1215

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.

1215

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

A) cannot be determined with the information given.

B) lower.

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.

1215

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

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

B) may be equal depending on the coupon rate.

C) are equal.

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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.

1215

Which of the following statements about duration is CORRECT?

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

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

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.

1215

What is the duration of a floating rate bond that has six years remaining to maturity and has semi-annual coupon payments. Assume a flat-term structure of 6%. Which of the following is closest to the correct duration?

A) 6.000.

B) 4.850.

C) 0.500.

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The duration of a floating rate bond is equal to the time until the next coupon payment takes place. As the coupon rate changes semi-annually with the level of the interest rate, a floating rate bond has the same duration as a pure discount bond with time to maturity equal to the time to the next coupon payment of the floating rate bond.

1215

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) 5.00.

B) 4.35.

C) 3.76.

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

1215

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.

1215

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) 10.

C) 5.

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