Investments
Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 15, Problem 9PS
Summary Introduction

To determine: The market’s expectation of the yield curve as per the expectations hypothesis from now to 1 year and further calculate the expected values of next year yields on bonds after one year, two years and three years.

Introduction:

Yield-curve analysis: It is a technique to calculate the difference in interest rate between the note value and the term of to maturity.

Expert Solution & Answer
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Answer to Problem 9PS

The forward rate after one year is 7%; after two years it is 7.5% and after three years it is 8.51%.

Explanation of Solution

We have been given the following information:

    BondYears to MaturityYTM (%)
    A15
    B26
    C36.5
    D47

We have to calculate the expected rate. Expected rate is called as expected hypothesis. The following formula can be used for calculation.

  1+Forward rateExpected return=( ( 1+Yield to maturit y Number of years ) Number of years ( 1+Yield to maturit y Number of years1 ) Number of years1)

Calculation of expected rate after one year:

  Forward rate1year=( ( 1+Yield to maturit y Number of years ) Number of years ( 1+Yield to maturit y Number of years1 ) Number of years1 )1=( ( 1+Yield to maturit y 2 ) 2 ( 1+Yield to maturit y 1 ) 1 )1=( ( 1+6% ) 2 ( 1+5% ) 1 )1=( ( 1+0.06 ) 2 ( 1+0.05 ) 1 )1=( ( 1.06 ) 2 ( 1.05 ) 1 )1=1.12361.051=1.07001=0.0700

When converted into percentages, it becomes 7%.

Calculation of expected rate after two years

  Forward rate2years=( ( 1+Yield to maturit y Number of years ) Number of years ( 1+Yield to maturit y Number of years1 ) Number of years1 )1=( ( 1+Yield to maturit y 3 ) 3 ( 1+Yield to maturit y 2 ) 2 )1=( ( 1+6.5% ) 3 ( 1+6 ) 2 )1=( ( 1+0.065 ) 3 ( 1+0.06 ) 2 )1=( ( 1.065 ) 3 ( 1.06 ) 2 )1=1.20791.12361=1.07501=0.0750

When converted into percentages, it becomes 7.5%.

Calculation of expected rate after 3 years:

The percentages have to be converted into decimals by dividing it by 100.

  =( ( 1+0.07 ) 4 ( 1+0.065 ) 3 )1=( ( 1.07 ) 4 ( 1.065 ) 3 )1=1.310796011.207949631=1.08511=0.0851

When converted into percentages, it becomes 8.51%.

Therefore, the forward rate after one year is 7%; after two years it is 7.5% and after three years it is 8.51%.

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