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

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

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

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

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

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

Which one of the following bonds has the shortest duration?

A) Zero-coupon, 13-year maturity.

B) Zero-coupon, 10-year maturity.

C) 8% coupon, 10-year maturity.

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If bonds are identical except for maturity, and coupon, the one with the shortest maturity and highest coupon will have the shortest duration. The rationale for this is similar to that for price volatility. Duration is approximately equal to the point in years where the investor receives half of the present value of the bond's cash flows. Therefore, the earlier the cash flows are received, the shorter the duration.
The relationship of maturity to duration is direct - the shorter the time to maturity, the shorter the duration. A shorter-term bond pays its cash flows earlier than a longer-term bond, decreasing the duration. Here, one of the 10-year bonds will have the shortest duration.
The relationship of coupon to duration is indirect - the higher the coupon rate, the shorter the duration. A higher coupon bond pays higher annual cash flows than a lower coupon bond and thus has more influence on duration. Here, the 10-year bond with the highest coupon (8.00%) will have the shortest duration. Note: In addition to having the highest price volatility, zero-coupon bonds have the longest duration (at approximately equal to maturity). This is because zero coupon bonds pay all cash flows in one lump sum at maturity.

optiix

All other things being equal, which one of the following bonds has the greatest volatility?

A) 20-year, 15% coupon.

B) 20-year, 10% coupon.

C) 5-year, 10% coupon.

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This question is asking: given a change in yield, which of the bonds will exhibit the greatest price change? Of the four choices, the bond with the longest maturity and lowest coupon will have the greatest price volatility.
All else equal, the bond with the longer term to maturity is more sensitive to changes in interest rates. Cash flows that are further into the future are discounted more than near-term cash flows. Here, this means that one of the 20-year bonds will have the highest volatility. Similar reasoning applies to the coupon rate. A lower coupon bond delivers more of its total cash flow (the bond's par value) at maturity than a higher coupon bond. All else equal, a bond with a lower coupon than another will exhibit greater price volatility. Here, this means that of the 20-year bonds, the one with the 10% coupon rate will exhibit greater price volatility than the bond with the 15% coupon.

optiix

Which set of conditions will result in a bond with the greatest volatility?

A) A high coupon and a short maturity.

B) A low coupon and a long maturity.

C) A high coupon and a long maturity.

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If bonds are identical except for maturity and coupon, the one with the longest maturity and lowest coupon will have the greatest volatility.
The relationship of maturity to volatility is direct - the longer the time to maturity, the greater the volatility. A longer-term bond pays its cash flows later than a shorter-term bond, increasing the volatility. This is because a bond’s price is determined by discounting the value of the cash flows. A longer-term bond pays its cash flows later than a shorter-term bond, and longer-term cash flows are discounted more heavily.
The relationship of coupon to volatility is indirect - the lower the coupon rate, the greater the volatility. This is because a bond’s price is determined by discounting the value of the cash flows. A lower coupon bond pays less cash flows over the bond's life and more at maturity than a higher coupon bond. As noted above, longer-term cash flows are discounted more heavily.

optiix

Duration measures the:

A) length of time until a bond matures.

B) timing of cash flows weighted by the proportionate value of each flow's present value.

C) cash flows weighted by the timing of the cash flows.

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The sensitivity of a bond’s price to changes in yield is known as a bond’s effective duration. Macaulay’s duration is calculated by the timing of cash flows weighted by the proportionate value of each flow’s present value.