andytrader

Why is convexity a good thing for a bond holder? Because when compared to a low convexity bonds a high convexity bond:

A) is usually underpriced.

B) is more sensitive to interest rate changes, increasing the potential payoff.

C) has better price changes regardless of the direction of the yield change.

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Relative to a bonds with low convexity, the price of a bond with high convexity will increase more when rates decline and decrease less when rates rise.

andytrader

Convexity is more important when rates are:

A) high.

B) unstable.

C) low.

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Since interest rates and the price of bonds are inversely related, unstable interest rates will lead to larger price fluctuations in bonds. The larger the change in the price of a bond the more error will be introduced in determining the new price of the bond if only duration is used because duration assumes the price yield relationship is linear when in fact it is a curved convex line. If duration alone is used to price the bond, the curvature of the line magnifies the error introduced by yield changes, and makes the convexity adjustment even more important.

andytrader

A 7% coupon bond with semiannual coupons has a convexity in years of 80. The bond is currently priced at a yield to maturity (YTM) of 8.5%. If the YTM decreases to 8%, the predicted effect due to convexity on the percentage change in price would be:

A) +50 basis points.

B) +20 basis points.

C) +40 basis points.

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Convexity adjustment: +(Convexity)(change in i)2
Convexity adjustment = +(80)(-0.005)(-0.005) = +0.0020 or 0.20% or +20 basis points.

andytrader

With respect to an option-free bond, when interest-rate changes are large, the duration measure will overestimate the:

A) fall in a bond's price from a given increase in interest rates.

B) increase in a bond's price from a given increase in interest rates.

C) final bond price from a given increase in interest rates.

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When interest rates increase by 50-100 basis points or more, the duration measure overestimates the decrease in the bond’s price.

andytrader

For a given change in yields, the difference between the actual change in a bond’s price and that predicted using the duration measure will be greater for:

A) a bond with less convexity.

B) a bond with greater convexity.

C) a short-term bond.

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Duration is a linear measure of the relationship between a bond’s price and yield. The true relationship is not linear as measured by the convexity. When convexity is higher, duration will be less accurate in predicting a bond’s price for a given change in interest rates. Short-term bonds generally have low convexity.

andytrader

For a given bond, the duration is 8 and the convexity is 50. For a 60 basis point decrease in yield, what is the approximate percentage price change of the bond?

A) 4.98%.

B) 4.62%.

C) 2.52%.

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The estimated price change is -(duration)(∆y) + (convexity) × (∆y)2 = -8 × (-0.006) + 50 × (-0.0062) = +0.0498 or 4.98%.

andytrader

A bond has a duration of 10.62 and a convexity of 91.46. For a 200 basis point increase in yield, what is the approximate percentage price change of the bond?

A) -17.58%.

B) -24.90%.

C) -1.62%.

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The estimated price change is:
-(duration)(∆y) + (convexity) × (∆y)2 = -10.62 × 0.02 + 91.46 × (0.022) = -0.2124 + 0.0366 = -0.1758 or –17.58%.

andytrader

If a Treasury bond has a duration of 10.27 and a convexity of 71.51. Which of the following is closest to the estimated percentage price change in the bond for a 125 basis point increase in interest rates?

A) -13.956%.

B) -9.325%.

C) -11.718%.

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The estimated percentage price change = the duration effect plus the convexity effect.
The formula is:
[–duration × (Δy)] + [convexity × (Δy)2].
Therefore, the estimated percentage price change is:
[–(10.27)(1.25%)] + [(71.51)(0.0125)2] = –12.8375 + 1.120% = –11.7175%.

andytrader

An investor gathered the following information about an option-free U.S. corporate bond:

• Par Value of $10 million
• Convexity of 45
• Duration of 7

If interest rates increase 2% (200 basis points), the bond’s percentage price change is closest to:

A) -14.0%.

B) -12.2%.

C) -15.8%.

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Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration × (change in yields)] + [convexity × (change in yields)2] = [(-7)(0.02) + (45)(0.02)2] = -0.12 = -12.2%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments.

andytrader

Assume that a straight bond has a duration of 1.89 and a convexity of 15.99. If interest rates decline by 1% what is the total estimated percentage price change of the bond?

A) 1.56%.

B) 2.05%.

C) 1.89%.

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The total percentage price change estimate is computed as follows:
Total estimated price change = -1.89 × (-0.01) × 100 + 15.99 × (-0.01)2 × 100 = 2.05%