Duration

Using the following information, what is the duration of the bond being described? Maturity is 11 years. Par value is $1,000. The coupon rate is 8.25%. The bond is currently selling in the market at $1,094. The bond pays interest annually.

7.8 years solve for YTM calculate Duration from formula sheet

Duration definition

Duration is the time remaining when a security's discounted future cash flow remains at risk.

To immunize a bond portfolio over a specific investment horizon, an investor would do which of the following?

Match the average weighted duration of the bond portfolio to the investment horizon. Duration, not maturity is used to immunize a portfolio. The average weighted duration rather than the duration of each specific bond is used for successful portfolio immunization.

The bigger the duration, the _______ the sensitivity to interest rate changes.

The bigger the duration, the more price sensitive the bond is to interest rate changes.

Bond A has a 6% annual coupon and is due in 2 years. Its value in today's market is $900. Bond B has a 10% annual coupon and is due in 4 years. It is priced to yield 12%. Bond C is a zero-coupon bond priced to yield 11% in 8 years. Assuming the duration of Bond A is 1.94 years, which of the following statements about the effect of a 1% decline in interest rates is true? a. Bond C, having a longer duration that Bond A, would have a larger percent increase in price than Bond A. b. The percent change in price of a bond is independent of the duration of a bond. c. It is NOT possible to determine the percent change in price of Bond A versus Bond C because the duration of Bond C is NOT given. d. Bond A would have a greater percent change in price than Bond C because it has a shorter duration.

The correct answer is A. In this instance, there's no need to do any calculations. They're already (inherently) done. Because it gives the duration of Bond A (directly) and Bond C (indirectly as zero coupon bonds always have a duration equal to their maturity), the longer duration bond (Bond C) will have the greatest sensitivity to interest rate changes (because of the longer duration). Bond B is ignored simply because it's not found in the answers as a choice. Thus, answer A is correct. Answer B is not correct because the percent price change is dependent on duration. Answer C is not correct because duration is given (indirectly by giving the maturity and the fact it's a zero). Answer D is incorrect simply because it's not true of duration. If you choose to calculate: Multiply the change of rate by the duration to arrive at the percent change in price (see formula sheet for percent change formula). For each percent of change, multiply by the duration to arrive at the total percent change. Then calculate that percentage into a price change. **This may exceed the 1.5 minutes per question suggested on the exam.

You are faced with several fixed income investment options. Which of these bonds has the greatest interest rate risk? A) U.S. Treasury bond with an 11.625% coupon, due in five years with a price of $1,225.39 and a yield to maturity of 6.3%. B) U.S. Treasury strip bond (zero-coupon) due in five years with a price of $735.12 and a yield to maturity of 6.25%. C) corporate B-rated bond with a 9.75% coupon, due in five years with a price of $1,038.18 and a yield to maturity of 8.79%.

The correct answer is B. With the term being equal, the bond with the lowest coupon will have the biggest duration. The bigger the duration, the more price sensitive the bond is to interest rate changes. Bond B has the lowest coupon, zero.

Which of the following is the better indicator for evaluating a bond's sensitivity to interest rate risk? A) Duration, because it measures interest rate and reinvestment rate changes. B) Covariance, because it measures the relationship between interest rate changes and bond price changes. C) Yield to maturity, because it takes capital gains, losses and periodic coupon payments into account. D) Weighted-average maturity, because it recognizes the full term of the bond.

a. duration.

if there's an equation where i need to calculate duration and there is no YTM available...

c is for cat mark, then skip if there's time come back and do the calculation

Which of these bonds initially immunizes a bond portfolio if the investors time horizon is 8 years? A.20 year zero coupon B.Series of Tbills C.Coupon paying bond maturing in 8 years D.Coupon paying bond maturing in 10 years

d. Option "A" - The term / duration is 20 years, which is well beyond the investors time horizon. Option "B" - The duration is too short (less than 12 month). Option "C" - The duration is something less than 8 which is too short. Option "D" - This is the only bond where the duration may equal the investor's time horizon, so it is the best answer.

immunization bonds

if zero coupon just show the exact, if not zero coupon show after.

What does duration measure?

interest rate and reinvestment rate changes.

Julie Quatsoe owns an LMN, Inc. bond with a par value of $1,000. LMN is a AA-rated bond that matures in seven years. Julie receives $55 of interest income from LMN semiannually. Comparable debt, i.e., is AA-rated, 7-year maturity, yields 12%. The bond's duration is five years. Assume the Federal Reserve is concerned about inflation and increases the discount rate. As a consequence, market interest rates on 7-year AA-rated bonds change from 12% to 13%. How will the price of Julie's bond change?

it will decrease by appx. 5% You may use the "rule of thumb", that is, multiply the percent increase (or decrease) by the years of duration and this will give you the percent change in price of the bond. It is best, however, to calculate this with the appropriate change of the price of a bond's formula (from the CFP Board formula sheet). ( - duration) X [ % change / (1+ytm) ]

if i need to calculate duration. what should i do?

just guess, and then mark the question to calculate later. * remember that zero coupon duration = time to maturity.

Duration is based on coupon rate. The _____ the coupon payment, the shorter the duration

larger

A zero-coupon bond's duration is always its ____

maturity

Your client has asked you to assist her in examining possible additions to her bond portfolio. She has expressed a desire to minimize risk at this stage in her planning process, and to assure income beginning at the point of her retirement, and lasting throughout. She has a tentative retirement date in seven years at age 65. She will then have an eighteen year life expectancy. Which of the following is an appropriate addition to her current portfolio? A. 25-year AAA-rated corporate bonds with a seven-year maturity. B. 20 year AAA-rated municipal bonds with a seven-year duration. C. 25-year AAA-rated corporate zeroes with a seven-year duration. D. 20-year US Treasury zeroes with a seven-year maturity. E. 25-year AAA-rated corporate bonds with a seven-year duration.

only E. The client is looking for income to begin in 7 years. Therefore anything maturing in 7 years will not provide that income. Zeroes provide no income. She wants something out 25 years, not 20 years. Thus, option "V" is the only appropriate answer.

John Risotto has a cash need at the end of nine years. Would all these investments best meet his need and serves to immunize the portfolio initially? a. An 11-year maturity coupon bond. b. A 9-year maturity coupon Treasury note. c. A series of Treasury bills.

only a. the process of portfolio immunization entails not maturity of a security, but its duration. Duration is based on coupon rate. The larger the coupon payment, the shorter the duration. This being the case, a bond generally pays higher interest than a note, and a note pays higher than short-term Treasury bills. Given this information, one could reasonably expect a shorter duration (than time to maturity), while receiving better immunization from the bond.

is the % price change relavant to the duration of a bond?

yes.