Convertible Bond Asset Swaps

Barclays Capital

An Introduction to Convertible Bond Asset Swaps Convertible Bond Research 8 August 2002

As the growth in the market for convertible bonds continues across the globe, the Convertible Bond Asset Swap has become an increasingly popular mechanism to match the specific risk-reward requirements of investors to the many properties of a convertible bond.

A Convertible Bond Asset Swap (CBAS) separates the convertible bond into two distinct components, a Convertible Bond Option (CBO) and a Callable Asset Swap (CAS), with notably different characteristics. The Convertible Bond Option retains the “optionality” of the convertible bond and, as such, is aimed at investors who are predominantly interested in the embedded equity option of a convertible bond. The Callable Asset Swap would be of particular interest to investors who wish to invest in the credit of the convertible bond issuer without the risk associated with the underlying equity.

This report aims to introduce the reader to the convertible bond asset swap and to explain both its structure as well as the advantages and risks of entering into such a transaction. It is assumed that the reader is familiar with convertible bonds and their properties, although we recommend the Barclays Capital publication, Convertible Bonds: A Technical Introduction, for those wishing to review.

For further information on convertible bond asset swaps and on the services provided by Barclays Capital, please visit our website at www.barcap.com/cbonds.

Quantitative Research Luke Olsen +44 (0)20 7773 8310 [email protected] Convertible Research Douglas Decker, CFA +44 (0)20 7773 8302 [email protected] Haidje Rustau +44 (0)20 7773 8301 [email protected] Judy Ho +44 (0)20 7773 9682 [email protected] Convertible Bond Sales Karam Deol +44 (0)20 7773 8320 [email protected] Alan Welch +44 (0)20 7773 8320 [email protected]

2 Convertible Bond Research Barclays Capital

Table of Contents Introduction 3 Key Features of Convertible Bond Asset Swaps 3 Why Do Fixed Income Investors Enter into Callable Asset Swaps? 4 Who is a Typical Callable Asset Swap Investor? 4 Why Do Equity Derivative Investors Purchase Convertible Bond Options? 4 Who is a Typical Convertible Bond Option Holder? 4

The Mechanics of a Convertible Bond Asset Swap 5 Callable Asset Swap 5 Convertible Bond Option 9

Why Would the Option Holder Exercise Their Option? 11 Protection for the CAS Investor From Immediate Exercise of the CBO 11

Intrinsic Value of the Convertible Bond Asset Swap 13 Callable Asset Swap 13 Convertible Bond Option 13

Market Sensitivities of the Convertible Bond Asset Swap 14 Equity Price Sensitivity 14 Equity Volatility 15 Default Risk of the Issuer – Credit Spread 15 Credit Spread Volatility 15 Interest Rates (Risk Free) 16

Summary 17

Glossary 18

Barclays Capital Convertible Bond Research 3

Introduction Key Features of Convertible Bond Asset Swaps

• The convertible bond is split into a fixed income component, the callable asset swap (CAS), and an option to buy the convertible bond (CBO).

• The CAS is created when the fixed income investor buys the convertible bond, sells an option to repurchase the bond and enters into an interest rate swap to exchange the fixed coupons for floating coupons of LIBOR plus a credit spread. This transaction results in a structure where cash flows due to the investor are equivalent to a callable floating rate note. The callable nature of the structure removes the sensitivity to the underlying equity of the convertible bond and enables the investor to receive a higher spread over LIBOR than would be achieved in a conventional non-callable asset swap on a straight bond.

• The CBO holder is the owner of an option to purchase the convertible bond at a price equivalent to the value of the fixed income component of a convertible bond with a specified credit spread. This convertible bond option is not just an option on the underlying equity but on the convertible bond itself, so its value depends on the factors that influence the price of the convertible. However, the option holder is protected against adverse movements in the convertible bond over and above the option premium.

• The CBAS is structured to mature at either the maturity of the convertible bond or, if the convertible bond can be “put” back to the issuer for early redemption, then to the next “put” date.

• Convertible bonds that are suitable for structuring as a CBAS typically have between six months and five years remaining to the first put date or maturity.

• To ensure the CAS investor receives a minimum return from their investment, a “make whole” penalty may be included to discourage the CBO holder from exercising their option before a set date.

• Market convention when quoting the price of a CBAS is to quote the spread over LIBOR that the CAS investor would receive. This also applies to the convertible bond option where the spread is used to determine the strike price at which the convertible bond can be repurchased. The bid is the spread over LIBOR at which an investor is willing to buy the credit (enter into a CAS). The offer is the spread at which the CBO holder is willing to offer the credit.

• The CBAS can only be terminated early if the option holder exercises their right to repurchase the convertible bond. If a CAS investor wishes to flatten the position before termination, the investor could enter into an opposite CBAS transaction, effectively netting the two positions.

• CBAS are OTC structures, so while a standard structure is generally followed, the terms and conditions can be tailored for each convertible issue or investor.

The convertible bond asset swap separates

a convertible bond into two separate

components, a fixed income component

and an option to purchase the

convertible bond


Why Do Fixed Income Investors Enter into Callable Asset Swaps?

• Due to supply and demand imbalances, many convertible bond issues trade at higher implied spreads over LIBOR than equivalent issues within the straight corporate bond and / or credit default swap markets. The CAS allows fixed income investors to profit from this market anomaly.

• The investor realises a higher yield on a CAS investment versus the convertible bonds due to the compensation received for the call option that they have sold to the CBO holder. The yield pick-up depends upon the credit risk and volatility of the issuer’s credit.

• Convertible bonds generally have a different maturity profile versus straight bonds of the same issuer, offering a diversification benefit along the yield curve.

• The CAS may offer diversification by sector, country and credit quality not available via the straight corporate bond market.

• Fixed income investors can benefit from their unique credit insights for an issuer without taking the equity risk inherent in convertibles.

• Some fixed income funds have mandates that forbid any investment in equity-related products. By removing the equity risk, a CAS allows investors to isolate the fixed income component of the convertible bonds.

Who is a Typical Callable Asset Swap Investor?

• Commercial banks;

• Money market funds;

• Insurance companies;

• Fixed income bond funds;

• Pension funds; and

• Investment banks.

Why Do Equity Derivative Investors Purchase Convertible Bond Options?

• The credit risk of the issuer is mitigated / hedged.

• The convertible bond option buyer may take a view on either the underlying equity or the volatility of the equity.

• Downside is limited to the option premium paid when purchasing the CBO.

• Buyers of the CBO may have more expertise in equity derivatives than credit analysis and hence seek to isolate the equity component.

• The CBO investor must only finance the cost of the convertible bond option rather than the whole convertible bond position. This can allow far greater leverage for an investor than by owning the convertible bonds outright.

Who is a Typical Convertible Bond Option Holder?

• Hedge funds;

• Mutual funds;

• Equity / warrant funds;

• Investment trusts; and

• Trading desks.

CAS investors are able to receive a higher

yield than both straight and

convertible bonds

CBO investors are able to limit their exposure

to the credit risk of the convertible bond

issuer


The Mechanics of a Convertible Bond Asset Swap Callable Asset Swap

Initialisation of the Trade In a Callable Asset Swap, the CAS investor enters into the following transaction (see Figure 1):

• Pay par and receive the convertible bond.

• Enter into an interest rate swap whereby they receive LIBOR + the agreed spread on par (the floating leg) and pay the fixed coupon from the convertible bond. The value of LIBOR used for the floating leg is typically set at the beginning of a three-month period, for payment at the end of the period.

• Write to the counterparty an option to repurchase the convertible bonds at par, adjusted for the accrued floating leg and the mark-to-market value of the interest rate swap (see later).

Figure 1: Initial Transaction in a Callable Asset Swap

Callable Asset Swap Investor

Barclays Bank PLC

Par (100%)

Convertible Bond

CB Option

Callable Asset Swap Investor

Barclays Bank PLC

Par (100%)

Convertible Bond

CB Option

Source: Barclays Capital.

Cash Flows for the Duration of the Trade Over its lifetime, the Callable Asset Swap investor will pay / receive the following cash flows (see Figure 2):

• Receive the fixed coupons from the convertible bond.

• As part of the interest rate swap, receive floating payments of LIBOR + Spread and pay the fixed coupons from the convertible bond.

Figure 2: Cash Flows Throughout the Duration of a Callable Asset Swap.

Callable Asset Swap

Investor

BarclaysBank PLC

Fixed Coupons

Floating Leg, LIBOR +Credit Spread

Convertible Bond

Fixed Coupons

Callable Asset Swap

Investor

BarclaysBank PLC

Fixed Coupons

Floating Leg, LIBOR +Credit Spread

Convertible Bond

Fixed Coupons


The CAS is structured to represent a callable

floating rate note paying LIBOR plus a

spread

The CAS investor swaps the coupons

from the convertible bond for payments of

LIBOR plus the agreed spread


The overall cash flows resemble a floating rate note paying LIBOR + Spread

Termination of the Trade The trade will be terminated in one of two ways: either the callable asset swap will mature or the option to repurchase the convertible bonds will be exercised.

If the CBAS transaction matures (either at maturity or put date of the convertible bond) with the CBO unexercised, the issuer will redeem the bonds (see Figure 3).

Figure 3: Redemption of the Convertible Bond at Maturity of the Callable Asset Swap

Callable Asset Swap

Investor

Convertible Bond

Par (100%)


If the CBO holder wishes to repurchase the convertible bonds, or the issuer calls the convertible bonds, the investor (see Figure 4):

• Returns the convertible bond to Barclays Bank PLC, who will cancel the interest rate swap.

• Receives par from Barclays Bank PLC.

• Receives the accrued floating rate payment from the last floating rate payment date to the settlement date of the option transaction (ie, until the convertible bonds are in the possession of Barclays Bank PLC).

• Receives or pays the mark-to-market value of the interest rate swap, which is usually a small amount and is due to movements in the yield curve since the last floating rate payment date (see below).

Figure 4: Cash Flows if the Convertible Bond Option is Exercised

Callable Asset Swap

Investor

Barclays Bank PLC

Par (100%) + Accrued Floating Leg ± Unwind MTM Value of the Swap

Convertible Bond


To unwind the interest rate swap, an equal and opposite interest rate swap must be effectively entered into (see Figure 5), thus cancelling all future cash flows. However, if the settlement date of the option transaction occurs between floating leg payment dates then there will be a cash flow mismatch at the next payment date. This mismatch will be comprised of the accrued floating leg due to the client and, if interest rates have moved, a payment from / to the investor of the mark-to-market value of the interest rate swap. Because these cash flows are due at the next floating leg payment date, they are discounted from the payment date to the option settlement date.

If the CAS matures without the option

having been exercised then the issuer

redeems the convertible bonds

If the option is exercised then the

option holder repurchases the bonds from the CAS investor

at a defined price


Figure 5: Cancellation of Interest Rate Swap Using an Equal and Opposite Swap

Floating Leg Coupons

Fixed Leg Coupons

F+Spread


Fixed Leg Coupons

L+Spread

α β

Settlement Date of the Option Exercise

Transaction

Original Interest

Rate Sw ap

Interest Rate Sw ap to cancel

the original Interest Rate

Sw ap


Fixed Leg Coupons

F+Spread


Fixed Leg Coupons

L+Spread

α β

Settlement Date of the Option Exercise

Transaction

Original Interest

Rate Sw ap

Interest Rate Sw ap to cancel

the original Interest Rate

Sw ap

Where, F = Floating Rate for the current Calculation Period.

L = Floating Rate for the Calculation Period from the Settlement Date of the Option Transaction to the next applicable Floating Rate Payment Date.

Spread = the negotiated Credit Spread at the inception of the CBAS. α = the actual number of days in the Calculation Period from the last

applicable Floating Rate Payment Date to the Settlement Date of the Option Transaction.

β = the actual number of days in the Calculation Period from the Settlement Date of the Option Transaction to the next applicable Floating Rate Payment Date.

D = Days in a year according to day basis used. The exact cash payments are:

Accrued floating rate payment is ( )( )DSpreadFPVF α×+×× %100

Mark-to-market value of the interest rate swap is ( )( )DLFPVF β×−×× %100

Where ( )DLPVF

β×+=

11

, the discount factor from the next floating rate payment

date to the settlement date of the option transaction.

As noted earlier, the structure can be easily tailored to meet the requirements of the client and the features of the underlying convertible bond. For example, many convertible bonds redeem at a price above par. In this case, the interest rate swap is structured to include a back-end payment that is paid by the callable asset swap investor to Barclays Bank PLC. This ensures that, at maturity, the net cash flow to the callable asset swap investor is par. If the convertible bond option is exercised, this back-end payment is cancelled.

Example The Olivetti 1.5% 2004 convertible bond was issued at a price of 100% but redeems at 105.078%. The bond pays a coupon of 1.5% annually on 1 January each year until maturity on 1 January 2004. The following describes the mechanics of a callable asset swap entered into at a spread of 180 basis points.

Special features of the convertible bond and / or client requirements

can be accommodated within the CBAS

structure

Example of a CAS structure for the

Olivetti 1.5% 2004 convertible bond


• The investor initially pays par and receives the convertible bond from Barclays Bank PLC (see Figure 6).

Figure 6: Initial Transaction for the Callable Asset Swap

Callable Asset Swap

Investor

Barclays Bank PLC

Par (100%)

Olivetti 1.5% 2004

Callable Asset Swap

Investor

Barclays Bank PLC

Par (100%)

Olivetti 1.5% 2004


• The investor enters into an interest rate swap with Barclays Bank PLC, whereby they receive LIBOR + 1.80% quarterly and pay the fixed coupons (see Figure 7). The back-end redemption amount of 5.078% is included in the interest rate swap.

Figure 7: Ongoing Cash Flows for the Callable Asset Swap

Callable Asset Swap

Investor

BarclaysBank PLC

1.5% Payable annually

3 Month LIBOR +

1.80% payable quarterly in arrears

Convertible Bond

1.5%Payable annually

Callable Asset Swap

Investor

BarclaysBank PLC

1.5% Payable annually

3 Month LIBOR +

1.80% payable quarterly in arrears

Convertible Bond

1.5%Payable annually


• The result for the CAS investor is a callable floating rate note with a face value of 100% that pays a floating coupon of three-month LIBOR + 1.80%, quarterly in arrears.

• If the convertible bond matures then the issuer will redeem the convertible bond at a price of 105.078%. However, the fixed back-end payment of 5.078% payable by the investor results in the net redemption for the callable asset swap investor of 100% (see Figure 8).

Figure 8: Cash Flow if the Convertible Bond Matures

Callable Asset Swap

Investor

Barclays Bank PLC

5.078%

Convertible Bond

105.078%



If the convertible bond option is exercised, the callable asset swap investor returns the convertible bond in exchange for par plus accrued interest and the unwind cost of the interest rate swap, as noted earlier (see Figure 9).

Figure 9: Cash Flows if the CBO is Exercised

Callable Asset Swap

Investor

Barclays Bank PLC

Par (100%) + Accrued Floating Leg ± Unwind

MTM Value of the Swap

Olivetti 1.5% 2004


Convertible Bond Option

At the beginning of the transaction, the CBO buyer sells convertible bonds and receives an option to repurchase the convertibles at a strike price dependent upon the negotiated spread. The option holder receives a cash amount equal to the “investment value” for the convertible bonds, which is effectively the value of the fixed income component.

This investment value is calculated by considering the CBO holder’s position as being equal and opposite to that of the callable asset swap investor. Hence, the investor receives par and enters into a swap receiving the fixed coupons from the convertible bond and paying the floating leg of LIBOR + Spread until maturity. In practice, an interest rate swap is not entered into, and instead, the net present value of the swap is calculated and deducted from par to give the “investment value” (see Figure 10).

Figure 10: Initial Transaction for a Convertible Bond Option Holder

Barclays Capital

Securities Ltd.


Holder

Investment Value

Convertible Bond


The “investment value” received by the option buyer is:

PV (LIBOR + Spread)100% + PV (Fixed Coupons)-� � (Note: this is the “dirty” price for the investment value as it includes the accrued fixed coupon since the last coupon payment date. To quote a “clean” investment value, we subtract the accrued fixed coupon. In practice, the investment value is quoted with the same convention as the underlying bond.)

Hence the net cost of the convertible bond option is: Convertible Bond Option = Convertible Bond – Investment Value

When the option holder exercises the option, the transaction is reversed and the investor pays the investment value of the convertible bond to repurchase the convertible bonds. The investment value is determined using the agreed spread at the inception of the trade and the settlement date of the option exercise transaction. Thus, the “investment value” is effectively the strike price of the convertible bond option. The

The CBO is structured so that the investor

effectively purchases an option to buy back the convertible bonds

If the option is exercised, the investor

pays the “investment value” to repurchase

the convertible bonds


greater the negotiated credit spread, the lower the investment value and the higher the option value. As time to maturity decreases, the investment value approaches par, although it will fluctuate with interest rates.

Example In Figure 11, we provide an example of the investment value calculations for a simple convertible bond asset swap, using the Olivetti 1.5% 2004 convertible bond to illustrate. Each floating leg is calculated using EURIBOR and the negotiated credit spread of 180 bp. All payments are then discounted back to the settlement date of the transaction. (NB. We quote the clean investment value below)

Figure 11: Calculation of Investment Value for Olivetti 1.5% 2004

Olivetti 1.5% 2004

Par Amount 100 Investment Value 98.657

Nominal 1000

Coupon 1.50% Accrued Coupon 0.785

Redemption Price 105.078 Net Present Value 99.442

Spread (bp) 180

Today 08 Jul 02

Settlement Date 11 Jul 02

Maturity 01 Jan 04

FLOATING LEG FIXED LEG

Date Fl. Rate Spread Amount PV Amount PV 01-Oct-02 3.43% 1.80% 1.191 1.182

01-Jan-03 3.56% 1.80% 1.370 1.347 1.500 1.475

01-Apr-03 3.79% 1.80% 1.397 1.361

01-Jul-03 3.97% 1.80% 1.459 1.407

01-Oct-03 4.18% 1.80% 1.529 1.459

01-Jan-04 4.35% 1.80% 1.572 1.484 6.578 6.207


On entering into the transaction, the investor sells the convertible bond to Barclays Capital Securities for the investment value of 98.657% of par, and acquires the convertible bond option. If the investor exercises the option, they will pay the investment value to repurchase the convertible bonds. An investor who owned the convertible bond option and wished to exercise their option on the above date would have to pay 98.657% of par to repurchase the bonds.

A callable asset swap investor could buy the credit for the “investment value” given above rather than enter into an interest rate swap and pay par, if they wished to receive fixed rather than floating cash flows.

Example calculation of the investment value

for the Olivetti 1.5% 2004 convertible bond


Why Would the Option Holder Exercise Their Option? At maturity of the CBAS, the option holder would exercise the right to repurchase the convertible bonds if the option is “in the money”. If the CBAS is structured to mature on a put date of the convertible, the option will be in the money if the convertible is trading above the put price. The value of the option can be realised by exercising the option and repurchasing the convertible bond, then immediately selling the convertible. If the CBAS is structured to mature when the convertible bond matures, then the option holder will exercise if parity of the convertible bond is greater than the redemption amount. The value of the option is realised by repurchasing the convertible bonds and converting into the underlying equity.

Exercise prior to maturity of the CBO can occur for a number of reasons:

• If the convertible bond issuer calls the bonds for early redemption then the option is automatically exercised.

• If the option holder no longer wants exposure to the convertible bond then the holder can exercise the option and sell the repurchased convertible bonds, thus realising the option’s value.

• If the credit quality of the issuer improves significantly then the option holder can exercise the option and enter into another asset swap at a tighter spread. This crystallises the profit from credit quality improvement and reduces the maximum loss that can occur if the convertible bond price subsequently declines.

• A lack of liquidity in the convertible bond may result in an artificially high price. An option holder can exercise their option to repurchase the bonds and sell them to capture this pricing anomaly.

Protection for the CAS Investor From Immediate Exercise of the CBO

Since the CBO can be exercised from the trade date, the option holder could exercise immediately if market conditions move swiftly in their favour. For the CAS owner, this exercise would curtail any cash flows. Therefore, certain penalties are typically established to protect the credit buyer from early exercise of the CBO. The two most common features are the “make whole” and “bullet” penalties.

“Make Whole” Penalty The “make whole” penalty that would be payable by the CBO holder typically exists for three to six months after inception of the CBAS and guarantees that the credit buyer receives a cash flow of the accrued spread up to the “make whole” date, regardless of whether the option is exercised before this date.

Hence the “make whole” penalty formula is:

“Make Whole” Penalty = DPVFSpread ω××

Where, ω = Number of days between the settlement date of the option exercise and the end of the “make whole” period

PVF = Discount factor from the “make whole” date to the settlement date of the option exercise (see above).

D = Days in a year according to day basis used

If the option is exercised, the cash price received by the callable asset swap investor is as follows (see Figure 12).

The option holder will exercise at maturity of

the CBAS if the convertible bond value

is greater than the redemption price

Under certain circumstances it

would be beneficial for the option holder to

exercise prior to maturity of the CBAS

To protect the CAS investor from early

exercise a number of penalties are used to discourage the CBO

holder


Figure 12: Cash Value of the Credit Spread to be Received by the Investor if the Option is Exercised

Settlement Date of the Option Transaction

100%

Net cash value of the credit spread payments

Make Whole date


100%

Net cash value of the credit spread payments

Make Whole date


“Bullet” Penalty Similar to the “make whole” penalty, the “bullet” penalty requires the option holder to pay an additional penalty (typically 0.5-1.0% of par) if the option is exercised within a set period. Most CBAS structures have either a “make whole” or “bullet” penalty, but rarely both.

“Recall” Spread Lastly, the “recall spread” also discourages early exercise of the option. In this case, the CBO holder must repurchase the bonds at a tighter spread (typically 5-10 bps) than the initially negotiated spread. This increases the investment value and hence the repurchase cost of the convertible bonds. In absolute cash terms, this penalty diminishes to zero as the time to maturity decreases (see Figure 13).

Figure 13: Recall Spread Increases the Investment Value and Hence the Repurchase Price

Investment Value


100%Maturity

Original Credit Spread

Recall Credit Spread

Investment Value


100%Maturity

Original Credit Spread

Recall Credit Spread



Intrinsic Value of the Convertible Bond Asset Swap Callable Asset Swap

For the CAS investor, the value of their position must be:

Callable Asset Swap = Convertible Bond Price + NPV of Interest Rate Swap – CBO

This reflects the CAS investor’s position of holding the convertible bond, being short an option to repurchase this convertible bond and having entered into an interest rate swap paying fixed coupons and receiving LIBOR plus the agreed spread. The value of the position will be 100% of par if the CBO has an intrinsic value greater than zero (see below). However, if the credit spread of the issuer widens and the CBO has an intrinsic value of zero then the value of the CAS investor’s position will be less than 100% of par. This reflects the investor’s position of being exposed to the default risk of the issuer yet benefiting from the premium they have received for selling the option.


Whilst calculation of the CBO’s theoretical value (including its “time value”) requires a more quantitative approach, it is straightforward to calculate its intrinsic value.

Convertible Bond Option = Max (Convertible Bond Price – Investment value, 0)

This equation represents the profit that would be made from immediately exercising the option, purchasing the convertible bond for its investment value, and selling it immediately for its market price. Thus, if the market price of the convertible bond falls below the strike price, it would not be beneficial for the option holder to exercise (the intrinsic value of the option is zero). However, although the intrinsic value is zero, there may be time value associated with the probability of the convertible bond price rising above the investment value before maturity.

The mark-to-market value of the CAS can

be determined by considering each

component of the CAS seperately

Intrinsic value of the CBO is the greater of

CB price less the Investment Value and

zero


Market Sensitivities of the Convertible Bond Asset Swap We present here a simplified description of how each risk factor will affect the value of both the Callable Asset Swap and the Convertible Bond Option, when all other variables are kept constant. For brevity, we use the terminology “in the money” to describe an option that has a positive intrinsic value, while “out of the money” is used for an option of zero intrinsic value.

Equity Price Sensitivity

The CBO is sensitive to the underlying value of the equity in the same way as a convertible bond. An increase in the equity price will increase the value of the convertible bond and hence the convertible bond option (see Figure 14). The option should have similar theoretical values of delta and gamma as the convertible bond, provided there has been no change in the credit quality of the issuer.

If the option is “in the money”, then the callable asset swap investor will be insensitive to equity price changes. The position is effectively capped at par, since investors receive par if the option is exercised. If the option moves “out of the money” due to an adverse change in credit quality, there can be some dependence on the underlying equity. However, in this scenario the sensitivity to the underlying equity will be minimal in comparison to the sensitivity to the default risk of the issuer.

Figure 14: Sensitivity of the Convertible Bond Option to the Underlying Stock Price.

Equity Price

Convertible Bond Price

Investment Value of the CB Option

Value of Convertible Bond Option

Investment value of the Convertible Bond

In the money Convertible Bond Option

Out of the money Convertible Bond Option

Equity Price

Convertible Bond Price

Investment Value of the CB Option

Value of Convertible Bond Option

Investment value of the Convertible Bond

In the money Convertible Bond Option

Out of the money Convertible Bond Option


A qualitative description of the

various risk factors that will affect the

mark-to-market value of the CBO and CAS

investor’s position

CBO

CAS


Equity Volatility

An increase in the volatility of the underlying equity will increase the value of the convertible bond and, consequently, the value of the convertible bond option.

The callable asset swap has no sensitivity to equity volatility if the option is “in the money”. If the option is out of the money then the sensitivity to volatility will be minimal and lower than even the sensitivity to the underlying equity.

Default Risk of the Issuer – Credit Spread

For a convertible bond option holder, an improvement in the issuer’s credit quality increases the value of the convertible bond and the convertible bond option. Conversely, if the credit deteriorates sufficiently, the option’s value will approach zero (see Figure 15), but whereas the CBO investor’s downside is limited to the option premium a CB investor’s downside is the whole value of the CB.

The callable asset swap investor has the opposite position. An improvement in credit quality of the issuer would not benefit the investor if the option is “in the money”, as the value of the position is capped at par. However, for an “out of the money” option, the investor is sensitive to credit quality. An increase in the default risk of the issuer will be detrimental to the CAS investor’s position. Note that the option premium effectively gives the callable asset swap investor a cushion against adverse credit spread movements of the issuer.

Figure 15: Profit and Loss for both Convertible Bond and CBO Investors from Changes in the Default Risk of the Issuer

P&L

Credit Improves

Credit Deteriorates

CBOCB

P&L

Credit Improves

Credit Deteriorates

CBOCB


Credit Spread Volatility

For the convertible bond option holder an increase in credit spread volatility is positive because the CBO is effectively an option on the credit quality of the issuer. An improvement in the credit quality of the issuer increases the value of the convertible bond but any deterioration is capped because the convertible bond option can never be worth less than zero. The value of this credit spread option is significantly higher for a convertible bond with a low parity.

For the CAS investor, credit spread volatility is negative because the investor is effectively short a credit spread option to the CBO holder. The investor’s position is

CBO

CAS

CBO

CAS

CBO

CAS


capped at par if credit quality improves whilst an increase in the default risk of the issuer is detrimental to the investor’s position.

Interest Rates (Risk Free)

The interest rate sensitivity of a convertible bond option depends on the difference in interest rate sensitivity of the convertible bond and of its investment value. Generally, the interest rate sensitivity of a convertible bond is less than that of the equivalent straight bond. Therefore, an increase in interest rates reduces the investment value more than the convertible bond value. As a result, an increase in interest rates will increase the intrinsic value of the convertible bond option and vice versa. However, since the value of the option cannot be less than zero, the investor effectively has an option on interest rates.

Like a callable floating rate note, the callable asset swap has little sensitivity to interest rate movements.

CBO

CAS


Summary The Convertible Bond Asset Swap repackages a convertible bond into a fixed income component and an option to repurchase the convertible bond. This structure allows investors with differing risk / reward requirements to isolate the different components of a convertible bond. The chief advantage of the convertible bond asset swap is that it allows a variety of investors to unlock value that is embedded within the convertible bond. Without taking equity risk, the fixed income investor buys exposure to the credit of a convertible bond, which typically trades wider than comparable straight corporate bonds. The convertible bond option holder is able to gain equity exposure without credit risk.

The fixed income investor enters into the Callable Asset Swap, a position equivalent to a callable floating rate note, by paying par and receiving the convertible bond. Then, the investor enters into an interest rate swap, swapping the fixed coupons of the bond for a floating leg of LIBOR plus the agreed spread. Finally, the investor has also sold a call option on the CB allowing the counterparty to repurchase the bonds for a price of par plus accrued. For this, they receive a further yield pick-up over the convertible bond, depending on the properties of the bond.

The CBO investor purchases an American-style option to repurchase the convertible bond at a price equal to the corresponding investment value of a callable asset swap struck at the agreed credit spread. This structure allows the investor to limit exposure to adverse credit movements of the issuer, while still participating in the equity component of the convertible bond. The convertible bond option also implicitly incorporates an option on the credit quality of the issuer.

To discourage the convertible bond option holder from exercising their option shortly after entering into the transaction and reducing returns for the fixed income investor, a number of penalties may be included. A “make whole” penalty guarantees a minimum return to the callable asset swap investor. A “recall” penalty requires the option holder to exercise the option at a higher strike price than that originally struck. It is analogous to paying the bid / offer spread in a conventional bond position.

The theoretical valuation of a convertible bond option requires a quantitative approach. However, it is straightforward to calculate the intrinsic value of the option (and hence the callable asset swap). The details are found within the preceding text.

In conclusion, we have shown that the Convertible Bond Asset Swap is a relatively simple structure with very interesting properties for many investors. As this market continues to grow, both fixed income and equity investors will be able enter into attractive investments that are tailored to their investment criteria.

Acknowledgements: The authors would like to thank the Barclays Capital Convertible Bond and CBAS traders for their valuable contributions to this document. For further market and / or technical enquiries please contact the CBAS traders through your nominated sales representative.


Glossary Convertible Bond Asset Swap.

Convertible Bond Option is an American-style call option to repurchase the convertible bonds at the “investment value”.

Callable Asset Swap is the fixed income component of a convertible bond. Constructed by swapping the fixed coupons of the convertible for a floating coupon and selling a call option on the convertible bonds.

The strike price of the CBO, calculated by considering the net present value of a transaction that receives par, receives fixed coupons from the convertible bond and pays floating coupons of LIBOR plus the agreed Spread. Values the fixed income component of the Convertible Bond.

A penalty introduced to ensure that the CAS investor receives cash value of the credit spread up to a negotiated date, the “make whole” date.

A penalty to discourage rapid turnover of a CBAS position by the CBO holder. The recall spread is the credit spread used to calculate the investment value, and hence strike price, at which the CBO holder can repurchase the convertible bonds when they exercise their option.

CBAS

CBO

CAS

Investment Value

Make Whole

Recall Spread

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Convertible Bond Asset Swaps

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