ShooterMcCFA

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 price

Premium over straight value

A) $87.92 0.0446

B) $75.00 0.1029

C) $84.17 0.1222

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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.

ShooterMcCFA

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.

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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.

ShooterMcCFA

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.

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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.

dkishore1

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.

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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.

dkishore1

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.

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All of these are true except the possibility of the issuer to force conversion. The bondholder has the option to convert.

dkishore1

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.

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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.

dkishore1

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).

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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.

dkishore1

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.

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The putable bond price tree is as follows:

		100.00
A → 99.00
99.00		100.00
	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.

dkishore1

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.

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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.

dkishore1

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.

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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