While few papers deal specifically with the CreditGrades model or capital structure arbitrage, vast amounts of literature examine credit instruments and the pricing of credit risk. From the early work of Jones, Mason and Rosenfeld (1984), researchers have struggled to model bond default premiums. Elton et al. (2001) show that expected default only accounts for a small fraction of the premium in corporate bond rates over treasury rates while Collin-Dufresne, Goldstein and Martin (2001) show that bond spread changes are impacted by local demand and supply shocks which are independent of credit risk. Literature demonstrates that the CDS market provides a timelier measure of credit risk than the bond market. In particular, Zhu (2006) finds that deviation of CDS and bond spreads is largely due to the higher responsiveness of CDS spreads to credit conditions. According to Norden and Weber (2009), the CDS market contributes more to price discovery than the bond market. As well as suggesting that CDS is a cleaner indicator of credit risk than bond spread, Blanco, Brennan and Marsh (2005) show that in firms where CDS spreads and bond spreads form a valid equilibrium relationship, the CDS market contributes around 80% of price discovery. Furthermore, even in the few cases where they do not, CDS spreads are still more likely to Granger-cause bond spread changes than the reverse. Similarly, Longstaff, Mithal and Neis (2005) suggest that CDS spreads provide a relatively precise measure of the default component of corporate spreads while a significant non-default component relates to bond- specific and macroeconomic measures of bond market liquidity. Considering other financial instruments, Norden and Wagner (2008) demonstrate that changes in CDS spreads are the dominant determinants of loan spreads, explaining loan rates much better than bonds of the same rating and other traditional explanatory factors.

From the initial work of Altman (1968) which identified firm characteristics associated with corporate bankruptcy, a great deal of empirical work has focussed on methods of predicting default probabilities. One approach to credit assessment involves reduced form models, first introduced by Litterman and Iben (1991), which assume market participants hold the same level of information, and default time is thus unpredictable. Further development undertaken by a number of researchers, including Jarrow and Turnbull (1995), aimed to provide a methodology for pricing and hedging derivatives involving credit risk. While reduced form models can compare credit risk, they do not specify the economic medium behind the default process (Zhou, 2001) or explicitly explain structural elements of firms which contribute to default. The CreditGrades model belongs to a different class of models known as structural models. These models are generally based on the Black and Scholes (1973) and Merton (1974) contingent claims framework, under which equity and debt represent an option on the firm’s assets with default probabilities predominantly estimated from market and balance sheet parameters. Although originally specified so that default occurs at maturity, both Black and Cox (1976) and Longstaff and Schwartz (1995) extended the analysis such that a firm defaults when its value first crosses an exogenous default threshold. This principle also underlies the dynamics of the CreditGrades model. By introducing uncertainty into the default barrier, the CreditGrades model matches the observed CDS spreads more closely than the Merton (1974) model which underestimates short-dated spreads given its assumption that changes in asset values follow a geometric Brownian- motion diffusion process. Modelling uncertain default barriers is consistent with Duffie and Lando’s (2001) argument that around the time of default, accounting information updates revealed to the market create uncertainty in the value of the assets. The authors also use the notion that investors are unable to directly a observe firm’s assets to provide a link between reduced form and structural-based models. While the use of an uncertain default barrier offers one solution, jumps can also explain sudden changes in market values (Zhou, 2001). Upward and downward jumps are often modelled asymmetrically, for example, Hilberink and Rogers (2002), use a L´evy process which only permits downward jumps in a firm’s value. An alternative structural model proposed by Leland (1994) and Leland and Toft (1996) considers an endogenous default threshold where the optimal capital structure for each firm and the value of long-term risky debt is explicitly linked to each firm’s risk, taxes, bankruptcy costs, interest rates, payout rates and bond covenants. For example, Fan and Sundaresan (2000) assume that shareholders and creditors of distressed firms negotiate to avoid inefficient liquidation and may inject new equity before debt maturity. By comparing a reduced-form model to two structural models, Arora, Bohn and Zhu (2005) show that a Hull-White reduced-form model largely underperforms sophisticated structural models in default prediction and estimation of CDS spread levels. Using the CreditGrades model with lagged stock returns, Byström (2006) shows that structural models are also effective at predicting CDS spread changes. This is consistent with Norden and Weber (2009) who consider monthly, weekly and daily co-movements between markets and conclude that stock returns tend to lead changes in both CDS spreads and bond spreads. Ericsson, Jacobs and Oviedo (2009) find that by regressing structural- model inputs such as firm volatility, firm leverage and the risk-free rate on CDS spreads, they can explain approximately 60% of the levels and 23% of the daily changes in CDS spreads of investment grade obligors. Pu’s (2008) results are broadly consistent with 22% of the variation of the changes in CDS spreads of investment grade and 35% of speculative grade obligors being explained by a set of market factors.

Our capital structure arbitrage strategy is a form of fixed-income arbitrage that exploits mispricing between firm’s debt and equity. Duarte, Longstaff and Yu

(2007) note that it is one of the five most widely used-fixed income arbitrage strategies used by market participants. However, the ability of traders to profit from relative mispricing has been previously restricted by the difficulties in taking short positions in a firm’s debt and a lack of liquidity in parts of the bond market. While not focussing specifically on the CreditGrades model, Ericsson, Reneby and Wang (2007) show that the emergence of the CDS market overcomes many of these difficulties. They show that Leland’s (1994), Leland and Toft’s (1996) and Fan and Sundaresan’s (2000) structural models fit market CDS spreads much more closely than bond spreads with any difficulties encountered in estimating default risk caused by illiquidity in the bond market. Although Currie and Morris (2002) note that many market participants see capital structure arbitrage strategies as the most significant development since the invention of the CDS itself, Yu (2006) notes a complete lack of prior academic research providing evidence either for or against capital structure arbitrage strategies. Using the 5-year North American daily CDS spreads from 2001 to 2004, he implements a convergence-style strategy which uses the CreditGrades model to identify trades in the CDS market and hedges the positions in the equity market. His results indicate that while substantial losses can occur at individual trades level, an equally weighted portfolio of arbitrage trades produces returns similar to other fixed-income hedge fund benchmarks. Duarte, Longstaff and Yu (2007) extend the work of Yu (2006) and conduct a review of the risk and return of a number of widely used fixed-income strategies using a larger dataset. They conclude that the potential profitability of a convergence-style capital structure arbitrage strategy is the highest of all fixed-income strategies considered, yet it also involves the highest level of risk. Extending the analysis of Yu (2006) and Duarte, Longstaff and Yu (2007), Cserna and Imbierowicz (2009) consider the profitability of a similar capital structure arbitrage strategy, but utilise the models of Leland and Toft (1996) and Zhou (2001) in addition to the CreditGrades model. Once transaction costs were taken into account, they found that the strategy produced significant positive returns over the sample period from 2002 to 2006 when CDS spreads were estimated using the CreditGrades or the Leland and Toft model, but not the Zhou model. They do, however, concede that their analysis was conducted over a period of low volatility and suggest it would be interesting to analyse the strategy in a more volatile market. model. Once transaction costs were taken into account, they found a singleshort-term day and not hedged in theand autocorrelation equity not market. medium-term relative mispricing, with positio significant positive returns over the sample period from 2002 to 20 a single day and not hedged in the equity market. estimated using the CreditGrades or the Leland and Toft model, bu Byström (2006) also do, exploits however,inefficiencies concede thatin the CDSanalysis their market using the was conducted over a p CreditGrades model. However, his trading strategy is based on the autocorrelation in the CDS data and thussuggest ignoresitfundamental changes intothe would be interesting obligor’s analyse assets. in a more volat the strategy Furthermore, his study is predominantly based on short-term autocorrelation and

The CreditGrades model requires the estimation of three parameters. As

recommended by Finger et al. (2002), we set λ to 0.3 and R to 0.5 with the 3.1

model Model Implementation inputs the estimation of three parameters. As recom and Calibration 3 Model Description

global recovery rate ( L ),value optimal the of standard deviation each firm of the determined by global recovery minimising the mean squared error (MSE) between the estimated and the actual spreads in the in-sample period. ecovery rate (R), equity volatility Consequently, (σS) anddefault the expected a risk-free ( LD rate (r). boundary The) asset for each firm depends on both the level of the firm’s debt and an implied estimate of L . Given the ollow geometric the Brownian importance motion such of an accurate that: of each firm’s L , we extend Yu’s (2006) estimation 10-day calibration period to two-months. We focus on the 5-year CDS as they offer the highest level of liquidity V dt (Ericsson, Jacobs and Oviedo, 2009). Consistent with previous research D t (1) conducted in other markets, such as Finger et al. (2002), we use the 5-year Australian interest rate swap as a risk-free proxy as it matches the maturity of the contracts. Moreover, derivative traders regard the swap zero curve as the risk-free rate (Hull, Predescu and White, 2004). While Finger et al. (2002) suggest using all of the short-term and long- term debts and half of all other liabilities except accounts payable as a proxy of the firm’s debts, recent studies on capital structure arbitrage including Yu (2006), Duarte, Longstaff and Yu (2007) and Cserna and Imbierowicz (2009) use total liabilities. We also choose total liabilities as it represents a more parsimonious input and is consistent with Vassalou and Yuhang’s (2004) argument that total liabilities affect the ability of firms to refinance short-term debts. Moreover, the calibration steps detailed above ensure that firm defaults when its asset value drops below a market-implied proportion of total liabilities, not its entire value.

An effective trading strategy ensures that model spreads do not lag actual CDS spreads and are generally close fitting and correlated with the market spreads so that significant deviations can be attributed to potentially profitable trading opportunities and not simply a badly specified and calibrated model. The differences between actual and model spreads determine market-entry decisions while the sensitivity of model spreads to changes in the equity price determine the equity hedge ratios. We split the hold-out sample into two periods – a low volatility ‘pre-crisis’ period with stable spreads from January 2006 to December 2007 and a high volatility ‘crisis’ period from January 2008 to December 2009 with elevated spreads caused by the Global Financial Crisis. The performance is presented in Table 2. We used three accuracy measures, mean error (ME), root mean squared error (RMSE) and mean absolute deviation (MAD) consistent with Bowerman, O’Connell and Koehler (2005).5

Mean Absolute Percentage Error (MAPE) was not utilised, given that it imposed a significantly heavier penalty on positive errors than negative errors and had an extremely skewed distribution if the actual series was close to zero (Hyndman and Koehler (2006)), which was the case with the CDS spread data.

The Spearman rank correlations between daily changes in actual CDS spreads, equity prices, volatility inputs and estimated CDS spreads for each firm are presented in Table 3. As expected, CDS spread changes have a significant negative correlation with equity price changes, with an average correlation of

-0.21. Consequently, we anticipated that equity should provide a reasonable hedge against changes in CDS spreads driven by market sentiment. Although increases in equity volatility signal increased risk and should be associated with a greater probability of default, we observed that only changes in IMP_VOL had a significant positive relationship with changes in CDS spreads, with an average correlation of 0.13. Changes in historical volatility inputs were only correlated with changes in CDS spreads by 0.03 to 0.05, on average, depending on the calculation method. Finally, we found a significant positive correlation between changes in the CreditGrades model CDS spreads and the changes in actual CDS spreads, confirming the model had explanatory power. The average correlation ranged between 0.19 and 0.22, but interestingly, the IMP_VOL correlation coefficient was smaller than the historical volatility coefficients.

The Granger causality tests examine whether actual spreads lead or lag estimated spreads. 6 Our lag structure was guided by Norden and Weber (2009) who suggest that two lags for weekly data and five lags for daily data are appropriate in capturing the overall information processing and aggregation time across the CDS, bond and stock markets. However, given that correlations between the actual and the CDS spreads increased substantially as sampling frequency decreased, we also considered monthly data with two lags. The results presented in Table 4 provide little evidence of a lead-lag relationship. Although at the monthly level, estimates using IMP_VOL were more likely to lead actual spreads than estimates using historical volatility, the reverse was true at the daily and weekly level. As with previous sections, analysis was also conducted without financial firms, with results largely unchanged.

Without a clear lead-lag relationship between the equity and the CDS markets, we implemented a relatively simple convergence-style trading strategy to profit from any mispricing between the two securities. The strategy involved taking a simultaneous position in both the equity and the CDS markets to profit from medium-term relative mispricing between the markets. Although similar to the strategy implemented by Yu (2006), we made a number of modifications.

We identified trading opportunities for all firms using three trading triggers (α) across four volatility inputs. Although increasing the size of α translates to fewer open trades, the number of trades for each α remains relatively constant through time. The summary statistics of holding period returns for α=0.5, 1 and 2 across the four volatility inputs are presented in Table 5. The total number of trades executed differs significantly across the simulations, ranging from 105 trades (250_VOL with α=2) to 541 trades (IMP_VOL with α=0.5). The trading strategy is profitable across all simulations before transaction costs are considered, on average, with returns for each trade ranging from a mean of 0% (1000_VOL with α=2) to a mean of 44% (IMP_VOL with α=2). However, with transaction costs, a third of the simulations produce a loss. Furthermore, using only $0.50 of the initial capital to cover each $1 nominal position in the CDS market results in transaction costs of approximately 10% of the initial capital per trade where the spread at entry and exit is relatively similar but can exceed 10% if spreads increase significantly while positions are held. Nevertheless, trades based on the IMP_VOL input (average holding period return ranging from 17% to 27% depending on α) and to a lesser extent 250_ VOL input (average holding period returns ranging from 9% to 13% depending on α) are still profitable. Although smaller α results in a larger number of trades; the effect on profitability is unclear with enhanced profitability under some volatility inputs and reduced profitability under others. The IMP_VOL input generated a greater number of trades for each α, consistent with conclusions from section 5.1 that market CDS spreads lie further away from the estimated spreads using IMP_VOL input than those estimated spreads using the historical volatility inputs. It is evident that regardless of the volatility input or α, the capital structure arbitrage strategy can be very risky at the individual trade level. In each of the simulations detailed in Table 5, there is at least one trade in which losses exceed the amount of initial capital allocated as collateral for that trade. Such losses can result from the continuing divergence between CDS and equity markets following the identification of a trading opportunity and an inadequate hedge to offset changes in CDS spreads. However, the number of trades in each simulation Impact of Financial Crisis on the Profitability Capital Structure Arbitrage in Australia: 67-97 85 in which the initial capital was completely depleted was relatively low (1 to 16 before ,and 4 to 23 after transaction costs were incorporated) compared to the total number of trades made (148 to 541).

Given the riskiness of individual trades, we followed the lead of Yu (2006) in creating a capital structure arbitrage index consisting of an equally weighted portfolio of all the individual trades across all obligors open each day. The portfolio returns, compounded and analysed at the monthly frequency are presented in Table 6. While it would be difficult to invest in such an index, it allows us to analyse the risk and return in a portfolio context and determine how closely returns are linked to common market risk factors. Given the substantial number of trades across the entire sample, trades occurred in all 48 months. While still risky, returns are substantially less volatile compared to the previous section, with the capital allocated to the index not depleted in any individual month in any of the simulations.

Given that we can identify relative mispricing between equity and CDS markets on an individual obligor basis, we extended this analysis to the index level. According to Byström (2006) the iTraxx CDS Indices are highly tradable and more liquid than contracts for individual obligors. Although they represent 44% of the turnover in the credit derivatives market (Australian Financial Markets Association (2010)), to the best of our knowledge no previous study has modelled CDS Indices using estimates of the constituents. We focused on the equally-weighted iTraxx Australia Index with 25 constituents.8 We found that the estimated index fits the actual index levels relatively well across all volatility inputs. For example, MAD between estimated and actual iTraxx levels was only 30 bps with the conventional 1000_VOL input, which compared favourably to the 63 bps average cross-sectional MAD between the estimated and actual spreads of individual obligors documented in Table 2. Interestingly, due to the accurate fit, using α from the previous sections and in much of the earlier literature only identified extremely few (if any) trades. As such, and given the lack of any guidance from previous studies, we chose α of 0.1, 0.2 and 0.3 for the index analysis. As previously, to minimise data snooping, we did not optimise these values.

We estimated the iTraxx Australia Index from 24 equally-weighted firms. Recently listed Crown Limited was omitted from the sample as long-term historical volatility was not available. However, its spreads were relatively close to that of the index. Impact of Financial Crisis on the Profitability Capital Structure Arbitrage in Australia: 67-97 89

Considering the proportion of the S&P/ASX 200 index capitalisation that the sample firms constituted, and the ease of taking futures positions in this index, we selected this index as an equity hedge to the iTraxx Index. The appropriate hedge ratio for the iTraxx Index at each point in time was calculated as an average of the model-estimated hedge ratios for each individual sample firm. Although the index bid-ask spread was lower than the spread for individual contracts, we maintained a 5% bid-ask spread to ensure consistency with previous sections. Table 8 presents a summary of the holding period returns across each α and volatility input. Even after transaction costs, the strategy led to positive average returns across the majority of scenarios. Consistent with section 5.5, strategies using the timelier IMP_VOL and 250_VOL inputs were significantly more profitable than those based on the EW_VOL and 1000_VOL inputs. Interestingly, while the IMP_VOL input was most profitable before transaction costs, CDS spreads increased significantly while many of the positions were open, increasing transaction costs relative to initial capital and resulting in the 250­_­VOL input generally being the most profitable after transaction costs.

5.81 Effectiveness of stop-loss and profit-taking trade out rules

We carried out a number of robustness checks to verify the sensitivity of our results to modifications in the trading strategy. To test the effectiveness of our additional stop-loss and profit-taking trade out rules, the trading profits were recalculated using only the convergence and timing trade-out rules of Yu (2006) and Duarte, Longstaff and Yu (2007). Table 9 contains a summary of the individual trade and index profitability, respectively.