mouse123

Which of the following is most accurate about a bond with positive convexity?

A) Positive changes in yield lead to positive changes in price.

B) Price increases and decreases at a faster rate than the change in yield.

C) Price increases when yields drop are greater than price decreases when yields rise by the same amount.

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A convex price/yield graph has a larger increase in price as yield decreases than the decrease in price when yields increase. This comes from the definition of a convex graph.

mouse123

Negative convexity is most likely to be observed in:

A) callable bonds.

B) zero coupon bonds.

C) treasury bonds.

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All noncallable bonds exhibit the trait of being positively convex and callable bonds have a negative convexity.  Callable bonds have a negative convexity because once the yield falls below a certain point, as yields fall, prices will rise at a decreasing rate, thus giving the curve a negative convex shape.

mouse123

Convexity is important because:

A) it measures the volatility of non-callable bonds.

B) the slope of the price/yield curve is not linear.

C) the slope of the callable bond price/yield curve is backward bending at high interest rates.

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Modified duration is a good approximation of price changes for an option-free bond only for relatively small changes in interest rates. As rate changes grow larger, the curvature of the bond price/yield relationship becomes more prevalent, meaning that a linear estimate of price changes will contain errors. The modified duration estimate is a linear estimate, as it assumes that the change is the same for each basis point change in required yield. The error in the estimate is due to the curvature of the actual price path. This is the degree of convexity. If we can generate a measure of this convexity, we can use this to improve our estimate of bond price changes.

Kingpin804

Which of the following statements best describes the concept of negative convexity in bond prices? As interest rates:

A) fall, the bond's price increases at an increasing rate.

B) rise, the bond's price decreases at a decreasing rate.

C) fall, the bond's price increases at a decreasing rate.

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Negative convexity occurs with bonds that have prepayment/call features. As interest rates fall, the borrower/issuer is more likely to repay/call the bond, which causes the bond’s price to approach a maximum. As such, the bond’s price increases at a decreasing rate as interest rates decrease.

Kingpin804

At a market rate of 7%, a $1,000 callable par value bond is priced at $910, while a similar bond that is non-callable is priced at $960. What is the value of the embedded call option?

A) $40.

B) $50.

C) $30.

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The value of the embedded call option is simply stated as:  
value of the straight bond component – callable bond value = value of embedded call option.
$960 – $910 = $50

Kingpin804

An analyst is evaluating the following two statements about putable bonds:

Statement #1: As yields fall, the price of putable bonds will rise less quickly than similar option-free bonds (beyond a critical point) due to the decrease in value of the embedded put option.
Statement #2: As yields rise, the price of putable bonds will fall more quickly than similar option-free bonds (beyond a critical point) due to the increase in value of the embedded put option.

The analyst should:

A) disagree with both statements.

B) agree with both statements.

C) agree with only one statement.

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Both statements are false. As yields fall, the value of the embedded put option in a putable bond decreases and (beyond a critical point) the putable bond behaves much the same as an option-free bond. As yields rise, the value of the embedded put option increases and (beyond a critical point) the putable bond decreases in value less quickly than a similar option-free bond.

Kingpin804

An investor gathered the following information about two 7% annual-pay, option-free bonds:

• Bond R has 4 years to maturity and is priced to yield 6%
• Bond S has 7 years to maturity and is priced to yield 6%
• Both bonds have a par value of $1,000.

Given a 50 basis point parallel upward shift in interest rates, what is the value of the two-bond portfolio?

A) $2,044.

B) $2,030.

C) $2,086.

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Given the shift in interest rates, Bond R has a new value of $1,017 (N = 4; PMT = 70; FV = 1,000; I/Y = 6.50%; CPT → PV = 1,017). Bond S’s new value is $1,027 (N = 7; PMT = 70; FV = 1,000; I/Y = 6.50%; CPT → PV = 1,027). After the increase in interest rates, the new value of the two-bond portfolio is $2,044 (1,017 + 1,027).

Kingpin804

With market interest rates at 6%, an analyst observes a 5-year, 5% coupon, $1,000 par value callable bond selling for $950. At the same time the analyst observes a non-callable bond, identical in all other respects to the callable bond, selling for $980. The analyst should estimate that the value of the call option on the callable bond is closest to:

A) $50.

B) $30.

C) $20.

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The difference in price between the two bonds is the value of the option: $980 − $950 = $30.

Kingpin804

Which of the following bonds experience the greatest precentage price change when the market interest rates rise?

A) A high coupon, long maturity bond.

B) A low coupon, short maturity bond.

C) A low coupon, long maturity bond.

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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.

According to these three features the greatest price change will come from the bond with a low coupon and long maturity.

Kingpin804

Which of the following bonds is likely to exhibit the greatest volatility due to interest rate changes? A bond with a:

A) low coupon and a long maturity.

B) high coupon and a long maturity.

C) low coupon and a short maturity.

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There are three features that determine the magnitude of the bond price volatility:
(1) The lower the coupon, the greater the bond price volatility.
(2) The longer the term to maturity, the greater the price volatility.
(3) The lower the initial yield, the greater the price volatility.
So the bond with a low coupon and long maturity will have the greatest price volatility.