LOS d, (Part 1): Compute and interpret the effective duration of a bond, given information about how the bond's price will increase and decrease for given changes in interest rates.

Q1. An investor finds that for every 1% increase in interest rates, a bond’s price decreases by 4.21% compared to a 4.45% increase in value for every 1% decline in interest rates. If the bond is currently trading at par value, the bond’s duration is closest to:

A)   4.33.

B)   8.66.

C)   43.30.

Q2. An international bond investor has gathered the following information on a 10-year, annual-pay U.S. corporate bond:

• Currently trading at par value
• Annual coupon of 10%
• Estimated price if rates increase 50 basis points is 96.99%
• Estimated price is rates decrease 50 basis points is 103.14%

The bond’s duration is closest to:

A)   3.14.

B)   6.15.

C)   6.58.

Q3. 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 effective duration of the bond?

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)   3.49.

B)   1.56.

C)   1.74.

Q4. If bond prices fall 5% in response to a 0.5% increase in interest rates, what is the bond's effective duration?

A)   -5.

B)   -10.

C)   +10.

Q5. When interest rates increase, the duration of a 30-year bond selling at a discount:

A)   increases.

B)   does not change.

C)   decreases.

Q6. A bond with a yield to maturity of 8.0% is priced at 96.00. If its yield increases to 8.3% its price will decrease to 94.06. If its yield decreases to 7.7% its price will increase to 98.47. The effective duration of the bond is closest to:

A)   7.66.

B)   2.75.

C)   4.34.

LOS d, (Part 1): Compute and interpret the effective duration of a bond, given information about how the bond's price will increase and decrease for given changes in interest rates.fficeffice" />

Q1. An investor finds that for every 1% increase in interest rates, a bond’s price decreases by 4.21% compared to a 4.45% increase in value for every 1% decline in interest rates. If the bond is currently trading at par value, the bond’s duration is closest to:

A)   4.33.

B)   8.66.

C)   43.30.

Correct answer is A)

Duration is a measure of a bond’s sensitivity to changes in interest rates.
Duration = (V_- – V₊) / [2V₀(change in required yield)] where:
V_- = estimated price if yield decreases by a given amount
V₊ = estimated price if yield increases by a given amount
V₀ = initial observed bond price
Thus, duration = (104.45 – 95.79)/(2 × 100 × 0.01) = 4.33. Remember that the change in interest rates must be in decimal form.

Q2. An international bond investor has gathered the following information on a 10-year, annual-pay ffice:smarttags" />U.S. corporate bond:

• Currently trading at par value
• Annual coupon of 10%
• Estimated price if rates increase 50 basis points is 96.99%
• Estimated price is rates decrease 50 basis points is 103.14%

The bond’s duration is closest to:

A)   3.14.

B)   6.15.

C)   6.58.

Correct answer is B)

Duration is a measure of a bond’s sensitivity to changes in interest rates.
Duration = (V_- – V₊) / [2V₀(change in required yield)] where:
V_- = estimated price if yield decreases by a given amount
V₊ = estimated price if yield increases by a given amount
V₀ = initial observed bond price
Thus, duration = (103.14 ? 96.99) / (2 × 100 × 0.005) = 6.15. Remember that the change in interest rates must be in decimal form.

Q3. 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 effective duration of the bond?

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)   3.49.

B)   1.56.

C)   1.74.

Correct answer is A)        

The effective duration is computed as follows:

Effective duration =	105.56 ? 98.46	= 3.49
	2 × 101.76 × 0.01

Q4. If bond prices fall 5% in response to a 0.5% increase in interest rates, what is the bond's effective duration?

A)   -5.

B)   -10.

C)   +10.

Correct answer is C)

Approximate percentage price change of a bond = - (duration) (delta y) =
-5 = - (duration) (0.5) = 10.

Q5. When interest rates increase, the duration of a 30-year bond selling at a discount:

A)   increases.

B)   does not change.

C)   decreases.

Correct answer is C)

The higher the yield on a bond the lower the price volatility (duration) will be. When interest rates increase the price of the bond will decrease and the yield will increase because the current yield = (annual cash coupon payment) / (bond price). As the bond price decreases the yield increases and the price volatility (duration) will decrease.

Q6. A bond with a yield to maturity of 8.0% is priced at 96.00. If its yield increases to 8.3% its price will decrease to 94.06. If its yield decreases to 7.7% its price will increase to 98.47. The effective duration of the bond is closest to:

A)   7.66.

B)   2.75.

C)   4.34.

Correct answer is A)

The change in the yield is 30 basis points.

Duration = (98.47 ? 94.06) / (2 × 96.00 × 0.003) = 7.6563.

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