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Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

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Nicholas Manganaro

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

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I am using QLXL I compiled from QuantLib 1.2.1. I am running it on a machine with Windows 7 Ultimate & SP1.

I am trying to confirm that some basic calculations make sense before generating results to use as the basis for another line of analysis.

I want to thank Jean-Mattieu and Senevi for their thread, and pursue a line of inquiry on Duration and Convexity using Senevi’s sample security.

In using Senevi’s terms and conditions, including the move to “Unadjusted” for BDC, I get the yield he sourced from Bloomberg (to 6 digits), without creating a new compounding convention. That said, I admire the thoroughness displayed in creating the smarter input, and wonder if/how I might be able to implement such a change with QLXL as part of a function, so I will still be able to match the market yield as the bonds I analyze get closer to maturity without having to rely on a VBA if/then. Nonetheless, I do not see the SimpleThenCompounded convention made available through the interface, so perhaps the question is moot.

I get the Macaulay duration and convexity values from QLXL Senevi shows as his outputs, which do not match the Bloomberg values. It is interesting to note that the built-in Excel Macaulay duration function does match the Bloomberg values to 3 digits:

B’berg Macaulay Dur’n 1.928

Excel Macaulay Dur’n 1.9275741842

QLXL Macaulay Dur’n from yld 1.9129221698

QLXL Modified Dur’n from yld 1.91003

Effective duration, from bumping the yield up + down 5 bps, recalculating the bond prices and dividing the difference in the prices by 0.1 = 1.923.

While it may be that there is a problem applying the appropriate discounting factors in calculating the QuantLib duration, these outputs seem to show that the QuantLib output to be overly discounted, not under-discounted.

I did some fiddling along the same line with convexity from yield. I get an effective convexity measure from the changes in QLXL Macaulay duration at the price points resulting from the yield bumping process which is not too far off from the B’berg result previously sited by Senevi:

Bloomberg cvx: 0.047

“effective” cvx: 0.0471389

QLXL cvx: 4.6061

The QLXL convexity number does not tie out with the other two, but if derived from an interim QL duration result, that is not a huge surprise.

I would appreciate any tips to overcome these relatively small frustrations. Would compiling QLXL 1.3 bring me closer to reliable outputs for these basic calculations?

-Nick

From: Senevi J Kankanamge Don [[hidden email]]
Sent: Friday, November 08, 2013 5:55 AM
To: Jean-Mathieu Vermosen; [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi,

Thanks for your response.

We compare true yield in BBG.

As you said, I had to set BusinessDayConvention paymentConvention = Unadjusted to avoid discrepancies.

Ultimately we implemented a new method isSettlementLastCouponPeriod() in ql/instruments/bonds/fixedratebond.hpp which returns whether the settlement falls into the last coupon period or not.

Then we did…

bool bIsSettlementLastCouponPeriod = bond.isSettlementLastCouponPeriod(settlementDate);

Compounding compoundingMethod = bIsSettlementLastCouponPeriod ? SimpleThenCompounded : Compounded;

Real ql_clean_price = BondFunctions::cleanPrice( bond, ql_yield, bondDayCount, compoundingMethod, frequency, settlementDate);

Now QuantLib yield match 100% with Bloomberg.

Duration and convexity don’t match with Bloomberg. It appears that QuantLib doesn’t take the weight of present values into account in computing these two figures whereas Bloomberg does.

Thanks

-Senevi

From: Jean-Mathieu Vermosen [[hidden email]]
Sent: Wednesday, November 06, 2013 2:37 PM
To: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hey there,

Which yield are you comparing to in BBG ? Treasury yield convention doesn’t adjust payments for holidays, so make sure that

BusinessDayConvention paymentConvention = ModifiedFollowing;

you passed to the FixedRateBond constructor is not creating discrepancies in the cash-flow table (Just checked the code, it’s used in FixedRateLeg class for cash-flow generation). Otherwise you would prefer to compare to the true yield under the YA screen (after turning the flag to Following: ModifiedFollowing is for the swap guy).

The duration/convexity figures looks quite far from there target. As far as I remember Bloomberg is not adjusting for convention across bonds of different setup (except for the frequency in some screens). Then it might requires further investigation or to contact our friends from the hep desk to check the convention behind...

Best,

Jean-Mathieu Vermosen

On Nov 4, 2013, at 10:25 AM, Senevi J Kankanamge Don <[hidden email]> wrote:

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

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Jean-Mathieu Vermosen-2

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi Nick,

not quite sure about the 1.2.1, but it’s defined in the current quantlibobject version:

create.registerType("SimpleThenCompounded", new QuantLib::Compounding(QuantLib::SimpleThenCompounded));

It’s supposed to be defined somewhere in the qlo/enumerations/register/register_types.cpp

Rgds,

On Dec 9, 2013, at 3:29 PM, Nicholas Manganaro <[hidden email]> wrote:

Resend from other e-mail account.
--------------------------------------------------------------------
I am using QLXL I compiled from QuantLib 1.2.1. I am running it on a machine with Windows 7 Ultimate & SP1.
I am trying to confirm that some basic calculations make sense before generating results to use as the basis for another line of analysis.
I want to thank Jean-Mattieu and Senevi for their thread, and pursue a line of inquiry on Duration and Convexity using Senevi’s sample security.

In using Senevi’s terms and conditions, including the move to “Unadjusted” for BDC, I get the yield he sourced from Bloomberg (to 6 digits), without creating a new compounding convention. That said, I admire the thoroughness displayed in creating the smarter input, and wonder if/how I might be able to implement such a change with QLXL as part of a function, so I will still be able to match the market yield as the bonds I analyze get closer to maturity without having to rely on a VBA if/then. Nonetheless, I do not see the SimpleThenCompounded convention made available through the interface, so perhaps the question is moot.

I get the Macaulay duration and convexity values from QLXL Senevi shows as his outputs, which do not match the Bloomberg values. It is interesting to note that the built-in Excel Macaulay duration function does match the Bloomberg values to 3 digits:
B’berg Macaulay Dur’n                 1.928
Excel Macaulay Dur’n                     1.9275741842
QLXL Macaulay Dur’n from yld   1.9129221698
QLXL Modified Dur’n from yld    1.91003
Effective duration, from bumping the yield up + down 5 bps, recalculating the bond prices and dividing the difference in the prices by 0.1 = 1.923.

While it may be that there is a problem applying the appropriate discounting factors in calculating the QuantLib duration, these outputs seem to show that the QuantLib output to be overly discounted, not under-discounted.

I did some fiddling along the same line with convexity from yield. I get an effective convexity measure from the changes in QLXL Macaulay duration at the price points resulting from the yield bumping process which is not too far off from the B’berg result previously sited by Senevi:
Bloomberg cvx:                 0.047
“effective” cvx:                 0.0471389
QLXL cvx:                             4.6061

The QLXL convexity number does not tie out with the other two, but if derived from an interim QL duration result, that is not a huge surprise.

I would appreciate any tips to overcome these relatively small frustrations. Would compiling QLXL 1.3 bring me closer to reliable outputs for these basic calculations?

-Nick

From: Senevi J Kankanamge Don [[hidden email]]
Sent: Friday, November 08, 2013 5:55 AM
To: Jean-Mathieu Vermosen; [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi,

Thanks for your response.

We compare true yield in BBG.

As you said, I had to set BusinessDayConvention paymentConvention = Unadjusted to avoid discrepancies.

Ultimately we implemented a new method isSettlementLastCouponPeriod() in ql/instruments/bonds/fixedratebond.hpp which returns whether the settlement falls into the last coupon period or not.

Then we did…

bool bIsSettlementLastCouponPeriod = bond.isSettlementLastCouponPeriod(settlementDate);
            Compounding compoundingMethod = bIsSettlementLastCouponPeriod ? SimpleThenCompounded : Compounded;

            Real ql_clean_price = BondFunctions::cleanPrice( bond, ql_yield, bondDayCount, compoundingMethod, frequency, settlementDate);

Now QuantLib yield match 100% with Bloomberg.

Duration and convexity don’t match with Bloomberg. It appears that QuantLib doesn’t take the weight of present values into account in computing these two figures whereas Bloomberg does.

Thanks
-Senevi

From: Jean-Mathieu Vermosen [[hidden email]]
Sent: Wednesday, November 06, 2013 2:37 PM
To: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hey there,

Which yield are you comparing to in BBG ? Treasury yield convention doesn’t adjust payments for holidays, so make sure that

BusinessDayConvention paymentConvention = ModifiedFollowing;

you passed to the FixedRateBond constructor is not creating discrepancies in the cash-flow table (Just checked the code, it’s used in FixedRateLeg class for cash-flow generation). Otherwise you would prefer to compare to the true yield under the YA screen (after turning the flag to Following: ModifiedFollowing is for the swap guy).

The duration/convexity figures looks quite far from there target. As far as I remember Bloomberg is not adjusting for convention across bonds of different setup (except for the frequency in some screens). Then it might requires further investigation or to contact our friends from the hep desk to check the convention behind...

Best,

Jean-Mathieu Vermosen

On Nov 4, 2013, at 10:25 AM, Senevi J Kankanamge Don <[hidden email]> wrote:

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg                          QuantLib
Yield                                      0.302775                              0.3027679582
Macaulay Duration          1.928                                     1.9129221698
Convexity                            0.047                                     0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

        double ql_price = 99.8984375;

        Date settlementDate = Date(25, Oct, 2013);
        Date firstCouponDate = Date(31, Mar, 2014);
        Date datedDate = Date(30, Sep, 2013);
        Date maturityDate = Date(30, Sep, 2015);

        //
        // Parameters required to define the bond
        //
        Natural settlementDays = 0;
        Real faceAmount = 100;
        DayCounter bondDayCount = ActualActual(ActualActual::Bond);
        BusinessDayConvention paymentConvention = ModifiedFollowing;
        Real redemption = 100.0;
        Compounding compoundingMethod = SimpleThenCompounded;
        DateGeneration::Rule dateGeneration = DateGeneration::Forward;
        Frequency frequency = Semiannual;
        Real accuracy = 1.0e-11;
        Size maxEvaluations = 100;

        //
        // Create the Schedule
        //
        Schedule fixedBondSchedule(
                                    datedDate,                                  // Dated Date
                                    maturityDate,                               // Maturity Date
                                    Period(Semiannual),                         // Period
                                    UnitedStates(UnitedStates::GovernmentBond), // Calendar
                                    Unadjusted,                                 // BusinessDayConvention - convention
                                    Unadjusted,                                 // BusinessDayConvention - terminationDateConvention
                                    dateGeneration,                             // DateGeneration::Rule rule
                                    false,                                      // endOfMonth
                                    firstCouponDate);                           // First Date

        //
        // Create the Fixed Rate Bond
        //
        FixedRateBond bond(
                            settlementDays,                        // Settlement Days
                            faceAmount,                            // Face Amount
                            fixedBondSchedule,                     // Schedule
                            std::vector<Rate>(1, ql_coupon),       // Coupons
                            bondDayCount,                          // DayCounter
                            paymentConvention,                     // BusinessDayConvention
                            redemption);                           // Redemption

        Real ql_yield       = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

        InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );
        Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

        Compounding compoundingMethod4Duration = Compounded;
        Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks
-Senevi
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Nicholas Manganaro

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Jean-Mathieu,

Thanks for your speedy response.

While I see your reference in the QuantLibAddin folder, I could not something similar in the QuantLibXL folder generated during the compilation process.

As a result, the type did not work as an input for QLXL in my recent experiment using MS Office 2010, 32 bit.

Is there a reference source for a way to create or expose the enumerations through the QL_XL add-in?

-Nick

From: Jean-Mathieu Vermosen [mailto:[hidden email]]
Sent: Monday, December 09, 2013 4:42 PM
To: Nicholas Manganaro
Cc: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi Nick,

not quite sure about the 1.2.1, but it’s defined in the current quantlibobject version:

create.registerType("SimpleThenCompounded", new QuantLib::Compounding(QuantLib::SimpleThenCompounded));

It’s supposed to be defined somewhere in the qlo/enumerations/register/register_types.cpp

Rgds,

On Dec 9, 2013, at 3:29 PM, Nicholas Manganaro <[hidden email]> wrote:

Resend from other e-mail account.

--------------------------------------------------------------------

I am using QLXL I compiled from QuantLib 1.2.1. I am running it on a machine with Windows 7 Ultimate & SP1.

I am trying to confirm that some basic calculations make sense before generating results to use as the basis for another line of analysis.

I want to thank Jean-Mattieu and Senevi for their thread, and pursue a line of inquiry on Duration and Convexity using Senevi’s sample security.

I get the Macaulay duration and convexity values from QLXL Senevi shows as his outputs, which do not match the Bloomberg values. It is interesting to note that the built-in Excel Macaulay duration function does match the Bloomberg values to 3 digits:
B’berg Macaulay Dur’n                 1.928
Excel Macaulay Dur’n                     1.9275741842
QLXL Macaulay Dur’n from yld   1.9129221698
QLXL Modified Dur’n from yld    1.91003
Effective duration, from bumping the yield up + down 5 bps, recalculating the bond prices and dividing the difference in the prices by 0.1 = 1.923.

While it may be that there is a problem applying the appropriate discounting factors in calculating the QuantLib duration, these outputs seem to show that the QuantLib output to be overly discounted, not under-discounted.

I did some fiddling along the same line with convexity from yield. I get an effective convexity measure from the changes in QLXL Macaulay duration at the price points resulting from the yield bumping process which is not too far off from the B’berg result previously sited by Senevi:
Bloomberg cvx:                 0.047
“effective” cvx:                 0.0471389
QLXL cvx:                             4.6061

The QLXL convexity number does not tie out with the other two, but if derived from an interim QL duration result, that is not a huge surprise.

I would appreciate any tips to overcome these relatively small frustrations. Would compiling QLXL 1.3 bring me closer to reliable outputs for these basic calculations?

-Nick

From: Senevi J Kankanamge Don [[hidden email]]
Sent: Friday, November 08, 2013 5:55 AM
To: Jean-Mathieu Vermosen; [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi,

Thanks for your response.

We compare true yield in BBG.

As you said, I had to set BusinessDayConvention paymentConvention = Unadjusted to avoid discrepancies.

Ultimately we implemented a new method isSettlementLastCouponPeriod() in ql/instruments/bonds/fixedratebond.hpp which returns whether the settlement falls into the last coupon period or not.

Then we did…

bool bIsSettlementLastCouponPeriod = bond.isSettlementLastCouponPeriod(settlementDate);
            Compounding compoundingMethod = bIsSettlementLastCouponPeriod ? SimpleThenCompounded : Compounded;

            Real ql_clean_price = BondFunctions::cleanPrice( bond, ql_yield, bondDayCount, compoundingMethod, frequency, settlementDate);

Now QuantLib yield match 100% with Bloomberg.

Duration and convexity don’t match with Bloomberg. It appears that QuantLib doesn’t take the weight of present values into account in computing these two figures whereas Bloomberg does.

Thanks
-Senevi

From: Jean-Mathieu Vermosen [[hidden email]]
Sent: Wednesday, November 06, 2013 2:37 PM
To: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hey there,

Which yield are you comparing to in BBG ? Treasury yield convention doesn’t adjust payments for holidays, so make sure that

BusinessDayConvention paymentConvention = ModifiedFollowing;

you passed to the FixedRateBond constructor is not creating discrepancies in the cash-flow table (Just checked the code, it’s used in FixedRateLeg class for cash-flow generation). Otherwise you would prefer to compare to the true yield under the YA screen (after turning the flag to Following: ModifiedFollowing is for the swap guy).

The duration/convexity figures looks quite far from there target. As far as I remember Bloomberg is not adjusting for convention across bonds of different setup (except for the frequency in some screens). Then it might requires further investigation or to contact our friends from the hep desk to check the convention behind...

Best,

Jean-Mathieu Vermosen

On Nov 4, 2013, at 10:25 AM, Senevi J Kankanamge Don <[hidden email]> wrote:

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg                          QuantLib
Yield                                      0.302775                              0.3027679582
Macaulay Duration          1.928                                     1.9129221698
Convexity                            0.047                                     0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

        double ql_price = 99.8984375;

        Date settlementDate = Date(25, Oct, 2013);
        Date firstCouponDate = Date(31, Mar, 2014);
        Date datedDate = Date(30, Sep, 2013);
        Date maturityDate = Date(30, Sep, 2015);

        //
        // Parameters required to define the bond
        //
        Natural settlementDays = 0;
        Real faceAmount = 100;
        DayCounter bondDayCount = ActualActual(ActualActual::Bond);
        BusinessDayConvention paymentConvention = ModifiedFollowing;
        Real redemption = 100.0;
        Compounding compoundingMethod = SimpleThenCompounded;
        DateGeneration::Rule dateGeneration = DateGeneration::Forward;
        Frequency frequency = Semiannual;
        Real accuracy = 1.0e-11;
        Size maxEvaluations = 100;

        //
        // Create the Schedule
        //
        Schedule fixedBondSchedule(
                                    datedDate,                                  // Dated Date
                                    maturityDate,                               // Maturity Date
                                    Period(Semiannual),                         // Period
                                    UnitedStates(UnitedStates::GovernmentBond), // Calendar
                                    Unadjusted,                                 // BusinessDayConvention - convention
                                    Unadjusted,                                 // BusinessDayConvention - terminationDateConvention
                                    dateGeneration,                             // DateGeneration::Rule rule
                                    false,                                      // endOfMonth
                                    firstCouponDate);                           // First Date

        //
        // Create the Fixed Rate Bond
        //
        FixedRateBond bond(
                            settlementDays,                        // Settlement Days
                            faceAmount,                            // Face Amount
                            fixedBondSchedule,                     // Schedule
                            std::vector<Rate>(1, ql_coupon),       // Coupons
                            bondDayCount,                          // DayCounter
                            paymentConvention,                     // BusinessDayConvention
                            redemption);                           // Redemption

        Real ql_yield       = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

        InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );
        Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

        Compounding compoundingMethod4Duration = Compounded;
        Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks
-Senevi
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Nicholas Manganaro-2

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Digging around, I found the following reference in the document for QuantLibAddin, which I’m trying to follow:

http://quantlib.org/quantlibaddin/extend_enum_tutorial.html

Since the type is in ..\QuantLibAddin\gensrc\metadata\enumerations\enumeratedtypes.xml and ..\QuantLibAddin\gensrc\metadata\types\types.xml, I do not think I have to add anything under instruction #2 to get “SimpleThenCompounded” to be exposed to Excel, but when I look at

..\QuantLib\ql\pricingengines\bond\bondfunctions.hpp there are only three compounded conventions in the description (which may well just be a text string), and only 3 work in the QLXL function.

Where would the exclusion of the “SimpleThenCompounded” element of the “Compounded” type happen? And how can I undo the exclusion once identified?

Digging, but not buried.

-Nick

From: Nicholas Manganaro [mailto:[hidden email]]
Sent: Monday, December 09, 2013 5:51 PM
To: 'Jean-Mathieu Vermosen'
Cc: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Jean-Mathieu,

Thanks for your speedy response.

While I see your reference in the QuantLibAddin folder, I could not something similar in the QuantLibXL folder generated during the compilation process.

As a result, the type did not work as an input for QLXL in my recent experiment using MS Office 2010, 32 bit.

Is there a reference source for a way to create or expose the enumerations through the QL_XL add-in?

-Nick

From: Jean-Mathieu Vermosen [[hidden email]]
Sent: Monday, December 09, 2013 4:42 PM
To: Nicholas Manganaro
Cc: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi Nick,

not quite sure about the 1.2.1, but it’s defined in the current quantlibobject version:

create.registerType("SimpleThenCompounded", new QuantLib::Compounding(QuantLib::SimpleThenCompounded));

It’s supposed to be defined somewhere in the qlo/enumerations/register/register_types.cpp

Rgds,

On Dec 9, 2013, at 3:29 PM, Nicholas Manganaro <[hidden email]> wrote:

Resend from other e-mail account.

--------------------------------------------------------------------

I am using QLXL I compiled from QuantLib 1.2.1. I am running it on a machine with Windows 7 Ultimate & SP1.

I am trying to confirm that some basic calculations make sense before generating results to use as the basis for another line of analysis.

I want to thank Jean-Mattieu and Senevi for their thread, and pursue a line of inquiry on Duration and Convexity using Senevi’s sample security.

I get the Macaulay duration and convexity values from QLXL Senevi shows as his outputs, which do not match the Bloomberg values. It is interesting to note that the built-in Excel Macaulay duration function does match the Bloomberg values to 3 digits:
B’berg Macaulay Dur’n                 1.928
Excel Macaulay Dur’n                     1.9275741842
QLXL Macaulay Dur’n from yld   1.9129221698
QLXL Modified Dur’n from yld    1.91003
Effective duration, from bumping the yield up + down 5 bps, recalculating the bond prices and dividing the difference in the prices by 0.1 = 1.923.

While it may be that there is a problem applying the appropriate discounting factors in calculating the QuantLib duration, these outputs seem to show that the QuantLib output to be overly discounted, not under-discounted.

I did some fiddling along the same line with convexity from yield. I get an effective convexity measure from the changes in QLXL Macaulay duration at the price points resulting from the yield bumping process which is not too far off from the B’berg result previously sited by Senevi:
Bloomberg cvx:                 0.047
“effective” cvx:                 0.0471389
QLXL cvx:                             4.6061

The QLXL convexity number does not tie out with the other two, but if derived from an interim QL duration result, that is not a huge surprise.

I would appreciate any tips to overcome these relatively small frustrations. Would compiling QLXL 1.3 bring me closer to reliable outputs for these basic calculations?

-Nick

From: Senevi J Kankanamge Don [[hidden email]]
Sent: Friday, November 08, 2013 5:55 AM
To: Jean-Mathieu Vermosen; [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi,

Thanks for your response.

We compare true yield in BBG.

As you said, I had to set BusinessDayConvention paymentConvention = Unadjusted to avoid discrepancies.

Ultimately we implemented a new method isSettlementLastCouponPeriod() in ql/instruments/bonds/fixedratebond.hpp which returns whether the settlement falls into the last coupon period or not.

Then we did…

bool bIsSettlementLastCouponPeriod = bond.isSettlementLastCouponPeriod(settlementDate);
            Compounding compoundingMethod = bIsSettlementLastCouponPeriod ? SimpleThenCompounded : Compounded;

            Real ql_clean_price = BondFunctions::cleanPrice( bond, ql_yield, bondDayCount, compoundingMethod, frequency, settlementDate);

Now QuantLib yield match 100% with Bloomberg.

Duration and convexity don’t match with Bloomberg. It appears that QuantLib doesn’t take the weight of present values into account in computing these two figures whereas Bloomberg does.

Thanks
-Senevi

From: Jean-Mathieu Vermosen [[hidden email]]
Sent: Wednesday, November 06, 2013 2:37 PM
To: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hey there,

Which yield are you comparing to in BBG ? Treasury yield convention doesn’t adjust payments for holidays, so make sure that

BusinessDayConvention paymentConvention = ModifiedFollowing;

you passed to the FixedRateBond constructor is not creating discrepancies in the cash-flow table (Just checked the code, it’s used in FixedRateLeg class for cash-flow generation). Otherwise you would prefer to compare to the true yield under the YA screen (after turning the flag to Following: ModifiedFollowing is for the swap guy).

The duration/convexity figures looks quite far from there target. As far as I remember Bloomberg is not adjusting for convention across bonds of different setup (except for the frequency in some screens). Then it might requires further investigation or to contact our friends from the hep desk to check the convention behind...

Best,

Jean-Mathieu Vermosen

On Nov 4, 2013, at 10:25 AM, Senevi J Kankanamge Don <[hidden email]> wrote:

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg                          QuantLib
Yield                                      0.302775                              0.3027679582
Macaulay Duration          1.928                                     1.9129221698
Convexity                            0.047                                     0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

        double ql_price = 99.8984375;

        Date settlementDate = Date(25, Oct, 2013);
        Date firstCouponDate = Date(31, Mar, 2014);
        Date datedDate = Date(30, Sep, 2013);
        Date maturityDate = Date(30, Sep, 2015);

        //
        // Parameters required to define the bond
        //
        Natural settlementDays = 0;
        Real faceAmount = 100;
        DayCounter bondDayCount = ActualActual(ActualActual::Bond);
        BusinessDayConvention paymentConvention = ModifiedFollowing;
        Real redemption = 100.0;
        Compounding compoundingMethod = SimpleThenCompounded;
        DateGeneration::Rule dateGeneration = DateGeneration::Forward;
        Frequency frequency = Semiannual;
        Real accuracy = 1.0e-11;
        Size maxEvaluations = 100;

        //
        // Create the Schedule
        //
        Schedule fixedBondSchedule(
                                    datedDate,                                  // Dated Date
                                    maturityDate,                               // Maturity Date
                                    Period(Semiannual),                         // Period
                                    UnitedStates(UnitedStates::GovernmentBond), // Calendar
                                    Unadjusted,                                 // BusinessDayConvention - convention
                                    Unadjusted,                                 // BusinessDayConvention - terminationDateConvention
                                    dateGeneration,                             // DateGeneration::Rule rule
                                    false,                                      // endOfMonth
                                    firstCouponDate);                           // First Date

        //
        // Create the Fixed Rate Bond
        //
        FixedRateBond bond(
                            settlementDays,                        // Settlement Days
                            faceAmount,                            // Face Amount
                            fixedBondSchedule,                     // Schedule
                            std::vector<Rate>(1, ql_coupon),       // Coupons
                            bondDayCount,                          // DayCounter
                            paymentConvention,                     // BusinessDayConvention
                            redemption);                           // Redemption

        Real ql_yield       = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

        InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );
        Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

        Compounding compoundingMethod4Duration = Compounded;
        Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks
-Senevi
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Nicholas Manganaro-2

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

In reply to this post by Nicholas Manganaro

Sorry for the barrage, but . .

Should I expect the 1.2.0 versions of gensrc and ObjectHandler to work with QuantLib 1.3 to allow me to compile a fully featured, 32 bit update to the QuantLibXL add-in, providing I am using a supported version of Visual Studio, i.e. 2008 or 2010?

Or is this perceived problem actually controlled by a setting that controls the way the Framework exposes the types through the interface?

-Nick

From: Nicholas Manganaro [mailto:[hidden email]]
Sent: Monday, December 09, 2013 11:18 PM
To: '[hidden email]'
Subject: RE: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Digging around, I found the following reference in the document for QuantLibAddin, which I’m trying to follow:

http://quantlib.org/quantlibaddin/extend_enum_tutorial.html

..\QuantLib\ql\pricingengines\bond\bondfunctions.hpp there are only three compounded conventions in the description (which may well just be a text string), and only 3 work in the QLXL function.

Where would the exclusion of the “SimpleThenCompounded” element of the “Compounded” type happen? And how can I undo the exclusion once identified?

Digging, but not buried.

-Nick

From: Nicholas Manganaro [[hidden email]]
Sent: Monday, December 09, 2013 5:51 PM
To: 'Jean-Mathieu Vermosen'
Cc: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Jean-Mathieu,

Thanks for your speedy response.

While I see your reference in the QuantLibAddin folder, I could not something similar in the QuantLibXL folder generated during the compilation process.

As a result, the type did not work as an input for QLXL in my recent experiment using MS Office 2010, 32 bit.

Is there a reference source for a way to create or expose the enumerations through the QL_XL add-in?

-Nick

<SNIP>

Senevi J Kankanamge Don

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

In reply to this post by Nicholas Manganaro

Hi Nick,

Thanks for your feedback.

I was doing my testing on QuantLib-1.3 and I found that I could not get modified duration, Macaulay duration and convexity to match with Bloomberg no matter what parameters are changed. I attribute this to the fact that Bloomberg uses different formulae compared to QuantLib. Further if the settlement is in the final period, Bloomberg uses a different formula but QuantLib does not.

Although I have never built QLXL, I don’t believe building on QLXL 1.3 will bring you closer to Bloomberg.

Thanks

-Senevi

From: Nicholas Manganaro [mailto:[hidden email]]
Sent: Monday, December 09, 2013 8:29 PM
To: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Resend from other e-mail account.

--------------------------------------------------------------------

I am using QLXL I compiled from QuantLib 1.2.1. I am running it on a machine with Windows 7 Ultimate & SP1.

I am trying to confirm that some basic calculations make sense before generating results to use as the basis for another line of analysis.

I want to thank Jean-Mattieu and Senevi for their thread, and pursue a line of inquiry on Duration and Convexity using Senevi’s sample security.

B’berg Macaulay Dur’n 1.928

Excel Macaulay Dur’n 1.9275741842

QLXL Macaulay Dur’n from yld 1.9129221698

QLXL Modified Dur’n from yld 1.91003

Effective duration, from bumping the yield up + down 5 bps, recalculating the bond prices and dividing the difference in the prices by 0.1 = 1.923.

Bloomberg cvx: 0.047

“effective” cvx: 0.0471389

QLXL cvx: 4.6061

The QLXL convexity number does not tie out with the other two, but if derived from an interim QL duration result, that is not a huge surprise.

I would appreciate any tips to overcome these relatively small frustrations. Would compiling QLXL 1.3 bring me closer to reliable outputs for these basic calculations?

-Nick

Hi,

Thanks for your response.

We compare true yield in BBG.

As you said, I had to set BusinessDayConvention paymentConvention = Unadjusted to avoid discrepancies.

Ultimately we implemented a new method isSettlementLastCouponPeriod() in ql/instruments/bonds/fixedratebond.hpp which returns whether the settlement falls into the last coupon period or not.

Then we did…

bool bIsSettlementLastCouponPeriod = bond.isSettlementLastCouponPeriod(settlementDate);

Compounding compoundingMethod = bIsSettlementLastCouponPeriod ? SimpleThenCompounded : Compounded;

Real ql_clean_price = BondFunctions::cleanPrice( bond, ql_yield, bondDayCount, compoundingMethod, frequency, settlementDate);

Now QuantLib yield match 100% with Bloomberg.

Duration and convexity don’t match with Bloomberg. It appears that QuantLib doesn’t take the weight of present values into account in computing these two figures whereas Bloomberg does.

Thanks

-Senevi

Hey there,

Which yield are you comparing to in BBG ? Treasury yield convention doesn’t adjust payments for holidays, so make sure that

BusinessDayConvention paymentConvention = ModifiedFollowing;

Best,

Jean-Mathieu Vermosen

On Nov 4, 2013, at 10:25 AM, Senevi J Kankanamge Don <[hidden email]> wrote:

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

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