optiix

Why do bond portfolio managers use the concept of duration?

A) It allows structuring a portfolio to take advantage of changes in credit quality.

B) It assesses the time element of bonds in terms of both coupon and term to maturity.

C) It enables direct comparisons between bond issues with different levels of risk.

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Portfolio managers are very interested in a bond’s sensitivity to changes in interest rates. Bonds can be different in terms of maturity and coupon level, while both characteristics impact the change in the bond’s price given changes in interest rates. Duration is a measure that can assesses the time element of bonds in terms of both coupon and term to maturity.

optiix

With an option-free zero-coupon bond the effective duration is:

A) approximately equal to its years to maturity.

B) unrelated to its time to maturity.

C) approximately equal to the number of semiannual periods to maturity.

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For an option-free zero coupon bond, effective and modified duration will be almost identical and both will be approximately equal to the bond's years to maturity.

optiix

Which of the following statements concerning bond duration is least accurate? Duration:

A) decreases as the coupon increases.

B) is the weighted-average maturity of the cash flows of the bond.

C) increases as market yields rise.

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Duration decreases as market yields rise.

optiix

In December 2004, an investor purchases a zero-coupon bond issued in 1998 and maturing in December 2008. What is the bond's approximate duration?

A) 10 years.

B) Cannot be determined.

C) 4 years.

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For a zero-coupon bond duration is approximately equal to the number of years to maturity. Here, there are 4 years until maturity, so the effective duration is approximately equal to 4 years. We use the term approximately because this ignores the curvature of the price/yield curve.

optiix

All else held equal, the duration of bonds selling at higher yields compared to bonds selling at lower yields will be:

A) lower.

B) cannot be determined with the information given.

C) greater.

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Duration is inversely related to yield to maturity (YTM).The higher the YTM, the lower the duration. This is because the change in the bond's price (or present value) is inversely related to changes in interest rates. When market yields rise, the value (or cash flow) of a bond decreases without decreasing the time to maturity.
Duration is also a function of volatility (risk).  Higher volatility (risk) = higher duration.  A higher coupon bond has a lower duration relative to a similar bond with a lower coupon because the bond holder is getting more of their cash value sooner (because of the higher coupon).  This lowers the overall risk of the bond resulting in a lower duration.

optiix

For coupon-paying bonds, duration and years to maturity:

A) may be equal depending on the coupon rate.

B) are equal.

C) are unequal with duration less than years to maturity.

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For coupon paying bonds, duration is less than maturity.
Duration is approximately equal to the point in years where the investor receives half of the present value of the bond's cash flows. Since zero-coupon bonds only have one cash flow at maturity, the duration is approximately equal to maturity. Any coupon amount will shorten duration because some cash flow is received prior to maturity.

optiix

Which of the following statements about duration is CORRECT?

A) A bond's percentage change in price and dollar change in price are both tied to the underlying price volatility.

B) The result of the formula for effective duration is for a 0.01% change in interest rates.

C) The formula for effective duration is: (price when yields fall − price when yields rise) / (initial price × change in yield expressed as a decimal).

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The statement that a bond's percentage change in price and dollar change in price are both tied to the underlying price volatility is correct.
The effective duration formula result is for a 1.00% change in interest rates (100 basis points equals 1.00%, or 0.01 in decimal form). The denominator is multiplied by 2.

optiix

Assuming a flat term structure of interest rates of 5%, the duration of a zero-coupon bond with 5 years remaining to maturity is closest to:

A) 4.35.

B) 5.00.

C) 3.76.

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The duration of a zero coupon bond is approximately equal to its time to maturity.

optiix

Which of the following bonds has the shortest duration? A bond with a:

A) 10-year maturity, 10% coupon rate.

B) 20-year maturity, 6% coupon rate.

C) 10-year maturity, 6% coupon rate.

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All else constant, a bond with a longer maturity will be more sensitive to changes in interest rates. All else constant, a bond with a lower coupon will have greater interest rate risk.

optiix

An option-free bond has a market price and par value equal to $1,000. For small changes in the yield of this bond, its price will change one dollar for every basis point change in the yield. What is the duration of the bond?

A) 1.

B) 5.

C) 10.

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Duration = [1001 − 999] / [2 × 1000 × 0.0001] = 10.