Assume it is January 1, 2024. Shubha is managing her financial portfolio and calculates that her...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Assume it is January 1, 2024. Shubha is managing her financial portfolio and calculates that her liabilities - including credit card payments, student loans, and car payments - have a modified duration of 7 years. Moreover, the present value of her liabilities is $25,000. She decides she would like to buy $25,000 worth of bonds as assets which, on average, have the same modified duration as her liabilities. This is known as portfolio immunization. Concerned about future changes in yields, she wants to match her 7- year liability duration by utilizing a bond barbell strategy. Specifically, she decides to buy 3-year, zero coupon bonds and 12-year zero coupon bonds. The yield curve on January 1, 2024 looks as follows: Maturity (in years) 1 2 3 11 12 1% 2.5% 4.5% 5.3% 5.5% Yield a) (3 points) Find the bond prices and modified durations of both bonds. Which bond has a duration that is closest to the duration of Shubha's liabilities? b) (4 points) Find the portfolio weights needed to ensure Shubha's assets and liabilities on average have the same duration. Before Shubha has a chance to purchase any bonds, all rates increase by .5% (50 bps). c) (4 points) Use modified duration to predict the percentage price changes of both bonds. Which bond has the larger predicted percentage price change? Hint: The percentage price change is (New Price - Old Price)/Old Price. New Price - Old Price is defined as the change in price. d) (3 points) Compare the predicted percentage price changes with the actual percentage price changes. Which bond's predicted percentage price change is closer to its actual percentage price change? e) (4 points) What should Shubha's new portfolio weights be, given Shubha's desire for her assets and liabilities to have the same modified duration? Which bond now has the higher portfolio weight? Explain why this makes sense, given the bonds' new modified durations. f) (2 points) How many of each bond should she buy? Use the actual new price to determine this number, not the estimated value. Assume a year has passed and all rates have again increased by .5% (50 bps). Within the year Shubha has paid off some of her debt, but due to rising interest rates, the amount and duration of her liabilities has changed. Specifically, she now owes $26,412.79, which has a modified duration of 6.5 years. g) (3 points) Find the new prices and the new total value of Shubha's bond portfolio. Also, find the portfolio weights of both bonds. h) (3 points) Find the modified duration and average modified duration of Shubha's bond portfolio. Is she currently under-immunized (i.e., average asset duration < liability duration) or over- immunized (i.e., average asset duration > liability duration)? i) (4 points) What should Shubha's new portfolio weights be, given Shubha's desire to be immunized (i.e., average asset duration = liability duration)? j) (Bonus 5 points) What value of each bond should Shubha buy/sell to obtain the portfolio weights determined in part i)? After buying/selling bonds, how many of each bond will she have in her portfolio? Assume it is January 1, 2024. Shubha is managing her financial portfolio and calculates that her liabilities - including credit card payments, student loans, and car payments - have a modified duration of 7 years. Moreover, the present value of her liabilities is $25,000. She decides she would like to buy $25,000 worth of bonds as assets which, on average, have the same modified duration as her liabilities. This is known as portfolio immunization. Concerned about future changes in yields, she wants to match her 7- year liability duration by utilizing a bond barbell strategy. Specifically, she decides to buy 3-year, zero coupon bonds and 12-year zero coupon bonds. The yield curve on January 1, 2024 looks as follows: Maturity (in years) 1 2 3 11 12 1% 2.5% 4.5% 5.3% 5.5% Yield a) (3 points) Find the bond prices and modified durations of both bonds. Which bond has a duration that is closest to the duration of Shubha's liabilities? b) (4 points) Find the portfolio weights needed to ensure Shubha's assets and liabilities on average have the same duration. Before Shubha has a chance to purchase any bonds, all rates increase by .5% (50 bps). c) (4 points) Use modified duration to predict the percentage price changes of both bonds. Which bond has the larger predicted percentage price change? Hint: The percentage price change is (New Price - Old Price)/Old Price. New Price - Old Price is defined as the change in price. d) (3 points) Compare the predicted percentage price changes with the actual percentage price changes. Which bond's predicted percentage price change is closer to its actual percentage price change? e) (4 points) What should Shubha's new portfolio weights be, given Shubha's desire for her assets and liabilities to have the same modified duration? Which bond now has the higher portfolio weight? Explain why this makes sense, given the bonds' new modified durations. f) (2 points) How many of each bond should she buy? Use the actual new price to determine this number, not the estimated value. Assume a year has passed and all rates have again increased by .5% (50 bps). Within the year Shubha has paid off some of her debt, but due to rising interest rates, the amount and duration of her liabilities has changed. Specifically, she now owes $26,412.79, which has a modified duration of 6.5 years. g) (3 points) Find the new prices and the new total value of Shubha's bond portfolio. Also, find the portfolio weights of both bonds. h) (3 points) Find the modified duration and average modified duration of Shubha's bond portfolio. Is she currently under-immunized (i.e., average asset duration < liability duration) or over- immunized (i.e., average asset duration > liability duration)? i) (4 points) What should Shubha's new portfolio weights be, given Shubha's desire to be immunized (i.e., average asset duration = liability duration)? j) (Bonus 5 points) What value of each bond should Shubha buy/sell to obtain the portfolio weights determined in part i)? After buying/selling bonds, how many of each bond will she have in her portfolio?
Expert Answer:
Answer rating: 100% (QA)
a To find the bond prices and modified durations we can use the formula Bond Price Face Value 1 YieldMaturity Modified Duration Maturity 1 Yield For the 3year zero coupon bond Bond Price 25000 1 00453 ... View the full answer
Related Book For
Contemporary Business Mathematics with Canadian Applications
ISBN: 978-0134141084
11th edition
Authors: S. A. Hummelbrunner, Kelly Halliday, Ali R. Hassanlou, K. Suzanne Coombs
Posted Date:
Students also viewed these finance questions
-
A\ Excel Assignment 1 Questions\ 1\ 2\ INSTRUCTIONS\ Sort the data in EA1 Data by Date [from oldest to newest] and then by Product [from PROD-001 to PROD-\ 3 200]. The data should be sorted by both...
-
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
-
A self-care plan can help you enhance your health and wellbeing, manage your stress, and maintain professionalism as a worker with young people. Learn to identify activities and practices that...
-
Charles has a savings account with a balance, today, of 100,000 SAR in his investment account. He expects to obtain a yearly return of 12% in his investments. How long will it take for Charles to...
-
Fauxhemain Ltd mass-produces antique-style furniture using an assembly line process. All direct materials are introduced at the start of the process, and conversion cost is incurred evenly throughout...
-
A 20 by 20 cm slab of copper 5 cm thick at a uniform temperature of 260C suddenly has its surface temperature lowered to 35C. Using the concepts of thermal resistance and capacitance and the...
-
Requirements 1. Using the following selected accounts of Juba Electrical, Inc., at September 30, 2010, prepare the entitys closing entries: 2. What is Juba Electricals ending Retained Earnings...
-
The following transactions were incurred by Howley Fabricators during January, the first month of its fiscal year. Requirements 1. Record the proper journal entry for each transaction. a. $ 180,000...
-
Today, during the class time you had the oportunity to meet Alicia Vianga, Founder and ED of' After Breast Cancer Society". If you will have the oportunity to be part of the event organizer for one...
-
Part C: Communication [20 marks] -99 1. Investment A offers a fixed annual interest rate of 6%, compounded annually for 15 years. Investment B offers the same fixed annual interest rate of 6%,...
-
A project team member has performed outstandingly during the duration of the project. Their efforts have gone beyond what is expected. As a project team manager, what strategy should you take to...
-
How to write a thesis on a research project assignment? The topic is what are the stereotypes living with epilepsy?
-
Which of the following accurately describes a requirement for a business to qualify as a qualified small business corporation a . The corporation must be a CCPC that uses at least the shares are sold...
-
How to write a proposal on classism for picking majors of study?
-
Golden Wedding Dress Company designs custom wedding dresses for brides to be. The person preparing the adjusting entries at year-end was unable to complete the adjustments due to illness. You have...
-
Mandy takes some money from the business bank account to pay some of her personal expenses. What is the part of the business's accounting equation will change?
-
Solve the following pair of linear equations by the cross multiplication method: x + 2y = 2; x 3y = 7
-
Which of the ocean zones shown would be home to each of the following organisms: lobster, coral, mussel, porpoise, and dragonfish? For those organisms you identify as living in the pelagic...
-
Determine the value of a $1300 non-interest- bearing note four months before its maturity date of July 13, 2017, if money is worth 7%.
-
The net price of an article is $63.31. What is the suggested retail price (the list price) if a discount of 35% was allowed?
-
Keys Company has a target of establishing a fund of $50 000. If $10 000 is deposited at the end of every six months, and the fund earns interest at 4% compounded quarterly, how long will it take to...
-
Consider a bivariate time series \(\boldsymbol{z}_{t}\), where \(z_{1 t}\) is the change in monthly U.S. treasury bills with maturity 3 months and \(z_{2 t}\) is the inflation rate, in percentage, of...
-
Consider the growth rates, in percentages, of the quarterly real GDP of United Kingdom, Canada, and the United States used in the chapter. Fit a VAR(4) model to the series, simplify the model by...
-
Consider the U.S. quarterly gross private saving (GPSAVE) and gross private domestic investment (GPDI) from first quarter of 1947 to the third quarter of 2012. The data are from the Federal Reserve...
Study smarter with the SolutionInn App