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标题: Fixed Income【Reading 50】Sample [打印本页]
作者: spartan1    时间: 2012-4-2 17:11     标题: [2012 L2] Fixed Income【Session 14- Reading 50】Sample

The following are the yields on various bonds. The relevant benchmark is that of Treasury securities.
Treasury Bond Yield   4.00%
Bond Sector Yield   4.50%
Comparable Bond Yield   6.00%
ABC Bond Yield   6.50%

Is the ABC bond undervalued or overvalued and why? Using relative value analysis, the ABC bond is:
A)
undervalued because its yield is greater than that of Treasuries.
B)
undervalued because its spread is greater than that of comparable bonds.
C)
overvalued because its spread is greater than that of comparable bonds.


The purpose of relative value analysis is to determine whether a bond is fairly valued. The bond’s spread over some benchmark is compared to that of a required spread to determine whether the bond is fairly valued. The required spread will be that available on comparable securities. In this example, the relevant benchmark was Treasury securities. The spread for ABC bonds over Treasuries was 2.5%. The spread for comparable bonds over Treasuries was 2.0%. The higher spread for ABC bonds means that they are relatively undervalued (their price is low because their yield is higher).
作者: spartan1    时间: 2012-4-2 17:12

The following are the yields on various bonds. The relevant benchmark is that of the bond sector.
Treasury Bond Yield   3.00%
Bond Sector Yield   3.25%
Comparable Bond Yield   5.75%
ABC Bond Yield   5.50%

Is the ABC bond undervalued or overvalued and why? Using relative value analysis, the ABC bond is:
A)
overvalued because its spread is less than that of comparable bonds.
B)
undervalued because its yield is less than that of Treasuries.
C)
undervalued because its spread is less than that of comparable bonds.


The purpose of relative value analysis is to determine whether a bond is fairly valued. The bond’s spread over some benchmark is compared to that of a required spread to determine whether the bond is fairly valued. The required spread will be that available on comparable securities. In this example, the relevant benchmark was the bond sector. The spread for ABC bonds over the bond sector was 2.25%. The spread for comparable bonds over the bond sector was 2.50%. The lower spread for ABC bonds means that they are relatively overvalued (their price is high because their yield is lower).
作者: spartan1    时间: 2012-4-2 17:12

The purpose of relative value analysis is to determine:
A)
the return differential from riding the yield curve.
B)
whether a bond is fairly valued using a benchmark yield.
C)
whether a stock is fairly valued using present value calculations.


The purpose of relative value analysis is to determine whether a bond is fairly valued. The bond’s spread over some benchmark is compared to that of a required spread to determine whether the bond is fairly valued. The required spread will be that available on comparable securities.
作者: spartan1    时间: 2012-4-2 17:12

Which of the following benchmarks would generate the greatest spread when used to examine a bond yield?
A)
A U.S. Treasury security.
B)
Bond sector benchmark.
C)
The issuer of a specific company.


The U.S. Treasury security would generate the highest spread because the yield on Treasury securities will be the lowest as they have the lowest credit and liquidity risk. The yields on a bond sector benchmark and for a specific company will be higher.
作者: spartan1    时间: 2012-4-2 17:13

Which of the following spreads will reflect the option risk in a callable bond?
A)
The Z-spread only.
B)
Both the nominal spread and the Z-spread.
C)
The OAS only.


The OAS is the option-adjusted spread. It is determined using a binomial tree where a spread (the OAS) is added to the benchmark yield to find the arbitrage-free value for the callable or putable bond. The arbitrage-free value is the imputed value equal to the current bond price. The OAS is referred to as an option-adjusted spread because the cash flows in the tree are adjusted to reflect the option of the bond (e.g. a callable bond’s price is capped at the call price when interest rates drop). The nominal spread is simply the bond’s yield minus the benchmark yield. The Z-spread is the spread that, when added to the spot rates from a yield curve, results in an imputed value equal to the bond’s current price. The nominal spread and the Z-spread do not adjust the cash flows for the bond’s option. Thus the calculated yield spread using both these measures will reflect the option risk in the bond, as well as the bond’s credit and liquidity risk. Because the OAS calculation adjusts the cash flows for the bond’s option-like characteristics, the calculated OAS is just a reflection of the bond’s credit and liquidity risk, relative to the benchmark spot rates.
作者: spartan1    时间: 2012-4-2 17:14

The use of which of the following benchmarks to generate a spread would not reflect credit risk?
A)
A U.S. Treasury benchmark.
B)
A global industry-yield benchmark.
C)
An issuer-specific benchmark.


An issuer-specific benchmark (another bond of the same company) would not reflect credit risk because the benchmark would incorporate the credit risk of the firm. Using a U.S. Treasury benchmark would reflect credit risk because the bond to be evaluated would have higher credit risk than either benchmark. The yield in a global industry is not typically used as a benchmark.
作者: spartan1    时间: 2012-4-2 17:14


Using the following interest rate tree of semiannual interest rates what is the value of an option free bond that has one year remaining to maturity and has a 5% semiannual coupon rate?
        7.30%
6.20%
        5.90%
A)
98.67.
B)
98.98.
C)
97.53.


The option-free bond price tree is as follows:

100.00

A → 98.89

98.67100.00
99.56
100.00


As an example, the price at node A is obtained as follows:
PriceA = (prob × (Pup + (coupon / 2)) + prob × (Pdown + (coupon / 2)) / (1 + (rate / 2)) = (0.5 × (100 + 2.5) + 0.5 × (100 + 2.5) / (1 + (0.0730 / 2)) = 98.89. The bond values at the other nodes are obtained in the same way.
The calculation for node 0 or time 0 is
0.5[(98.89 + 2.5) / (1+ 0.062 / 2) + (99.56 + 2.5) / (1 + 0.062 / 2)] =
0.5(98.3414 + 98.9913) = 98.6663
作者: spartan1    时间: 2012-4-2 17:15

Using the following interest rate tree of semiannual interest rates what is the value of an option free semiannual bond that has one year remaining to maturity and has a 6% coupon rate?
         6.53%
6.30%
         5.67%
A)
98.52.
B)
97.53.
C)
99.81.


The option-free bond price tree is as follows:

100.00

A ==> 99.74

99.81100.00
100.16
100.00


As an example, the price at node A is obtained as follows:
PriceA = (prob × (Pup + coupon/2) + prob × (Pdown + coupon/2))/(1 + rate/2) = (0.5 × (100 + 3) + 0.5 × (100 + 3))/(1 + 0.0653/2) = 99.74. The bond values at the other nodes are obtained in the same way.
The calculation for node 0 or time 0 is
0.5[(99.74 + 3)/(1+ 0.063/2) + (100.16 + 3)/(1 + 0.063/2)] =
0.5 (99.60252 + 100.00969) = 99.80611
作者: spartan1    时间: 2012-4-2 17:15

For a putable bond, callable bond, or putable/callable bond, the nodal-decision process within the backward induction methodology of the interest rate tree framework requires that at each node the possible values will:
A)

not be higher than the call price or lower than the put price.
B)

include the face value of the bond.
C)

be, in number, two plus the number of embedded options.


At each node, there will only be two values. At each node, the analyst must determine if the initially calculated values will be below the put price or above the call price. If a calculated value falls below the put price: Vi,U = the put price. Likewise, if a calculated value falls above the call price, then Vi,L = the call price. Thus the put and call price are lower and upper limits, respectively, of the bond’s value at a node.
作者: spartan1    时间: 2012-4-2 17:16

A bond with a 10% annual coupon will mature in two years at par value. The current one-year spot rate is 8.5%. For the second year, the yield volatility model forecasts that the one-year rate will be either 8% or 9%. Using a binomial interest rate tree, what is the current price?
A)

102.659.
B)

101.837.
C)

103.572.


The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:
V1,U=[(100+10)/1.09+(100+10)/1.09]/2= 100.917
V1,L=[(100+10)/1.08+(100+10)/1.08]/2= 101.852
Thus
V0=[(100.917+10)/1.085+(101.852+10)/1.085]/2= 102.659
作者: spartan1    时间: 2012-4-2 17:24

Which of the following is a correct statement concerning the backward induction technique used within the binomial interest rate tree framework? From the maturity date of a bond:
A)
the corresponding interest rates are weighted by the bond's duration to discount the value of the bond.
B)
the corresponding interest rates and interest rate probabilities are used to discount the value of the bond.
C)
a deterministic interest rate path is used to discount the value of the bond.


For a bond that has N compounding periods, the current value of the bond is determined by computing the bond’s possible values at period N and working “backwards” to the present. The value at any given node is the probability-weighted average of the discounted values of the next period’s nodal values.
作者: spartan1    时间: 2012-4-2 17:26

With respect to interest rate models, backward induction refers to determining:
A)

convexity from duration.
B)

one portion of the yield curve from another portion.
C)

the current value of a bond based on possible final values of the bond.


Backward induction refers to the process of valuing a bond using a binomial interest rate tree. For a bond that has N compounding periods, the current value of the bond is determined by computing the bond’s possible values at period N and working "backwards."
作者: spartan1    时间: 2012-4-2 17:27

For an option-free bond where the coupons and maturity value are known and assuming constant interest rate volatility, which of the following sets of information will allow an analyst to construct the entire tree? The:
A)

beginning interest rate at the root only.
B)

lowest interest rate in each nodal period.
C)

interest rate at the root and in the final nodal period.


Given the lowest interest rate in each nodal period, the interest rates at the other nodes can be calculated. The interest rate at any node above the lowest is larger than the one below it by a factor of e2 × σ. Neither of the other sets of information are sufficient for constructing the tree.
作者: spartan1    时间: 2012-4-2 17:27

A binomial model or any other model that uses the backward induction method cannot be used to value a mortgage-backed security (MBS) because:
A)
the prepayments occur linearly over the life of an interest rate trend (either up or down).
B)
the cash flows for an MBS only depend on the current rate, not the path that rates have followed.
C)
the cash flows for the MBS are dependent upon the path that interest rates follow.


A binomial model or any other model that uses the backward induction method cannot be used to value an MBS because the cash flows for the MBS are dependent upon the path that interest rates have followed.
作者: dkishore1    时间: 2012-4-2 17:29

Using the following tree of semiannual interest rates what is the value of a 5% callable bond that has one year remaining to maturity, a call price of 99 and pays coupons semiannually?
        7.76%
6.20%
        5.45%
A)
99.01.
B)
97.17.
C)
98.29.


The callable bond price tree is as follows:
100.00

A → 98.67

98.29100.00

99.00

100.00

As an example, the price at node A is obtained as follows:
PriceA = min[(prob × (Pup + (coupon / 2)) + prob × (Pdown + (coupon/2)) / (1 + (rate / 2)), call price] = min[(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + (0.0776 / 2)), 99} = 98.67. The bond values at the other nodes are obtained in the same way.
作者: dkishore1    时间: 2012-4-2 17:30

Using the following tree of semiannual interest rates what is the value of a callable bond that has one year remaining to maturity, a call price of 99 and a 5% coupon rate that pays semiannually?

7.59%
6.35%
5.33%
A)
99.21.
B)
98.65.
C)
98.26.


The callable bond price tree is as follows:
100.00
98.75
98.26 100.00
99.00
100.00

The formula for the price at each node is:
Price = min{(prob × (Pup + coupon/2) + prob × (Pdown + coupon/2)) / (1 + rate/2), call price}.
Up Node at t = 0.5: min{(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + 0.0759/2), 99} = 98.75.
Down Node at t = 0.5: min{(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + 0.0533/2), 99} = 99.00.
Node at t = 0.0: min{(0.5 × (98.75 + 2.5) + 0.5 × (99 + 2.5)) / (1 + 0.0635/2), 99} = 98.26.
作者: dkishore1    时间: 2012-4-2 17:31

A callable bond with an 8.2% annual coupon will mature in two years at par value. The current one-year spot rate is 7.9%. For the second year, the yield-volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. The call price is 101. Using a binomial interest rate tree, what is the current price?
A)

100.558.
B)

100.279.
C)

101.000.


The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value for all the nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:
V1,U =[(100+8.2)/1.076+(100+8.2)/1.076]/2 = 100.558
V1,L =[(100+8.2)/1.068+(100+8.2)/1.068]/2= 101.311
Since V1,L is greater than the call price, the call price is entered into the formula below:
V0=[(100.558+8.2)/1.079)+(101+8.2)/1.079)]/2 = 101.000.
作者: dkishore1    时间: 2012-4-2 17:31

Which of the following is the appropriate "nodal decision" within the backward induction methodology of the interest tree framework for a callable bond?
A)
Min(call price, discounted value).
B)
Min(par value, discounted value).
C)
Max(call price, discounted value).


When valuing a callable bond using the backward induction methodology, the relevant cash flow to use at each nodal period is the coupon to be received during that nodal period plus the computed value or the call price, whichever is less.
作者: dkishore1    时间: 2012-4-2 17:32

For a callable bond, the value of an embedded option is the price of the option-free bond:
A)

minus the price of a callable bond of the same maturity, coupon and rating.
B)

plus the price of a callable bond of the same maturity, coupon and rating.
C)

plus the risk-free rate.


The value of the option embedded in a bond is the difference between that bond and an option-free bond of the same maturity, coupon and rating. The callable bond will have a price that is less than the price of a non-callable bond. Thus, the value of the embedded option is the option-free bond’s price minus the callable bond’s price.
作者: dkishore1    时间: 2012-4-2 17:32

Suppose that the value of an option-free bond is equal to 100.16, the value of the corresponding callable bond is equal to 99.42, and the value of the corresponding putable bond is 101.72. What is the value of the call option?
A)
0.74.
B)
0.64.
C)
0.21.


The call option value is just the difference between the value of the option-free bond and the value of the callable bond. Therefore, we have:
Call option value = 100.16 – 99.42 = 0.74.
作者: dkishore1    时间: 2012-4-2 17:32

How is the value of the embedded call option of a callable bond determined? The value of the embedded call option is:
A)
the difference between the value of the option-free bond and the callable bond.
B)
equal to the amount by which the callable bond value exceeds the option-free bond value.
C)
determined using the standard Black-Scholes model.


The callable bond is equivalent to the option-free bond except that the issuer has the option to call the bond at the call price before maturity. Therefore, for the holder of the bond, the bond is worth the same as the option-free bond reduced by the value of the option.
作者: dkishore1    时间: 2012-4-2 17:33

Which of the following is equal to the value of the putable bond? The putable bond value is equal to the:
A)
option-free bond value minus the value of the put option.
B)
callable bond plus the value of the put option.
C)
option-free bond value plus the value of the put option.


The value of a putable bond can be expressed as Vputable = Vnonputable + Vput.
作者: dkishore1    时间: 2012-4-2 17:33

The value of a callable bond is equal to the:
A)
option-free bond value minus the value of the call option.
B)
callable bond value minus the value of the put option minus the value of the call option.
C)
callable bond plus the value of the embedded call option.


The value of a bond with an embedded call option is simply the value of a noncallable (Vnoncallable) bond minus the value of the option (Vcall). That is: Vcallable = Vnoncallable – Vcall.
作者: dkishore1    时间: 2012-4-2 17:34

How does the value of a callable bond compare to a noncallable bond? The bond value is:
A)
lower.
B)
lower or higher.
C)
higher.


Since the issuer has the option to call the bonds before maturity, he is able to call the bonds when their coupon rate is high relative to the market interest rate and obtain cheaper financing through a new bond issue. This, however, is not in the interest of the bond holders who would like to continue receiving the high coupon rates. Therefore, they will only pay a lower price for callable bonds.
作者: dkishore1    时间: 2012-4-2 17:34

A callable bond and an option-free bond have the same coupon, maturity and rating. The callable bond currently trades at par value. Which of the following lists correctly orders the values of the indicated items from lowest to highest?
A)

$0, embedded call, callable bond, option-free bond.
B)

Embedded call, callable bond, $0, option-free bond.
C)

Embedded call, $0, callable bond, option-free bond.


The embedded call will always have a positive value prior to expiration, and this is especially true if the callable bond trades at par value. Since investors must be compensated for the call feature, the value of the option-free bond must exceed that of a callable bond with the same coupon and maturity and rating.
作者: dkishore1    时间: 2012-4-2 17:35

A callable bond, a putable bond, and an option-free bond have the same coupon, maturity and rating. The call price and put price are 98 and 102 respectively. The option-free bond trades at par. Which of the following lists correctly orders the values of the three bonds from lowest to highest?
A)

Callable bond, option-free bond, putable bond.
B)

Option-free bond, putable bond, callable bond.
C)

Putable bond, option-free bond, callable bond.


The put feature increases the value of a bond and the call feature lowers the value of a bond, when all other things are equal. Thus, the putable bond generally trades higher than a corresponding option-free bond, and the callable bond trades at a lower price.
作者: dkishore1    时间: 2012-4-2 17:35

As the volatility of interest rates increases, the value of a callable bond will:
A)
rise.
B)
rise if the interest rate is below the coupon rate, and fall if the interest rate is above the coupon rate.
C)
decline.



As volatility increases, so will the option value, which means the value of a callable bond will decline. Remember that with a callable bond, the investor is short the call option.
作者: dkishore1    时间: 2012-4-2 17:36

On a given day, a bond with a call provision rose in value by 1%. What can be said about the level and volatility of interest rates?
A)
The only possible explanation is that level of interest rates fell.
B)
A possibility is that the level of interest rates remained constant, but the volatility of interest rates fell.
C)
A possibility is that the level of interest rates remained constant, but the volatility of interest rates rose.


As volatility declines, so will the option value, which means the value of a callable bond will rise.
作者: dkishore1    时间: 2012-4-2 17:36

As the volatility of interest rates increases, the value of a putable bond will:
A)
rise.
B)
decline.
C)
rise if the interest rate is below the coupon rate, and fall if the interest rate is above the coupon rate.


As volatility increases, so will the option value, which means the value of a putable bond will rise. Remember that with a putable bond, the investor is long the put option.
作者: dkishore1    时间: 2012-4-2 17:37

Which part of the nominal spread does the option-adjusted spread (OAS) capture?
A)
credit and liquidity risk.
B)
interest rate and volatility risk.
C)
option risk.


The OAS removes the amount that is due to option risk from the nominal spread leaving just the credit and liquidity risk.
作者: dkishore1    时间: 2012-4-2 17:37

Which kind of risk remains if the option-adjusted spread is deducted from the nominal spread?
A)
credit risk.
B)
option risk.
C)
liquidity risk.


The OAS captures the amount of credit risk and liquidity risk.
作者: dkishore1    时间: 2012-4-2 17:38

An analyst has constructed an interest rate tree for an on-the-run Treasury security. Given equal maturity and coupon, which of the following would have the highest option-adjusted spread?
A)

A putable corporate bond with a AAA rating.
B)

A putable corporate bond with a Aaa rating.
C)

A callable corporate bond with a Baa rating.


The bond with the lowest price will have the highest option-adjusted spread. All other things equal, the callable bond with the lowest rating will have the lowest price.
作者: dkishore1    时间: 2012-4-2 17:38

Which of the following correctly explains how the effective duration is computed using the binomial model. In order to compute the effective duration the:
A)
binomial tree has to be shifted upward and downward by the same amount for all nodes.
B)
yield curve has to be shifted upward and downward in a parallel manner and the binomial tree recalculated each time.
C)
the nodal probabilities are shifted upward and downward and the binomial tree recalculated each time.


Apply parallel shifts to the yield curve and use these curves to compute new forward rates in the interest rate tree. The resulting bond values are then used to compute the effective duration.
作者: dkishore1    时间: 2012-4-2 17:39

Which of the following most accurately explains how the effective convexity is computed using the binomial model. In order to compute the effective convexity the:
A)
yield curve has to be shifted upward and downward in a parallel manner and the binomial tree recalculated each time.
B)
binomial tree has to be shifted upward and downward by the same amount for all nodes.
C)
volatility has to be shifted upward and downward and the binomial tree recalculated each time.


Apply parallel shifts to the yield curve and use these curves to compute new forward rates in the interest rate tree. The resulting bond values are then used to compute the effective convexity.
作者: dkishore1    时间: 2012-4-2 17:39

An analyst has constructed an interest rate tree for an on-the-run Treasury security. The analyst now wishes to use the tree to calculate the duration of the Treasury security. The usual way to do this is to estimate the changes in the bond’s price associated with a:
A)
parallel shift up and down of the forward rates implied by the binomial model.
B)
parallel shift up and down of the yield curve.
C)
shift up and down in the current one-year spot rate all else held constant.


The usual method is to apply parallel shifts to the yield curve, use those curves to compute new sets of forward rates, and then enter each set of rates into the interest rate tree. The resulting volatility of the present value of the bond is the measure of effective duration.
作者: dkishore1    时间: 2012-4-2 17:40

An analyst has constructed an interest rate tree for an on-the-run Treasury security. The analyst now wishes to use the tree to calculate the convexity of a callable corporate bond with maturity and coupon equal to that of the Treasury security. The usual way to do this is to calculate the option-adjusted spread (OAS):
A)
compute the convexity of the Treasury security, and divide by (1+OAS).
B)
compute the convexity of the Treasury security, and add the OAS.
C)
shift the Treasury yield curve, compute the new forward rates, add the OAS to those forward rates, enter the adjusted values into the interest rate tree, and then use the usual convexity formula.


The analyst uses the usual convexity formula, where the upper and lower values of the bonds are determined using the tree.
作者: dkishore1    时间: 2012-4-2 17:41

Steve Jacobs, CFA, is analyzing the price volatility of Bond Q. Q’s effective duration is 7.3, and its effective convexity is 91.2. What is the estimated price change for Bond Q if interest rates fall/rise by 125 basis points?
FallRise
A)
+7.70%−10.55%
B)
+10.55%−7.70%
C)
−10.55%+7.70%


Estimated change if rates fall by 125 basis points:

(-7.3 × -0.0125) + (91.2)(0.0125)2 = 0.1055 or 10.55%


Estimated change if rates rise by 125 basis points:

(-7.3 × 0.0125) + (91.2)(0.0125)2 = -0.0770 or -7.70%
作者: dkishore1    时间: 2012-4-2 17:41

A CFA charter holder observes a 12-year 7 ¾ percent semiannual coupon bond trading at 102.9525. If interest rates rise immediately by 50 basis points the bond will sell for 99.0409. If interest rates fall immediately by 50 basis points the bond will sell for 107.0719. What are the bond's effective duration (ED) and effective convexity (EC).
A)
ED = 8.031, EC = 2445.120.
B)
ED = 40.368, EC = 7.801.
C)
ED = 7.801, EC = 40.368.


ED = (V- − V+) / (2V0(∆y))
= (107.0719 − 99.0409) / (2 × 102.9525 × 0.005) = 7.801
EC = (V- + V+ − 2V0) / (2V0(∆y)2)
= (107.0719 + 99.0409 − (2 × 102.9525)) / [(2 × 102.9525 × (0.005)2)] = 40.368
作者: dkishore1    时间: 2012-4-2 17:41

A putable bond with a 6.4% annual coupon will mature in two years at par value. The current one-year spot rate is 7.6%. For the second year, the yield volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. The bond is putable in one year at 99. Using a binomial interest rate tree, what is the current price?
A)

98.246.
B)

98.885.
C)

98.190.


The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value at all nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:
Vi,U = [(100 + 6.4) / 1.076 + (100+6.4) / 1.076] / 2 = 98.885
Vi,L = [(100 + 6.4) / 1.068 + (100 + 6.4) / 1.068] / 2 = 99.625.
Since 98.885 is less than the put price, Vi,U = 99
V0 = [(99 + 6.4) / 1.076) + (99.625 + 6.4) / 1.076)] / 2 = 98.246.
作者: dkishore1    时间: 2012-4-2 17:42

Using the following tree of semiannual interest rates what is the value of a putable bond that has one year remaining to maturity, a put price of 99, coupons paid semiannually with payments based on a 5% annual rate of interest?
         7.59%
6.35%
         5.33%
A)
99.00.
B)
98.75.
C)
97.92.


The putable bond price tree is as follows:

100.00

A → 99.00

99.00100.00
99.84
100.00


As an example, the price at node A is obtained as follows:
PriceA = max[(prob × (Pup + coupon / 2) + prob × (Pdown + (coupon / 2)) / (1 + (rate / 2)), put price] = max[(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + (0.0759 / 2)) ,99] = 99.00. The bond values at the other nodes are obtained in the same way.
The calculated price at node 0 =
[0.5(99.00 + 2.5) + 0.5(99.84 + 2.5)] / (1 + (0.0635 / 2)) = $98.78 but since the put price is $99 the price of the bond will not go below $99.
作者: dkishore1    时间: 2012-4-2 17:43

Which of the following is the appropriate "nodal decision" within the backward induction methodology of the interest tree framework for a putable bond?
A)
Max(par value, discounted value).
B)
Min(put value, discounted value).
C)
Max(put price, discounted value).


When valuing a putable bond using the backward induction methodology, the relevant cash flow to use at each nodal period is the coupon to be received during that nodal period plus the computed value or exercise price, whichever is greater.
作者: dkishore1    时间: 2012-4-2 17:43


Using the following tree of semiannual interest rates what is the value of a putable semiannual bond that has one year remaining to maturity, a put price of 98 and a 4% coupon rate? The bond is putable today.
         7.59%
6.35%
         5.33%
A)
98.00.
B)
98.75.
C)
97.92.


The putable bond price tree is as follows:

  

100.00

A ==> 98.27

  

98.00

  

100.00

  

99.35

  

100.00


As an example, the price at node A is obtained as follows:
PriceA = max{(prob × (Pup + coupon/2) + prob × (Pdown + coupon/2))/(1 + rate/2), putl price} = max{(0.5 × (100 + 2) + 0.5 × (100 + 2))/(1 + 0.0759/2),98} = 98.27. The bond values at the other nodes are obtained in the same way.

The price at node 0 = [0.5 × (98.27+2) + 0.5 × (99.35+2)]/ (1 + 0.0635/2) = $97.71 but since this is less than the put price of $98 the bond price will be $98.

作者: dkishore1    时间: 2012-4-2 17:44

For a convertible bond, which of the following is least accurate?
A)
The issuer can decide when to convert the bonds to stock.
B)
The conversion ratio times the price per share of common stock is a lower limit on the bond's price.
C)
A convertible bond may be putable.


All of these are true except the possibility of the issuer to force conversion. The bondholder has the option to convert.
作者: dkishore1    时间: 2012-4-2 17:44

Which of the following is equal to the value of a noncallable / nonputable convertible bond? The value of the corresponding:
A)
callable bond plus the value of the call option on the stock.
B)
straight bond.
C)
straight bond plus the value of the call option on the stock.


The value of a noncallable/nonputable convertible bond can be expressed as:
Option-free convertible bond value = straight value + value of the call option on the stock.
作者: ShooterMcCFA    时间: 2012-4-2 17:45

For a convertible bond without any other options, the call feature implied by the convertibility feature will do all of the following EXCEPT:
A)
increase the value of the bond over that of a comparable option-free bond.
B)
cause negative convexity.
C)
place a lower limit on the possible values of the bond.



Negative convexity is caused by the bond being callable where the issuer has the embedded call option. Negative convexity does not apply to convertible bonds. The convertibility feature gives the bondholder a call option on the shares of common stock of the issuer. This increases the price of the bond and places a lower limit on the possible values of the bond. However, that lower limit will change with the price of the common stock.
作者: ShooterMcCFA    时间: 2012-4-2 17:46

Which of the following factors must be included in an option-based valuation approach to price a callable convertible bond?
A)
Interest rates, stock prices and their correlation.
B)
Stock prices only.
C)
Interest rates and stock prices only.


The valuation of convertible bonds with embedded call and/or put options requires a model that links the movement of interest rates and stock prices.
作者: ShooterMcCFA    时间: 2012-4-2 17:46

A convertible bond has a conversion ratio of 12 and a straight value of $1,010. The market value of the bond is $1,055, and the market value of the stock is $75. What is the market conversion price and premium over straight value of the bond?
Market conversion pricePremium over straight value
A)
$87.920.0446
B)
$75.000.1029
C)
$84.170.1222


The market conversion price is:
(market price of the bond) / (conversion ratio) = $1,055 / 12 = $87.92.
The premium over straight price is:
(market price of bond) / (straight value) − 1 = ($1,055 / $1,010) − 1 = 0.0446.
作者: ShooterMcCFA    时间: 2012-4-2 17:46

For a convertible bond with a call provision, with respect to the bond's convertibility feature and the call feature, the Black-Scholes option model can apply to:
A)
only one feature.
B)
both features.
C)
neither features.


The Black-Scholes model applies to the convertibility feature just as it does to the common stock. The Black-Scholes model is not appropriate for the call feature because the volatility of the bond cannot be assumed constant.
作者: ShooterMcCFA    时间: 2012-4-2 17:47

What is the market conversion price of a convertible security?
A)
The value of the security if it is converted immediately.
B)
The price that an investor pays for the common stock if the convertible bond is purchased and then converted into the stock.
C)
The price that an investor pays for the common stock in the market.


The market conversion price, or conversion parity price, is the price that the convertible bondholder would effectively pay for the stock if she bought the bond and immediately converted it.
market conversion price = market price of convertible bond ÷ conversion ratio.
作者: ShooterMcCFA    时间: 2012-4-2 17:47

Suppose the market price of a convertible security is $1,050 and the conversion ratio is 26.64. What is the market conversion price?
A)
$1,050.00.
B)
$26.64.
C)
$39.41.


The market conversion price is computed as follows:
Market conversion price = market price of convertible security/conversion ratio = $1,050/26.64 = $39.41
作者: ShooterMcCFA    时间: 2012-4-2 17:48

Which of the following statements is most accurate concerning a convertible bond? A convertible bond's value depends:
A)
only on interest rate changes.
B)
on both interest rate changes and changes in the market price of the stock.
C)
only on changes in the market price of the stock.


The value of convertible bond includes the value of a straight bond plus an option giving the bondholder the right to buy the common stock of the issuer. Hence, interest rates affect the bond value and the underlying stock price affects the option value.
作者: ShooterMcCFA    时间: 2012-4-2 17:48

Which of the following correctly describes one of the basic features of a convertible bond? A convertible bond is a security that can be converted into:
A)
common stock at the option of the issuer.
B)
common stock at the option of the investor.
C)
another bond at the option of the issuer.


The owner of a convertible bond can exchange the bond for the common shares of the issuer.
作者: ShooterMcCFA    时间: 2012-4-2 17:49

Which of the following scenarios will lead to a convertible bond underperforming the underlying stock? The:
A)
stock price is stable.
B)
stock price falls.
C)
stock price rises.


A convertible bond underperforms the underlying common stock when that stock increases in value. This is because of the conversion premium which means that the bond will increase less than the increase in stock price. If the stock price falls, the convertible bond should outperform the stock because of the floor created by the straight-value. If the stock is stable, the bond is likely to outperform the stock because of the higher current yield of the bond. If the bond is upgraded, the bond should increase in value. There is no reason that upgrading the bond should lead to the bond underperforming the stock.
作者: ShooterMcCFA    时间: 2012-4-2 17:50

The primary benefit of owning a convertible bond over owning the common stock of a corporation is the:
A)
bond has lower downside risk.
B)
bond has more upside potential.
C)
conversion premium.


The straight value of the bond forms a floor for the convertible bond’s price. This lowers the downside risk. The conversion premium is a disadvantage of owning the convertible bond, and it is the reason the bond has lower upside potential when compared to the stock.
作者: ShooterMcCFA    时间: 2012-4-2 17:50

Suppose that the stock price of a common stock increases by 10%. Which of the following is most accurate for the price of the recently issued convertible bond? The value of the convertible bond will:
A)
increase by 10%.
B)
increase by less than 10%.
C)
remain unchanged.


When the underlying stock price rises, the convertible bond will underperform because of the conversion premium.
作者: ShooterMcCFA    时间: 2012-4-2 17:50

How do the risk-return characteristics of a newly issued convertible bond compare with the risk-return characteristics of ownership of the underlying common stock? The convertible bond has:
A)
lower risk and higher return potential.
B)
higher risk and higher return potential.
C)
lower risk and lower return potential.


Buying convertible bonds in lieu of direct stock investing limits downside risk due to the price floor set by the straight bond value. The cost of the risk protection is the reduced upside potential due to the conversion premium.



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