EXPLORING SOME ALTERNATIVE FIXED-INCOME STRATEGIES Philippe PRIAULET HSBC-CCF and University of EVRY...

EXPLORING SOME ALTERNATIVE

FIXED-INCOME STRATEGIES

Philippe PRIAULET

HSBC-CCF and University of EVRY

2 AVRIL 2004

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


Bond picking strategies


• 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.


• 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.


• 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+1.

2- 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.

1tS

MinMax

MinSt1


• 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 = -0.0888% and Max = 0.0677%. One day later, the new spread is 0.0775% so that the ratio is equal to 1.063. The bond is cheap.

Historical Distribution

0

2

4

6

8

10

12

14

16

-0.1

0%

-0.0

8%

-0.0

6%

-0.0

4%

-0.0

2%

0.0

0%

0.0

2%

0.0

4%

0.0

6%

0.0

8%

Classes

Fré

qu

en

cy


• 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.


• 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.


• 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.


• Graph results

Evolution of the Net Asset Value from 31/05/95 to 31/12/01

50 000 000

55 000 000

60 000 000

65 000 000

70 000 000

75 000 000

80 000 000

85 000 000

90 000 000

31/05/95 26/03/96 20/01/97 16/11/97 12/09/98 09/07/99 04/05/00 28/02/01 25/12/01

Defensive Fund

Offensive Fund

Monetary Fund


• 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)

0,00%

0,50%

1,00%

1,50%

2,00%

2,50%

3,00%

3,50%

4,00%


• An uncorrelated strategy / An attractive Sharpe ratio

Money Market

French govt 10Y

MSCI Euro corporate

MSCI Euro Debt SP 500 CAC 40

DefensiveFund

Money Market 1,00 0,34 0,39 0,33 -0,06 -0,21 0,22French govt 10Y 1,00 0,87 0,94 0,00 0,03 -0,06MSCI Euro corporate 1,00 0,80 0,06 0,04 0,11MSCI Euro Debt 1,00 0,12 0,13 -0,01SP 500 1,00 0,68 0,08CAC 40 1,00 -0,12Defensive Fund 1,00

Money market

French govt 10Y

MSCI Euro corporate

MSCI Euro Debt SP 500 CAC 40

Def. Fund

risk 0,29% 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%

Sharpe 0,912 0,758 1,115 0,460 0,467 1,097


• Risk measures

Skewness 3.84Kurtosis 17.58

Downside deviation 0.18%Upside deviation 0.46%

Maximum drawdown 0.97%Sortino ratio 3.08


• 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.

Max PON Min PON MoyennePON

Max POA MoyennePOA

Min POV MoyennePOV

1.96 -1.67 0.05 10.53 1.02 -11.25 -0.97


• 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 million2- 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 million5- Total of losses for negative arbitrages: Eur 1.4 million

6- Maximum gain for one arbitrage: Eur 3446167- Maximum loss for one arbitrage: Eur -138452


• 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.


Swap barbells and butterflies


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 50-50 and maturity-weighted swap barbells and butterflies identify more than 80% of profitable trades


P/L estimation of swap barbells and butterflies

For any $Duration-neutral butterfly, the approximate total return in $ is given by :

(1)

Where: Dm, Ds, Dl are the $Duration of the body, short- and long-wings, rm, rs and rl

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

lllsssmmm rDrDrDLP &

lsmmm

lsmmm

lmm

lls

mm

ssmmm

rrrDLP

rrrDLP

rD

Dr

D

DrDLP

1&

1&

&

0 llssmm DDD

mm

ss

D

D



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)

lsm rrrSpread )1(


-70

-65

-60

-55

-50

-45

Nov 03 Dec 03 Jan 04 Feb 04 Mar 04

Yie

ld S

pre

ad (

bp

)

2-5-10yr EUR Barbell @ β =0.1


-55

-50

-45

-40

-35

-30


Yie

ld S

pre

ad (

bp

)


-35

-33

-31

-29

-27

-25

-23

-21

-19

-17

-15


Yie

ld S

pre

ad (

bp

)


-18

-16

-14

-12

-10

-8

-6

-4

-2

0


Yie

ld S

pre

ad (

bp

)


0

2

4

6

8

10

12

14


Yie

ld S

pre

ad (

bp

)


16

18

20

22

24

26

28

30


Yie

ld S

pre

ad (

bp

)


33

35

37

39

41

43

45


Yie

ld S

pre

ad (

bp

)


50

52

54

56

58

60

62


Yie

ld S

pre

ad (

bp

)


68

69

70

71

72

73

74

75

76

77

78


Yie

ld S

pre

ad (

bp

)



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 Mm, Ms and Ml are the Maturities of the body, short- and long-wings

2ls

mrr

r

lsl

mls

sl

smm r

MM

MMr

MM

MMr

22

& mlsmmm

rrrrDLP

sl

sm

MM

MM


P/L estimation of swap barbells and butterflies Maturity-weighted butterfly

same weights as a 50/50 swap when Mm- Ms = Ml - Mm

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

smml

smsmml rr

MM

MMrrrr

1



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 50-50 weighting (such as 2-5-10 year, 2-5-30 year and 2-7-15 year) present stronger mean-reverting characteristics when a MV-weighting is used instead

lsm rrrVarMin )1(


P/L estimation of swap barbells and butterflies Minimum Variance Butterfly

8

10

12

14

16

18

20

22

24

26

28

Oct 03 Nov 03 Dec 03 Jan 04 Feb 04 Mar 04

50-5

0 Y

ield

Sp

read

(b

p)

92

94

96

98

100

102

104

106

108

110

112

MV

Yie

ld S

pre

ad (

bp

)

50-50 EUR 2-5-10 barbell (LHS)Minimum variance (MV) EUR 2-5-10 barbell (RHS)


Example: USD 2-5-10 50-50 barbell

30 July 03: Spread = 32bp Z-score = 2.7

8 August 03: Spread = 20bp Z-score = 0.9

Total return = 55bp

-5

0

5

10

15

20

25

30

35

Mar 03 Apr 03 May 03 Jun 03 Jul 03 Aug 03

Yie

ld S

pre

ad (

bp

)

2-5-10 yr USD barbell


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)

USD EUR GBPZ-score In 2.5 2.5 2.5Z-score Out 1.0 1.0 1.0Stop-time 40 working days 50 working days 60 working days


US statistics* for period 2000-2003

Source: HSBC *50-50 & maturity-weighted

-75

-50

-25

0

25

50

75

100

125

2000 2001 2002 2003 Total

To

tal

Ret

urn

s (b

p)

Max/Min Average Observations within +/-1sd


USD statistics* on different combinations

-5

0

5

10

15

20

25

30

35

40

45

45% 56% 67% 78% 89% 100%

Profitable Trades (%)

Ave

rag

e T

ota

l R

etu

rn (

bp

)

2-5-7

2-3-4

15-20-30

10-15-20

5-7-10



USD cumulative total returns*

0

10

20

30

40

50

60

70

80

2000 2001 2002 2003

Cu

mu

lati

ve T

ota

l R

etu

rns

(%)

USD cumulative total returns



USD annual cumulative returns*

0

10

20

30

40

50

60

70

80

90

Total 2000 2001 2002 2003

An

nu

al C

um

ula

tive

Ret

urn

s (%

)



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



USD - Monthly distribution of trades

Source: HSBC

0

5

10

15

20

25

30

35

40

45

50

Mar 00 Dec 00 Sep 01 Jun 02 Mar 03 Dec 03

Nu

mb

er o

f T

rad

es

Maturity

50/50


EUR statistics for period 2000-2003*

-100

-80

-60

-40

-20

0

20

40

60

80

2000 2001 2002 2003 Total

To

tal

retu

rns

(bp

)

-100

-80

-60

-40

-20

0

20

40

60

80




EUR statistics on different combinations*

-2

0

2

4

6

8

10

12

14

16

60% 70% 80% 90% 100%


Ave

rag

e T

ota

l R

etu

rn (

bp

)

2-5-10

2-7-15

3-5-7

15-20-307-10-15



GBP statistics for period 2000-2003*

-150

-100

-50

0

50

100

2000 2001 2002 2003 Total

To

tal

retu

rns

(bp

)

-150

-100

-50

0

50

100




GBP statistics on different combinations*

-10

-5

0

5

10

15

20

25

40% 60% 80% 100%


Ave

rag

e T

ota

l R

etu

rn (

bp

)

7-15-20

3-5-7

7-10-15

15-20-30



Revealing anomalies in forward and volatility curves


• 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)


• 30 yr CMS forwards against 2 yr CMS forwards


• Forwards implying inversion of 30-2 yr curve


• EUR CMS curve steepener

The two previous figures show that the spread 30yr-2yr becomes negative after 2009, reaching a maximum of -57bp on 2019. 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.


• 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 2009-2019.


• 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.

t

dsst

tvol0

2 )(1

)(

222 ).()(.)(. tTBEtTtvoltTvolT

tTBE


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.

tT

tvoltTvolTBEtT

22 )(.)(.

22 )(.)(. tvoltTvolT


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%.

mmBE63 yyBE21 yyBE32 yyBE75 yyBE107

29.6%12.9% 0% 9.8% 7%


• HSBV Bloomberg site


• References

L. Martellini, P. Priaulet and S. Priaulet, “Understanding the butterfly strategy”, Journal of Bond Trading and Management, 1(1), 9-19, 2002.

L. Martellini, P. Priaulet and S. Priaulet, “Fixed-Income Securities: Valuation, Risk Management and Portfolio Strategies”, Wiley, 2003.

F. Fabozzi, C. Dialynas, L. Martellini and P. Priaulet, “Indexing, Structured and Active Fixed-Income Portfolio Management”, Wiley, forthcoming 2005.


• 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."

EXPLORING SOME ALTERNATIVE FIXED-INCOME STRATEGIES Philippe PRIAULET HSBC-CCF and University of EVRY...

Documents

Transcript of EXPLORING SOME ALTERNATIVE FIXED-INCOME STRATEGIES Philippe PRIAULET HSBC-CCF and University of EVRY...