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Chapter 4: Q. 7 (page 133)

When is the current yield a good approximation of the yield to maturity?

Short Answer

Expert verified

It is close to maturity near about 10 years.

Step by step solution

01

Step 1. Introduction

Current yield is an investment's annual income (hobby or dividends) divided through the contemporary fee of the security. This degree examines the contemporary fee of a bond, as opposed to searching at its face value.

02

Step 2. Explanation

When the bond price is very close to par or the maturity is over 10 years, the present yield will be a good approximation of the yield to maturity. This is because the present discounted values of cash flows further in the future are so little that the value of a long-term coupon bond is near to that of a perpetual with the same coupon rate.

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Most popular questions from this chapter

True or False: With a discount bond, the return on the bond is equal to the rate of capital gain.

The U.S. Treasury issues some bonds as Treasury Inflation Indexed Securities, or TIIS, which are bonds adjusted for inflation; hence the yields can be roughly interpreted as real interest rates. Go to the St. Louis Federal Reserve FRED database, and find data on the following TIIS bonds and their nominal counterparts. Then answer the questions below.

  • 5-year U.S. Treasury (DGS5) and 5-year TIIS (DFII5)
  • 7-year U.S. Treasury (DGS7) and 7-year TIIS (DFII7)
  • 10-year U.S. Treasury (DGS10) and 10-year TIIS (DFII10)
  • 20-year U.S. Treasury (DGS20) and 20-year TIIS (DFII20)
  • 30-year U.S. Treasury (DGS30) and 30-year TIIS (DFII30)

a. Following the Great Recession of 2008鈥� 2009, the 5-, 7-, 10-, and even the 20-year TIIS yields became negative for a period of time. How is this possible?

b. Using the most recent data available, calculate the difference between the yields for each of the pairs of bonds (DGS5 鈥� DFII5, etc.) listed above. What does this difference represent?

c. Based on your answer to part (b), are there significant variations among the differences in the bond-pair yields? Interpret the magnitude of the variation in differences among the pairs.

What is the formula used to calculate the yield to maturity on a 20-year coupon bond with a current yield of 12% and \(1,000 face value that sells for \)2,500

If the interest rate is 15%, what is the present value of a security that pays you \(1,100 next year, \)1,250 the year after, and $1,347 the year after that?

Under what conditions will a discount bond have a negative nominal interest rate? Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate?
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