How does time to maturity affect the duration of a bond

Assignment Help Finance Basics
Reference no: EM131223255

Assignment

Zero rates and arbitrage pricing, and introduction to duration

Please turn in one copy per group. Please do not submit this printout along with your homework. Please show your work. Please write all of your names and your section number on your submission. It is recommended that you use Excel to solve this homework.

Bootstrapping

The following annual coupon bond prices with face values of $100 from a "risk-free" institution have been observed in the market as of 11/01/2015:

Maturity Date

Annual coupon rate

Price in decimals

11/01/2016

3.5%

100.00000

11/01/2017

3.5%

100.47299

11/01/2018

3.5%

101.39991

11/01/2019

3.5%

102.54795

11/01/2020

3.5%

103.97606

11/01/2021

3.5%

105.22412

1. Using bootstrapping, calculate the zero rates implied by the market prices above. Round answers to near the nearest basis point.

2. Using the zero rates above, calculate the discount factors in question 1. above

3. Using the zero rates, calculate the arbitrage-free price of a 3-year, 4% annual coupon bond with a par value of $100 maturing on 11/01/2018

4. Using the zero rates, calculate the coupon rate the "risk-free" institution would need to offer on a three-year annual coupon bond to result in an issuance price of par or $100. Round solution of c to nearest basis point. Here, given a set of zero rates, you'll need to guess a coupon rate ‘c' that sets the price of the bond equal to par.

Duration

5. Consider the following bonds:

Bond

YTM (%)

Coupon Rate (%)

Years to maturity

A

5

5

5

B

5

5

10

C

2

5

5

D

5

8

5

a. Calculate the duration for each of these $100 par, annual coupon bonds
b. How does time to maturity affect the duration of a bond? Why?
c. How does YTM affect the duration of a bond? Why?
d. How does the coupon rate affect the duration of a bond? Why?

Empirical

For this exercise we're going to analyze some historical data on zero-coupon bonds over the last 60 or so years. Included in this homework is a spreadsheet called "Zeros.xlsx". After the "Date" column, each column lists the price of a zero-coupon bond with a par value of $100 of a particular maturity, in years. For example on December 31, 1952, the price of a 1-year zero maturing on December 31, 1953 is $98.022 (Cell C3); the price of a 2-year zero maturing on December 31, 1954 is $95.713 (Cell D3); and so on. Notice that after a year the price of the 1-year zero is exactly $100, as the bond matures (Cell B4); analogously, after a year, the 2-year zero is now priced as a one-year zero at $98.438 (Cell C4); and so on.

1. Calculate the zero rates for each maturity from years 1 to 5 for each year. Plot them on a chart.

2. There is significant time variation in these rates. The National Bureau of Economic Research (NBER) "dates" business cycles: https://www.nber.org/cycles.html. What happens to the spread between the one-year zero rate and the five-year zero rates during recessions; that is, which rate falls relatively more, the one-year rate or the five-year rate? Why do you think that is?

Now we're going to look at some properties of the annual returns of these zero-coupon bonds. These aren't the "approximate" returns in the lecture slides because we'll be explicitly accounting for the one-year lapse in maturity. To calculate the annual return on zero-coupon bond you simply need to use this formula

Annual Return_today=(P_today-P_(last year))/P_(last year)

For example, the three-year zero as of December 31, 1952 was priced $93.587 (Cell E3). In one year's time the bond was now a two-year zero priced at $96.47 (Cell D4). Its annual return over the year, then, was

Annual Return_19531231=(P_19531231-P_19521231)/P_19521231 =(($96.47-$93.587))/$93.587=0.0308 or 3.08%

Loosely speaking, similar shifts of "one-cell-left-and-one-cell-down" (Cell E3 becomes D4, and so on) results hold for every other annual return. Note that you'll lose one time series observation when calculate returns for an asset; that is, if you have T price observations, you'll only have T-1 return observations.

3. Calculate the entire annual return series for each zero-coupon bond. In the end you'll have five annual return series, one for each maturity. Each annual return series should be 60 observations.Don't submit these time series!

4. Using Excel, calculate the average return for each of the zeros. Also calculate the standard deviations. To calculate the average return, use Excel's "=AVERAGE(...)" function. To calculate the standard deviation, use Excel's "STDEV(...)" function. For each maturity, report the zeros average return and standard deviation of those returns in table.

5. If we take standard deviation as a crude measure of risk, which bonds are riskier, the short-term bonds or the long-term bonds? Are you compensated for this risk in the form of a higher average return?

Reference no: EM131223255

Questions Cloud

Roles of security devices in each layer : Roles of Security Devices for WWTC: I will divided the network design into five layers and described the roles of security devices in each layer.
Monetary policy reaction and dynamic aggregate demand curve : What would you expect to happen to the long-run real interest rate? - What impact would this have on the monetary policy reaction curve and the dynamic aggregate demand curve?
Declared and assigned the value true or false : Assume that a boolean variable named a has been declared and assigned the value true or false. You should also assume that two hint variables named b and c have been declared and assigned some integer values.
Describe the components of the healthcare system in us : Identify the major economics related research questions and challenges being asked in the areas of health insurance provision, the pharmaceutical industry, the physician services industry and the long term care industry;
How does time to maturity affect the duration of a bond : How does time to maturity affect the duration of a bond? Why? How does YTM affect the duration of a bond? Why? How does the coupon rate affect the duration of a bond? Why?
Movement along or a shift in monetary policy reaction curve : State whether each of the given will result in a movement along or a shift in the monetary policy reaction curve and in which direction the effect will be.
Evaluate financial performance and financial position : Show the original figures as well as any ratios or percentage changes that you calculate. An efficient way to present these figures and ratios is in Word tables or in sections of Excel spreadsheets that are pasted into Word documents.
Resources to try at our institute jubail technical institute : Please let us access free resources to try at our institute Jubail Technical Institute (www.jti.edu.sa). If it is approved by higher managment later, we can have deal or an agreement with you for further course of action.
Experience in creating tables and using ms word : For this discussion, Creating tables can be a valuable way of displaying information in a Word document. For this discussion, you will talk about your experience in creating tables and using MS Word to perform calculations.

Reviews

Write a Review

 

Finance Basics Questions & Answers

  Market-based indicators for making investment

Please comment and discuss. For example, what advantages or disadvantages of market-based indicators for making investment (bonds, loans, stock) decisions?

  What is the expected rate of return on the market

You own a stock that has an expected return of 16.48 percent and a beta of 1.33. The U.S. Treasury bill is yielding 3.65 percent and the inflation rate is 2.95 percent. What is the expected rate of return on the market?

  Prepare a bank reconciliation

The following are summary financial information for Parker Corporation, and Boulder, Corporation, for three recent years:

  Approaches to job design that are the most important

Select two (2) out of the four (4) approaches to job design that are the most important for you to consider. Suggest two (2) challenges that you may encounter when designing a job using each of the selected approaches.

  What would be the increase or decrease in company net income

Analysis of Hair Care Company's citrus hair conditional reveals that it is losing $5,000 annually. The company sells 5,000 units citrus hair conditioner each year at $10 per unit. What would be the increase or decrease in company net income if citr..

  Managerial and financial strengths and weaknesses

Address internal resource analysis such as managerial and financial strengths and weaknesses. Please include short-term and long-term strategic goals.

  Recommendation to pay for children education

"Tom and Betty have AGI of $150,000 and have not planned for their children s education. Their children are ages 18 and 17 and the parents anticipate paying $20,000 per year, per child for education expenses. Which of the following is the most app..

  Suppose there is a financial asset abc which is the

suppose there is a financial asset abc which is the underlying asset for a futures contract with settlement six months

  Important determinant of an investment

Question 1. The most important determinant of an investment's portfolio risk is which of the following?

  How you stayed within your budget

You will use the theoretical studies of computer hardware and software and apply them to a study of real-world IT products. include references for your costs to document how you stayed within your budget

  Dollars worth of sales are generated

A firm hs net working capital of $462, net fixed assets of $2,217, sales of $6,000, and current liabilities of $800. How many dollars worth of sales are generated from every $1 in total assets?

  What annual rate of return did the firm earn

Marcus, Inc. purchased a rare coin for $219,000 three years ago. Today, they resold that coin for $297,500. What annual rate of return did the firm earn on this investment?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd