### 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
trade^{1}. The synthetic structure can be constructed using
liquid "easy to trade^{2}" 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.

*ARTConsulting/Research*

Back to Consulting *ARBLab*
Samples Page