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A bond is trading at a price of 100 with a yield of 8%. If the yield increases by 1 basis point. the price of the bond will decrease to 99.95. If the yield decreases by 1 basis point. the price of the bond will increase to 100.04. What is the modified duration of the bond?

a) 5.0

b) -5.0

c) 4.5

d) -4.5 Example 1-6: FRl\1 Exam 1998--Question 22

What is the price impact of a 10-basis-point increase in yield on a 10-year par bond with a modified duration of 7 and convexity of 50?

a) -0.705

b) -0.700

c) -0.698

d) -0.690 Example 1-8: FRl\1 Exam 1998--Question 20

Coupon curve duration is a useful method for estimating duration from market prices of a mortgage-backed security (MBS). Assume the coupon curve of prices for Ginnie Maes in June 2001 is as follows: 6% at 92. 7% at 94. and 8% at 96.5. What is the estimated duration of the 7s?

a) 2.45

b) 2.40

c) 2.33

d) 2.25 Example 1-9: FRl\'1 Exam 1998--Question 21

Coupon curve duration is a useful method for estimating convexity from market prices of an MBS. Assume the coupon curve of prices for Ginnie Maes in June 2001 is as follows: 6% at 92. 7% at 94. and 8% at 96.5. What is the estimated convexity of the 7s?

a) 53

b)26

c) 13

d) -53

Example 1-10: FRM Exam 2001-Question 71

Calculate the modified duration of a bond with a Macauley duration of 13.083 years. Assume market interest rates are 11.5% and the coupon on the bond is paid semiannually.

a) 13.083

b) 12.732

c) 12.459

d) 12.371 Example I-II: FRl\'1 Exam 2002-Question 118

A Treasury bond has a coupon rate of 6% per annum (the coupons are paid semiannually) and a semiannually compounded yield of 4% per annum. The bond matures in 18 months and the next coupon will be paid 6 months from now. Which number is closest to the bond's Macaulay duration?…...

...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...

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...Chapter Nine Interest Rate Risk II Chapter Outline Introduction Duration: A Simple Introduction A General Formula for Duration • The Duration of Interest Bearing Bonds • The Duration of a Zero-Coupon Bond • The Duration of a Consol Bond (Perpetuities) Features of Duration • Duration and Maturity • Duration and Yield • Duration and Coupon Interest The Economic Meaning of Duration • Semiannual Coupon Bonds Duration and Interest Rate Risk • Duration and Interest Rate Risk Management on a Single Security • Duration and Interest Rate Risk Management on the Whole Balance Sheet of an FI Immunization and Regulatory Considerations Difficulties in Applying the Duration Model • Duration Matching can be Costly • Immunization is a Dynamic Problem • Large Interest Rate Changes and Convexity Summary Appendix 9A: The Basics of Bond Valuation Appendix 9B: Incorporating Convexity into the Duration Model • The Problem of the Flat Term Structure • The Problem of Default Risk • Floating-Rate Loans and Bonds • Demand Deposits and Passbook Savings • Mortgages and Mortgage-Backed Securities • Futures, Options, Swaps, Caps, and Other Contingent Claims Solutions for End-of-Chapter Questions and Problems: Chapter Nine ***signed to the questions 2 3 16 20 1. What is the difference between book value accounting and market value accounting? How do interest rate......

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...analysis of the relationship between the marital status of an employee and the period of time taken off from work due to injuries sustained at the workplace Abstract The primary aim of this paper is to analyze the statistical relationship between the marital status of an employee and the period of time said employee takes off from work due to injuries sustained at the workplace. The analysis will be conducted on the basis of data consisting of 7,150 observations and 13 variables. This paper will aim to observe as many factors which have bearing on the duration of benefits, as is reasonably possible, with a specific focus on the role of the marital status of an employee. Such an endeavor will necessitate the observation of a variety of aspects consisting of emotional, physical and sexual factors. The overarching aim of our analysis is to draw the attention of employers towards the different factors which impact durat (the time duration of the provision of benefits) and pique the interest of other researchers to conduct further studies on the issue we have raised in our current undertaking. Introduction The primary assumption of this paper shall be that married individuals have greater tendency to prolong the time they take off due to injuries, as compared to unmarried individuals, because their spouses are also members of the active workforce. Accordingly, married individuals can afford to take more time off because they are not the sole breadwinners of their......

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...Debt Instruments and Markets Professor Carpenter Convexity Concepts and Buzzwords • Dollar Convexity • Convexity • Curvature • Taylor series • Barbell, Bullet Readings • Veronesi, Chapter 4 • Tuckman, Chapters 5 and 6 Convexity 1 Debt Instruments and Markets Professor Carpenter Convexity • Convexity is a measure of the curvature of the value of a security or portfolio as a function of interest rates. • Duration is related to the slope, i.e., the ﬁrst derivative. • Convexity is related to the curvature, i.e. the second derivative of the price function. • Using convexity together with duration gives a better approximation of the change in value given a change in interest rates than using duration alone. Price‐Rate Func:on Example: Security with Positive Convexity Price Linear approximation of price function Approximation error Interest Rate (in decimal) Convexity 2 Debt Instruments and Markets Professor Carpenter Correc:ng the Dura:on Error • The price‐rate function is nonlinear. • Duration and dollar duration use a linear approximation to the price rate function to measure the change in price given a change in rates. • The error in the approximation can be substantially reduced by making a convexity correction. Taylor Series • The Taylor Theorem from calculus says that the value of a function can be approximated near a given point ......

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...Bond Portfolios 1. Duration can be thought of as a weighted average of the ‘maturities’ of the cash flows paid to holders of the perpetuity, where the weight for each cash flow is equal to the present value of that cash flow divided by the total present value of all cash flows. For cash flows in the distant future, present value approaches zero (i.e., the weight becomes very small) so that these distant cash flows have little impact, and eventually, virtually no impact on the weighted average. 2. A low coupon, long maturity bond will have the highest duration and will, therefore, produce the largest price change when interest rates change. 3. An intermarket spread swap should work. The trade would be to long the corporate bonds and short the treasuries. A relative gain will be realized when the rate spreads return to normal. 4. Change in Price = – (Modified Duration Change in YTM) Price = -Macaulay's Duration1+ YTM Change in YTM Price Given the current bond price is $1,050, yield to maturity is 6%, and the increase in YTM and new price, we can calculate D: $1,025 – $1,050 = – Macaulay's Duration1+ 0.06 0.0025 $1,050 D = 10.0952 5. d. None of the above. 6. The increase will be larger than the decrease in price. 7. While it is true that short-term rates are more volatile than long-term rates, the longer duration of the longer-term bonds makes their rates of return more volatile. The higher duration magnifies the......

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...Running Head: Calculate Convexity Calculate Convexity Leann Joseph Southern New Hampshire University Author Note: This short paper was done as an assignment in fulfillment of the requirements for: Southern New Hampshire University’s FIN 645 Analytical Tools in Portfolio 14TW3 Running Head: Calculate Convexity 3-2 Assignment Using an Excel spreadsheet, calculate the convexity for the two bonds you selected for the Module Two Assignment. Conduct an analysis of their duration and convexity and expound on the difference between the two concepts. Since I did not choose two bonds in Module Two Assignment, I considered the following bonds: **Using the dollar value of the bond and a $1000 face value, I considered a bond that has the following: Coupon rate-5 % Years remaining to maturity-5 Priced to yield- 4% Semi-annual interest Effective Duration: Yield 3% 4% 5% Value 109.222 104.491 100.000 Effective duration = (109.22218 – 100)/(2*104.49129*0.01) = 4.41289 The approximate change in price if the yield increases from 4% to 5% is: 4.41289 x 0.01 x –1 = –4.41289% Considering a bond that has the following: Coupon rate-5 % Years remaining to maturity-10 Priced to yield-4% Semi-annual interest Running Head: Calculate Convexity Effective duration: Yield 3% 4% 5% Value 117.168 108.175 100.000 Effective duration = (117.16864 - 100)/(2 (108.17572) (0.01)) = 7.935533 The approximate change in price if the yield increases from 4% to 5%:......

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...Assignment Print View http://ezto.mheducation.com/hm_finance.tpx award: 1.00 point A pension fund has an average duration of its liabilities equal to 14 years. The fund is looking at 5-year maturity zero-coupon bonds and 4% yield perpetuities to immunize its interest rate risk. How much of its portfolio should it allocate to the zero-coupon bonds to immunize if there are no other assets funding the plan? → 57.14% 42.86% 35.71% 26.00% Duration of the perpetuity = 1.04/0.04 = 26 years Duration of the zero = 1 years 14 = (wz)(5) + (1 – wz)26; wz = 57.14% Learning Objective: 11-04 Formulate fixed-income immunization strategies for various investment horizons. Multiple Choice Difficulty: 3 Hard award: 1.00 point You own a bond that has a duration of 5 years. Interest rates are currently 6%, but you believe the Fed is about to increase interest rates by 29 basis points. Your predicted price change on this bond is ________. (Select the closest answer.) +1.37% → –1.37% –4.72% +4.72% D* = 5/1.06 = 4.72 ∆P/P = –D*(∆y) = –4.72(0.29%) = –1.37% Learning Objective: 11-02 Compute the duration of bonds; and use duration to measure interest rate sensitivity. Multiple Choice Difficulty: 2 Medium 1 of 13 11/29/2014 1:56 PM Assignment Print View http://ezto.mheducation.com/hm_finance.tpx award: 1.00 point You have purchased a guaranteed investment contract (GIC) from an insurance firm that promises to pay you a 7% compound rate of return......

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...INVESTMENTS: DURATION BASED APPROACH Introduction: Duration Based Approach in investment depends on the investment goals and time frames, the amount of risks that can be taken and the income and tax structure. Investments on the basis of duration could be classified as: Short-Term, Medium Term or Long Term . * Short Term Investment: Investments made by an individual or organisation that will expire within one year. Commonly, these accounts contain stocks and bonds that are considered highly liquid assets. Example- Investing money for going in a vacation within a year, investing in company’s yearly inventories. * Medium term: An intermediate duration asset holding period or investment horizon. The exact time period to be considered as medium term depends on the investor's personal choices, as well as on the asset class under consideration. Bonds that have a maturity period of between 5 to 10 years are considered to be intermediate -term bonds In the fixed-income market. Example – Investing money for buying a house in 5 years, investing in machineries which will last for 5 years. * Long Term Investments: The account on the asset side of the balance sheet of any company which represents the investments that the company intends to hold for more than ten year. It includes real estate, stocks, bonds and cash. Example – Investing money in retirement scheme benefits, investing in long term assets of factories. Measurement of duration: * Effective duration can be......

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...Investment Advisory Commission Duration Basics Introduction Duration is a term used by fixed-income investors, financial advisors, and investment advisors. It is an important measure for investors to consider, as bonds with higher durations (given equal credit, inflation and reinvestment risk) may have greater price volatility than bonds with lower durations. It is an important tool in structuring and managing a fixed-income portfolio based on selected investment objectives. Investment theory tells us that the value of a fixed-income investment is the sum of all of its cash flows discounted at an interest rate that reflects the inherent investment risk. In addition, due to the time value of money, it assumes that cash flows returned earlier are worth more than cash flows returned later. In its most basic form, duration measures the weighted average of the present value of the cash flows of a fixed-income investment. All of the components of a bond—price, coupon, maturity, and interest rates—are used in the calculation of its duration. Although a bond’s price is dependent on many variables apart from duration, duration can be used to determine how the bond’s price may react to changes in interest rates. This issue brief will provide the following information: < A basic overview of bond math and the components of a bond that will affect its volatility. < The different types of duration and how they are calculated. < Why duration is an important measure......

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...sensitivity Duration Cash-flow matching Duration matching: immunization Convexity Prof. Lasse H. Pedersen 2 Interest-Rate Sensitivity First order effect: Bond prices and yields are negatively related Maturity matters: Prices of long-term bonds are more sensitive to interest-rate changes than short-term bonds Convexity: An increase in a bond’s YTM results in a smaller price decline than the price gain associated with a decrease of equal magnitude in the YTM. Prof. Lasse H. Pedersen 3 Duration The duration (D) of a bond with cashflows c(t) is defined as minus the elasticity of its price (P) with respect to 1 plus its yield (y): dP 1 + y T c(t ) D=− = ∑ f (t ) t , where f (t ) = dy P (1 + y ) t P 1 We see that the duration is equal to the average of the cash-flow times t weighted by f(t), the fraction of the present value of the bond that comes from c(t) ! The relative price-response to a yield change is therefore: ∆P ∆y D modified P ≅ −D 1+ y =− 1+ y { ∆y = − D ∆y modified duration Prof. Lasse H. Pedersen 4 Example: Duration of a Coupon Bond What is the duration of a 3-year coupon bond with a coupon rate of 8% and a YTM of 10% ? If the YTM changes to 10.1%, what would be the (relative) change in price ? If the YTM changes to 11%, what would be the (relative) change in price ? Prof. Lasse H. Pedersen 5 Duration Facts The duration of a portfolio is the weighted average of the......

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...There are two main types of memory, short term and long term memory; short term memory has a limited capacity and duration. Capacity is, the amount of information someone can store in their memory. The capacity of short term memory is between 5-9 things. Coding is the format of which things are stored in our memory. Duration is the amount of time we can remember something for. Short term memory has duration of between 18-30 seconds. There have been various amounts of research done by different people on capacity, duration and coding. Firstly research on capsid was done by joseph Jacobs. Jacobs developed the theory that how much someone could remember could be tested by using digit span. During this test a research would read 4 digits and a participant would have to read the 4 digits back, if the participants read them back correctly the researcher would then 5 digits and the participant would do the same before. This process was repeated increasing the number of letters by one each time until the participant got one of them wrong. This process was done with numbers and letters, doing this determines the duration of someone’s digit span. With this research Jacobs found that the mean across all participants was number of times was 9.3, the mean across letters was 7.3. This research was very useful but it did have its downfall. Jacobs research was lacking in validity, there could have been a lot of confounding variables that wouldn’t have been controlled things like, the......

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...Financial Mathematics for Actuaries Chapter 8 Bond Management Learning Objectives 1. Macaulay duration and modiﬁed duration 2. Duration and interest-rate sensitivity 3. Convexity 4. Some rules for duration calculation 5. Asset-liability matching and immunization strategies 6. Target-date immunization and duration matching 7. Redington immunization and full immunization 8. Cases of nonﬂat term structure 2 8.1 Macaulay Duration and Modiﬁed Duration • Suppose an investor purchases a n-year semiannual coupon bond for P0 at time 0 and holds it until maturity. • As the amounts of the payments she receives are diﬀerent at diﬀerent times, one way to summarize the horizon is to consider the weighted average of the time of the cash ﬂows. • We use the present values of the cash ﬂows (not their nominal values) to compute the weights. • Consider an investment that generates cash ﬂows of amount Ct at time t = 1, · · · , n, measured in payment periods. Suppose the rate of interest is i per payment period and the initial investment is P . 3 • We denote the present value of Ct by PV(Ct ), which is given by Ct . PV(Ct ) = t (1 + i) and we have P = n X (8.1) PV(Ct ). (8.2) t=1 • Using PV(Ct ) as the factor of proportion, we deﬁne the weighted average of the time of the cash ﬂows, denoted by D, as D = = n X t=1 n X t " PV(Ct ) P twt , # (8.3) t=1 where PV(Ct ) wt = . P 4 (8.4) P •...

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...M2) Explain how the action plan has helped support own development over the duration of the programme. My action plan has helped support my development over the duration of the programme. During the BTEC Health & Social Care programme I have gained great knowledge and that is something I did not think I could achieve. I have learned to research on certain subjects and gather so much information in order to complete assignments and tasks. This will help me to go university and study the course of my choice. Even the targets I have set for myself have helped me to be more serious about my career path and my future. Setting the action plan has helped me to apply for university through UCAS; I have also learned how to write my personal statement and my curriculum vitae. I have realised that my teachers and friends have been a great support towards all this and motivated in every way possible. The targets I have set for myself have helped me gain certain skills which will help me enormously. I have gained great work experience within the health and social care sector. I believe my voluntary work will also give me great experience and help me to get into university. I have received great support in order to achieve good qualifications and I understand that there are different routes for everything we do in life. Whilst I was on this programme my behaviour and attitude towards everything has become positive even though it was quite negative sometimes. Since I had set...

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...Target dollar duration can be found by multiplying the target duration by the dollar value of the portfolio. The target dollar duration is then compared to the current dollar duration and the difference is the dollar exposure that must be provided by a position in the futures contract. The following relationship holds: If target dollar duration > current dollar duration, buy futures If target dollar duration < current dollar duration, sell futures Dollar duration per futures contract: an illustration Assume the price of an interest rate futures contract is 70 and that the underlying interest rate instrument has a par value of $100,000. Thus, the futures delivery price is $70,000 ($100,000 x 0.7). Suppose that a change in interest rates of 100 basis points results in a futures price change of about 3% per contract, then the dollar duration per futures contract is $2,100. Hedging Hedging is a special case of controlling interest rate risk. In a hedge, the manager seeks a target duration or target dollar duration of zero. Hedging with futures calls for taking a futures position as a temporary substitute for transactions to be made in the cash market at a later date. If cash and futures prices are perfectly positively correlated, any loss realized by the hedger from one position will be exactly offset by a profit on the other position. A short hedge is used to protect against a decline in the cash price of a bond. To execute a short hedge, futures contracts......

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...Running head: INADEQUATE SELF-EFFICACY, EXCLUSIVITY AND DURATION Inadequate Self-Efficacy, Exclusivity and Duration of Breastfeeding in Primiparous Mothers Erika Warren Grand Canyon University: NRS 441V Professional Research Project August 12, 2012 Inadequate Self-Efficacy, Exclusivity and Duration of Breastfeeding in Primiparous Mothers When addressing the topic of breastfeeding there is one thing that is indubitable, that breast milk is the best option for feeding a newborn. The numerous benefits of breastfeeding have been studied and documented and the practice of breastfeeding has been embraced and is recommended by nearly all health organizations world-wide as the feeding method of choice. Breast milk provides nutrients and illness combating antibodies as well as being easier to digest. Some research has shown breast milk to have far reaching benefits such as reducing the risk of sudden infant death syndrome (SIDS), childhood leukemia, atopic dermatitis, and Type 1 diabetes (U.S. Department of Health and Human Services Office on Women’s Health, 2011). Yet despite the evidence, the number of women who exclusively breastfeed for at least 6 months, primiparous mothers in particular falls short of the World Health Organization’s (WHO) recommendation (American Association of Family Physicians News Staff, 2010). There are many factors that contribute to the lack of breastfeeding initiation or premature discontinuation, one of which is lack......

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