Board logo

标题: Fixed Income【Reading 59】Sample [打印本页]
作者: Kingpin804    时间: 2012-3-31 15:22     标题: [2012 L1] Fixed Income【Session 16 - Reading 59】Sample

Which of the following approaches in measuring interest rate risk is most accurate when properly performed?
A)
Duration approach.
B)
Duration/convexity approach.
C)
Full Valuation approach.


The most accurate approach method for measuring interest rate risk is the so-called full valuation approach. Essentially this boils down to the following four steps: (1) begin with the current market yield and price, (2) estimate hypothetical changes in required yields, (3) recompute bond prices using the new required yields, and (4) compare the resulting price changes. Duration and convexity are summary measures and sacrifice some accuracy.
作者: Kingpin804    时间: 2012-3-31 15:22

Which of the following steps is NOT used in the full valuation approach in measuring interest rate risk?
A)
Calculate the bond's convexity.
B)
Compare resulting price changes.
C)
Estimate hypothetical changes in required yields.


The most straightforward approach method for measuring interest rate risk is the so-called full valuation approach. Essentially this boils down to the following four steps: (1) begin with the current market yield and price, (2) estimate hypothetical changes in required yields, (3) recompute bond prices using the new required yields, and (4) compare the resulting price changes.
作者: Kingpin804    时间: 2012-3-31 15:23

Holding other factors constant, the interest rate risk of a coupon bond is higher when the bond's:
A)
current yield is higher.
B)
coupon rate is higher.
C)
yield to maturity is lower.


There are three features that determine the magnitude of the bond price volatility:
In this case the only determinant that will cause a higher interest rate risk is having a low yield to maturity (initial yield). A higher coupon yield and a higher current yield will cause for lower interest rate risk.
作者: Kingpin804    时间: 2012-3-31 15:23

If interest rates fall, the:
A)
value of call option embedded in the callable bond falls.
B)
callable bond's price rises faster than that of a noncallable but otherwise identical bond.
C)
callable bond's price rises more slowly than that of a noncallable but otherwise identical bond.


When a callable bond's yield falls to a certain point, when the yields fall the price will increase at a decreasing rate. Compare this to a noncallable bond where, as the yield falls the price rises at an increasing rate.
作者: Kingpin804    时间: 2012-3-31 15:24

In comparing the price volatility of putable bonds to that of option-free bonds, a putable bond will have:
A)
less price volatility at low yields.
B)
less price volatility at higher yields.
C)
more price volatility at higher yields.


The only true statement is that putable bonds will have less price volatility at higher yields. At higher yields the put becomes more valuable and reduces the decline in price of the putable bond relative to the option-free bond. On the other hand, when yields are low, the put option has little or no value and the putable bond will behave much like an option-free bond. Therefore at low yields a putable bond will not have more price volatility nor will it have less price volatility than a similar option-free bond.
作者: Kingpin804    时间: 2012-3-31 15:24

A $1,000 face, 10-year, 8.00% semi-annual coupon, option-free bond is issued at par (market rates are thus 8.00%). Given that the bond price decreased 10.03% when market rates increased 150 basis points (bp), which of the following statements is CORRECT? If market yields:
A)
decrease by 150bp, the bond's price will decrease by more than 10.03%.
B)
decrease by 150bp, the bond's price will increase by more than 10.03%.
C)
decrease by 150bp, the bond's price will increase by 10.03%.


All other choices are false because of positive convexity - bond prices rise faster than they fall. Positive convexity applies to both dollar and percentage price changes. For any given absolute change in yield, the increase in price will be more than the decrease in price for a fixed-coupon, noncallable bond. As yields increase, bond prices fall, and the price curve gets flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond prices rise, and the price curve gets steeper, and changes in yield have a larger effect on bond prices. Here, for an absolute 150bp change, the price increase would be more than the price decrease. For a 100bp increase, the price decrease would be less than that for a 150bp increase.
作者: Kingpin804    时间: 2012-3-31 15:25

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.


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.
作者: Kingpin804    时间: 2012-3-31 15:25

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.


There are three features that determine the magnitude of the bond price volatility:
According to these three features the greatest price change will come from the bond with a low coupon and long maturity.
作者: Kingpin804    时间: 2012-3-31 15:25

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.


The difference in price between the two bonds is the value of the option: $980 − $950 = $30.
作者: Kingpin804    时间: 2012-3-31 15:26

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


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).
作者: Kingpin804    时间: 2012-3-31 15:26

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.


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.
作者: Kingpin804    时间: 2012-3-31 15:27

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.


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
作者: Kingpin804    时间: 2012-3-31 15:27

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.


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.
作者: mouse123    时间: 2012-3-31 15:29

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.


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.
作者: mouse123    时间: 2012-3-31 15:29

Negative convexity is most likely to be observed in:
A)
callable bonds.
B)
zero coupon bonds.
C)
treasury bonds.


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.
作者: mouse123    时间: 2012-3-31 15:30

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.


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.
作者: mouse123    时间: 2012-3-31 15:30

Positive convexity in bond prices implies all but which of the following statements?
A)
As yields increase, changes in yield have a smaller effect on bond prices.
B)
Bond prices approach a ceiling as interest rates fall.
C)
The price volatility of non-callable bonds is inversely related to the level of market yields.


The convexity of bond prices means that bond prices as a function of interest rates approach a floor as interest rates rise.
作者: mouse123    时间: 2012-3-31 15:30

If a put feature expires on a bond so that it becomes option-free, then the curve depicting the price and yield relationship of the bond will become:
A)
less convex.
B)
more convex.
C)
inversely convex.


When the option expires, the prices at the lower end of the curve will become lower. This will make the curve less convex.
作者: mouse123    时间: 2012-3-31 15:31

Can a fixed income security have a negative convexity?
A)
Only when the price/yield curve is linear.
B)
No.
C)
Yes.


Yes, fixed income securities can have a negative security. The only type of fixed income security with a negative convexity will be callable bonds.  
作者: mouse123    时间: 2012-3-31 15:31

How does the price-yield relationship for a callable bond compare to the same relationship for an option-free bond? The price-yield relationship is:
A)
concave for the callable bond and convex for an option-free bond.
B)
concave for low yields for the callable bond and always convex for the option-free bond.
C)
the same for both bond types.


Since the issuer of a callable bond has an incentive to call the bond when interest rates are very low in order to get cheaper financing, this puts an upper limit on the bond price for low interest rates and thus introduces the concave relationship between yields and prices.
作者: mouse123    时间: 2012-3-31 15:31

How does the price-yield relationship for a putable bond compare to the same relationship for an option-free bond? The price-yield relationship is:
A)
more convex at some yields for the putable bond than for the option-free bond.
B)
the same for both bond types.
C)
more convex for a putable bond than for an option-free bond.


Since the holder of a putable has an incentive to exercise his put option if yields are high and the bond price is depressed, this puts a lower limit on the price of the bond when interest rates are high. The lower limit introduces a higher convexity of the putable bond compared to an option-free bond when yields are high.
作者: mouse123    时间: 2012-3-31 15:32

Jayce Arnold, a CFA candidate, is studying how the market yield environment affects bond prices. She considers a $1,000 face value, option-free bond issued at par. Which of the following statements about the bond’s dollar price behavior is most likely accurate when yields rise and fall by 200 basis points, respectively? Price will:
A)
increase by $149, price will decrease by $124.
B)
decrease by $149, price will increase by $124.
C)
decrease by $124, price will increase by $149.


As yields increase, bond prices fall, the price curve gets flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond prices rise, the price curve gets steeper, and changes in yield have a larger effect on bond prices. Thus, the price increase when interest rates decline must be greater than the price decrease when interest rates rise (for the same basis point change). Remember that this applies to percentage changes as well.
作者: mouse123    时间: 2012-3-31 15:32

Which of the following bonds may have negative convexity?
A)
Mortgage backed securities.
B)
Callable bonds.
C)
Both of these choices are correct.


Negative convexity is the idea that as interest rates decrease they get to a certain point where the value of certain bonds (bonds with negative convexity) will start to increase in value at a decreasing rate.
Interest rate risk is the risk of having to reinvest at rates that are lower than what an investor is currently receiving.
Mortgage backed securities (MBS) may have negative convexity because when interest rates fall mortgage owners will refinance for lower rates, thus prepaying the outstanding principle and increasing the interest rate risk that investors of MBS may incur.
Callable bonds are similar to MBS because of the possibility that the principle is being returned to the investor sooner than expected if the bond is called causing a higher level of interest rate risk.
作者: mouse123    时间: 2012-3-31 15:33

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.


There are three features that determine the magnitude of the bond 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.
作者: mouse123    时间: 2012-3-31 15:33

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.


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.
作者: mouse123    时间: 2012-3-31 15:33

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.


When bond prices go up faster than they go down, it is called positive convexity.
作者: mouse123    时间: 2012-3-31 15:34

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.


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.
作者: mouse123    时间: 2012-3-31 15:34

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.


The duration is computed as follows:
Duration = 105.50 − 100 = 5.37
2 × 102.50 × 0.005
作者: mouse123    时间: 2012-3-31 15:35

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.


The effective duration is computed as follows:
Effective duration = 105.56 − 98.46 = 3.49
2 × 101.76 × 0.01
作者: mouse123    时间: 2012-3-31 15:35

An international bond investor has gathered the following information on a 10-year, annual-pay U.S. corporate bond:
The bond’s duration is closest to:
A)
3.14.
B)
6.15.
C)
6.58.


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.
作者: mouse123    时间: 2012-3-31 15:35

Consider an annual coupon bond with the following characteristics:
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.


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.
作者: mouse123    时间: 2012-3-31 15:36

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.


The formula for effective duration is: (V- – V+) / (2V0Δy). Therefore, effective duration is: ($1.110 – $1.053) / (2 × $1.081 × 0.005) = 5.27.
作者: mouse123    时间: 2012-3-31 15:36

Calculate the effective duration for a 7-year bond with the following characteristics:
A)
3.1.
B)
6.8.
C)
6.5.


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


where:
The duration of this bond is calculated as:

作者: mouse123    时间: 2012-3-31 15:37

An investor finds that for every 1% increase in interest rates, a bond’s price decreases by 4.21% compared to a 4.45% increase in value for every 1% decline in interest rates. If the bond is currently trading at par value, the bond’s duration is closest to:
A)
4.33.
B)
8.66.
C)
43.30.


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 = (104.45 – 95.79)/(2 × 100 × 0.01) = 4.33. Remember that the change in interest rates must be in decimal form.
作者: mouse123    时间: 2012-3-31 15:37

A non-callable bond with 18 years remaining maturity has an annual coupon of 7% and a $1,000 par value. The current yield to maturity on the bond is 8%. Which of the following is closest to the effective duration of the bond?
A)
8.24.
B)
9.63.
C)
11.89.

First, compute the current price of the bond as:

FV = $1,000; PMT = $70; N = 18; I/Y = 8%; CPT → PV = –$906.28

Next, change the yield by plus-or-minus the same amount. The amount of the change can be any value you like. Here we will use ±50 basis points. Compute the price of the bond if rates rise by 50 basis points to 8.5% as:

FV = $1,000; PMT = $70; N = 18; I/Y = 8.5%; CPT → PV = –$864.17

Then compute the price of the bond if rates fall by 50 basis points to 7.5% as:

FV = $1,000; PMT = $70; N = 18; I/Y = 7.5%; CPT → PV = –$951.47

The formula for effective duration is:

(V- – V+) / (2V0Δy)

Therefore, effective duration is:

($951.47 – $864.17) / (2 × $906.28 × 0.005) = 9.63.
作者: mouse123    时间: 2012-3-31 15:38

A non-callable bond with 4 years remaining maturity has an annual coupon of 12% and a $1,000 par value. The current price of the bond is $1,063.40. Given a change in yield of 50 basis points, which of the following is closest to the effective duration of the bond?
A)
2.94.
B)
3.27.
C)
3.11.

First, find the current yield to maturity of the bond as:

FV = $1,000; PMT = $120; N = 4; PV = –$1,063.40; CPT → I/Y = 10%

Then compute the price of the bond if rates rise by 50 basis points to 10.5% as:

FV = $1,000; PMT = $120; N = 4; I/Y = 10.5%; CPT → PV = –$1,047.04

Then compute the price of the bond if rates fall by 50 basis points to 9.5% as:

FV = $1,000; PMT = $120; N = 4; I/Y = 9.5%; CPT → PV = –$1,080.11

The formula for effective duration is:

(V-–V+) / (2V0Δy)

Therefore, effective duration is:

($1,080.11 – $1,047.04) / (2 × $1,063.40 × 0.005) = 3.11
作者: mouse123    时间: 2012-3-31 15:39

Joshua Reynaldo is a fixed income portfolio manager for Golden Apple Capital Management. The portfolio is valued at $900 million, of which $840 million is currently invested. Fiona Campbell, the firm’s strategist, is becoming concerned about the possibility of an increase in interest rates. Reynaldo agrees, and this makes him nervous because the effective duration of his current portfolio investments is 10.315. However, his portfolio is presented to clients as a long-term fund, so there are limits to how short he can make the duration of the portfolio and still stay within the investment policy guidelines.
Reynaldo needs to invest the $60 million cash currently in the portfolio, and wants to do it in a way that will minimize the portfolio’s downside risk in a rising rate environment. He considers two different bonds. Both trade at their $1,000 par value and make coupon payments semiannually.
The first bond is a 12-year issue of Yorkville Technologies. Reynaldo likes the bond because of its attractive 5.9% coupon. He is concerned, however, because Yorkville is only rated Baa and Campbell is expecting a deterioration in credit quality as part of her economic outlook.
The second bond is also a 12-year maturity, but issued by Mountain States Electric & Gas, an Aaa utility. The 5.2% yield is not as attractive as the lower quality issue, but the Mountain States bond would represent a safe haven if credit spreads begin to widen, as both he and Campbell expect. Reynaldo’s only concern about the Mountain States bond is that it is callable any time at 102.
Discussing these possibilities with Campbell, Reynaldo tells her, “I ran my calculations assuming rates rise or fall by 50 basis points, and found that the effective convexity of the Mountain States bond is ten times the effective convexity of the Yorkville bond.” Campbell adds, “But the signs are opposite – the Mountain States bond has negative convexity and the Yorkville bond has positive convexity.”
Reynaldo continues, “I haven’t done a full valuation yet, but using my figures for duration and assuming convexity is 46, it looks like a 100 basis point rise in rates would cause the price of the Yorkville bond to fall by 6.73%.” Campbell, looking over his shoulder at his calculations, adds, “The dollar value of an 01 for the Yorkville bond is only 0.063, though.”
Reynaldo decides to invest in the Yorkville bond.Which statement about how duration tends to predict price changes for large swings in yield is most accurate? Duration:
A)
overestimates the increase in price for increases in yield.
B)
overestimates the increase in price for decreases in yield.
C)
underestimates the increase in price for decreases in yield.


For large swings in yield, duration tends to underestimate the increase in price when yield decreases and overestimate the decrease in price when yield increases. This is because duration is a linear estimate and does not account for the curvature in the price/yield relationship.
Using a 50 basis point change in interest rates, what is the difference in effective duration between the Mountain States bond and the Yorkville bond? The effective duration of the:
A)
Mountain States bond is 0.34 lower than the effective duration of the Yorkville bond.
B)
Mountain States bond is 0.34 higher than the effective duration of the Yorkville bond.
C)
Yorkville bond is 2.21 higher than the effective duration of the Mountain States bond.


In order to calculate effective duration, we first need to know the bond price if interest rates rise or fall by 50 basis points.
For the Yorkville bond:
N = 24; PMT = (0.059 coupon × $1,000 par value / 2 payments per year =) 29.50; FV = 1,000
If rates rise by 50 basis points, I = ((5.9% + 0.50 =) 6.4% / 2 payments per year =) 3.2%; PV = -958.56.
Since the bond has a par value of $1,000, the estimated price will be (958.56 / 1,000 × 100 =) 95.86.
If rates fall by 50 basis points, I = ((5.9% − 0.50 =) 5.4% / 2 payments per year = ) 2.7%; PV = -1043.74.
Since the bond has a par value of $1,000, the estimated price will be (1043.74 / 1,000 × 100 =) 104.37.
Now that we have the prices, we can use the formula for effective duration (ED):
ED = (104.37 – 95.86) / (2 × 100 × 0.005)
ED = 8.51 / 1
ED = 8.51
For the Mountain States bond:
N = 24, PMT = (0.052 coupon × $1,000 par value / 2 payments per year =) 26.00, FV = 1,000
If rates rise by 50 basis points, I = ((5.2% + 0.50 =) 5.7% / 2 payments per year =) 2.85%; PV = -956.97.
Since the bond has a par value of $1,000, the estimated price will be (956.97 / 1,000 × 100 =) 95.70.
If rates fall by 50 basis points, I = ((5.2% − 0.50 =) 4.7% / 2 payments per year =) 2.35%; PV = -1045.46.
Since the bond has a par value of $1,000, the estimated price will be (1045.46 / 1,000 × 100 =) 104.55
However, since the bond is callable at 102, the price will be 102, not 104.55.
ED = (102 – 95.70) / (2 × 100 × 0.005)
ED = 6.30 / 1
ED = 6.30
The ED of the Yorkville bond is (8.51 – 6.30 =) 2.21 higher than the ED of the Mountain States bond.

If Reynaldo must invest his $60 million cash in either the Yorkville bond or the Mountain States bond, or some combination of the two, what is the lowest value he can achieve for the effective duration of the total portfolio?
A)
10.194.
B)
10.046.
C)
9.624.


If he purchases the Yorkville bond:
Portfolio duration = (w1 × ED1) + (w2 × ED2)
Portfolio duration = ((840 / 900) × 10.315) + ((60 / 900) × 8.51)
Portfolio duration = (0.933 × 10.315) + (0.067 × 8.51)
Portfolio duration = 9.624 + 0.570
Portfolio duration = 10.194
If he purchases the Mountain States bond:
Portfolio duration = (w1 × ED1) + (w2 × ED2)
Portfolio duration = ((840 / 900) × 10.315) + ((60 / 900) × 6.30)
Portfolio duration = (0.933 × 10.315) + (0.067 × 6.30)
Portfolio duration = 9.624 + 0.422
Portfolio duration = 10.046
Note, however, that we did not need to calculate the duration of the portfolio if he purchases the Yorkville bond. Since we know that the Mountain States bond has lower effective duration than the Yorkville bond, we know that the lowest effective duration for the total portfolio would be achieved by investing all $60 million in the Mountain States bond.

Regarding the statements made by Reynaldo and Campbell about the expected price change in the Yorkville bond:
A)
both are incorrect.
B)
both are correct.
C)
only one is correct.


For the Yorkville bond:
Percentage price change = (-8.51 × 0.010 × 100) + (46.0 × 0.0102 × 100)
Percentage price change = -8.51 + 0.46
Percentage price change = -8.05
Reynaldo’s statement is incorrect.
To calculate the dollar value of an 01 we need to know the price of the bond if interest rates rise (or fall) by 1 basis point:
N = 24; PMT = (0.059 coupon × $1,000 par value / 2 payments per year =) 29.50; FV = 1,000
If rates rise by 1 basis point, I = ((5.90 + 0.01 =) 5.91% / 2 payments per year =) 2.955%; PV = -999.149, for a price of 99.915.
PVBP = 100 – 99.915 = 0.085
Campbell’s statement is also incorrect.

Reynaldo and Apple are training a new analyst, Norah Spears. They ask Spears what she knows about duration and convexity. Spears replies with four statements:

Statement 1:
Modified duration is a better measure than effective duration for bonds with embedded options.

Statement 2:
The convexity adjustment corrects for the error embedded in the duration.

Statement 3:
Modified duration ignores the negative convexity of a callable bond.

Statement 4:
Convexity of option-free bonds is always added to duration to modify the errors in calculating price volatility.

Which of the following regarding Spears’ statements is most accurate?
A)
Spears is correct with respect to Statement 2, but incorrect with respect to Statement 4.
B)
Spears is correct with respect to Statement 3, but incorrect with respect to Statement 1.
C)
Spears is correct with respect to all four statements.


Effective duration is a better measure than modified duration for bonds with embedded options because modified duration does not explicitly recognize the change in cash flows that will occur in a bond with embedded options as yield changes. Therefore, Statement 1 is incorrect. The other four statements made by Spears are correct.
作者: mouse123    时间: 2012-3-31 15:39

A 30-year semi-annual coupon bond issued today with market rates at 6.75% pays a 6.75% coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?
A)
3.84%.
B)
1.28%.
C)
12.80%.


Approximate % change in price =
(price if yield down − price if yield up) / (2 × initial price × yield change expressed as a decimal).
Here, the initial price is par, or $1,000 because we are told the bond was issued today at par. So, the calculation is: (1039.59 − 962.77) / (2 × 1000 × 0.003) = 76.82 / 6.00 = 12.80.
作者: mouse123    时间: 2012-3-31 15:40

A bond with a yield to maturity of 8.0% is priced at 96.00. If its yield increases to 8.3% its price will decrease to 94.06. If its yield decreases to 7.7% its price will increase to 98.47. The effective duration of the bond is closest to:
A)
2.75.
B)
7.66.
C)
4.34.


The change in the yield is 30 basis points.
Duration = (98.47 − 94.06) / (2 × 96.00 × 0.003) = 7.6563.
作者: mouse123    时间: 2012-3-31 15:40

A bond's yield to maturity decreases from 8% to 7% and its price increases by 6%, from $675.00 to $715.50. The bond's effective duration is closest to:
A)
7.0.
B)
5.0.
C)
6.0.


Effective duration is the percentage change in price for a 1% change in yield, which is given as 6.
作者: mouse123    时间: 2012-3-31 15:41

When interest rates increase, the duration of a 30-year bond selling at a discount:
A)
increases.
B)
does not change.
C)
decreases.


The higher the yield on a bond the lower the price volatility (duration) will be. When interest rates increase the price of the bond will decrease and the yield will increase because the current yield = (annual cash coupon payment) / (bond price). As the bond price decreases the yield increases and the price volatility (duration) will decrease.
作者: mouse123    时间: 2012-3-31 15:41

If bond prices fall 5% in response to a 0.5% increase in interest rates, what is the bond's effective duration?
A)
+10.
B)
-5.
C)
-10.


Approximate percentage price change of a bond = - (duration) (delta y) =
-5 = - (duration) (0.5) = 10.
作者: mouse123    时间: 2012-3-31 15:42

A non-callable bond with 10 years remaining maturity has an annual coupon of 5.5% and a $1,000 par value. The current yield to maturity on the bond is 4.7%. Which of the following is closest to the estimated price change of the bond using duration if rates rise by 75 basis points?
A)
-$61.10.
B)
-$47.34.
C)
-$5.68.


First, compute the current price of the bond as: FV = 1,000; PMT = 55; N = 10; I/Y = 4.7; CPT → PV = –1,062.68. Then compute the price of the bond if rates rise by 75 basis points to 5.45% as: FV = 1,000; PMT = 55; N = 10; I/Y = 5.45; CPT → PV = –1,003.78. Then compute the price of the bond if rates fall by 75 basis points to 3.95% as: FV = 1,000; PMT = 55; N = 10; I/Y = 3.95; CPT → PV = –1,126.03.
The formula for effective duration is: (V-–V+) / (2V0Δy). Therefore, effective duration is: ($1,126.03 – $1,003.78) / (2 × $1,062.68 × 0.0075) = 7.67.
The formula for the percentage price change is then: –(duration)(Δy). Therefore, the estimated percentage price change using duration is: –(7.67)(0.75%) = –5.75%. The estimated price change is then: (–0.0575)($1,062.68) = –$61.10
作者: mouse123    时间: 2012-3-31 15:42

A non-callable bond has an effective duration of 7.26. Which of the following is the closest to the approximate price change of the bond with a 25 basis point increase in rates using duration?
A)
-0.018%.
B)
1.820%.
C)
-1.820%.


The formula for the percentage price change is: –(duration)(Δy). Therefore, the estimated percentage price change using duration is: –(7.26)(0.25%) = –1.82%.
作者: mouse123    时间: 2012-3-31 15:42

What happens to bond durations when coupon rates increase and maturities increase?
As coupon rates increase,
duration:		As maturities increase,
duration:
  
A)
increases  increases
B)
decreases   increases
C)
decreases   decreases


As coupon rates increase the duration on the bond will decrease because investors are recieving more cash flow sooner. As maturity increases, duration will increase because the payments are spread out over a longer peiod of time.
作者: mouse123    时间: 2012-3-31 15:43

Given a bond with a modified duration of 1.93, if required yields increase by 50 basis points, the expected percentage price change would be:
A)
-1.025%.
B)
1.000%.
C)
-0.965%.


Approximate percentage price change of a bond = (-)(duration)(Δ y)
(-1.93)(0.5%) = -0.965%
作者: mouse123    时间: 2012-3-31 15:43

Par value bond XYZ has a modified duration of 5. Which of the following statements regarding the bond is CORRECT? If the market yield:>
A)
increases by 1% the bond's price will decrease by $50.
B)
increases by 1% the bond's price will increase by $50.
C)
increases by 1% the bond's price will decrease by $60.


Approximate percentage price change of a bond = (-)(Duration)(Δy)
(-5)(1%) = -5%
($1000)(-0.05) = –$50
作者: mouse123    时间: 2012-3-31 15:44

An $850 bond has a modified duration of 8. If interest rates fall 50 basis points, the bond's price will:
A)
increase by $4.00.
B)
increase by $34.00.
C)
increase by 22.5%.

ΔP/P = (-)(MD)(Δi) ΔP = (-)(P)(MD)(Δi)
ΔP = (-)(8)(850)(-0.005) = +$34
作者: mouse123    时间: 2012-3-31 15:46

A bond has the following characteristics:
If the market interest rate decreases by 0.75%, what will be the percentage change in the bond's price?
A)
0.750%.
B)
-12.675%.
C)
+12.675%.


Approximate percentage price change of a bond = (-)(effective duration)(Δy)
= (-16.9)(-0.75%) = +12.675%
作者: mouse123    时间: 2012-3-31 15:47

A bond with a semi-annually coupon rate of 3% sells for $850. It has a modified duration of 10 and is priced at a yield to maturity (YTM) of 8.5%. If the YTM increases to 9.5%, the predicted change in price, using the duration concept decreases by:
A)
$85.00.
B)
$77.56.
C)
$79.92.


Approximate percentage price change of a bond = (-)(duration)(Δy)
Δy = 9.5% − 8.5% = 1%
(-10)(1%) = -10%
($850)(-0.1) = -$85
作者: mouse123    时间: 2012-3-31 15:47

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 approximate percentage price change of the bond using effective duration and assuming interest rates decrease by 0.5%?
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)
1.74%.
B)
0.174%.
C)
0.0087%.


The effective duration is computed as follows:


Using the effective duration, the approximate percentage price change of the bond is computed as follows:
Percent price change = -3.49 × (-0.005) × 100 = 1.74%
作者: mouse123    时间: 2012-3-31 15:47

Which of the following statements about duration is NOT correct
A)
Effective duration is the exact change in price due to a 100 basis point change in rates.
B)
For a specific bond, the effective duration formula results in a value of 8.80%. For a 50 basis point change in yield, the approximate change in price of the bond would be 4.40%.
C)
The numerator of the effective duration formula assumes that market rates increase and decrease by the same number of basis points.


Effective duration is an approximation because the duration calculation ignores the curvature in the price/yield graph.
作者: mouse123    时间: 2012-3-31 15:48

When calculating duration, which of the following bonds would an investor least likely use effective duration on rather than modified duration?
A)
Option-free bond.
B)
Callable bond.
C)
Convertible bond.


The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.
作者: andytrader    时间: 2012-3-31 15:49

A bond with an 8% semi-annual coupon and 10-year maturity is currently priced at $904.52 to yield 9.5%. If the yield declines to 9%, the bond’s price will increase to $934.96, and if the yield increases to 10%, the bond’s price will decrease to $875.38. Estimate the percentage price change for a 100 basis point change in rates.
A)
6.58%.
B)
4.35%.
C)
2.13%.


The formula for the percentage price change is: (price when yields fall – price when yields rise) / 2 × (initial price) × 0.005 = ($934.96 – 875.38) / 2($904.52)(0.005) = $59.58 / $9.05 = 6.58%. Note that this formula is also referred to as the bond’s effective duration.
作者: andytrader    时间: 2012-3-31 15:49

Which of the following statements about modified duration and effective duration is NOT correct?
A)
Modified duration should be used for bonds with embedded options.
B)
Effective duration should be used for bonds with embedded options.
C)
The modified duration measure assumes that yield changes do not change the expected cash flows.


Using modified duration as a measure of the price sensitivity of a security with embedded options to changes in yield would be misleading. With embedded options, yield changes may change the expected cash flows.
作者: andytrader    时间: 2012-3-31 15:50

When compared to modified duration, effective duration:
A)
is equal to modified duration for callable bonds but not putable bonds.
B)
factors in how embedded options will change expected cash flows.
C)
places less weight on recent changes in the bond's ratings.


The point of effective duration is to consider expected changes in cash flow from features such as embedded options.
作者: andytrader    时间: 2012-3-31 15:50

The goal of computing effective duration is to get a:
A)
preliminary estimate of modified duration.
B)
more accurate measure of the bond's price sensitivity when embedded options exist.
C)
measure of duration that is effectively constant for the life of the bond.


The point of effective duration is to consider expected changes in cash flow from features such as embedded options. When embedded options exist, the effective duration will give a better measure of the bond’s price sensitivity to interest rate changes.
作者: andytrader    时间: 2012-3-31 15:50

An investor gathered the following information on two U.S. corporate bonds:

For each bond, which duration calculation should be applied?

Bond JBond M
A)
Modified DurationEffective Duration only
B)
Effective DurationEffective Duration only
C)
Effective DurationModified Duration or Effective Duration


The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.
作者: andytrader    时间: 2012-3-31 15:51

Which of the following explains why modified duration should least likely be used for bonds with call options? Modified duration assumes that the cash flows on the bond will:
A)
change with the bond's embedded options.
B)
be affected by a convertible bond.
C)
not change.


Modified duration assumes that the cash flows on the bond will not change (i.e., that we are dealing with non-callable bonds). This greatly differs from effective duration, which considers expected changes in cash flows that may occur for bonds with embedded options.
作者: andytrader    时间: 2012-3-31 15:52

Why should effective duration, rather than modified duration, be used when bonds contain embedded options?
A)
Modified duration considers expected changes in cash flows.
B)
Either could be used if the bond has embedded options.
C)
Effective duration considers expected changes in cash flows.


Modified duration assumes that the cash flows on the bond will not change (i.e., that we are dealing with non-callable bonds). This greatly differs from effective duration, which considers expected changes in cash flows that may occur for bonds with embedded options.
作者: andytrader    时间: 2012-3-31 15:52

Effective duration is more appropriate than modified duration as a measure of a bond's price sensitivity to yield changes when:
A)
the bond has a low coupon rate and a long maturity.
B)
yield curve changes are not parallel.
C)
the bond contains embedded options.


Effective duration takes into consideration embedded options in the bond. Modified duration does not consider the effect of embedded options. For option-free bonds, modified duration will be similar to effective duration. Both duration measures are based on the value impact of a parallel shift in a flat yield curve.
作者: andytrader    时间: 2012-3-31 15:52

Which of the following statements about duration is most accurate?
A)
Modified duration is the most appropriate measure of interest rate sensitivity for bonds with embedded options.
B)
Effective duration accounts for changes in a bond’s cash flows resulting from interest rate changes.
C)
Effective duration is calculated from past price changes in response to changes in yield.


Neither Macaulay nor modified duration is an appropriate measure of interest rate risk for bonds with embedded options. Macaulay duration does not take the current YTM into account as modified duration does. Effective duration, however, explicitly takes into account changes in a bond’s cash flows due to interest rate changes and is calculated from expected price changes in response to a given increase or decrease in yield.
作者: andytrader    时间: 2012-3-31 15:53

Vijay Ranjin, CFA, is a portfolio manager with Golson Investment Group. He manages a fixed-coupon bond portfolio with a face value of $120.75 million and a current market value of $116.46 million. Golson’s economics department has forecast that interest rates are going to change by 50 basis points. Based on this forecast, Ranjin estimates that the portfolio’s value will increase by $2.12 million if interest rates fall and will decrease by $2.07 million if interest rates rise. Which of the following choices is closest to the portfolio’s effective duration?
A)
4.3.
B)
0.4.
C)
3.6.


Effective duration = (price when interest rates fall − price when interest rates rise) / (2 × initial price × basis point change)
= (118.58 – 114.39) / (2 × 116.46 × 0.005) = 3.60.
作者: andytrader    时间: 2012-3-31 15:53

Which of the following statements about portfolio duration is NOT correct? It is:
A)
a measure of interest rate risk.
B)
a simple average of the duration estimates of the securities in the portfolio.
C)
the weighted average of the duration estimates of the securities in the portfolio.


Portfolio duration uses a weighted average figure, not a simple average.
作者: andytrader    时间: 2012-3-31 15:54

Suppose you have a three-security portfolio containing bonds A, B and C. The effective portfolio duration is 5.9. The market values of bonds A, B and C are $60, $25 and $80, respectively. The durations of bonds A and C are 4.2 and 6.2, respectively. Which of the following amounts is closest to the duration of bond B?
A)
7.4.
B)
1.4.
C)
9.0.


Plug all the known figures and then solve for the one unknown figure, the duration of bond B.
Proof: (60/165 × 4.2) + (25/165 × 9.0) + (80/165 × 6.2) = 5.9
作者: andytrader    时间: 2012-3-31 15:55

A bond portfolio consists of a AAA bond, a AA bond, and an A bond. The prices of the bonds are $1,050, $1,000, and $950 respectively. The durations are 8, 6, and 4 respectively. What is the duration of the portfolio?
A)
6.00.
B)
6.07.
C)
6.67.


The duration of a bond portfolio is the weighted average of the durations of the bonds in the portfolio. The weights are the value of each bond divided by the value of the portfolio:

portfolio duration = 8 × (1050 / 3000) + 6 × (1000 / 3000) + 4 × (950 / 3000) = 2.8 + 2 + 1.27 = 6.07.
作者: andytrader    时间: 2012-3-31 15:55

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.


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.
作者: andytrader    时间: 2012-3-31 15:55

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.


Bond duration is calculated using market values; changes in book values are irrelevant.
作者: andytrader    时间: 2012-3-31 15:56

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.


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).
作者: andytrader    时间: 2012-3-31 15:56

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.


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.
作者: andytrader    时间: 2012-3-31 15:57

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.


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.
作者: andytrader    时间: 2012-3-31 15:57

Convexity is more important when rates are:
A)
high.
B)
unstable.
C)
low.


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.
作者: andytrader    时间: 2012-3-31 15:58

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.

Convexity adjustment: +(Convexity)(change in i)2
Convexity adjustment = +(80)(-0.005)(-0.005) = +0.0020 or 0.20% or +20 basis points.
作者: andytrader    时间: 2012-3-31 15:59

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.


When interest rates increase by 50-100 basis points or more, the duration measure overestimates the decrease in the bond’s price.
作者: andytrader    时间: 2012-3-31 15:59

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.


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.
作者: andytrader    时间: 2012-3-31 16:00

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%.


The estimated price change is -(duration)(∆y) + (convexity) × (∆y)2 = -8 × (-0.006) + 50 × (-0.0062) = +0.0498 or 4.98%.
作者: andytrader    时间: 2012-3-31 16:00

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%.


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%.
作者: andytrader    时间: 2012-3-31 16:01

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%.


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%.
作者: andytrader    时间: 2012-3-31 16:03

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


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.
作者: andytrader    时间: 2012-3-31 16:03

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%.


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%
作者: andytrader    时间: 2012-3-31 16:03

Which of the following statements about the market yield environment is most accurate?
A)
As yields increase, bond prices rise, the price curve flattens, and further increases in yield have a smaller effect on bond prices.
B)
For a given change in interest rates, bond price sensitivity is lowest when market yields are already high.
C)
Positive convexity applies to the percentage price change, not the absolute dollar price change.


The price volatility of noncallable (option-free) bonds is inversely related to the level of market yields. In other words, when the yield level is high, bond price volatility is low and vice versa.
The statement beginning with, As yields increase. . . should continue . . .bond prices fall. Positive convexity (bond prices increase faster than they decrease for a given change in yield) applies to both absolute dollar changes and percentage changes.
作者: andytrader    时间: 2012-3-31 16:04

Consider a bond with a duration of 5.61 and a convexity of 21.92. Which of the following is closest to the estimated percentage price change in the bond for a 75 basis point decrease in interest rates?
A)
4.33%.
B)
4.21%.
C)
4.12%.


The estimated percentage price change is equal to the duration effect plus the convexity effect. The formula is: [–duration × (Δy)] + [convexity × (Δy)2]. Therefore, the estimated percentage price change is: [–(5.61)(–0.0075)] + [(21.92)(-0.0075)2] = 0.042075 + 0.001233 = 0.043308 = 4.33%.
作者: andytrader    时间: 2012-3-31 16:05

A bond has a convexity of 25.72. What is the approximate percentage price change of the bond due to convexity if rates rise by 150 basis points?
A)
0.71%.
B)
0.26%.
C)
0.58%.


The convexity effect, or the percentage price change due to convexity, formula is: convexity × (Δy)2. The percentage price change due to convexity is then: (25.72)(0.015)2 = 0.0058.
作者: andytrader    时间: 2012-3-31 16:05

A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes:
A)
down 15.00%.
B)
up 1.46%.
C)
down 1.46%.


∆P = [(-MD × ∆y) + (convexity) × (∆y)2] × 100
∆P = [(-6 × 0.0025) + (62.5) × (0.0025)2] × 100 = -1.461%
作者: andytrader    时间: 2012-3-31 16:06

A bond has a modified duration of 7 and convexity of 50. If interest rates decrease by 1%, the price of the bond will most likely:
A)
increase by 6.5%.
B)
increase by 7.5%.
C)
decrease by 7.5%.


Percentage Price Change = –(duration) (∆i) + convexity (∆i)2
therefore
Percentage Price Change = –(7) (–0.01) + (50) (–0.01)2=7.5%.
作者: andytrader    时间: 2012-3-31 16:06

A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes:
A)
up 4.00%.
B)
down 1.46%.
C)
down 15.00%.


ΔP/P = (-)(MD)(Δi) +(C) (Δi)2
= (-)(6)(0.0025) + (62.5) (0.0025)2 = -0.015 + 0.00039 = - 0.01461
作者: andytrader    时间: 2012-3-31 16:07

A bond’s duration is 4.5 and its convexity is 43.6. If interest rates rise 100 basis points, the bond’s percentage price change is closest to:
A)
-4.50%.
B)
-4.94%.
C)
-4.06%.


Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration × (change in yields)] + [convexity × (change in yields)2] = (-4.5)(0.01) + (43.6)(0.01)2 = -4.06%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments.
作者: andytrader    时间: 2012-3-31 16:08

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)
-2.875%.
B)
+0.075%.
C)
-2.125%.


Convexity adjustment: +(C) (Δi)2
Con adj = +(120)(-0.0025)(-0.0025) = +0.000750 or 0.075%
作者: andytrader    时间: 2012-3-31 16:09

One major difference between standard convexity and effective convexity is:
A)
effective convexity is Macaulay's duration divided by [1 + yield/2].
B)
effective convexity reflects any change in estimated cash flows due to embedded bond options.
C)
standard convexity reflects any change in estimated cash flows due to embedded options.


The calculation of effective convexity requires an adjustment in the estimated bond values to reflect any change in estimated cash flows due to the presence of embedded options. Note that this is the same process used to calculate effective duration.
作者: andytrader    时间: 2012-3-31 16:09

William Morgan, CFA, manages a fixed-income portfolio that contains several bonds with embedded options. Morgan would like to evaluate the sensitivity of his portfolio to large interest rate changes and will therefore use a convexity measure in addition to duration. The convexity measure that will best estimate the price sensitivity of Morgan’s portfolio is:
A)
modified convexity.
B)
either effective or modified convexity.
C)
effective convexity.


Effective convexity is the appropriate measure because it takes into account changes in cash flows due to embedded options, while modified convexity does not.
作者: andytrader    时间: 2012-3-31 16:09

The distinction between modified convexity and effective convexity is that:
A)
effective convexity accounts for changes in cash flows due to embedded options, while modified convexity does not.
B)
different dealers may calculate modified convexity differently, but there is only one formula for effective convexity.
C)
modified convexity becomes less accurate as the change in yield increases, but effective convexity corrects for this.


Effective convexity is the appropriate measure to use for bonds with embedded options because it takes into account the effect of the embedded options on the bond’s cash flows.
作者: andytrader    时间: 2012-3-31 16:10

Which of the following statements is most accurate concerning the differences between modified convexity and effective convexity?
A)
Modified convexity takes into account changes in cash flows due to embedded options, while effective convexity does not.
B)
For an option-free bond, modified convexity is slightly greater than effective convexity.
C)
Effective convexity is most appropriate for bonds with embedded options.


Effective convexity is most appropriate for bonds with embedded options because it takes into account changes in cash flows due to changes in yield, while modified convexity does not. For an option-free bond, modified convexity and effective convexity should be very nearly equal.
作者: andytrader    时间: 2012-3-31 16:11

The price value of a basis point (PVBP) for a 7-year, 10% semiannual pay bond with a par value of $1,000 and yield of 6% is closest to:
A)
$0.92.
B)
$0.28.
C)
$0.64.

PVBP = initial price – price if yield changed by 1 bps.

Initial price:

Price with change:

FV = 1000

FV = 1000

PMT = 50

PMT = 50

N = 14

N = 14

I/Y = 3%

I/Y = 3.005

CPT PV = 1225.92

CPT PV = 1225.28

PVBP = 1,225.92 – 1,225.28 = 0.64
PVBP is always the absolute value.

作者: clearlycanadian    时间: 2012-3-31 16:13

The price value of a basis point (PVBP) of a bond is $0.75. If the yield on the bond goes up by 1 bps, the price of the bond will:
A)
increase by $0.75.
B)
decline by $0.75.
C)
increase or decrease by $0.75.


Inverse relationships exist between price and yields on bonds. The larger the PVBP, the more volatile the bond’s price.
作者: clearlycanadian    时间: 2012-3-31 16:13

In addition to effective duration, analysts often use measures such as Value–at–Risk (VaR) to estimate the price sensitivity of bonds to changes in interest rates because these measures also incorporate the effects of:
A)
time to maturity.
B)
embedded options.
C)
yield volatility.


The volatility of a bond’s yield should be considered along with the bond’s effective duration when estimating its price sensitivity to interest rates. Measures of price risk such as VaR account for yield volatility. Effective duration includes the effects of time to maturity and embedded options.



欢迎光临 CFA论坛 (http://forum.theanalystspace.com/) Powered by Discuz! 7.2