Reading 66: Introduction to the Measurement of Interest Rate 2010, face, percentage, currently, change

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LOS g: Describe the convexity measure of a bond.

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.

 

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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.

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How does the convexity of a bond influence the yield on the bond? All else the same, for a bond with high convexity investors will require:

A) a lower yield.

B) a higher or lower yield depending on the bond's duration.

C) a higher yield.

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Convexity is to the advantage of the bond holder because a high-convexity bond's price will decrease less when rates increase

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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.

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

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

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

C) fall in a bond's 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.

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Convexity is more important when rates are:

A) unstable.

B) high.

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

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If a bond has a convexity of 120 and a modified duration of 10, what is the convexity adjustment associated with a 25 basis point interest rate decline?

A) +0.075%.

B) -2.875%.

C) -2.125%.

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Convexity adjustment: +(C) (Δi)²

Con adj = +(120)(-0.0025)(-0.0025) = +0.000750 or 0.075%

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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%.

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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) -24.90%.

B) -17.58%.

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%.

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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) -11.718%.

B) -13.956%.

C) -9.325%.

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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%.> >