1. Regime Change and Convertible Arbitrage Risk
Mark C. Hutchinson12 and Liam A. Gallagher3
1 Department of Accounting, Finance and Information Systems, UCC
2 Centre for Investment Research, UCC
3 DCU Business School, DCU
Centre for Investment Research

2. Paper Contributions
Present evidence that the relationship between convertible arbitrage hedge fund returns and default and term structure risk factors is non-linear.
Model this relationship using LSTAR methodology showing two alternate risk regimes – Positive alpha regime and Negative alpha regime.
Demonstrate increase in efficiency of this model over linear AR(1).
Conclude that prior lit documenting abnormal performance is due to strategy operating in low risk regime for sample period.
Centre for Investment Research

3. What is convertible arbitrage?
Purchase “undervalued” convertible bond (CB) (a hybrid security which is a combination of a bond and equity option.). Hedge the equity option with a short position in the underlying stock.
Capture income from the yield on the bond.
Capture “undervaluation” in the option component by dynamically hedging the short position in the underlying stock.
Evidence suggests that hedge funds make up > 50% of the demand for CB issues. ($100bn to $200bn AUM).
Centre for Investment Research

4. Background
Evidence indicates convertible arbitrage hedge funds generate significant abnormal returns. (CH, 2004; FH 2002 etc.)
Suggests either
Financial markets exhibit significant mispricing of CBs. or
Prior studies have failed to adequately model the returns.
There is now a growing literature documenting non-linearity in hedge fund returns.
Centre for Investment Research

5. Convertible Arbitrage Data Set
To model the convertible arbitrage hedge fund strategy we specify five indices of convertible arbitrage hedge funds, four portfolios made up of convertible arbitrage hedge funds from the HFR database and a simulated convertible arbitrage portfolio.
All of the series have different start dates.
The sample period runs from the start of each series to December 2002.
The indices specified are the CSFB Tremont Convertible Arbitrage Index, the HFRI Convertible Arbitrage Index, the Van Hedge Convertible Arbitrage Index, the Barclay Group Convertible Arbitrage Index and the CISDM Convertible Arbitrage Index.
Centre for Investment Research

6. Simulated Series
CBARB, the simulated portfolio is an equally weighted portfolio constructed of long positions in convertible bonds combined with delta neutral hedged short positions in the underlying stocks.
H&G(2007 & 2008) examine this series in more detail.
This series is included for robustness as it is free of the biases of hedge fund indices – instant history bias, selection bias, survivorship bias and smoothing.
Centre for Investment Research

7. Convertible arbitrage series summary statistics
Centre for Investment Research

8. Comparison
Centre for Investment Research

9. Fig. 1. Cumulative Returns of the convertible arbitrage series
Centre for Investment Research

10. Centre for Investment Research

11. Convertible arbitrage series correlation matrix
Centre for Investment Research

12. Our theoretical expectation
Relationship between convertible arbitrage and bond market risk factors is non-linear.
Strategy is long a CB and short the underlying stock. Equity exposure is hedged but the strategy is exposed to downside credit risk – Effectively short a credit put option.
When the CB is below a certain threshold it has equity and bond characteristics. Above this threshold it has equity characteristics.
Centre for Investment Research

13. STAR Models - Why?
Models incorporate two alternate regimes, corresponding with the theoretical relationship between convertible arbitrage returns and bond market risk factors.
They incorporate a smooth transition from one risk regime to another. In financial markets with many participants operating independently and at different time horizons, movements in asset prices and risk weightings are likely to be smooth rather than sharp.
When estimating the STAR model no ex ante knowledge of the threshold variable level, c, is required. This threshold level is estimated simultaneously with the coefficients of the model.
Centre for Investment Research

14. STAR Methodology – 3 Steps
1. Specify and estimate a linear model.
2. Test linearity by estimating the following auxiliary regression.
The null hypothesis of linearity, H0: β1 = β 2 = β 3 = 0.
3. Choose between LSTAR and ESTAR based on a series of nested F tests related to regression (5).
Centre for Investment Research

15. Our Linear AR(1) model Where
YLAGt is the one period lag of the hedge fund series return at time t.
RMRFt is the excess return on the market portfolio
SMBt the size risk factor
HMLt the book-to-market equity risk factor
DEFt and TERMt represent default and term structure risk factors
Centre for Investment Research

16. Risk factor summary statistics and correlation matrix
Centre for Investment Research

17. Linear AR(1) Model Centre for Investment Research

18. LSTAR Model Specification
Linearity tests and nested F-tests indicate the correct specification is an LSTAR model. where xt is the risk factors specified in the linear model (i.e. YLAG, RMRF, SMB, HML, DEF, TERM) zt is the transition variable – the one period lag of returns, yt-1. c is the threshold level.
Centre for Investment Research

19. Smooth transition autoregressive regression model
Centre for Investment Research

20. Brief history of financial crisis 1990 to 2002
1990 to 1992 – collapse of ERM
1994 – Mexican Peso crisis
1998 – Asian, Russian and LTCM crisis
2001 to 2002 – Dot Com and Argentina crisis
Centre for Investment Research

21. Fig 2. Transition function for the smooth transition autoregressive (STAR) models (selection)
Centre for Investment Research

22. Key Findings
Consistent with theoretical expectations, the results for all of the convertible arbitrage series provide evidence to support the existence of a non-linear relationship between convertible arbitrage returns and explanatory risk factors.
We identify two alternate risk regimes for the strategy; a negative alpha regime; and, a positive alpha regime.
Centre for Investment Research

23. Key Findings – Negative Alpha Regime
In the negative alpha regime, with zt < c (i.e. prior month convertible arbitrage returns are below the threshold level) the convertible arbitrage series have increased risk coefficients and negative alpha. In this regime the portfolio generally exhibits increased exposure to fixed income risks.
This regime also appears to coincide with incidences of market stress, with a corresponding decrease in liquidity, such as the 1994 Peso crisis and the 1998 Asian currency crisis.
Centre for Investment Research

24. Key Findings – Positive Alpha Regime
In the positive alpha regime, with zt > c (i.e. prior month convertible arbitrage returns are above the threshold level) the default and term structure risk coefficients generally decrease and the strategy exhibits positive alpha. In this regime the portfolio exhibits less fixed income risk characteristics and is characterised by relatively benign financial markets.
Centre for Investment Research

25. Conclusions
The presence of these two risk regimes has important implications for investors in convertible arbitrage hedge funds.
Though these funds have historically offered high returns with relatively low standard deviation and exposure to market risk factors, this appears due to the favourable market conditions since 1990.
The evidence presented in this paper indicates that in future periods of market stress the strategy will become significantly exposed to fixed income risk factors, and, more importantly, under-perform a passive investment in these factors.
Centre for Investment Research

26. What has happened since this paper in 2007 & 2008
Centre for Investment Research

27. What has happened in 2007 & 2008
Convertible Arbitrage is down 50% over the last twelve months.
Since late 2007 the convertible arbitrage strategy has been in the higher risk, negative return, negative performance regime.
Centre for Investment Research