honeycfa

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.

honeycfa

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

A) 20-year, 15% coupon.

B) 5-year, 10% coupon.

C) 20-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.

honeycfa

Which one of the following bonds has the shortest duration?

A) 8% coupon, 10-year maturity.

B) Zero-coupon, 13-year maturity.

C) Zero-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.

honeycfa

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

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

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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.

honeycfa

Which of the following statements about duration is least accurate?

A) There is a direct relationship between yield to maturity and duration.

B) There is an inverse relationship between coupon and duration.

C) The effective duration of a zero coupon bond is equal to its maturity.

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Bonds with larger coupons have a smaller duration, all other things the same. A zero coupon bond has an effective duration equal to its maturity. Duration measures the approximate change in price given a change in interest rates. Therefore, the duration of the bond does not change with the yield to maturity of the bond.

honeycfa

Which of the following statements about duration of a bond is least accurate?

A) The dollar change in price for a 1% change in yield is approximately equal to the product of the duration and the current value of the bond divided by 100.

B) If a bond has an effective duration of 7.5, it means that a 1% change in rates will result in a 7.5% change in price.

C) The duration of a floater is equal to the time to the next reset date.

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Because of convexity, it will be approximately a 7.5% change in price, not an actual 7.5% change in price. The readings are very explicit about this distinction.

honeycfa

Duration measures the:

A) length of time until a bond matures.

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

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

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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.

honeycfa

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

A) A high coupon and a short maturity.

B) A high coupon and a long maturity.

C) A low coupon and a long maturity.

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.