mouse123

Consider two bonds, A and B. Both bonds are presently selling at par. Each pays interest of $120 annually. Bond A will mature in 5 years while bond B will mature in 6 years. If the yields to maturity on the two bonds change from 12% to 10%, both bonds will:

A) increase in value, but bond A will increase more than bond B.

B) increase in value, but bond B will increase more than bond A.

C) decrease in value, but bond B will decrease more than bond A.

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There are three features that determine the magnitude of the bond price volatility:

• The lower the coupon, the greater the bond price volatility.
• The longer the term to maturity, the greater the price volatility.
• The lower the initial yield, the greater the price volatility.

Since both of these bonds are the same with the exception of the term to maturity, the bond with the longer term to maturity will have a greater price volatility.  Since bond value has an inverse relationship with interest rates, when interest rates decrease bond value increases.

mouse123

Positive convexity means that:

A) as interest rates change, bond prices will increase at an increasing rate and decrease at a decreasing rate.

B) the graph of a callable bond flattens out as the market value approaches the call price.

C) the price of a fixed-coupon bond is inversely related to changes in interest rates.

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Positive convexity refers to the principle that for a given change in market yields, bond price sensitivity is lowest when market yields are high and highest when market yields are low.
Although the statements that begin, the graph of a callable bond . . . and the price of a fixed-coupon bond . . . are true, they are not the best choices to describe positive convexity.

mouse123

Non-callable bond prices go up faster than they go down. This is referred to as:

A) positive convexity.

B) negative convexity.

C) inverse features.

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When bond prices go up faster than they go down, it is called positive convexity.

mouse123

Negative convexity for a callable bond is most likely to be important when the:

A) price of the bond approaches the call price.

B) bond is first issued.

C) market interest rate rises above the bond's coupon rate.

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Negative convexity illustrates how the relationship between the price of a bond and market yields changes as the bond price rises and approaches the call price. The convex curve that we generally see for non-callable bonds bends backward to become concave (i.e., exhibit negative convexity) as the bond approaches the call price.

mouse123

Assume that the current price of a bond is 102.50. If interest rates increase by 0.5% the value of the bond decreases to 100 and if interest rates decrease by 0.5% the price of the bond increases to 105.5. What is the effective duration of the bond?

A) 5.37.

B) 5.50.

C) 5.48.

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The duration is computed as follows:

Duration =	105.50 − 100	= 5.37
	2 × 102.50 × 0.005

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 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) 1.56.

B) 3.49.

C) 1.74.

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The effective duration is computed as follows:

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

mouse123

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.

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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.

mouse123

Consider an annual coupon bond with the following characteristics:

• Face value of $100
• Time to maturity of 12 years
• Coupon rate of 6.50%
• Issued at par
• Call price of 101.75 (assume the bond price will not exceed this price)

For a 75 basis point change in interest rates, the bond's duration is:

A) 5.09 years.

B) 8.79 years.

C) 8.17 years.

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Since the bond has an embedded option, we will use the formula for effective duration. (This formula is the same as the formula for modified duration, except that the “upper price bound” is replaced by the call price.) Thus, we only need to calculate the price if the yield increases 75 basis points, or 0.75%.
Price if yield increases 0.75%: FV = 100; I/Y = 6.50 + 0.75 = 7.25; N = 12; PMT = 6.5; CPT → PV = 94.12The formula for effective duration is

Where:
V-	= call price/price ceiling
V+	= estimated price if yield increases by a given amount, Dy
V0	= initial observed bond price
Dy	= change in required yield, in decimal form

Here, effective duration = (101.75 – 94.12) / (2 × 100 × 0.0075) = 7.63 / 1.5 = 5.09 years.

mouse123

A noncallable bond with seven years remaining to maturity is trading at 108.1% of a par value of $1,000 and has an 8.5% coupon. If interest rates rise 50 basis points, the bond’s price will fall to 105.3% and if rates fall 50 basis points, the bond’s price will rise to 111.0%. Which of the following is closest to the effective duration of the bond?

A) 6.12.

B) 5.54.

C) 5.27.

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The formula for effective duration is: (V- – V+) / (2V0Δy). Therefore, effective duration is: ($1.110 – $1.053) / (2 × $1.081 × 0.005) = 5.27.

mouse123

Calculate the effective duration for a 7-year bond with the following characteristics:

• Current price of $660
• A price of $639 when interest rates rise 50 basis points
• A price of $684 when interest rates fall 50 basis points

A) 3.1.

B) 6.8.

C) 6.5.

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The formula for calculating the effective duration of a bond is:

where:

• V- = bond value if the yield decreases by ∆y
• V+ = bond value if the yield increases by ∆y
• V0 = initial bond price
• ∆y = yield change used to get V- and V+, expressed in decimal form

The duration of this bond is calculated as: