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

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

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

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

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

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

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

B) a higher yield.

C) a lower 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 and will increase more when rates decrease than a low-convexity bond's price.

andytrader

Which of the following is the most significant limitation of the portfolio duration measure? The assumption of:

A) a nonparallel shift in the yield curve.

B) a linear approximation of the actual price-yield function.

C) a parallel shift in the yield curve.

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The most significant limitation of portfolio duration is the assumption that the yield for all maturities changes by the same amount (a parallel shift in the yield curve).

andytrader

Which of the following is NOT a limitation of the portfolio duration measure?

A) It is subject to huge swings in value since book values may change over time.

B) It assumes that the yield for all maturities changes by the same amount.

C) It is subject to huge swings in value since market values may change over time.

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Bond duration is calculated using market values; changes in book values are irrelevant.

andytrader

Which of the following is a limitation of the portfolio duration measure? Portfolio duration only considers:

A) a linear approximation of the actual price-yield function for the portfolio.

B) the market values of the bonds.

C) a nonparallel shift in the yield curve.

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Duration is a linear approximation of a nonlinear function. The use of market values has no direct effect on the inherent limitation of the portfolio duration measure. Duration assumes a parallel shift in the yield curve, and this is an additional limitation.