Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Duration reflects whether the future cash payments of an asset are relatively short-term (low duration) or long-term (high duration). A way to measure duration is

image text in transcribedimage text in transcribed

Duration reflects whether the future cash payments of an asset are relatively short-term (low duration) or long-term (high duration). A way to measure duration is given by the following formula: . duration = EF=17 (1 + i)" EF=1 (1 + i)? . where cp, is the cash payment t periods in the future, T is the time to maturity of the asset, and i is the interest rate at which one discounts the future cash payments. Note that following formulas might be helpful aT+1 a1 - a) = -T- (1 - a)2 (1 - a) T=1 and T at a(1 - a") (1 - a) T=1 (5 points) A coupon bond has a face value of $10000 which will be paid at maturity. The coupon bond also has a coupon payment every year of $500 until maturity. The time to maturity is 20 years. What is the duration of that bond? Show work. (5 points) Suppose the price of the consol is $1000. Calculate the duration of a consol that pays $100 each year. Show work. (5 points) Suppose the current coupon payment is $10. Suppose future coupon payments of the consol are indexed to inflation and inflation is expected to be 2% in the future. The current yield to maturity on the consol is 10%. What is the duration of this consol? Show work. Duration reflects whether the future cash payments of an asset are relatively short-term (low duration) or long-term (high duration). A way to measure duration is given by the following formula: . duration = EF=17 (1 + i)" EF=1 (1 + i)? . where cp, is the cash payment t periods in the future, T is the time to maturity of the asset, and i is the interest rate at which one discounts the future cash payments. Note that following formulas might be helpful aT+1 a1 - a) = -T- (1 - a)2 (1 - a) T=1 and T at a(1 - a") (1 - a) T=1 (5 points) A coupon bond has a face value of $10000 which will be paid at maturity. The coupon bond also has a coupon payment every year of $500 until maturity. The time to maturity is 20 years. What is the duration of that bond? Show work. (5 points) Suppose the price of the consol is $1000. Calculate the duration of a consol that pays $100 each year. Show work. (5 points) Suppose the current coupon payment is $10. Suppose future coupon payments of the consol are indexed to inflation and inflation is expected to be 2% in the future. The current yield to maturity on the consol is 10%. What is the duration of this consol? Show work

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Startup CEO A Field Guide To Scaling Up Your Business

Authors: Matt Blumberg

2nd Edition

1119723663, 978-1119723660

More Books

Students also viewed these Finance questions