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EXPLORING SOME ALTERNATIVE FIXED-INCOME STRATEGIES Philippe PRIAULET HSBC-CCF and University of EVRY 2 AVRIL 2004

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Fixed Income Strategy 22 CONTENTS Bond picking strategies Results of a systematic trading strategy on the T-bond French market Swap barbells and butterflies Results of a systematic trading strategy on the US, EUR and GBP markets Revealing anomalies in forward and volatility curves Anomalies in forward curves Swaption and caplet break-evens

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Fixed Income Strategy 33 Bond picking strategies

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Fixed Income Strategy 44 The bond relative value analysis The goal of that analysis is to detect rich and cheap securities that historically present abnormal yields to maturity, taking as reference a theoretical zero-coupon yield curve fitted with bond prices. The method can be developed both for Treasury and corporate bonds. We take here the example of the French Treasury bond market. We build a strategy that belongs to alternative fixed-income strategies, and back-test it from 1995 to 2001.

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Fixed Income Strategy 55 How it works ? Bond rich-cheap analysis proceeds in five steps 1- We construct the adequate current zero-coupon yield curve with a spline model using data for assets with the same characteristics in terms of liquidity and risk. 2- Then compute a theoretical price for each asset to obtain the spread between the market yield to maturity and the theoretical yield to maturity. 3- For each asset, we implement a Z-score analysis so as to distinguish actual inefficiencies from abnormal yields. This statistical analysis provides signals of short or long positions to take in the market. 4- Short and long positions are unwound according to a criterion that is defined a priori.

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Fixed Income Strategy 66 Z-score analysis At date t and for a given bond, we use the historical of the 60 last spreads. 1- We define the value Min such that x% of the spreads are below that value, and the value Max such that x% of the spreads are above that value. is the value of the spread at date t When converges to 1 or exceeds 1, the bond is considered cheap. On the other hand, when this ratio converges to zero or becomes negative, the bond is considered expensive. For other values of this ratio, we conclude that the bond is fairly priced.

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Fixed Income Strategy 77 Example of Z-score analysis Suppose that we obtain the following historical distribution for the spread of a given bond over the last 60 working days For x = 5, Min = % and Max = %. One day later, the new spread is % so that the ratio is equal to The bond is cheap.

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Fixed Income Strategy 88 When to unwind the position ? The issue lies in the decision timing to reverse the position in the market. Many choices are possible. We expose here two of them: - it can be the first time when the position generates a profit net of transaction costs - another idea is to define new values Min (Max) such that y% of the spreads are below this value. For example, if the signal is detected for x = 1, the position can be reversed in the market for y = 15, which means that the spread has now a more normal level.

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Fixed Income Strategy 99 Back-test of a systematic method on the French market - We boost the performance of a monetary fund of Eur 50 million by benefiting of arbitrage opportunities detected by our model. - Two different funds are created: one is defensive with a leverage coefficient of 2 as the other one is offensive with a leverage coefficient of 4. - The Z-score analysis is performed over a 100-day period. The value x, which provides the signal to enter the position is equal to 3%. The fixed level, which is chosen to reverse the position is equal to 25%. - Short and long positions are financed by means of the repo market. The repo rate raises by 50bp when the bond is cheap and decreases by 50bp when the bond is expensive.

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Fixed Income Strategy 10 Back-test of a systematic method on the French market (2) - An arbitrage opportunity is a pair of bonds which meets the three following rules: * one bond cheap and one bond expensive * the difference of maturity between the two bonds is inferior to 1 year. * we buy a nominal of Eur 50 million of the cheap bond and sell the expensive bond for a nominal amount N such that the global position is $duration neutral. - We applicate a stop-time of 30 calendar days on each position.

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Fixed Income Strategy 11 Graph results

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Fixed Income Strategy 12 Regular performances nb of months with positive performance for the defensive fund: 84 (100%) mean of monthly total returns: 0.48% higher total return: 3.47% (sept. 95) lower total return: 0.04% (oct. 95)

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Fixed Income Strategy 13 An uncorrelated strategy / An attractive Sharpe ratio Money Market French govt 10Y MSCI Euro corporate MSCI Euro DebtSP 500CAC 40 Defensive Fund Money Market1,000,340,390,33-0,06-0,21 0,22 French govt 10Y1,000,870,940,000,03 -0,06 MSCI Euro corporate1,000,800,060,04 0,11 MSCI Euro Debt1,000,120,13 -0,01 SP 5001,000,68 0,08 CAC 401,00 -0,12 Defensive Fund 1,00 Money market French govt 10Y MSCI Euro corporate MSCI Euro DebtSP 500CAC 40 Def. Fund risk0,29%2,96%3,20%3,66%16,09%20,31%1,73% return 3,85%6,54%6,27%7,93%11,24%13,33%5,75% Sharpe0,9120,7581,1150,4600,4671,097

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Fixed Income Strategy 14 Risk measures Skewness3.84 Kurtosis17.58 Downside deviation0.18% Upside deviation0.46% Maximum drawdown0.97% Sortino ratio3.08

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Fixed Income Strategy 15 Leverage coefficients for the defensive fund PON: Difference between bonds bought and bonds sold as a multiple of the initial value of the funds (Eur 50 million) POA: Total of bonds bought as a multiple of the initial value of the funds (Eur 50 million) POV: Total of bonds sold as a multiple of the initial value of the funds (Eur 50 million) Leverage coefficients are multiplied by 2 for the offensive fund.

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Fixed Income Strategy 16 Statistics on arbitrages 172 arbitrage opportunities from 31/05/95 to 31/12/01 average length of an arbitrage: 2 weeks 1- Total of transaction costs: Eur 7.5 million 2- Total of repo costs: Eur -0.7 million 3- Total of gains: Eur 7.6 million 4- Total of gains for positive arbitrages: Eur 9 million 5- Total of losses for negative arbitrages: Eur 1.4 million 6- Maximum gain for one arbitrage: Eur Maximum loss for one arbitrage: Eur

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Fixed Income Strategy 17 Conclusion At the moment, the number of arbitrage opportunities detected by the market is about 15 in a year. To be really competitive, this method needs to be implemented on all the T- Bond markets of the Eurozone. The model is also robust to consider arbitrage opportunities on investment grade markets. See our Trade Ideas on HSBV (Bloomberg site of Fixed-Income Strategy) for such arbitrage opportunities.

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Fixed Income Strategy 18 Swap barbells and butterflies

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Fixed Income Strategy 19 Summary Barbell/butterfly characteristics Systematic positioning of numerous swap barbell/butterflies yields a high return Trade-based rules revolve around Z-score measures that are adjusted to signal entry and exist of positions. Results are consistent for USD, EUR and GBP Back-tests from 2000 to 2003 of 26 standard and maturity-weighted swap barbells and butterflies identify more than 80% of profitable trades

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Fixed Income Strategy 20 P/L estimation of swap barbells and butterflies For any $Duration-neutral butterfly, the approximate total return in $ is given by : (1) Where: D m, D s, D l are the $Duration of the body, short- and long-wings, r m, r s and r l the change in swap rates of the medium(body), short- and long-wings and m, s and l are the weights which must satisfy the following constraint : Rearranging (1) gives the following expression : with

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Fixed Income Strategy 21 P/L estimation of swap barbells and butterflies So the following spread measure is a good indicator of the performance of the butterfly : In a barbell (a butterfly), the spread measure is expected to decrease (to increase) Impact of the beta coefficient on the evolution of the spread measure Relative value trades based on the assumption that this spread shows mean-reversion properties A negative (positive) Z-score provides a signal to enter the butterfly (barbell)

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Fixed Income Strategy 22 P/L estimation of swap barbells and butterflies

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Fixed Income Strategy 23 P/L estimation of swap barbells and butterflies 50/50 swap buttefly specific case with beta equals to 0.5 spread measure given by : trade neutral to some small steepening and flattening movement as Maturity-weighted butterfly specific case with beta equals to spread measure given by : where M m, M s and M l are the Maturities of the body, short- and long-wings

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Fixed Income Strategy 24 P/L estimation of swap barbells and butterflies Maturity-weighted butterfly same weights as a 50/50 swap when M m - M s = M l - M m designed to take into account the fact that short-term rates are much more volatile than long-term rates neutral trade if the spread change between the long wing and the body is proportional to the spread change between the body and the short wing as shown by the following relationship : Regression-weighted buttterfly the coefficient beta is obtained by regressing the change in spread between the long wing and the body with the change in spread between the long wing and the short wing this coefficient minimizes the variance of P&L of the position

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Fixed Income Strategy 25 P/L estimation of swap barbells and butterflies Minimum Variance Butterfly the idea is to minimize the variance of the spread measure as to increase the mean- reverting properties of the trades the coefficient beta is the solution of the following minization program: and is simply equal to the regression coefficient of the spread between the long wing and the body and the spread between the the long wing and the short wing calculated over the last 100 working days Combinations that are traditionally very directional when structured with the weighting (such as year, year and year) present stronger mean- reverting characteristics when a MV-weighting is used instead

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Fixed Income Strategy 26 P/L estimation of swap barbells and butterflies Minimum Variance Butterfly

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Fixed Income Strategy 27 Example: USD barbell 30 July 03: Spread = 32bp Z-score = August 03: Spread = 20bp Z-score = 0.9 Total return = 55bp

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Fixed Income Strategy 28 Back-test results Back-tests of 26 standard swap barbells/butterflies with different Z-scores from 2.5 to 5.0 (in absolute value) to enter the trade, and from 0.5 to 2.0 to exit the position Additional constraints in terms of stop-time (between 20 and 60 working days) and number of trades (minimum of 150 trades) Optimization with two criteria: cumulative total return and % of profitable trades Best combinations (50-50 and maturity-weighted)

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Fixed Income Strategy 29 US statistics* for period Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 30 USD statistics* on different combinations Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 31 USD cumulative total returns* Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 32 USD annual cumulative returns* Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 33 USD - Statistics on trades Number of trades = 454 These trades were initiated on 209 different dates with a maximum concentration of signals equal to 10 as of 11 Sep 01 Average carry = 17 working days Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 34 USD - Monthly distribution of trades Source: HSBC

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Fixed Income Strategy 35 EUR statistics for period * Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 36 EUR statistics on different combinations* Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 37 GBP statistics for period * Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 38 GBP statistics on different combinations* Source: HSBC *50-50 & maturity-weighted

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Fixed Income Strategy 39 Revealing anomalies in forward and volatility curves

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Fixed Income Strategy 40 Anomalies in forward curves Forward rates are variables which are modelized for the pricing and hedging of fixed income derivatives The pricing of the most simple products such as plain vanilla swaps or CMS swaps is obtained by discounting these forward rates The detection of abnormal levels provide good opportunities to enter some trades Example of a trade idea on the Euro Market on April 03: EUR CMS curve steepener (see trade ideas on HSBV)

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Fixed Income Strategy yr CMS forwards against 2 yr CMS forwards

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Fixed Income Strategy 42 Forwards implying inversion of 30-2 yr curve

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Fixed Income Strategy 43 EUR CMS curve steepener The two previous figures show that the spread 30yr-2yr becomes negative after 2009, reaching a maximum of -57bp on Historical precedent suggest that this is very unlikely as since 1999, the flattest that the swap curve has been is in August 2000 when it reached +48bp. There is an opportunity to enter a 10 year (or more) maturity swap to receive the 30 year CMS rate and pay the 2 year CMS rate. The value of the swap is zero at inception. We implement a scenario analysis to judge the risk/return profile of that product.

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Fixed Income Strategy 44 Results of the scenario analysis The trade will be profitable as soon as the forward spread becomes positive. The trade has a positive time value so as time passes it becomes more and more profitable. Risks to this strategy centre on the forward spread becoming more negative over the next five years, making the value of the swap negative. Also the curve could become inverted during the period

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Fixed Income Strategy 45 Swaption break-evens We define the break-even of two swaptions on the same swap (for example a 10-year swap) with two different maturities t and T as the volatility which should be realized between t and T so that the two swaptions are correctly priced at the current date 0. Denoting by and vol(T) the volatilities of the two swaptions with maturities t and T, we have: where is the break-even between t and T.

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Fixed Income Strategy 46 Finally we obtain When the quantity is negative, we consider that the break-even is equal to zero. Detecting anomalies Irregular break-evens can reveal good opportunities to enter trades.

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Fixed Income Strategy 47 Example: On 8 July 2003, EUR swaption break-evens for the 2-year maturity swap were: The break-even is equal to zero which shows that the volatility of the 3-year maturity swaption is too low relatively to the volatility of the 2-year maturity swaption. Between 8 July 2003 and 29 July 2003, the volatility of the 2-year and 3-year maturity swaption increased by 0.1% and 1% respectively, with the consequences that the break-even was on 29 July 2003 at a more adequate level of 11.8%.

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Fixed Income Strategy 48 HSBV Bloomberg site

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Fixed Income Strategy 49 References L. Martellini, P. Priaulet and S. Priaulet, “Understanding the butterfly strategy”, Journal of Bond Trading and Management, 1(1), 9-19, L. Martellini, P. Priaulet and S. Priaulet, “Fixed-Income Securities: Valuation, Risk Management and Portfolio Strategies”, Wiley, F. Fabozzi, C. Dialynas, L. Martellini and P. Priaulet, “Indexing, Structured and Active Fixed-Income Portfolio Management”, Wiley, forthcoming 2005.

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Fixed Income Strategy 50 Disclaimer "Issued by CCF, a member of the HSBC Group. This material is for institutional and professional clients only and not for private customers. Courses and materials are for general information only and do not constitute recommendations or solicitation of any activity in relation to any investment. Accuracy or completeness of courses and materials cannot be guaranteed : any opinions therein are given in good faith but are subject to change without notice. Persons who attend a course or receive materials should make their own independent assessment of the merits or suitability of any investment referred to. No liability whatsoever is accepted by any member of HSBC Group for any direct or consequential loss arising from reliance upon information provided in a course or materials."

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