New research being carried out
jointly at Dublin City University Business School
and University College Cork provides important
findings for those considering an investment in
convertible bond arbitrage. Evidence is provided
that in severe market downturns convertible arbitrage
exhibits negative returns. This negative return
is due to increases in credit spreads. Evidence
is also found that in severe market upturns the
daily returns from a convertible bond arbitrage
portfolio are negatively related to equities.
In effect the returns to convertible bond arbitrage
are akin to writing naked out of the money put
and call options. Although this is not the first
study to document the put option like feature
in convertible arbitrage returns ^{1} , it is the first
to document the negative correlation between daily
convertible bond arbitrage and equity market returns
in extreme up markets. This negative correlation
is explained by the long volatility nature of
convertible bond arbitrage. In extreme up markets
implied volatility generally decreases having
a negative effect on portfolio returns. This is
an important finding for any investor considering
adding a convertible bond arbitrage fund to an
existing buy and hold long only equity portfolio.
While the overall market for
convertible bonds has been growing to an estimated
$351.9 billion by the end of December 2003 (BIS,
2004), the hedge fund industry has also been growing
at a phenomenal rate. Initially investors were
interested in large global/macro hedge funds and
the majority of the funds went into these strategies.
Fung and Hsieh (2000) estimate that in 1997 27
large hedge funds accounted for at least one third
of the assets managed by the industry. However,
since the burst of the dotcom bubble, perhaps
due to a reduction in appetite for risk, investors
have been increasingly interested in lower volatility
nondirectional arbitrage strategies. According
to Tremont Advisors, convertible arbitrage total
market value grew from just $768 million in 1994
to $25.6 billion in 2002, an astonishing growth
rate of 50% on average per annum.
Rather than using combinations
of derivatives which you would expect to intuitively
share the characteristics of a trading strategy's
returns, this study innovates by creating a convertible
arbitrage portfolio by combining financial instruments
in a manner akin to that ascribed to practitioners
who operate the strategy. The portfolio is created
by matching long positions in convertible bonds,
with short positions in the issuer's equity to
create a delta neutral hedged convertible bond
position which captures income and volatility.
Returns on each individual position are calculated
daily as follows.
Daily returns are then compounded
to produce a position value index for each hedged
convertible bond over the entire sample period.
The delta neutral hedged positions are then combined
into two convertible bond arbitrage portfolios,
one equally weighted, the other weighted by market
capitalisation of the convertible issuers' equity.
To confirm that the portfolios have the characteristics
of a convertible bond arbitrageur, the returns
of the convertible bond arbitrage portfolio and
the returns from two indices of convertible arbitrage
hedge funds are examined in a variety of market
conditions.
Table 1, taken from Hutchison and Gallagher (2005),
presents the correlation coefficients between
the monthly returns on the equally weighted convertible
bond arbitrage portfolio (Equal Portfolio), the
market capitalisation weighted portfolio (MC Portfolio),
the CSFB Tremont Convertible Arbitrage Index (CSFB
Tremont Convertible), the HFRI Convertible Arbitrage
Index (HFRI Convertible), the Russell 3000, the
Merrill Lynch Convertible Securities Index (ML
Convertible Securities) and the VIX Index (VIX).
The VIX index is an equity volatility index calculated
by the Chicago Board Option Exchange. It is calculated
by taking a weighted average of the implied volatilities
of 8 30day call and put options to provide an
estimate of equity market volatility. As the CSFB
Tremont data is unavailable prior to 1994, the
correlation coefficients cover returns from January
1994 to December 2002 ^{2}.
The equal weighted portfolio,
the market capitalisation weighted portfolio,
the CSFB Tremont index and the HFRI index are
all positively correlated with the Merrill Lynch
convertible index. With the exception of the CSFB
Tremont index they are also all positively correlated
with equities. The equal weighted portfolio is
positively correlated with the market capitalisation
weighted portfolio, the CSFB Tremont index and
the HFRI index over the entire sample period.
Surprisingly, the market capitalisation weighted
portfolio is not correlated with the CSFB Tremont
index, although it is positively correlated with
the HFRI index. Monthly returns on the VIX are
negatively correlated with both the equal weighted
portfolio and the market capitalization weighted
portfolio indicating that they are both negatively
correlated with implied volatility. Neither of
the hedge fund indices has any correlation with
the VIX. This is surprising as convertible bond
arbitrage is a long volatility strategy.
Table 1  Hutchinson and
Gallagher (2005)
Correlation between monthly convertible bond arbitrage
returns and market factors
click on the image for enlarged view
This table presents correlation
coefficients for monthly returns on the equally
weighted (Equal Portfolio) and market capitalisation
weighted (MC Portfolio) convertible bond arbitrage
portfolios, the CSFB Tremont Convertible Arbitrage
Index, the HFRI Convertible Arbitrage Index and
market factor returns. The Russell 3000 is a broad
based index of US equities. The Merrill Lynch
Convertible Securities Index is an index of US
convertible securities and the VIX is an equity
volatility index calculated by the Chicago Board
Option Exchange. It is calculated by taking a
weighted average of the implied volatilities of
8 30day call and put options to provide an estimate
of equity market volatility.
A further analysis of correlations
in different states of equity market return reported
in Hutchinson and Gallagher (2005) indicates that
the relationship between convertible arbitrage
and equity market returns is nonlinear. As discussed
previously we are not the first authors to come
to this conclusion. However, studies to date have
been restricted to analysing relatively low frequency
monthly returns data. To provide a closer examination
of this nonlinear effect we look in Table 2,
taken from Hutchinson and Gallagher (2005), at
the estimation of the market model using the equally
weighted portfolio limiting the sample to those
days when the equity risk premium is more than
two and a half standard deviations form its mean.
This represents a relatively infrequent seven
trading days per year but from an investors perspective
these may be the most important. Panel A looks
at those days when the equity risk premium is
at least two and a half standard deviations less
than its mean. The explanatory power of the regression
is higher than for the entire sample (adjusted
R2 of 13.7% v. 1.9%) and the convertible bond
arbitrage beta has again increased, to 0.137 from
0.048. Panel B of table 7 looks at those days
when the equity risk premium is at least two and
a half standard deviations greater than its mean
and the results are striking. The explanatory
power of the regression is high with an adjusted
R2 of 11.9%, and the beta is 0.267, providing
evidence of the negative relationship between
convertible bond arbitrage and equity returns
in extremely positive equity markets.
Table 2  Hutchinson and
Gallagher (2005)
Regression of daily equally weighted convertible
bond arbitrage returns
at market extremes
This table presents results from
the following regression of convertible bond arbitrage
returns.
Where is the daily return on
the equal weighted convertible bond arbitrage
portfolio, is the daily return on the Russell
3000 stock index and is the daily yield on a three
month treasury bill.
Panel A of the table presents
results after restricting the sample to those
days with excess market returns at least two and
a half standard deviations less than their mean.
Panel B presents results after restricting the
sample to those days with excess market returns
at least two and a half standard deviations greater
than their mean.
The analysis of convertible bond
arbitrage conducted in this research provides
some useful evidence on the characteristics of
this dynamic trading strategy. This evidence should
be particularly interesting to any institution
or individual considering an investment in convertible
bond arbitrage.
References
Agarwal, V. and
Naik, N.Y., 2004. Risks and portfolio decisions
involving hedge funds. Review of Financial Studies
17, 6398.
BIS, 2004. BIS
Quarterly Review. Bank of International Settlement
Publication, March.
Fung, W. and Hsieh,
D.A., 2000a. Measuring the market impact of hedge
funds. Journal of Empirical Finance 7, 136.
Hutchinson, M.
and Gallagher, L., 2005. Convertible Bond Arbitrage,
Working Paper.
^{1 }Agarwal
and Naik (2004) also document this feature of
convertible arbitrage using monthly hedge fund
asset values.
^{2 }Correlation coefficients were estimated
for the entire sample period 1990 to 2002 for
all variables excluding the CSFB Tremont data.
There was no change in the sign or significance
of any of the coefficients.
