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Asset Allocation and Arbitrage:

Convertible Bonds with Equity/Asset/Credit Swaps- Part 2c

Please note, as ART Consulting/Research is a fee based service, in the following the results have been "sanitised" to disguise the specific markets, trading factors, strategy parameters and many other essentials.  Of course, all of the analyses is based on real market conditions and real world trading considerations (trans cost, funding, etc).  For access to the "un-sanitised" results, and for analysis tailored to your needs please submit an email via  Request More Information.


There are many different trading strategies involving Convertible Bonds (CBs).  One observation is that CBs can be used as a vehicle for asset allocation (i.e. switching between equity grade investment and bond grade investment).  To benefit from such a strategy, the correct valuation of the structure, and any rebalancing considerations ,must be accurately calculated.  Such calculations require a deep understanding of the arbitrage relationships within such trading strategies.


Conversely, CBs arbitrage may be employed more effectively once the arbitrage relationships can be reliably expressed in terms of market conditions and replication strategies.


This abridged note provides only a cursory illustration of just a few holding period P&L results using different rebalancing and structuring strategies.  It cannot be emphasised too strongly that such trading strategies are very complex.  Moreover, what may appear to be an "arb" in theory can be, all too often, a "pure punt" in reality (and sometimes not a very good punt at all).  Many real market results can be counterintuitive to those coming from theory alone, as seen below, for example.


One consideration in this framework is the determination of how to use CBs.  For example, are there CBs available that meet certain real world trading criteria (e.g. liquidity etc).  Moreover, if the process is to encompass asset allocation, then those CBs that are dominated by the issuing company's idiosyncrasies  (as opposed to the wider market forces exploited in traditional asset allocation) may not be practical. 


An approach that bridges these requirements is trading "synthetic CBs".  That is, create a structure that "looks like a CB" in terms of having an equity-like optionality "coupled" to a bond grade investment.  The exact details of how to structure the correlation components and the many other "bells and whistles" seen in typical CBs (e.g. callable/putable, etc) are omitted, but those components should be structured to best reflect the purpose and goal of the trade1.  The synthetic structure can be constructed using liquid "easy to trade2" instruments such as listed options, equity swaps, vanilla IR swaps, asset swaps, etc.


As is customary at the ARBLab, PaR analysis is performed on various structuring and rebalancing strategies.  Other examples of PaR analysis and the  Pr/rO software are provided in the ARBLab Samples section, such as ARBLab: P&L Optimal Options Rebalancing - 1, while all of TG2RM1st - Chapter 12 is dedicated to the introduction of PaR analysis.


Here, three different strategies are considered.  They have been chosen to span the range of "pure asset allocation" through to "(real world) arbitrage".  Importantly, it will be seen that traditional rebalancing strategies used for risk management, or for so-called CBs volatility arbitrage, can be much worse under certain market conditions than nothing at all (i.e. the hedging/rebalancing strategies continuous to lock in losses, while preventing upside gains).  This is especially noticeable during very volatile markets, such as the several years chosen these examples.


The analysis uses real market data, and only the rebalance ratios are model calculated.  The PaR analysis requires the calculation of the net-holding period P&L for many trades, market conditions, and strategies.  Those P&L's are then analysed for consistent and attractive risk-adjusted return opportunities in terms of measurable market conditions.


The image to right (click to ENLARGE) shows 3502 net-P&L's resulting from 3502 trades, each being held and rebalanced as required by the structure/strategy under consideration.  It is noteworthy that just the data requirements for such an analysis are quite considerable, since each date in each strategy requires the spectrum of volatility skews/term-structures, yield curves, asset swap/credit default swap spreads and so forth.  The quality of the data is critical.

The vertical axis is "cash"  in terms of the net-holding period P&L in the primary domestic currency of the trades, per "unit" of notional.  Though much additional analysis is required, it is possible to show that these results imply the possibility of asset allocation strategies that can be quite profitable, especially when chosen in connection with Factor X, Y, and other analysis "dimensions" (these factors are real world measurable quantities such as prices, vols, moving averages, etc.).

One useful tool is fitting surface to the "cloud" of P&L's to better see the structure of the trade performance.  The image to the right is one type of surface derived from the data above.  Here, it is easier to see that the trade is profitable for certain combinations of Factor X and Y.  Note that those areas where the P&L is negative are simply combinations of Factor X and Y during which these strategies/rebalance should be traded "the other way around" (e.g. bought vs. sold, or sold vs. bought).

An alternate set of strategies, where there is greater reliance on structuring the bond to remove credit spread effects, and other components, can result in very major alteration of the trade performance.  That is, the combination of market and strategy conditions implied by the analysis to make money here (i.e. the combination of market Factors, etc) result in very different trading signals than those above.  This is not entirely surprising since the volatility in the bond market dominated the P&L's above, and here swaps have reduced the IR dominance.  Still, it is noteworthy how little structuring/rebalancing alteration may be required to have a profound affect on the trading strategy's performance.  Put differently, sometimes an apparently small and innocuous change in position keeping/structuring can fundamentally alter the risk/return characteristics of the strategy.

The image to the right shows the results for a "highly managed" position as may result from high frequency rebalancing strategies used in CBs arbs (e.g. traditional Delta/Gamma synthetic replication on the equity side, and possibly various dynamic methods on the bond side with V01 and spread strategies).  These strategies are, in this set of results, the "worst".  That is, the parameterisation shows that it is quite easy to get it "wrong", since there are high and low peaks adjacent to one another throughout the surface.  Some may consider this to be counterintuitive since the position is heavily "risk managed", but that fails to consider that in highly volatile markets, predominantly linear rebalancing (e.g. Delta and V01) can have very great slippage due to hedge inefficiency against non-linear positions, and so the rebalances are "chasing" the market, and simply locking in the losses.

As usual, caution is required.  The analysis here, though including thousands of trades, and incorporating many real world factors cannot be taken as any perfect predictor of the future, and additional specific analysis may be required for your due diligence.


For detailed research results on this issue please Request More Information and please feel free to indicate specifics of interest to you.


1 For example, a "Bond + Warrant" is often included in the CB family of trades, but this is not a strict CB.  With a strict CB, you may only own one or the other security at any one time, while with a B+W it is possible to end up holding both shares and bonds simultaneously.

2 "Easy to trade" instruments are those that are easily accessible, liquid, low transaction and warehousing costs, and so forth.


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Last modified: July 25, 2011