The Limits of Convertible Bond Arbitrage

The Limits of Convertible Bond ArbitrageEvidence from the Recent Crash

Clifford Asness, Adam Berger, Christopher Palazzolo

AQR Capital Management

The Limits of Convertible Bond Arbitrage

Background

Great case study about a a strategy that is as close to the conceptof arbitrage as they get.

Why can a market go to extremes in situations are can be ”clearly”arbitraged away?


Convertible Bonds.

Corporate bonds.

Can be converted, by the holder, into shares, so they arehybrid.

”Conversion price”: the price at which the holder is indifferentbetween the bond and the shares.For example: a bond with $1, 000 face, conversion ratio of 50shares per bond ⇒ cpnversion price = $20.

Value = the sum of the bond piece and the option piece.

This is what is called the ”fundamental value” of the bond.


Convertible Bonds.

Size of the market: approx $200b.

They tend to be illiquid.

High transaction costs.


Convertible Bond ”Cheapness”.

Issued by high-risk companies.

They monetize their high volatility.

They issue them at prices below the fundamental price.

Attractive to investors because they can hedge thecomponents: equity, credit, interest rates.

Can measure the discount at which they trade.

To get a measure as a whole they look at the median discount.

Historically they traded between 3% rich and 3% cheap.

Liquidity plays a big role in their cheapness.


Convertible Bond Arbitrage.

Buy the bond, sell the pieces: debt + equity (delta-hedge).

Selling the equity is easy, the credit art could be morechallenging, sometimes they sell more shares to hedge part ofthe credit.

This makes them prefer bond with more equity than creditthan viceversa:Example:

Face = $1, 000, conversion ratio = 50 shares and the stock istrading at $200. That means that the fundamental value ofthe bond os close to $10, 000.Same bond but the stock is now worth $1. Almost all of thevalue is due to the debt part.

Arbitrageurs prefer the first scenario.


Returns to Convertible Bond Arbitrage.

Historically, attractive returns.

From 1990 to 2007, HFR convertible arbitrage index deliveredan annualized return of 10%.

Annualized volatility = 5%.

Therefore, the Sharpe ratio was 1.2.

The S&P had a Sharpe ratio of 0.4 during the same period.

These returns benefit from the use of leverage. Since most ofthe risks can be hedge away the volatility of these strategies islow so they can leverage.


Imperfect Arbitrage.

Convertible arbitrage is not perfect, not riskless..

Two ways in which arbitrageurs lose money: default andunwinding.

Default: clearly if the bond defaults the arbitrageur has tounwind the hedges.Unwinding: for example in 1998 LTCM blew up. They wereforced to liquidate, among their strategies they had oneinvolving convertible bonds. Their unwinding forced otherleveraged holders to liquidate as well.


Convertible Bonds in the Credit Crisis.

As the crisis unfolded convertible bonds cheapened.

At the end of 2007 median bond cheapness was at 0.9%.

At the end of February 2008 it was at 1.4%.

In March 2008 Bear Sterns collapsed, however the bonds didnot cheapen much.

At the end of the second quarter they ended up at the levelthat they were during the LTCM crisis, 2.3%.

At the end of August 2008 they got to a discount of 3.7%, avery attractive level by ”historical” standards.

The HFR convertible arbitrage index fell 9% in the first eightmonth of 2008.


After Lehman Brothers.

The disaster started in September.

Inthe last four months of the year the index fell 27%.

Financing was withdrawn from the convertible bond market.

At the beginning of the year 75% of the bonds were held byarbitrageurs.

These portfolios were run with a leverage of 3− 5. This meansthat $100 of capital could own $300 to $500 worth of bonds.


After Lehman Brothers. Financing

Financing was provided by prime brokers (banks).

Where did the prime brokers get the money from?They used them as collateral to get loans usually fromEuropean banks.

An alternative to this was the use of internal funds. These,generally, are more expensive funds.


After Lehman Brothers. Financing

When Lehman collapsed, their secure lenders (the ones thathad collateral given by them in exchange of funds) had toliquidate their collateral.

Much of the collateral was easy to get rid of, convertibleswere not.

Given the difficulty to trade them, lenders stopped acceptingthem as collateral.

The prime brokers pushed the bonds back to their customerswho, because of the lack of short-term funding (and their useof leverage), were forced to liquidate them.


Liquidity Recedes.

The most vulnerable were the single-strategy managers, sincethey had no other assets to use as collateral.

Multistrategy managers could use other assets (stock forexample).

They estimate that convertible arbitrage portfolios shrank by50% in the weeks following Lehman’s collapse.


Liquidity Recedes. How Liquidity Reinforces the Selling.

Suppose that an investor is using a leverage ratio of 5x andhas $100 of capital.

The portfolio contains $500 worth of bonds.

If bonds fall by 5% the portfolio loses $25.

The investor now has a capital of $75.

At the given leverage ratio the investor can hold a portfolio of$375.

So, $100 worth of bonds have to be liquidated.


Crossover Buyers

Who was willing to buy the bonds?

Usually, convertible bond arbitrageurs acted as the buyer oflast resort.

Now, these people were forced sellers.

The bonds bottomed out at 12% cheapness.


Crossover Buyers

At this level the buyers included value equity investors andsome multistrategy hedge funds.

Also, the issuers themselves.


Stabilization

In early 2009 the market started to recover.

During this period equity prices were still falling.

Crossover players were buying and arbitrageurs had done mostof the selling.

For the first quarter of 2009 the HFR convertible arbitrageindex was up 11%.


The Return of Financing.

The initial stabilization was precarious.

Was not clear whether all the selling had been done.

Slowly ”normality” came back but the situation did not gback completely.

Lenders started to require ”haircuts” to account for thepotential problem in the case they had to liquidate thecollateral.

Half-way through the year the index was up 29%.


Implications.

Convertible arbitrage is an excellent example of a relativelylow-risk arbitrage.

A perfect arbitrage is supposed to give riskless profits.

Perfect arbitrages do not exist.

In theory, convertible arbitrage would have worked forinvestors who could have held their positions through thecrisis.

This should be a warning to prospective investors in any typeof arbitrage.

Strategies based on some type of future ”convergence” eventare usually lower risk than strategies that depend on thedirection of volatile markets, but this strategies are notriskless, particularly where leverage using short-term financingis involved.


Implications.

In retrospect, we see that opportunistic investors earnedoutsize returns.

These profits were not riskless, at that time there was a greatdeal of uncertainty about the future direction of theconvertible bond market.

In general, opportunistic investment strategies seek to provideliquidity to the markets in extreme periods by buying (selling)when the rest of the world wants to sell (buy).

Implementing these strategies is difficult.

By definition, they always appear very risky at the time theyemerge.


The Limits of Convertible Bond Arbitrage

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