2011 CFA Program Curriculum: Level 2, Volume 5

CFA Institute

Chapter 56 VALUING BONDS WITH EMBEDDED OPTIONS - all with Video Answers

Educators

Chapter Questions

Problem 1

Comment on the following statement:
"There are several arbitrage-free models for valuing callable bonds. These models differ significantly in terms of how interest rates may change in the next period. There are models that allow the rate in the next period to take on only one of two values. Such a model is called a binomial model. There are models that allow the rate in the next period to take on more than two possible values. For example, there is a model that allows the rate in the next period to take on three possible values. Such a model is called a trinomial model. All these models represent a significantly different approach to valuation and involve different procedures for obtaining the arbitrage-free value."

Check back soon!

Problem 2

Why is the procedure for valuing a bond with an embedded option called "backward induction"?

Check back soon!

00:37

Problem 3

Why is the value produced by a binomial model and any similar models referred to as an "arbitrage-free value"?

Aaron Russell

Numerade Educator

Problem 4

A. When valuing an option-free bond, short-term forward rates can be used. When valuing a bond with an embedded option, there is not one forward rate for a period but a set of forward rates for a given period. Explain why:
B. Explain why the set of forward rates for a given period depend on the assumed interest rate volatility.

Check back soon!

Problem 5

The on-the-run issue for the Inc.Net Company is shown below:
$$
\begin{array}{ccc}
\hline \text { Maturity (Years) } & \text { Yield to Maturity (\%) } & \text { Market Price } \\
\hline 1 & 7.5 & 100 \\
2 & 7.6 & 100 \\
3 & 7.7 & 100 \\
\hline
\end{array}
$$
Using the bootstrapping methodology, the spot rates are:
$$
\begin{array}{cc}
\hline \text { Maturity (Years) } & \text { Spot Rate (\%) } \\
\hline 1 & 7.500 \\
2 & 7.604 \\
3 & 7.710 \\
\hline
\end{array}
$$
Assuming an interest rate volatility of $10 \%$ for the 1 -year rate, the binomial interest rate tree for valuing a bond with a maturity of up to three years is shown below:
A. Demonstrate using the 2-year on-the-run issue that the binomial interest rate tree above is in fact an arbitrage-free tree.
B. Demonstrate using the 3-year on-the-run issue that the binomial interest rate tree above is in fact an arbitrage-free tree.
C. Using the spot rates given above, what is the arbitrage-free value of a 3-year $8.5 \%$ coupon issue of Inc.Net Company?
D. Using the binomial tree, determine the value of an $8.5 \%$ 3-year option-free bond.
E. Suppose that the 3 -year $8.5 \%$ coupon issue is callable starting in year 1 at par (100) (that is, the call price is 100 ). Also assume that the following call rule is used: if the price exceeds 100 , the issue will be called. What is the value of this 3 -year $8.5 \%$ coupon callable issue?
F. What is the value of the embedded call option for the 3 -year $8.5 \%$ coupon callable issue?

Check back soon!

Problem 6

In discussing the approach taken by its investment management firm in valuing bonds, a representative of the firm made the following statement:
"Our managers avoid the use of valuation methodologies such as the binomial model or other fancier models because of the many assumptions required to determine the value. Instead, our managers are firm believers in the concept of option-adjusted spread."

Check back soon!

Problem 7

- A portfolio manager must mark a bond position to market. One issue, a callable issue, has not traded in the market recently. So to obtain a price that can be used to mark a position to market, the manager requested a bid from a dealer and a value from a pricing service. The dealer bid's price was 92. The pricing service indicated a bid price of 93 would be a fair value. The manager could not understand the reason for the 1 point difference in the bid prices.

Upon questioning the trader at the dealer firm that gave a bid of 92 , the manager found that the trader based the price on the dealer's valuation model. The model used is the binomial model and the benchmark interest rates the model uses are the on-the-run Treasury issues. The manager then contacted a representative from the pricing service and asked what type of valuation model it used. Again, the response was that the binomial model is used and that the on-the-run Treasury issues are used as the benchmark interest rates.

The manager is puzzled why there is a 1 point difference even though the dealer and the pricing service used the same model and the same benchmark interest rates. The manager has asked you to explain why. Provide an explanation to the manager:

Check back soon!

Problem 8

The manager of an emerging market bond portfolio is approached by a broker about purchasing a new corporate bond issue in Brazil. The issue is callable, and the broker's firm estimates that the option-adjusted spread is 220 basis points. What questions would you ask the broker with respect to the 220 basis points OAS?

Check back soon!

Problem 9

In explaining the option-adjusted spread to a client, a manager stated the following: "The option-adjusted spread measures the yield spread using the Treasury on-the-run yield curve as benchmark interest rates." Comment on this statement.

Check back soon!

Problem 10

A. Explain why the greater the assumed interest rate volatility the lower the value of a callable bond?
B. Explain why the greater the assumed interest rate volatility the higher the value of a putable bond?

Check back soon!

Problem 11

An assistant portfolio manager described the process for valuing a bond that is both callable and putable using the binomial model as follows:
"The process begins by first valuing one of the embedded options, say the call option. Then the model is used to value the put option. The value of the corresponding option-free bond is then computed. Given the value of the call option, the value of the put option, and the value of the option-free bond, the value of the bond that is callable and putable is found by adding to the value of the option-free bond the value of the put option and then subtracting the value of the call option."

Explain why you agree or disagree with this assistant portfolio manager's description of the process for valuing a bond that is both callable and putable.

Check back soon!

01:24

Problem 12

Explain why, when the binomial model is used to obtain the values to be used in the formula for computing duration and convexity, the measures computed are an effective duration and effective convexity.

Sheryl Ezze

Numerade Educator

Problem 13

An assistant portfolio manager is trying to find the duration of a callable bond of FeedCo Corp. One vendor of analytical systems reported the duration for the issue is 5.4. A dealer firm reported that the duration is 4.5. The assistant portfolio manager was confused by the difference in the reported durations for the FeedCo Corp. issue. He discussed the situation with the senior portfolio manager. In the discussion, the assistant portfolio manager commented: "I don't understand how such a difference could occur: After all, there is a standard formula for computing any duration." How should the senior portfolio manager respond?

Check back soon!

Problem 14

In computing the effective duration and convexity of a bond with an embedded option, what assumption is made about the option-adjusted spread when rates change?

Check back soon!

Problem 15

Four portfolio managers are discussing the meaning of option-adjusted spread. Here is what each asserted:
Manager 1: "The option-adjusted spread is a measure of the value of the option embedded in the bond. That is, it is the compensation for accepting option risk."

Manager 2: "The option-adjusted spread is a measure of the spread relative to the Treasury on-the-run yield curve and reflects compensation for credit risk."

Manager 3: "The option-adjusted spread is a measure of the spread relative to the Treasury on-the-run yield curve and reflects compensation for credit risk and liquidity risk."

Manager 4: "The option-adjusted spread is a measure of the spread relative to the issuer's on-the-run yield curve and reflects compensation for credit risk and liquidity risk." Comment on each manager's interpretation of OAS.

Check back soon!

Problem 16

Suppose that a callable bond is valued using as the benchmark interest rates the on-the-run yield curve of the issuer and that the yield for the 10-year issue is $6 \%$. Suppose further that the option-adjusted spread computed for a 10 -year callable bond of this issuer is 20 basis points. Is it proper to interpret the OAS as meaning that the 10 -year callable bond is offering a spread of 20 basis points over the $6 \%$ yield on the 10 -year on-the-run issue? If not, what is the proper interpretation of the 20 basis point OAS?

Check back soon!

Problem 17

Suppose that a callable bond has an option-adjusted spread of zero. Does that mean the corporate bond is being overvalued in the market (i.e., (rading rich)?

Check back soon!

Problem 18

In valuing a floating rate note, it is necessary to make a modification to the backward induction method.
A. Why is the adjustment necessary?
B. What adjustment is made?
C. If the floating rate note has a cap, how is that handled by the backward induction method?

Check back soon!

Problem 19

A. In what sense does a convertible bond typically have multiple embedded options?
B. Why is it complicated to value a convertible bond?

Check back soon!

Problem 20

In the October 26, 1992, prospectus summary of the Staples $5 \%$ convertible subordinated debentures due 1999 , the offering stated: "Convertible into Common Stock at a conversion price of $$\$ 45$$ per share. . " Since the par value is $$\$ 1,000$$, what is the conversion ratio?

Check back soon!

Problem 21

Consider the convertible bond by Miser Electronics:
par value $$=\$ 1,000$$
coupon rate $=8.5 \%$
market price of convertible bond $$=\$ 900$$
conversion ratio $=30$
estimated straight value of bond $$=\$ 700$$
Assume that the price of Miser Electronics common stock is $$\$ 25$$ and that the dividend per share is $$\$ 1$$ per annum.
Calculate each of the following:
A. conversion value.
B. market conversion price.
C. conversion premium per share.
D. conversion premium ratio.
E. premium over straight value.
F. favorable income differential per share.
G. premium payback period.

Check back soon!

Problem 22

Suppose that the price of the common stock of Miser Electronics whose convertible bond was described in the previous question increases from $$\$ 25$$ to $$\$ 54$$.
A. What will be the approximate return realized from investing in the convertible bond if an investor had purchased the convertible for $$\$ 900$$ ?
B. What would be the return realized if $$\$ 25$$ had been invested in the common stock?
C. Why would the return be higher by investing in the common stock directly rather than by investing in the convertible bond?

Check back soon!

Problem 23

Suppose that the price of the common stock declines from $$\$ 25$$ to $$\$ 10$$.
A. What will be the approximate return realized from investing in the convertible bond if an investor had purchased the convertible for $$\$ 900$$ and the straight value does not change?
B. What would be the return realized if $$\$ 25$$ had been invested in the common stock?
C. Why would the return be higher by investing in the convertible bond rather than by investing in the common stock directly?

Check back soon!

Problem 24

The following excerpt is taken from an article entitled "Caywood Looks for Convertibles," that appeared in the January 13, 1992 issue of BondWeek, p. 7:
Caywood Christian Capital Management will invest new money in its $$\$ 400$$ million high-yield portfolio in "busted convertibles," doubleand triple-B rated convertible bonds of companies whose stock . . ., said James, Gaywood, CEO. Caywood likes these convertibles as they trade at discounts and are unlikely to be called, he said.
A. What is a "busted convertible"?
B. What is the premium over straight value that these bonds would trade?
C. Why does Mr. Caywood seek convertibles with higher investment grade ratings?
D. Why is Mr. Caywood interested in call protection?

Check back soon!

Problem 25

Explain the limitation of using premium over straight value as a measure of the downside risk of a convertible bond?

Check back soon!

Problem 26

A. The valuation of a convertible bond using an options approach requires a two-factor model. What is meant by a two-factor model and what are the factors?
B. In practice, is a two-factor model used to value a convertible bond?

Check back soon!

06:09

Problem 27

Today's ex-coupon price of a non-callable bond with four years to maturity and an $8 \%$ coupon rate like the Wentz bond is closest to:
A. 99.4623 .
B. 107.0094 .
C. 107.0437 .

Narayan Hari

Numerade Educator

Problem 28

Today's ex-coupon price of the callable Wentz bond is closest to:
A. 96.0000 .
B. 104.5688 .
C. 105.0263 .

Check back soon!

Problem 29

Holding all other factors constant, if Merton revises her analysis and uses a higher estimate of the volatility of interest rates, the price of the callable Wentz bond:
A. is likely to fall.
B. will not change.
C. is likely to increase.

Check back soon!

Problem 30

- Merton has calculated the price of the AGP Foods bond if its YTM increases to $9 \%$. The price is $$\$ 935.82$$. On the other hand, if the YTM of the bond falls to $7 \%$, the price of the bond would be $$\$ 1,070.24$$. Using these two prices, the price of the bond at an $8 \%$ YTM, and the $100 \mathrm{bps}$ change in interest rates, the effective duration of the AGP Foods bond is closest to:
A. 6.72 .
B. 7.00 .
c. 7.25 .

Check back soon!

Problem 31

Today's minimum market price of the Ashling Enterprises convertible bond is most likely:
A. $$\$ 993.32$$.
B. $$\$ 1,006.72$$.
C. $$\$ 1,152,00$$.

Check back soon!

01:46

Problem 32

Which of the following provides the best rationale for purchasing the
Ashling Enterprises convertible bond rather than the common stock of Ashling?
A. The convertible bond is more liquid than the common stock.
B. The convertible bond provides current income; the common stock does not.
C. The convertible bond is, in effect, a leveraged position in Ashling stock and therefore offers the opportunity for dramatically higher returns.

Majid Borumand

Numerade Educator

Problem 33

The total debt-to-capitalization and the EBITDA interest coverage ratios for Thor Products are closest to:
$$
\begin{array}{|c|c|c|}
\hline & \text { ot-to-Capitalization } & \text { EBITDA Interest Coverage } \\
\hline \text { A. } & 68.4 \% & 5.3 \\
\hline \text { B. } & 76.4 \% & 8.0 \\
\hline \text { c. } & 84.4 \% & 2.7 \\
\hline
\end{array}
$$

Check back soon!

01:02

Problem 34

Which of the three covenants on Thor's bonds is an affirmative covenant?
A. #1.
B. #2.
C. #3.

Narayan Hari

Numerade Educator

Problem 35

Are Jokinen's statements regarding the effects on callable bonds of an increase in interest rates and an increase in interest rate volatility, respectively, correct?

Check back soon!

Problem 36

From Exhibit 2, the current price of the Thor callable bond is closest to:
A. 102.05 .
B. $\quad 102.17$.
C. 103.01.

Check back soon!

Problem 37

The premium payback period (in years) for the France Telecom convertible bond is closest to:
A. 1.60 .
B. 1.81 .
C. 6.05 .

Check back soon!

Problem 38

Is Jokinen's statement about the currency exposure to investing in the dual currency bond (euro and Turkish lira) correct?
A. No, the bond has exposure to the Turkish lira from the date of purchase,
B. Yes, the bond has appreciation exposure to the Turkish lira only at maturity,
C. Yes, the bond has depreciation exposure to the Turkish lira only at maturity.

Check back soon!