Modeling Exchangeable Bonds WHITE PAPER MONIS CONVERTIBLE BONDS MODELING EXCHANGEABLE BONDS


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1 A Modeling Exchangeable Bonds WHITE PAPER MONIS CONVERTIBLE BONDS MODELING EXCHANGEABLE BONDS
2 Contents 1 Introduction 1 Setting up an exchangeable bond 3 Conclusion 4 Appendix
3 Modeling Exchangeable Bonds 1 Introduction There is much debate on how to set up and model an exchangeable bond. Unfortunately, the typical large move up or down in valuation for pledged or risky shares means that the users return to their standard convertible model. But this no longer needs to be the case. The valuation will become more accurate and acceptable as additional information is entered into the model. These missing data items include ring fence probability, recovery rate, underlying equity credit spread and default correlation. This paper will explain each item and indicate why each is necessary. In the interest of brevity much of the model explanation has been left for the appendix. Setting up an exchangeable bond Ring fence probability Version 12 of Monis allows the user to enter the probability of receiving their full entitlement of shares (i.e., parity value) in the event of bankruptcy. Where the model previously assumed 100 percent or zero percent depending on type, the user can now be more subtle. In the case of a pledge, is the user really 100 percent confident of getting shares in the event of bankruptcy? After all, the issuer must be very distressed to default, and in such situations investors prefer to be cautious. In addition, there are jurisdictions where the pledge has not been tested in law, like Spain, so the particular law governing any pledge may also give holders pause for thought. On the other hand, is zero percent correct for nonpledge structures? This may be right for a situation where the default is unexpected and sudden, such as the Parmalat bankruptcy. But what about the situation where the issuer s credit slowly deteriorates, which is more typical? Surely there will be an opportunity for a holder to exercise before default occurs. Further, ringfence probability may well become a method by which investors will calibrate their results. The impact of this will vary with structure and set up. However, a key determinant of its impact will be the issuer credit spread. The table below shows the impact of ring fence probability on typical terms: five year, with 130 call after three years, with 33 percent premium and 0.75 percent coupon (using vol = 28 percent, borrow = 0.4 percent and div yield = 0 percent, issuer bankruptcy recovery = 0, share credit spread = 0). 5 year 3y Call at 130% 0.75% Coupon 33% Premium Recovery = 0% Ring Fence Prob Credit Spread 100 Credit Spread % 80% 60% 40% 20% 0% CB The benefit of being exchangeable reduces as the ring fence probability reduces. Note, however, that other effects to be discussed later will impact on these results.
4 2 Modeling Exchangeable Bonds Recovery value Typically, users leave recovery value at zero percent. This is understandable for straight convertibles as it is the most conservative assumption: the higher the recovery, the higher the probability of default for any given credit spread and the larger the impact on share price growth (see understanding the jump to default model in the appendix for a fuller explanation). However, this is not necessarily the case for exchangeable bonds as the share price is independent of the issuer credit. Now the great advantage of a fully pledged exchangeable is that the holder is entitled to the full parity even if the issuer is in default. Effectively, the holder gets the maximum of parity or recovery * 100 (assuming par and redemption is 100 and ignoring accrued coupons). So an exchangeable is like a convertible but with this additional option on default, with the strike price of recovery value. Clearly, with the strike of zero, this option has a higher value. Remember, the bond floor of the exchangeable is fixed by the credit spread so the impact of recovery is primarily on this option. (See Simplified example showing impact of recovery rate in the appendix.) 5 year 3y Call at 130% 0.75% Coupon 33% Premium Recovery 0% 20% 40% 60% Ring Fence Prob 100% Ring Fence Prob 0% Credit spread impact on the standard convertible By using the default credit type of unconditional, the model for convertibles assumes a jump to default. This impacts the share price distribution, affecting volatility; which now relates to the random walk part of the share price movement only as the possibility of going to default is now included in the tree (PDE) structure (in comparison, the possibility of default in the B&S model must be captured in the volatility input value as there is no default branch). The jump to default also impacts on share price growth within the model. As there is a chance of share price going to zero (on default), the share price must grow faster in nondefault to bring the average back to the riskfree rate (adjusted by dividends, borrow, etc.). (See the appendix for a fuller explanation.) Share credit spread To achieve a share price distribution consistent with straight convertible bonds, the user should enter a credit spread for the share. This would impact the share price distribution in a similar way as the convertible and would tend to increase the value of the exchangeable bond as the jump to zero in default must be balanced by a higher growth rate in the nonbankruptcy part of the PDE or tree, so that the growth rate over all branches averages to the riskfree rate (adjusted for borrow and dividends). If the user wants to directly compare the exchangeable bond to options, then the share credit spread should be left as zero. The higher the recovery, the less benefit there is of having the choice of parity or bond recovery. Simply put, an option on the parity with a strike of 0 is more valuable than an option with a strike of year 3y Call at 130% 0.75% Coupon 33% Premium Share recovery = 0% Share Credit Spread Ring Fence Prob 100% Ring Fence Prob 0% The bond benefits from the higher related share price growth as the share credit spread increases. A nonzero share recovery rate would increase this effect. However, we tend to leave this as zero to be more conservative.
5 Modeling Exchangeable Bonds 3 Default correlation So far we have assumed that the underlying share and issuer are independent. This is commonly not the case. For example, a holding company may be selling some of its holdings or associates, and bankruptcy in one would suggest the higher chance of bankruptcy in the other. It is possible to incorporate default correlation to capture this impact. 5 year 3y Call at 130% 0.75% Coupon 33% Premium Recovery = 0% Share credit = 200bp Default Correlation 0% 50% 100% Ring Fence Prob 100% Ring Fence Prob 0% Conclusion Now that the tools exist to more accurately model exchangeable bonds, we would anticipate the market moving slowly in this direction and eventually adapting to the exchangeable model. Further reading White papers and other documents are available on our website: For Further information or discussion This subject is highly complex, and even with the appendix, in the interest of brevity the topic has only been touched on with simplified examples. Contact us for further discussion or explanations on this or any other convertible bondrelated topic by ing Monis. Note: in this case, as the share credit spread equals the issuer credit spread, the value of the exchangeable moves to the CB value as the default correlation goes to 100 percent. There are cases where the underlying represents a majority of the assets and the holding company has significant debt. Then the NAV of the company could be zero long before the underlying shares hit zero. In this case, a mandatory structure may be a more appropriate structure to model the risk. This is not covered in this note. Monis Data Service FIS Monis Data Service aims to capture the hard factual data of the convertible, leaving the client to add the subtleties. As such, we leave share credit spread and default correlation as zero. For ring fenced probability with no pledge, we tend to enter zero, but for pledged shares we typically enter a range around percent to ensure a reasonable valuation.
6 4 Modeling Exchangeable Bonds Appendix Understanding the jump to default model The Monis default credit setting of unconditional models the possibility of bankruptcy as a jump to default event. On default, the share price goes to zero and the bond price goes to the recovery value  after recover value insert (for a standard convertible). Hence we adjust the trinomial tree (or PDE) by adding a fourth branch that represents the jump to default. u 0 S 1 S 0 S 1 d 0 S 1 This extra (bankruptcy) branch is added to every point in the tree. The probability of bankruptcy can be worked back from the credit spread and recovery rate. As an example, if a bond has a credit spread of 100bps and a recovery rate of zero percent, with interest rates at zero percent, the probability of bankruptcy is approximately one percent per annum. (One percent payment to compensate for the risk of bankruptcy, which matches our expected one percent chance of losing 100 percent.) Impact The jump to default has two key impacts on the share price distribution. They affect the measure of volatility and the growth of share price. Measure of volatility The measure of volatility expected in the Monis model is not the same as that required for the Black and Scholes riskfree world. Users may need to adjust the volatility value if taken from the option market. The jump to default process already factors in the share price movement related to default. Therefore, the volatility input relates to the random walk part of the share price movement only and not to the potential collapse of the share price in bankruptcy. This is not the case for the volatility used to value an option (in the B&S riskfree world); in the B&S model, the volatility input needs to capture the full potential move of the share price, including any jump to default within its value. Therefore it would typically be higher. u 1 S 1 S 0 S 1 Bankruptcy d 1 S 1 Changes in share price growth for a straight convertible The second impact of jump to default is based on the fact that the share price must grow at a faster rate in the nondefault part of the tree (or PDE). Over the whole tree, the share price grows at the riskfree rate (adjusted for dividends, borrow, etc.) But the jump to default branches (where the share price goes to zero) pulls the expected growth rate down. Therefore, in the nondefault part of the tree the share price needs to grow at a higher rate. This increases the valuation as the expected parity in an exercise situation will be higher. This effect increases with higher credit spread and recovery rate values. Setting recovery to zero typically gives a lower valuation for a standard convertible and is therefore the default value. Increasing the recovery rate increases the probability of default hence the growth of the share price and the value of the convertible but it does not affect the bond floor. As an example, with interest rates at zero percent and a recovery rate of zero percent, a credit spread of 100bps equates to roughly a one percent chance of losing all your money or a two percent chance of losing half your money (in a year s time period). In either case, the bond floor is determined by the credit spread of 100bp alone. Therefore, increasing the recovery rate will impact on the share side of the convertible, as it affects the share growth, but not the bond side. In our example, if the probability of default is one percent per annum, the share price must grow roughly one percent p.a. more than the riskfree rate. If the recovery rate is 50 percent, then the probability of bankruptcy is two percent and the share price needs to grow around two percent p.a. over riskfree rates. The latter would increase the payout in the event of exercise pushing up the convertible value. Simplified example showing impact of recovery rate on fully pledged exchangeable bonds Consider a fully pledged one year out of the money exchangeable bond with low volatility, parity of 60 percent, coupon of one percent, credit spread of 100bp and interest rates of zero. In this structure there is no chance of normal conversion, but the pledge structure still adds value. The bond floor is 100, whatever the recovery rate, as it is set by the credit spread. Now if recovery rate is zero percent, then the probability of default is more or less one percent (the bond floor of 100 reflects the 99 percent chance of receiving 101 and one percent chance of receiving zero). If the recovery is 50 percent, then the probability of default is two percent (the bond floor now reflecting the 98 percent chance of receiving 101 and two percent chance of receiving 50 percent).
7 Modeling Exchangeable Bonds 5 In default, the exchangeable bond in the holder can claim parity of 60 percent in either case. But in the first case, this leads to the theoretical value of (99 percent * one percent * max(0,60)). In the second case, the exchangeable bond is only worth reflecting the 98 percent chance of receiving 101 and two percent chance of max (50 or 60). So increasing the recovery rate in this case reduces the added value of the convertible bond being a fully pledged exchangeable bond. Bond only payments 99% % Prob of default = 1% 0 2% 50 Finding these new attributes The attribute finder can be useful to help find attributes. But if you have any difficulties, please contact Monis support. Share recovery It can be argued that the user should enter share recovery, and the model allows this. However, it would be more conservative to use zero. Exchangeable payments % 98% 101 Model flexibility We have discussed specific features and the set up of the model. It is important to understand that there is no need to stay on the default set up. You can select the model set up that you wish to use % max (60 or 50) max (60 or 0) Prob of default = 1% on default holder recieves max of parity or recovery The simplified tree structure above shows the calculation for probability of default from the bond side only of the exchangeable bond (top) and the impact of this on the exchangeable bond s theoretical value (bottom). To keep our example simple, no other equity option value is included due to the low parity and low volatility.
8 About FIS FIS is a global leader in financial services technology, with a focus on retail and institutional banking, payments, asset and wealth management, risk and compliance, consulting and outsourcing solutions. Through the depth and breadth of our solutions portfolio, global capabilities and domain expertise, FIS serves more than 20,000 clients in over 130 countries. Headquartered in Jacksonville, Florida, FIS employs more than 55,000 people worldwide and holds leadership positions in payment processing, financial software and banking solutions. Providing software, services and outsourcing of the technology that empowers the financial world, FIS is a Fortune 500 company and is a member of Standard & Poor s 500 Index. For more information about FIS, visit twitter.com/fisglobal linkedin.com/company/fisglobal 2016 FIS FIS and the FIS logo are trademarks or registered trademarks of FIS or its subsidiaries in the U.S. and/or other countries. Other parties marks are the property of their respective owners. 0733
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