from a bank or another party, there is a possibility that the borrower will not repay the money. The purpose of interest is to......

Words: 1382 - Pages: 6

Option Pricing, Interest Rate Risk in U.S

...Option Pricing, Interest Rate Risk in U.S Diana PĂUN & Ramona GOGONCEA (2013). Interest Rate Risk Management and the Use of Derivative Securities. Economia Seria Management. Retrieved from: <http://www.management.ase.ro/reveconomia/2013-2/4.pdf> The study by these two authors aims at demonstrating how derivative financial instruments can be utilized to prudently manage interest rate risk majorly faced by numerous banks and financial institutions as well as enable the efficient application of monitoring and control tools. There are a couple of risk management methods at the disposal of banks including both balance sheet and off the balance sheet such as the gap method of managing interest rate risk for purposes of controlling short-term rates exposure, combined with derivatives such as options to manage the residual interest rate exposures. Interest rate risks emanate from interest rates sensitivity differentials of capital outflows and inflows. Due to the common view or misconception that high interest rates are the best way of fighting inflation, banks’’ engaging in monetary policy. Financial institutions play a major role in influencing interest rates since they engage in releasing capita to the public by buying assets in the primary markets and selling securities in the secondary market so as to fund purchase of assets. Furthermore, any interest-bearing asset for instance a loan or bond may face interest rate risk caused by changes in the value of assets......

Words: 2017 - Pages: 9

Interest Rate

...Interest rates are considered to be the price of holding money and the opportunity cost of any investment. After analyzing interest rates in our course do you think that interest rate in Egypt reflects the real opportunity cost of holding money? Why or why not? Please support your answer with all the references you have searched. Interest Rate is: The amount charged, expressed as a percentage of principal, by a lender to a borrower for the use of assets. Interest is charged by lenders as compensation for the loss of the asset's use. In the case of lending money, the lender could have invested the funds instead of lending them out. That’s why interest rate should cover the opportunity cost of lending the money to the borrower. Also, interest rate should cover the inflation rate in the economy, as by time the lender receives the principal again due to inflation, the money will be of less value than when first lent to the borrower. So, if the interest rate doesn’t cover both the opportunity cost and inflation, it’ll be irrational decision to lend the money. For example, if the lender can invest in some real estate and construction projects with an average return of 10% & if inflation is 10%, then the interest rate should be more than 20% to be rational choice for the lender to lend the money. Interest rate in Egypt: (Lending Interest Rate) So, The lending interest rate is now at 9.75% annually, so, does this rate covers the inflation rate & opportunity cost of......

Words: 332 - Pages: 2

Interest Rate

...swelling or financing expenses to secure the dauntlessness of costs moreover, the normal trust in the nation's money and the cash related technique also tries to offer help with improving the fiscal advancement and steadfastness and to give more business open entryways besides, to keep up obvious exchange rates with various countries money related structures. Monetary technique can either be expansionary or contractionary . In case it is expansionary it grows the total of supply of the trade out the economy brisk however if it s contractionary it broadens the money supply continuously . In the latest year morocco lessened its credit cost from 2.5% to 2.25% and a significant extended period of time back it was 6.5% and each one of this to urge nationals to stop saving money and to start eating up also, spending logically moreover to ask outside budgetary experts to place assets into the country and even locals will start getting progressively money and eat up more which will be a gigantic favorable position for the economy in light of the fact that my reducing the advance charge we diminish the cost of securing money and each one of this will outcome of cutting down the rate of unemployment and growing optional income for customers. A part of exchange components that we can use to upgrade the economy's advancement are : * Improving HR : The sum and the way of open individuals can clearly impact the improvement of the economy since a country can't have an......

Words: 831 - Pages: 4

Interest Rates

...Interest Rates Write two paragraphs with about how interest rate affects our purchasing decisions. Paragraph One Changes in interest rates can have positive and negatives effects. According with the interest rate that we have is the amount of money that we are going to paid every month for a loan. If we have a high interest rate we have a high monthly payment, and we need to make sure that we can afford that. If we have a low interest rate our monthly payment is less. If the interest rates change the incentive for individuals to take out loans to buy goods will also change. In the interest falls for example, then the charges for a loan to buy larger items likes cars, furniture, electrical equipment, and so on, is also likely to fall. As a result more people might be willing to buy such items and the business selling these items might see and unexpected rise in demand for their products. Equally, if the interest rate rises, people might be put off buying things, since it is now more expensive to pay back the loan. Business selling the same products above, might see and unexpected fall in the demand of their products. For the individuals and for the business the changes in the interest rates can have a big impact in their financial situation. Paragraph Two Further effects of changing interest rates can affect our mortgage. For many of us, the mortgage payment is the biggest single monthly outgoing and houses are not paid off......

Words: 351 - Pages: 2