andytrader

When compared to modified duration, effective duration:

A) is equal to modified duration for callable bonds but not putable bonds.

B) factors in how embedded options will change expected cash flows.

C) places less weight on recent changes in the bond's ratings.

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The point of effective duration is to consider expected changes in cash flow from features such as embedded options.

andytrader

Which of the following statements about modified duration and effective duration is NOT correct?

A) Modified duration should be used for bonds with embedded options.

B) Effective duration should be used for bonds with embedded options.

C) The modified duration measure assumes that yield changes do not change the expected cash flows.

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Using modified duration as a measure of the price sensitivity of a security with embedded options to changes in yield would be misleading. With embedded options, yield changes may change the expected cash flows.

andytrader

A bond with an 8% semi-annual coupon and 10-year maturity is currently priced at $904.52 to yield 9.5%. If the yield declines to 9%, the bond’s price will increase to $934.96, and if the yield increases to 10%, the bond’s price will decrease to $875.38. Estimate the percentage price change for a 100 basis point change in rates.

A) 6.58%.

B) 4.35%.

C) 2.13%.

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The formula for the percentage price change is: (price when yields fall – price when yields rise) / 2 × (initial price) × 0.005 = ($934.96 – 875.38) / 2($904.52)(0.005) = $59.58 / $9.05 = 6.58%. Note that this formula is also referred to as the bond’s effective duration.

mouse123

When calculating duration, which of the following bonds would an investor least likely use effective duration on rather than modified duration?

A) Option-free bond.

B) Callable bond.

C) Convertible bond.

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The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.

mouse123

Which of the following statements about duration is NOT correct

A) Effective duration is the exact change in price due to a 100 basis point change in rates.

B) For a specific bond, the effective duration formula results in a value of 8.80%. For a 50 basis point change in yield, the approximate change in price of the bond would be 4.40%.

C) The numerator of the effective duration formula assumes that market rates increase and decrease by the same number of basis points.

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Effective duration is an approximation because the duration calculation ignores the curvature in the price/yield graph.

mouse123

The price of a bond is equal to $101.76 if the term structure of interest rates is flat at 5%. The following bond prices are given for up and down shifts of the term structure of interest rates. Using the following information what is the approximate percentage price change of the bond using effective duration and assuming interest rates decrease by 0.5%?

Bond price: $98.46 if term structure of interest rates is flat at 6%
Bond price: $105.56 if term structure of interest rates is flat at 4%

A) 1.74%.

B) 0.174%.

C) 0.0087%.

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The effective duration is computed as follows:

Using the effective duration, the approximate percentage price change of the bond is computed as follows:

Percent price change = -3.49 × (-0.005) × 100 = 1.74%

mouse123

A bond with a semi-annually coupon rate of 3% sells for $850. It has a modified duration of 10 and is priced at a yield to maturity (YTM) of 8.5%. If the YTM increases to 9.5%, the predicted change in price, using the duration concept decreases by:

A) $85.00.

B) $77.56.

C) $79.92.

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Approximate percentage price change of a bond = (-)(duration)(Δy)
Δy = 9.5% − 8.5% = 1%
(-10)(1%) = -10%
($850)(-0.1) = -$85

mouse123

A bond has the following characteristics:

• Modified duration of 18 years
• Maturity of 30 years
• Effective duration of 16.9 years
• Current yield to maturity is 6.5%

If the market interest rate decreases by 0.75%, what will be the percentage change in the bond's price?

A) 0.750%.

B) -12.675%.

C) +12.675%.

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Approximate percentage price change of a bond = (-)(effective duration)(Δy)
= (-16.9)(-0.75%) = +12.675%

mouse123

An $850 bond has a modified duration of 8. If interest rates fall 50 basis points, the bond's price will:

A) increase by $4.00.

B) increase by $34.00.

C) increase by 22.5%.

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ΔP/P = (-)(MD)(Δi) ΔP = (-)(P)(MD)(Δi)
ΔP = (-)(8)(850)(-0.005) = +$34

mouse123

Par value bond XYZ has a modified duration of 5. Which of the following statements regarding the bond is CORRECT? If the market yield:>

A) increases by 1% the bond's price will decrease by $50.

B) increases by 1% the bond's price will increase by $50.

C) increases by 1% the bond's price will decrease by $60.

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Approximate percentage price change of a bond = (-)(Duration)(Δy)
(-5)(1%) = -5%
($1000)(-0.05) = –$50