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Reading 69: Introduction to the Measurement of Interest R

16.Regarding the statements made by Reynaldo and Campbell about the expected price change in the Yorkville bond:

A)   Reynaldo’s statement is incorrect; Campbell’s statement is correct.

B)   Reynaldo’s statement is correct; Campbell’s statement is incorrect.

C)   Reynaldo’s statement is correct; Campbell’s statement is correct.

D)   Reynaldo’s statement is incorrect; Campbell’s statement is incorrect.

17.Reynaldo and Apple are training a new analyst, Norah Spears. They ask Spears what she knows about duration and convexity. Spears replies with four statements:

Statement 1:

Modified duration is a better measure than effective duration for bonds with embedded options.

Statement 2:

The convexity adjustment corrects for the error embedded in the duration.

Statement 3:

Modified duration ignores the negative convexity of a callable bond.

Statement 4:

Convexity of option-free bonds is always added to duration to modify the errors in calculating price volatility.

Which of the following regarding Spears’ statements is TRUE

A)   Spears is correct with respect to all four statements.

B)   Spears is correct with respect to Statement 2, but incorrect with respect to Statement 4.

C)   Spears is correct with respect to Statement 3, but incorrect with respect to Statement 1.

D)   Spears is correct with respect to Statements 1 and 2, but is incorrect with respect to Statement 3.

18.A 30-year semi-annual coupon bond issued today with market rates at 6.75 percent pays a 6.75 percent coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?

A)   12.80%.

B)   1.28%.

C)   6.50%.

D)   3.84%.

答案和详解如下:

16.Regarding the statements made by Reynaldo and Campbell about the expected price change in the Yorkville bond:

A)   Reynaldo’s statement is incorrect; Campbell’s statement is correct.

B)   Reynaldo’s statement is correct; Campbell’s statement is incorrect.

C)   Reynaldo’s statement is correct; Campbell’s statement is correct.

D)   Reynaldo’s statement is incorrect; Campbell’s statement is incorrect.

The correct answer was D)

For the Yorkville bond:

Percentage price change = (-8.51 x 0.010 x 100) + (46.0 x 0.010
2 x 100)
Percentage price change = -8.51 + 0.46
Percentage price change = -8.05

Reynaldo’s statement is incorrect.

To calculate the dollar value of an 01 we need to know the price of the bond if interest rates rise (or fall) by 1 basis point:

N = 24, PMT = (0.059 coupon x $1,000 par value / 2 payments per year = ) 29.50, FV = 1000

If rates rise by 1 basis point, I = ((5.90 + 0.01 =) 5.91% / 2 payments per year = ) 2.955%
PV = -999.149, for a price of 99.915.

PVBP = 100 – 99.915 = 0.085

Campbell’s statement is also incorrect.

17.Reynaldo and Apple are training a new analyst, Norah Spears. They ask Spears what she knows about duration and convexity. Spears replies with four statements:

Statement 1:

Modified duration is a better measure than effective duration for bonds with embedded options.

Statement 2:

The convexity adjustment corrects for the error embedded in the duration.

Statement 3:

Modified duration ignores the negative convexity of a callable bond.

Statement 4:

Convexity of option-free bonds is always added to duration to modify the errors in calculating price volatility.

Which of the following regarding Spears’ statements is TRUE

A)   Spears is correct with respect to all four statements.

B)   Spears is correct with respect to Statement 2, but incorrect with respect to Statement 4.

C)   Spears is correct with respect to Statement 3, but incorrect with respect to Statement 1.

D)   Spears is correct with respect to Statements 1 and 2, but is incorrect with respect to Statement 3.

The correct answer was C)

Effective duration is a better measure than modified duration for bonds with embedded options because modified duration does not explicitly recognize the change in cash flows that will occur in a bond with embedded options as yield changes. Therefore, Statement 1 is incorrect. The other four statements made by Spears are correct.

18.A 30-year semi-annual coupon bond issued today with market rates at 6.75 percent pays a 6.75 percent coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?

A)   12.80%.

B)   1.28%.

C)   6.50%.

D)   3.84%.

The correct answer was A)

Approximate % change in price =

(price if yield down – price if yield up) / (2 * initial price * yield change expressed as a decimal).

Here, the initial price is par, or $1,000 because we are told the bond was issued today at par. So, the calculation is: (1039.59 – 962.77) / (2 * 1000 * 0.003) = 76.82 / 6.00 = 12.80.

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