Convertible Arbitrage Strategies: Dude, Where's My Arbitrage?
"Arbitrage is an investment strategy in which an investor simultaneously buys and sells an asset in different markets to take advantage of a price difference and generate a profit."
"Ultimately, pure arbitrage is a strategy in which an investor takes advantage of market inefficiencies. As technology has advanced and trading has become increasingly digitized, it’s grown more difficult to take advantage of these scenarios, as pricing errors can now be rapidly identified and resolved. This means the potential for pure arbitrage has become a rare occurrence."
However, when we get to Convertible Arbitrage the proposition becomes more opaque and even more complex. Investors are no longer seeking to 'simultaneously' buy and sell an asset and generate a profit. Rather, they are now taking a subjective bet on future changes in volatility, credit spreads, dividends, etc. to generate a potential profit. Therefore, this is not arbitrage.
As long as investors are crystal clear on this, then managers can call the strategy whatever they like.
Now, we can move on to the more serious matter of returns, risks and dispersion. In the title graphic, we have compared the performance of SPY (SPDR S&P 500 ETF Trust), HYG (iShares iBoxx $ High Yield Corporate Bond ETF), CWB (SPDR Bloomberg Convertible Securities ETF) and the BarclayHedge Convertible Arbitrage Index (https://portal.barclayhedge.com/cgi-bin/indices/displayHfIndex.cgi?indexCat=Barclay-Hedge-Fund-Indices&indexName=Convertible-Arbitrage-Index).
As expected, SPY significantly outperforms over time. Also as expected, CWB outperforms HYG. However, more interestingly, over time the Convertible Arbitrage Index outperforms HYG. Furthermore, convertible arbitrage delivers superior risk-adjusted returns and has a significantly lower correlation to the SPY than either CWB or HYG.
CORRELATION
CWB has a monthly return correlation of 0.86 with SPY. HYG has a monthly return correlation of 0.75 with SPY, while the Convertible Arbitrage Index has a monthly return correlation of 0.46 with SPY, as seen in the graphs below.
THE FAIRWATER APPROACH
Our CIO, Orlando Gemes has been active in global credit markets since 2000. In that time, he traded government bonds, corporate bonds (investment grade and high yield), financials, CDS, index and bespoke tranches, options, convertible bonds, esoteric ABS, and over the past decade, equities.
His insight is that capital structures are frequently dislocated. However, it is difficult to accurately, consistently and systematically identify these dislocations, as historically the data has not been publicly available nor is it clean. "Data cleaning is the process of fixing or removing incorrect, corrupted, incorrectly formatted, duplicate, or incomplete data within a dataset. When combining multiple data sources, there are many opportunities for data to be duplicated or mislabelled." - Salesforce .
To solve this challenge, Fairwater Capital LLP started a PhD program in 2019. Our PhDs have come from STEM disciplines, and more by coincidence, they all attended the 英国牛津大学 . We have also been hugely fortunate to develop a close relationship with the University.
In 2022, we hired a systems architect to build a data lake to enable us to aggregate large volumes of information on securities and companies. For the first two years, we focused on building the process and started collecting data on index tranches, CDS, options, bonds, and ETFs. We also built a range of systematic indicators. The data and the tools were built to eliminate bias and give us the ability to deliver repeatable alpha.
For the past two years, we have been focused on convertible bonds. Most banks and managers use a traditional convertible bond model. Some of the most advanced use more complex methodologies including modified Merton models. However, and somewhat to our surprise, our data clearly demonstrates that the use of a Black and Scholes model using 1 or 2-year ATM volatility has a very high correlation with the daily change in many convertible bonds (see the graph below). It becomes abundantly clear that most methodologies do not account for the correlation nor the change in correlation between the convertible bond price and the underlying company stock price.
As previously explained, convertible arbitrage is just a name. While convertible arbitrage has a lower correlation with SPY than CWB and HYG, it is far from zero. It is also noteworthy that returns from the Convertible Arbitrage Index are highly inconsistent and dispersed over both monthly and annual periods.
OPTION PRICING
LinkedIn has provided an extraordinary platform for sharing insights and information. We are also constantly reading and learning from books and the research of market leaders. Over the past year, we have taken particular note of Gregory Zuckerman 's 'The Man Who Solved the Market' on Jim Simons and Renaissance Technologies LLC ; Annie Duke 's 'Thinking in Bets'; Jack D. Schwager's 'Hedge Fund Market Wizards'; and finally, the monthly newsletters of David Dredge of Convex Strategies Pte Ltd .
Investors such as Convex Strategies Pte Ltd are focused on sourcing cheap convexity from the option and derivative markets. While some investors focus only on the upside of convexity, we observe that convexity is equally powerful in providing greater returns when the price of a security rises, as it is in losing less when the price of a security falls.
领英推荐
The global market for single stock options varies hugely in terms of volumes, liquidity, the range of strikes, and maturity profiles. The U.S. options market is the clear leader. The market then falls off a cliff in terms of the number of companies and contracts that trade. In Europe, the majority of trading is in companies that are part of the STOXX 50. In the STOXX 600, the number of companies and contracts that trade is considerably lower. The result of lower volumes and liquidity is that volatility surfaces and term structures are much less observable. This creates a range of challenges in these pricing options.
The call option embedded in a convertible bond is both out of the money and long duration at the issue date. Over time, the relationship between the stock price and the strike price often changes dramatically. Thus, the option can become anywhere from deep out of the money to deep in the money.
Returning to the books mentioned, in 'Hedge Fund Market Wizards,' Jamie Mai of Cornwall Capital is interviewed. Jamie was captured in Michael Lewis' book, The Big Short, and is famous for delivering a return of "about 80 times the initial premium they paid for subprime default protection."
We believe that the pricing of options of small and medium capitalisation companies where the option is either deep in or out of the money and/or long duration is highly inefficient. These are the common characteristics of the option embedded in a convertible bond.
Jamie Mai's following quotes support this thesis:
"Options are priced lowest when volatility has been very low. In my experience, however, the single best predictor of future increases of volatility is low historical volatility."
"Often, the longer the duration of the option, the lower the volatility, which makes no sense."
"Option models generally assume that forward prices are predictive of the future movements in the spot prices. Academic research and common sense suggest that this relationship is often invalid."
"Volatility is a terrible proxy for measuring potential price change over longer intervals of time."
In response to the question: So the basic concept is that option prices will tend to be priced too low in smoothly trending markets - "Yes, and this is another type of option mispricing. The broader principle is that the explicit and implicit assumptions that go into option pricing models often diverge from the underlying reality...Option math works a lot better over short intervals. Once you extend the time horizon, all sorts of exogenous variables are introduced that can throw a wrench into the option-pricing model."
While the U.S. market is meaningfully more efficient than Europe or Asia, the quotes from Jamie Mai highlight the wide range of challenges in option pricing, and thus the inefficiencies that exist. When a long-dated out of the money call option is combined with a credit spread in a convertible bond, the challenge is exacerbated.
In 'Thinking in Bets', Annie Duke contrasts poker and chess. "Chess contains no hidden information and very little luck." "Poker, in contrast, is a game of incomplete information." This is relevant in that many banks and investors in derivatives believe that the output of the models and thus the pricing is consistent and efficient. They believe they are playing chess, and we believe they are playing poker. Understanding and accepting this reality focuses our attention on the inefficiencies and drives our desire to seek superior solutions.
By aggregating and cleaning data, we can gain an information advantage when pricing both the convertible bond, but also the sum of the parts including the bond floor and the call option. Furthermore, the data allows us to study a wider range of characteristics than just delta, gamma, vega, theta and rho.
THE FAIRWATER RELATIVE VALUE STRATEGY
Our ambition at the outset was to develop an all-weather credit relative value strategy focused on convertible bonds that delivered repeatable alpha with minimal drawdowns and de minimis correlation to the SPY.
Thus far, our backtesting demonstrates that our strategy is capable of delivering on our ambitions. However, we wholly concede that the proof is only in the pudding, and we look forward to proving our thesis.