The goal of convertible
bond arbitrage is to consistently make money regardless of market
conditions and to do so with minimal volatility. The basic mechanics
of this market neutral approach is to take simultaneous long
and short positions in a convertible bond and its underlying
stock. By having the appropriate hedge between long and short
positions, the arbitrageur hopes to profit whether the market
goes up or down. Despite a focus on absolute returns rather
than beating market indices, convertible bond arbitrage strategies
have outdone the S&P 500 index with significantly lower
volatility over the past decade.
A little about Convertible Bonds
It is helpful to think of convertible bonds as consisting
of two components: a traditional ("straight") bond
that pays a regular coupon and an equity call option on the
underlying stock. Typically, when a company issues a convertible
bond, the conversion price  the effective price at which
the bond is converted into the underlying shares  is at a
premium (say, 15% or 25%) to the company's stock price. Companies
oftentimes find convertible bonds to be an attractive source
of funds because convertibles typically carry a lower coupon
than comparable straight bonds. In many jurisdictions, companies
also find that there is a tax advantage to issuing convertible
bonds in lieu of common equity. Convertible bond investors
are willing to receive lower coupon payments because convertibles
contain imbedded equity call options that allow investors
to convert the bonds into shares if share prices rise. In
effect, the difference in yields between a convertible bond
and a comparable straight bond is the price the investor must
pay to have a call option on the underlying stock.
The minimum value of a convertible bond is the "investment
value" of its bond component, which is the present value
of future coupon payments and principal repayment from the
bond. Because of this fact, a convertible bond should be worth
at least as much as the value of its underlying shares. A
convertible bond nears this "bond floor" when the
underlying stock falls far below the conversion price and
the equity option component becomes nearly worthless or far
"outofthemoney." It should be noted, however,
that if the issuing company's credit quality has deteriorated,
the convertible bond's minimum value will fall accordingly.
The upside of holding a convertible bond is the option to
convert the bond into shares if the underlying share price
rises above the issue's conversion price. As the underlying
share price rises above the bond's conversion price, the convertible
becomes "inthemoney." The higher the stock price,
the higher the convertible bond trades; the convertible bond's
maximum value is essentially the value of its underlying shares.
How to Profit from Convertible Bond Arbitrage
On a general level, the arbitrageur seeks to exploit mispricings
between a convertible bond and its underlying stock. If a
convertible is cheap relative to its underlying stock, the
arbitrageur will buy the convertible and sell short the underlying
shares. He will do the reverse if the convertible bond is
overvalued relative to its underlying shares. How much the
arbitrageur buys and sells of each security depends upon the
appropriate hedge ratio.
Hedging
Typically, the hedge ratio is determined by the "delta"
 the sensitivity of a convertible bond's price to a price
change in the underlying shares. For example, a delta of 50%
indicates that the convertible bond should rise or fall at
half the rate of its underlying shares. Given that a convertible's
minimum value is its "bond floor," while a share's
minimum value is zero, theoretically the delta must always
be less than 100%. As far as hedging goes, for a convertible
bond with a delta of 50%, one might sell short ¥50 of
stock for every ¥100 in convertibles bought if the investor
thought the convertibles were undervalued. It is important
to note that delta is not a constant number; it changes as
the underlying share price changes. This change in delta is
called "gamma." Because of gamma, an arbitrageur
must adjust his delta position  the ratio of his share to
convertible position  if he wishes to remain "delta
neutral" as the underlying share price changes.
Strategies
One convertible bond arbitrage strategy is volatility trading,
which is commonly attempted with convertible bonds that are
"atthemoney"  when the underlying stock price
is close to the bond's conversion price. Using a very simplified
example where we assume a starting delta of 50% and no hedging
adjustments, an arbitrageur might buy ¥100 of convertible
bonds and simultaneously sell short ¥50 of the underlying
stock. If the share price rises, the loss from the arbitrageur's
short position in the stock should be less than his gain from
the convertible bond's price appreciation. On the other hand,
if the share price falls, the gains from shorting the stock
should exceed the loss on the convertible bond. (Remember
that the convertible cannot fall below the "bond floor.")
Thus, the arbitrageur can make a relatively lowrisk profit
whether the underlying share price rises or falls without
speculating as to which direction the underlying share price
will move. As always, though, there are risks to this strategy,
including incorrect interest rate assumptions, issuer credit
deterioration, stock volatility, stock borrow recall and takeover
of the issuer without provisions for convertible bondholders.
Deep inthemoney convertible bonds are attractive for their
income advantage. These are usually highly leveraged trades,
as the proceeds from selling the underlying stock short can
be used to buy more convertibles because of the high delta.
High leverage is also necessary to make good returns in such
situations. The arbitrageur does not need to have a directional
view on the underlying share price, though he sometimes might
view this as a cheap put on the stock. Risks for this strategy
include unexpected dividend growth, bond recall, stock borrow
recall and repricing of the convertible.
Deep outofthemoney or "busted" convertible bonds
can be attractive to arbitrageurs as a fixed income play.
These convertibles have very little sensitivity (i.e., low
delta) to changes in the underlying share price and are often
mispriced because other hedge funds might have sold the convertibles
regardless of credit fundamentals. However, these convertibles
can be attractive because the investor receives the upside
of a significant rise in the share price (a cheap call option)
in addition to a bond yield equivalent to that of a straight
bond. This strategy carries interest rate, stock borrow and
default risk.
Some convertible bond arbitrage strategies combine the above
strategies and yet others have directional biases  through
their use of hedging  that allow arbitrageurs to capitalize
on expected rises or falls in the underlying stock price.
In short, there are numerous variations of convertible bond
arbitrage strategy.
