LOS f: Compute and interpret the duration and dollar duration of a bond.

Q1. Duration of a bond normally increases with an increase in:

A)   yield to maturity.

B)   coupon rate.

C)   time to maturity.

Q2. Which of the following statements about duration of a bond is least accurate?

A)   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.

B)   The dollar change in price is approximately equal to the product of the duration and the current value of the bond divided by 100.

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

Q3. 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.

Q4. Which set of conditions will result in a bond with the greatest volatility?

A)   A low coupon and a long maturity.

B)   A high coupon and a short maturity.

C)   A high coupon and a long maturity.

Q5. 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.

Q6. Which one of the following bonds has the shortest duration?

A)   Zero-coupon, 13-year maturity.

B)   8% coupon, 10-year maturity.

C)   Zero-coupon, 10-year maturity.

LOS f: Compute and interpret the duration and dollar duration of a bond.fficeffice" />

Q1. Duration of a bond normally increases with an increase in:

A)   yield to maturity.

B)   coupon rate.

C)   time to maturity.

Correct answer is C)

Duration is directly related to maturity and inversely related to the coupon rate and yield to maturity (YTM). 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 later the cash flows are received, the greater the duration. 

The longer the time to maturity, the greater the duration (and vice versa). A longer-term bond pays its cash flows later than a shorter-term bond, increasing the duration. The lower the coupon rate, the greater the duration (and vice versa). A lower coupon bond pays lower annual cash flows than a higher-coupon bond and thus has less influence on duration. The lower the YTM, the higher the duration. This is because the bond's price (or present value) is inversely related to interest rates. When market yields fall, the value (or cash flow) of a bond increases without increasing the time to maturity.

Q2. Which of the following statements about duration of a bond is least accurate?

A)   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.

B)   The dollar change in price is approximately equal to the product of the duration and the current value of the bond divided by 100.

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

Correct answer is A)        

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.

Q3. 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.

Correct answer is B)

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.

Q4. Which set of conditions will result in a bond with the greatest volatility?

A)   A low coupon and a long maturity.

B)   A high coupon and a short maturity.

C)   A high coupon and a long maturity.

Correct answer is A)

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.

Q5. 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.

Correct answer is C)

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.

Q6. Which one of the following bonds has the shortest duration?

A)   Zero-coupon, 13-year maturity.

B)   8% coupon, 10-year maturity.

C)   Zero-coupon, 10-year maturity.

Correct answer is B)        

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.

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