HPCL Report Final

Bond Mathematics 1

HINDUSTAN PETROLEUM COMPANY

LIMITED

Company profile:

Fortune 500 company

Mega Public Sector Undertaking

Hindustan Petroleum Corporation

Limited (HPCL) is an integrated

oil refining and marketing

companies in India. It is engaged

in the oil and gas exploration and

production, refining of crude oil

and marketing of petroleum

products. Currently, the company holds 16% market share and 10.3% of

India‘s refining capacity. The company owns and operates two coastal

refineries, one at Mumbai and the other in Vishakapatnam. The company

also holds an equity stake of 16.95% in Mangalore Refinery &

Petrochemicals Limited. The company is headquartered at Mumbai in

Maharashtra, India.

HPCL‘s Mumbai refinery has a capacity of 5.5 Million Metric Tons Per

Annum (mmtpa) and Vishakapatnam refinery has a capacity of 7.5 mmtpa.

Mangalore Refinery has a capacity of 9 mmtpa. HPCL owns and operates

the largest lube refinery in India with a capacity of 335 TMT.

The company reported revenues of

(Rupee) INR 1,294,757.90 million

during the fiscal year ended March

2009, an increase of 16.53% over

2008. The operating profit of the

company was INR 10,118.40

million during the fiscal year 2009,

a decrease of 28.92% from 2008.

The net profit of the company was

INR 7,573.90 million during the

fiscal year 2009, a decrease of

44.48% from 2008.

KEY DATA

2009 Sales:

1,31,802.65 Cr

Major Industry:

Oil Industry

Sub Industry:

Refineries

Country:

India

Currency

Indian Rupees

Fiscal Year Ends:

March

Employees

More than 11,245

Exchanges:

NSE BSE

Market Capitalization:

12092.38 Cr

Weighted avg. no. of

shares

33.86 crores

OFFICERS

Chairman & Managing Director

Mr.Arun Balakrishnan

Director- Marketing

Mr.S.Roy Choudhury

Director- Human Resources

Mr.V. Vizia Saradhi

Director- Finance

Mr.B.Mukherjee

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Company description:

Mission:

"HPCL, along with its joint ventures, will

be a fully integrated company in the

hydrocarbons sector of exploration and

production, refining and marketing;

focusing on enhancement of productivity,

quality and profitability; caring for

customers and employees; caring for

environment protection and cultural

heritage.

It will also attain scale dimensions by

diversifying into other energy related

fields and by taking up transnational

operations."

Vision:

To be a World Class Energy Company

known for caring and delighting the

customers with high quality products and

innovative services across domestic and

international markets with aggressive

growth and delivering superior financial

performance. The Company will be a

model of excellence in meeting social

commitment, environment, health and

safety norms and in employee welfare and

relations.

Table1.1

Business Units Description

Refineries Present Projects:

Facilities for Euro-III & IV grade Gasoline

New FCCU project at Mumbai Refinery

Environmental facilities

Bottom Up-gradation Projects

LOBS Project

MR/VR DHT

Single Point Mooring (SPM) Project at Visakh Refinery

Modernization Project for Mounded Storage System for LPG

/Propylene at Visakh Refinery

Aviation Infrastructure

Aviation Service Facility: Our Facility to supply JET A1 at Indian

Airports

Location of our ASFs: Aircraft Fueling Facilities of HP Aviation in

India

Equipment: Our Equipment to supply Aircraft Jet Fuel in India

Modernization And Upgradation: Keeping ATF Refueling facilities up-to-date

Jet Fuel Prices

Domestic Prices: Price of Jet A1 at various airports in India

International Prices: PLATTS based Pricing in India for International carriers

Bulk Fuel Fuels Offered:

Bitumen

Fuels

Marine-Bunker Fuels

Marine Lubes

Special Products

Bond Mathematics 3

Superior Kerosene Oil-Non PDS

LPG (HP Gas) LPG Offered:

Domestic LPG

Commercial LPG

Industrial & Bulk LPG

Auto LPG

Piped LPG

Rasoi Ghar

Lubes (HP Lubes) HP Lubricants are borne out of an intense and unrelenting R & D effort, which

aims at producing quality products that enhance automotive performance

standards. The range of HP Lubes is comprehensive and catering to the minutest

needs; from new generation cars to ploughing tractors and industrial machinery.

The range conforms strictly to OEM specifications, often taking the initiative in

customization of products.

Retail Retail Offered:

Auto LPG

CNG

Power

Turbo Jet

Trade The activities of IT&S relate to

Crude oil imports,

Petroleum Product Imports / Exports,

Shipping,

Production planning for Refineries,

Supplies for domestic Markets,

Product exchange with other Indian Oil Companies and Oil price risk management.

E & P HPCL, in consortium with E&P partners companies currently has 19 nos. blocks

in India, and 4 nos. overseas blocks in Oman, Australia and Egypt. HPCL intends

to leverage and consolidate its current position and formulate & implement a strategy for E&P business based on opportunities both within and outside India.

Currently HP E&P has presence in 4 countries including India and plans to

expand its portfolio in other countries which is a main area of focus of its

Strategic Investment plan mainly in Middle East, South East Asia & Africa.

Ventures Till Date JV‘s:

HPCL-Mittal Energy Ltd. (HMEL)

Hindustan Colas (HINCOL)

Prize Petroleum Company Limited

South Asia LPG Co Pvt. Ltd. ( SALPG)

Bhagyanagar Gas Limited (BGL)

Aavantika Gas Limited

Petronet India Limited (PIL)

Petronet MHB Limited (PMHBL)

Mangalore Refineries and Petrochemicals Limited (MRPL)

CREDA-HPCL Biofuel Limited (CHBL)

Sushrut Hospital and Research Centre

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HPCL financial analysis:

Figure1.1

Ratios- 2009:

Asset Ratios

Total assets/equity 4,39

Total liabilities/equity 3.39

Total liabilities/total assets 0.77

Sales/total assets 3.04

Liquidity Ratios

Quick ratio 2.03

Current ratio 2.87

Interest cover 1.47

65,218.83

76,920.26

96,918.15

112,098.27

131,803

2005 2006 2007 2008 2009

sales (in crores)

sales (in crores)

2,347.52

1113.36

3000.43

2557.35

4158.17

2005 2006 2007 2008 2009

PBDIT (in crores)

adjusted PBDIT

1277.33

405.63

1571.17

1134.88

574.98

2005 2006 2007 2008 2009

PAT (in crores)

reported net profit

0

50

100

150

200

250

300

350

DIVIDEND EPS BOOK VALUE

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Turnover ratios

Sales/inventory 12.96

Sales/receivables 20.26

Sales/working cap 7.91

Profitability ratios

Operating margin 2.27

Pretax income margin 0.63

Return on equity 3.08

Return on fixed assets 2.05

Return on total assets 0.75

As per the sales seen, there is a constant

increase in sales and volumes. The profit

should also increase but there is a decline

over last 2 years. This decrease is due to

the negative results of stock adjustments in

the P&L account, which says that HPCL‘s

shares have been undervalued and the

company was getting devalued. This can

be clearly seen in the trend of EPS and the

same is reflected in the net profits.

Asset ratios show that total assets have

22.7% equity and 77.3% debt. The

liabilities have been raised high against

Rs.1 of equity i.e Rs.3.39, which is not a

good sign. Sales/total assets is a good ratio

of 3.04. HPCL is earning good sales out of

this assets.

Liquidity ratios of HPCL are good. The

company has the ability to meet its short

term debt obligations. It has very high

short term solvency. There is a lot of

liquidity in the company leading to

opportunity costs. They can use this

money in more investments. Interest cover

ratio is quite fine and company earnings

seem to be consistent.

Turnover ratios show that sales inventory

ratio is above 6.94 indicating excessive

efficiency in sales performance. Similarly,

sales receivable ratio of 20.26 signifies

efficient debt management. However,

considering the liquid nature of industry it

operates, the ratio needs to be bought

down below 15.

Profitability ratios show that they are just

touching margins.ROE should be around

12%. To improve their profits HPCL has

to reduce its costs or has increase its

volumes and sales or can increase its

prices. But being a public company, it is

not that easy to increases prices as they

have to abide by the government policies

and subsidiaries. Despite of these subsidy

mechanisms, one can say that HPCL is

gaining good profits.

Growth ratios (2009)

Net sales growth (%) 18.83

Core EBITDA growth (%) 37.22

EBIT growth (%) 47.02

PAT growth (%) -49.34

EPS growth (%) -49.34

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Competitive analysis (2009):

The competitor‘s in the public sector: IOCL, BPCL and MRPL.

The competitor‘s in the private sector: RIL, CPCL

The competitor‘s in the MNC are: Essar, BP

The major competitors amongst these would be IOCL, BPCL and RIL

Figure1.2

0

50000

100000

150000

200000

250000

300000

350000

HPCL IOCL RIL BPCL

sales (in crores)

sales (in crores)

0

5000

10000

15000

20000

25000

30000

HPCL IOCL RIL BPCL

Adjusted PBDIT (in crores)

Adjusted PBDIT (in crores)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

HPCL IOCL RIL BPCL

PAT (in crores)

PAT (in crores)

0

200

400

600

800

1000

1200

HPCL IOCL RIL BPCL

Stock price

STOCK PRICE (June 2,2010)

Bond Mathematics 7

Table1.2

Valuation

Parameters

HPCL IOCL RIL BPCL

P/E 9.5 8.36 20.3 13.63

EV/NET

SALES

0.25 0.29 2.08 0.25

EV/EBITDA 8.28 8.36 12.12 8.09

The above results clearly show that RIL is a big player and a tough competitor to HPCL. RIL

market cap is high and all their valuation parameters are high, which indicates that to

compete with RIL, HPCL‘s best adoption should be to expand its business and sales. IOCL is

the next competitor to HPCL and BPCL is on same margins as HPCL, but all three

companies are better in profits than HPCL. HPCL should adopt to better business plans and

strategies to set a race with these companies.

Threat of Intense segment rivalry:

• Is witnessed in the holistic service offered by the retail outlet majors (IOCL,HPCL ,BPCL) If

IOCL has Swagat outlets HPCL and BPCL has Club HP and Pure for Sure outlets. It is noted

that most of these outlets have same facilities like Quality verification checks, Truck driver

amenities etc, leading to intense segment rivalry.

• However IOCL has the edge in terms of vast refining and distribution network, hence is the

market leader.

Threat of new entrants:

• In the current INDIAN scenario, entry and exit barriers are high and profit potential is high.

• But firms face more risk because poorer-performing firms stay in and fight it out. Like, IBP

was facing bleak prospects till the time INDIAN OIL purchased it with a premium of over

60%.

• Till the recent crude OIL spike, Reliance Retail petroleum, ESSAR OIL and SHELL gave a

head-on clash (frontal attack in select locations) with OIL PSU‘s.

• Adding to it newer plants come with better crude handling and therefore refinery margins are

good, thus reflected in the net margins.

Threat of Supplier’s growing bargaining power:

• Petroleum is synonymous with OPEC cartel.

• Big-wigs like Exxon-Mobil, Total, Occidental Petroleum, IOCL, and BPCL are not shielded

from the vagaries of OPEC.

• Though OPEC claims that it‘s the tax structure in the respective countries which makes

petroleum products expensive, crude OIL price varies in in accordance with production levels

of OPEC.

• Today due to Global meltdown, Crude OIL prices are declining.

Bond Mathematics 8

• But OPEC has already initiated significant production cuts whose effect might be felt in the

forthcoming months.

Threat of Substitute Products:

• Is from cleaner and efficient fuels like Compressed Natural Gas (CNG), where it was

implemented on a war-footing in Delhi to control emissions.

• Central Government‘s encouragement in the form of Bio-fuel purchase policy for 5% bio-

fuel blended Diesel fuel.

• Electric car – Reva also poses a challenge to the existing players.

Threat of buyer’s growing bargaining power:

• ‗Consumer is always the king ‗– is apt in the case of petroleum products in India.

• Consumer‘s interests‘ are protected by the Government by not raising the fuel prices beyond

a limit and indirectly consumer is exercising his bargaining power.

• Also all the OIL PSU‘s offer varied services to the consumer including intangible ones like

frequent quality checks and tangible ones like amenities ATM , Car care etc which was not

even a moot concept in the past

Bond Mathematics 9

Oil industry

Table1.3

Oil and Gas Exploration & Production

The economic crisis left an impact on the oil and gas industry globally. The economic

downturn that followed resulted in unprecedented demand destruction. The industry is on a

path of recovery due to fiscal measures announced by various governments. The major

deepwater basins of the world namely the East coast of India, Gulf of Mexico, Africa and

Brazil continue to witness huge levels of activity and investment. The structural theme for

investment in the sector remains valid. The world‘s insatiable need for reliable and affordable

energy continues to grow unabated. This calls for substantial investments, access to resources

and newer technologies to unlock resources from challenging locations.

The International Energy Agency (IEA), in its World Energy Outlook 2009, estimates that by

the year 2030, global energy demand is expected to increase by 49% from its current level.

Oil and natural gas are expected to remain primary energy sources and are expected to meet

51% of the global demand. Increasing concern for climate change augurs well for natural gas

as it is an environmentally benign fuel with carbon emissions far lower than other fossil fuels.

Bond Mathematics 10

IEA estimates that the world requires investments to the tune of $ 11 trillion in the oil and gas

sector over the next 20 years implying an annual investment of over $ 500 billion.

FY 2009-10 was a year of steady growth. Oil prices rose from an average of $ 46/barrel (bbl)

in January 2009 to touch $ 75/bbl in December 2009. Average WTI prices remained at $

70/bbl vis-à-vis $86/bbl for the previous year. Henry Hub natural gas price averaged at $

4/Million Metric British Thermal Unit (MMBTU) for FY 2009-10 as against an average of $

7.87/MMBTU in FY 2008-09.

The year 2009 also saw the global oil demand slip to 84.93 MBPD, a decrease of 1.5% over

2008. IEA forecasts that the global oil demand is set to increase by 1.67 MBPD or 2.0% to

86.60 MBPD in 2010.

Figure1.3

Kirirt parekh recommendations on future oil prices

An experts group, headed by former

Planning Commission member Kirit

Parikh, submitted its much awaited report

on pricing policy for four major oil

products, namely, petrol, diesel, kerosene

and LPG. The committee has

recommended that prices of petrol and

diesel to be market-determined, both at the

refinery gate and retail levels, whereas the

prices of kerosene and domestic LPG can

be partially raised

by Rs 6 per litre and Rs 100 per cylinder

respectively. For kerosene and LPG, the

committee has recommended linking fuel

prices with per capita income and selective

allocations to poorer families through

smart cards linked with unique identities

(UID) project.

29.6%

7.9%

10.9%5.3%

8.0%

1.8%

1.6%

0.1%

9.2%

25.5%

Refinery crude throughput, 2006

IOCL

BPCL

HPCL

KRL

CPCL

BRPL

NRL

ONGC

MRPL

RIL

Bond Mathematics 11

The committee has accepted the subsidy

formula proposed by Oil and Natural Gas

Corporation (ONGC) aimed at reducing

burden of oil companies. The formula

suggests an incremental rate of taxes on

higher crude oil price realization from the

nomination blocks of ONGC and Oil India

Ltd (OIL).

The proposed subsidy sharing formula

shall keep the government‘s subsidy

contribution from budget in the range of

Rs 19,780-23,340 crore at various crude

price levels. A summary of

recommendations and their impact has

been provided in Annexure. According to

D.R.Dogra, Managing Director & CEO ,

CARE Ltd. ― The impact on the oil and

gas industry, if any of the

recommendations by the committee is

implemented, will be extremely positive‖.

The complete deregulation of auto-fuels

and sharp hikes in the prices of cooking

fuels would help the government in

reducing fiscal deficit and thus curtail its

borrowings. The three public sector oil

marketing companies, namely, Indian Oil

Corporation, Bharat Petroleum

Corporation Ltd and Hindustan Petroleum

Corporation Ltd, would be able to reduce

their under-recoveries considerably.

However, the complete deregulation may

prompt private players such as Reliance,

Essar and Shell to re-open their retail fuel

outlets, putting pressure on market share of

public sector oil marketing companies

(OMCs). In the past, the entry of private

players in retail fuel market had resulted in

an erosion of about 10 per cent in the

market share of public sector OMCs. The

proposed hike in prices of cooking fuels

coupled with reduction in allocation of

kerosene under the public distribution

scheme (PDS) by 20 per cent would

reduce under-recoveries by about Rs

16,454 crore, whereas, the auto-fuel

deregulation would avert Rs 13,997 crore

of under-recoveries.

In the opinion of CARE Research, this is

a landmark report, but implementation is

the key. Although the report is in line with

the wish-list of most of the market

participants, implementation of the

recommendations needs to be keenly

watched for. ―The situation is tricky for the

Government, as it needs to strike a balance

between reducing the subsidy burden on

the public sector oil and gas undertakings,

reducing the fiscal deficit and managing

the current inflationary scenario, given the

economy being in the process of revival

and attempting to restore its buoyancy‖

added Mr Dogra. It may be noted that

similar kind of recommendations made by

the Chaturvedi committee in 2008 were

rejected by the government. Also,

practicability of the selective allocations to

poorer families through smart cards linked

with UID project also needs to be

evaluated by the government keeping in

view the infrastructure requirement for the

same. Although diesel is a major

contributor to the total underrecoveries, its

deregulation needs to be carefully

evaluated as the agriculture sector

(consuming 12 percent of diesel) and

transport industry (consuming 40 per cent

of diesel), the backbone of the Indian

economy, are the major consumer of the

fuel.

Bond Mathematics 12

Table1.4

Bond Mathematics 13

Conclusive report 2010

Looking at the financial results of the company for this year 2009-2010, company has

recommended Rs 12 of dividend/share as against Rs 5.25 last year. The dividend/share has

been increasing gradually which is a good significance for the shareholders. The sales/income

from operations have been decreased from 136885.22 Cr in year 2008-2009 to 119453.33 Cr

in year 2009-2010. The company‘s gross profits earned are 2564.29 Cr as against 2620.66 Cr.

But the PAT has doubled from 757.39 Cr in 2008-2009 to 1475.15 Cr in year 2009-2010.

The physical performance of market sales has increased from 25.39 million metric tonnes in

2008-2009 to 26.27 MMT in 2009-2010. The company‘s turnover has decreased from last

year highest achieved turnover of 121510.39 Cr to 113163.38 Cr in this year.

It is a matter of pride for the company to be ranked 311 amongst Global Fortune 500

Companies, 1002 amongst Forbes Global 2000 Companies and 111 in the list of World‘s

Most Reputed Companies brought out by the Global Reputation Institute. HPCL aims to

conduct our business with highest standards of corporate governance. HPCL has

implemented the ―Right to Information Act (RTI)‖ in letter as well as spirit. HPCL has also

implemented the Integrity Pact in liaison with ―Transparency International‖. The Integrity

Pact forbids vendors from using any type of unwarranted influence for furthering their

interests while in turn ensuring them fairness, transparency and equal opportunity in their

association with the Corporation.

1. The Company is engaged in the following business segments:

a) Downstream i.e. Refining and Marketing of Petroleum Products

b) Exploration and Production of Hydrocarbons

Segments have been identified taking into account the nature of activities and the

nature of risks and returns.

2. Segment Revenue comprises of the following:

a) Turnover (Net of Excise Duties)

b) Subsidy from Government of India

c) Other income (excluding interest income, dividend income and investment income)

3. There are no geographical segments.

Average Gross Refining Margins during the year ended March 2010, were US $ 2.68

per BBL as against US $ 3.97 per BBL during the corresponding previous year.

The prices of LPG (Domestic) and SKO (LPG) are subsidised as per the scheme

approved by the Government of India. Subsidy amounting to Rs. 609.43 crores

(2008-09 : Rs. 574.23 crores) for the year has been accounted at 1/3rd of the subsidy

rates for 2002-03.

In principle approval of Government of India for Budgetary Support amounting to

Rs. 5563.13 crores (2008-09 : Oil Bonds for Rs. 14,692.77 crores), has been received

and the same have been accounted under ‗Recovery under Subsidy Schemes‘.

During the year, ONGC and GAIL offered discount amounting to Rs. 3247.14 crores

(2008-09 : Rs. 7176.95 crores) on Crude Oil, SKO and LPG purchased from them.

Bond Mathematics 14

During the current year, investments in ―6.35% Oil Marketing Companies' GOI

Special Bonds 2024‖ amounting to Rs. 4603.73 crores have been reclassified from

‗Long Term Investments‘ to ‗Current Investments‘. Consequently, an amount of Rs.

756.88 crores has been provided in the books of accounts towards diminution in the

value for this investment.

The employee cost for the year 2009-10 is higher due to provision made for Rs.

318.25 crores towards revision in the salary for non-management staff, and

perquisites & retiral benefits for management employees.

Overall the emerging global scenario and economic slowdown has influenced HPCL to

greater extent. However consistent performance of the corporation and efficient management

has managed to maintain the profitability of the corporation at sustained levels.

HPCL still expects a wide road to be travelled towards achievement of its goal and target.

Bond Mathematics 15

BOND MARKET IN INDIA

The Bond Market in India with the liberalization has been transformed completely. The

opening up of the financial market at present has influenced several foreign investors holding

upto 30% of the financial in form of fixed income to invest in the bond market in India. The

bond market in India has diversified to a large extent and that is a huge contributor to the

stable growth of the economy. The bond market has immense potential in raising funds to

support the infrastructural development undertaken by the government and expansion plans

of the companies.

Sometimes the unavailability of funds become one of the major problems for the large

organization. The bond market in India plays an important role in fund raising for

developmental ventures. Bonds are issued and sold to the public for funds. Bonds are interest

bearing debt certificates. Bonds under the bond market in India may be issued by the large

private organizations and government company. The bond market in India has huge

opportunities for the market is still quite shallow. The equity market is more popular than the

bond market in India. At present the bond market has emerged into an important financial

sector.

The government securities market has witnessed significant transformation in the 1990s in

terms of market design. The most significant developments include introduction of auction-

based price determination for government securities, development of new instruments and

mechanisms for government borrowing as well as participation by new market participants,

increase in information dissemination on market borrowings and secondary market

transactions, screen based negotiations for trading, and the development of the yield curve for

government securities for marking-to-market portfolios of banks. During the last one decade,

RBI introduced the system of primary dealers (PDs) and satellite dealers (since discontinued

from December 2002), introduced delivery versus payment (DvP) in securities settlement,

expanded the number of players in the market with facility for non-competitive bidding in

auctions, and allowed wider participation in constituent Subsidiary General Ledger (SGL)

accounts. The government securities market also benefited from emergence of liquidity

arrangement through the Liquidity Adjustment Facility (LAF), expansion of the repo

markets, complete stoppage of automatic monetisation of deficits, and emergence of self

regulatory bodies, such as, the Primary Dealers Association of India (PDAI) and the Fixed

Income Money Markets and Derivatives Association (FIMMDA).Continuous reforms in the

G- Sec market are being undertaken for improving market design and liquidity.

Bond Mathematics 16

To enhance liquidity and efficiency, some important initiatives have been taken in the Indian

debt market such as:

introduction of repo/reverse repo operations in government securities to facilitate

participants of manage short term liquidity mismatches

operationalisation of Negotiated Dealing system (NDS), an automated electronic

trading platform

establishment of Clearing Corporation of India Ltd. (CCIL) for providing an efficient

and guaranteed settlement platform

introduction of G-secs in stock exchanges

introduction of Real time Gross Settlement System (RTGS) which addresses

settlement risk and facilitates liquidity management,

adoption of a modified Delivery-versus-Payment mode of settlement which provides

for net settlement of both funds and securities legs and

Announcement of an indicative auction calendar for Treasury Bills and Dated

Securities.

Central government securities: bonds and t-bills

The different types of bond market in India

Primary market:

•Issuance of securities through autions

•Issuance of securities with pre-announced coupon bonds

•Issuance of securities through tap sale

•Issuance of securities in conversion of maturing treasury bills/dated securities

Secondary markets:

•Trading on stock exchanges: NSE, BSE, OTCEI

•Most of the secondary market trades in government securities are negotiated between participants (Banks, FIs, PDs, MFs) having SGL accounts with RBI. These may be negotiated directly between counter parties or negotiated through brokers. NDS of RBI provides an electronic platform for negotiating trades in government securities. If a broker is involved, the trade is reported to the concerned exchange. Trades are also executed on electronic platform of the WDM segment of NSE. WDM segment of NSE provides trading and reporting facilities for government securities

•Repo and reverse repo

•Wholesale debt market

•Retail debt market

Corporate

bond

market

Municipal

bond

market

Governmen

t & agency

bond

market

Funding

bond

market

Mortgage

backed &

collateral

debt

obligation

bond

market

Bond Mathematics 17

Table 2.1

Market Segment Issuer Instruments

Government

securities

Central Government

Zero Coupon Bonds, Coupon

Bearing Bonds, Treasury

Bills, STRIPS

State Governments

Coupon Bearing Bonds

Public sector bonds Government Agencies / Statutory

Bodies

Govt. Guaranteed Bonds,

Debentures

Public Sector Units

PSU Bonds, Debentures,

Commercial Paper

Private sector

bonds

Corporates Debentures, Bonds,

Commercial Paper, Floating

Rate Bonds, Zero Coupon

Bonds, Inter-Corporate

Deposits

Banks Certificates of Deposits,

Debentures, Bonds

Financial Institutions Certificates of Deposits,

Bonds

The major reforms in the bond market in India

The system of auction introduced to sell the government securities

The introduction of delivery versus payment (DvP) system by the Reserve Bank of

India to nullify the risk of settlement in securities and assure the smooth functioning

of the securities delivery and payment

The computerization of the SGL

The launch of innovative products such as capital indexed bonds and zero coupon

bonds to attract more and more investors from the wider spectrum of the populace

Sophistication of the markets for bonds such as inflation indexed bonds

The development of the more and more primary dealers as creators of the

Government of India bonds market

The establishment of the a powerful regulatory system called the trade for trade

system by the Reserve Bank of India which stated that all deals are to be settled with

bonds and funds

A new segment called the Wholesale Debt Market (WDM) was established at the

NSE to report the trading volume of the Government of India bonds market

Issue of ad hoc treasury bills by the Government of India as a funding instrument was

abolished with the introduction of the Ways And Means agreement

Bond Mathematics 18

Participants and products in debt markets:

Table 2.2

Issuer Instrument Maturity Investors

Central government Dated securities 2-30 years RBI, Banks, Insurance

companies, Provident

Funds, Mutual Funds,

Individuals, PDs

Central government T-Bills 91/182/364 days RBI, Banks, Insurance

companies, Provident

Funds, Mutual Funds,

Individuals, PDs

State government Dated securities 5-13 years RBI, Banks, Insurance

companies, Provident

Funds, Mutual Funds,

Individuals, PDs

PSUs Bonds, Structured

Obligations

5-10 years Banks, Insurance

companies, Provident

Funds, Mutual Funds,

Individuals, Corporate

Corporate Debentures 1-12 years Banks, Corporate, Mutual

Funds

Corporate, PDs Commercial paper 7 days to 1 year Banks, Corporate Financial

institutions, Mutual funds,

Individuals, FIIs

Scheduled

commercial banks

Certificates of

deposit (CDs)

7 days to 1 year Banks, Corporations,

Individuals, companies,

Trusts, Funds, Associations,

FIs, NRIs Financial Institutions 1 year to 3 years

Scheduled

commercial banks

Bank Bonds 1-10 years Corporations, Individual

companies, Trusts, Funds,

Associations, FIs, NRIs

Municipal

Corporation

Municipal Bonds 0-7 years Banks, Corporations,

Individuals, Companies,

Trusts, Funds, Associations,

FIs, NRIs

Securities market and financial system

The securities market has two interdependent and inseparable segments, the new issues

(primary market) and the stock (secondary) market.

Primary market

The primary market provides the channel for sale of new securities from the actual

issuers to the primary investors based on their perception of the bond instrument.

Primary market provides opportunity to issuers of securities; government as well as

corporates, to raise resources to meet their requirements of investment and/or discharge some

obligation.

Bond Mathematics 19

They may issue the securities at face value, or at a discount/premium and these securities may

take a variety of forms such as equity, debt etc. They may issue the securities in domestic

market and/or international market. The primary market issuance is done either through

public issues or private placement. A public issue does not limit any entity in investing

while in private placement, the issuance is done to select people. In terms of the Companies

Act, 1956, an issue becomes public if it results in allotment to more than 50 persons. This

means an issue resulting in allotment to less than 50 persons is private placement. There are

two major types of issuers who issue securities. The corporate entities issue mainly debt and

equity instruments (shares, debentures, etc.), while the governments (central and state

governments) issue debt securities (dated securities, treasury bills).

The price signals, which subsume all information about the issuer and his business including

associated risk, generated in the secondary market, help the primary market in allocation of

funds.

Secondary market

Secondary market refers to a market where securities are traded after being initially

offered to the public in the primary market and/or listed on the Stock.

The secondary market enables participants who hold securities to adjust their holdings in

response to changes in their assessment of risk and return. They also sell securities for cash to

meet their liquidity needs. The secondary market has further two components, namely the

over-the-counter (OTC) market and the exchange-traded market. OTC is different from

the market place provided by the Over The Counter Exchange of India Limited. OTC markets

are essentially informal markets where trades are negotiated. Most of the trades in

government securities are in the OTC market. All the spot trades where securities are traded

for immediate delivery and payment take place in the OTC market. The exchanges do not

provide facility for spot trades in a strict sense. Closest to spot market is the cash market

where settlement takes place after some time. Trades taking place over a trading cycle, i.e. a

day under rolling settlement, are settled together after a certain time (currently 2 working

days). Trades executed on the leading exchange (National Stock Exchange of India Limited

(NSE) are cleared and settled by a clearing corporation which provides novation and

settlement guarantee.

Nearly 100% of the trades settled by delivery are settled in demat form. NSE also provides a

formal trading platform for trading of a wide range of debt securities including government

securities.

A variant of secondary market is the forward market, where securities are traded for future

delivery and payment. Pure forward is outside the formal market. The versions of forward in

formal market are futures and options. In futures market, standardised securities are traded

for future delivery and settlement. These futures can be on a basket of securities like an index

or an individual security. In case of options, securities are traded for conditional future

delivery. There are two types of options–a put option permits the owner to sell a security to

the writer of options at a predetermined price while a call option permits the owner to

purchase a security from the writer of the option at a predetermined price. These options can

also be on individual stocks or basket of stocks like index. Two exchanges, namely NSE and

the Bombay Stock Exchange, (BSE) provide trading of derivatives of securities.

The past few years in many ways have been remarkable for securities market in India. It has

grown exponentially as measured in terms of amount raised from the market, number

of stock exchanges and other intermediaries, the number of listed stocks, market

capitalisation, trading volumes and turnover on stock exchanges, and investor

population. Along with this growth, the profiles of the investors, issuers and intermediaries

Bond Mathematics 20

have change significantly. The market has witnessed fundamental institutional changes

resulting in drastic reduction in transaction costs and significant improvements in efficiency,

transparency and safety.

Reforms in the securities market, particularly the establishment and empowerment of SEBI,

market determined allocation of resources, screen based nation-wide trading,

dematerialisation and electronic transfer of securities, rolling settlement and ban on deferral

products, sophisticated risk management and derivatives trading, have greatly improved the

regulatory framework and efficiency of trading and settlement. Indian market is now

comparable to many developed markets in terms of a number of qualitative parameters.

Securities market & economic development

Three main sets of entities depend on securities market. While the corporate and governments

raise resources from the securities market to meet their obligations, the households invest

their savings in the securities.

Corporate Sector:

The 1990s witnessed emergence of the securities market as a major source of finance for

trade and industry. A growing number of companies are accessing the securities market rather

than depending on loans from FIs/banks. The corporate sector is increasingly depending on

external sources for meeting its funding requirements. There appears to be growing

preference for direct financing (equity and debt) to indirect financing (bank loan) within the

external sources.

The listing agreements have been amended recently requiring the companies to disclose

shareholding pattern on a quarterly basis. As per the shareholding pattern of companies listed

on NSE at end of March 2008, it is observed that on an average the promoters hold about

56.12% of total shares. Though the non-promoter holding is about 41.91%, Individuals held

only 13.07% and the institutional holding (FIIs, MFs, VCFs-Indian and Foreign) accounted

for 19.37%.

Governments:

Along with increase in fiscal deficits of the governments, the dependence on market

borrowings to finance fiscal deficits has increased over the years. During the year 1990-91,

the state governments and the central government financed nearly 14% and 18% respectively

of their fiscal deficit by market borrowing. In percentage terms, depend ence of the state

governments on market borrowing did not increase much during the decade 1991-2001.

However, their dependence on market borrowing has been increasing since then to reach 38%

during 2003-04. In case of central government, it increased to 73% by 2007-08, The central

government and the state governments now-a-days finance about three fourth and one fourth

of their fiscal deficits respectively through borrowings from the securities market.

Households:

According to RBI data, household sector accounted for 84.8% of gross domestic savings in

Fixed Income Investment instruments during 2006-07. They invested 55.7% of financial

savings in deposits, 24.2 % in insurance/provident funds, and 6.5% in securities market

including government securities, units of mutual funds and other securities (out of which

investment in Gilts has been 0.2%). Thus, the fixed income bearing instruments are the most

preferred assets of the household sector.

Bond Mathematics 21

Trading platforms for bonds

NSE

National Stock Exchange of India Limited (NSE) was given recognition as a stock exchange

in April 1993.

Objectives:

establishing a nationwide trading facility for all types of securities,

ensuring equal access to all investors all over the country through an appropriate

communication network,

providing a fair, efficient and transparent securities market using electronic trading

system,

enabling shorter settlement cycles and book entry settlements, and

Meeting the international benchmarks and standards.

Within a short span of life, above objectives have been realized and the Exchange has played

a leading role as a change agent in transforming the Indian Capital Markets to its present

form. NSE has set up infrastructure that serves as a role model for the securities industry in

terms of trading systems, clearing and settlement practices and procedures. The standards set

by NSE in terms of market practices, products, technology and service standards have

become industry benchmarks and are being replicated by other market participants. It

provides screen-based automated trading system with a high degree of transparency and equal

access to investors irrespective of l;geographical location. The high level of information

dissemination through on-line system has helped in integrating retail investors on a nation-

wide basis.

The Exchange currently operates three market segments, namely Capital Market

Segment, Wholesale Debt Market Segment and Futures and Options segment. NSE has

been playing the role of a catalytic agent in reforming the market in terms of microstructure

and market practices. Right from its inception, the exchange has adopted the purest form of

demutualised set up whereby the ownership, management and trading rights are in the hands

of three different sets of people. This has completely eliminated any conflict of interest and

helped NSE to aggressively pursue policies and practices within a public interest framework.

It has helped in shifting the trading platform from the trading hall in the premises of the

exchange to the computer terminals at the premises of the trading members located country-

wide and subsequently to the personal computers in the homes of investors and even to hand

held portable devices for the mobile investors. Settlement risks have been eliminated with

NSE‘s innovative endeavors in the area of clearing and settlement viz., reduction of

settlement cycle, professionalisation of the trading members, fine-tuned risk management

system, dematerialisation and electronic transfer of securities and establishment of clearing

corporation. As a consequence, the market today uses the state-of-art information technology

to provide an efficient and transparent trading, clearing and settlement mechanism.

NSE provides a trading platform for of all types of securities-equity and debt, corporate

and government and derivatives. On its recognition as a stock exchange under the

Securities Contracts (Regulation) Act, 1956 in April 1993, it commenced operations in the

Wholesale Debt Market (WDM) segment in June 1994, in the Capital Market (CM) segment

Bond Mathematics 22

in November 1994, and in Futures & Options (F&O) segment in June 2000. The Exchange

started providing trading in retail debt of Government Securities in January 2003.

NDS

The first step towards electronic bond trading in India was the introduction of the RBIs

Negotiated Dealing System in February 2002.

NDS, facilitates screen based negotiated dealing for secondary market transactions in

government securities and money market instruments, online reporting of transactions

in the instruments available on the NDS and dissemination of trade information to the

market. Government Securities (including T-bills), call money, notice/term money, repos in

eligible securities are available for negotiated dealing through NDS among the members.

NDS members concluding deals, in the telephone market in instruments available on NDS,

are required to report the deal on NDS system within 15 minutes of concluding the deal. NDS

interfaces with CCIL for settlement of government securities transactions for both outright

and repo trades done/reported by NDS members. Other instruments viz, call money,

notice/term money, commercial paper and certificate of deposits settle as per existing

settlement procedure.

Table 2.3

Bond Mathematics 23

With the objective of creating a broad-based and transparent market in government securities

and thereby enhancing liquidity in the system, the NDS was designed to provide:

Electronic bidding in primary market auctions (T-Bills, dated securities, state

government securities) by members,

Electronic bidding for OMO of RBI including repo auctions under LAF,

Screen based negotiated dealing system for secondary market operations,

Reporting of deals in government securities done among NDS members outside the

system (over telephone or using brokers of exchanges) for settlement,

Dissemination of trade information to NDS members,

Countrywide access of NDS through INFINET,

Electronic connectivity for settlement of trades in secondary market both for outright

and repos either through CCIL or directly through RBI, and Creation and maintenance

of basic data of instruments and members.

The functional scope of the NDS relating to trading includes:

giving/receiving a Quote,

placing a call and negotiation (with or without a reference to the quote),

entering the deals successfully negotiated, setting up preferred counterparty list and

exposure limits to the counterparties,

dissemination of on-line market information such as the last traded prices of

securities, volume of transactions, yield curve and information on live quotes,

interface with Securities Settlement System for facilitating settlement of deals done in

government securities and treasury bills

Facility for reporting on trades executed through the exchanges for information

dissemination and settlement in addition to deals done through NDS.

Figure 2.1

0 20 40 60 80 100

Aug/06

Nov/06

Feb/07

May/07

Aug/07

Nov/07

Feb/08

May/08

Aug/08

Nov/08

Feb/09

share of NDS call in total call volumes (%)

share of NDS call in total call volumes (%)

Bond Mathematics 24

Repo and reverse repo

Repo or Repurchase Agreements are short-term money market instruments. Repo is

nothing but collateralized borrowing and lending through sale/purchase operations in

debt instruments. Under a repo transaction, a holder of securities sells them to an investor

with an agreement to repurchase at a predetermined date and rate. In a typical repo

transaction, the counterparties agree to exchange securities and cash, with a simultaneous

agreement to reverse the transactions after a given period. To the lender of cash, the securities

lent by the borrower serves as the collateral; to the lender of securities, the cash borrowed by

the lender serves as the collateral. Repo thus represents a collateralized short term lending. A

reverse repo is the mirror image of a repo.

Banks and dealers use repos to finance inventories, to cover short positions, to create leverage

and to hedge or to speculate on interest rate movements. Investors such as mutual funds,

pension funds, insurance companies and corporate treasurers use repo markets to invest

surplus cash, to earn incremental returns on their portfolios or to raise cash for investments.

There are three types of repo, each with different costs and benefits that are reflected in the

repo rate and the haircut:

Figure 2.2

•the collateral is held on the balance sheet of the cash provider, granting immediate access in the event of default on the loan.

Bilateral repo:

•an agent stands between the security lender and cash provider and physically controls the securities offered as collateral.

Triparty repo:

•the security lender continues to hold the bond on their own balance sheet in a segregated account, raising the risk to the cash provider.

Hold-in-custody repo:

share in money market trading volumes, 2009

repo volume

call volume

CBLO volume

Call: Market in which brokers and dealers borrow

money to satisfy their credit needs, either to finance

their own inventory of securities or to cover their

customers' margin accounts.

CBLO: A money market instrument that represents an

obligation between a borrower and a lender as to the

terms and conditions of the loan. Collateralized

borrowing and lending obligations (CBLOs) are used

by those who have been phased out of or heavily

restricted in the interbank call money market.

Repo: For the party selling the security (and agreeing

to repurchase it in the future) it is a repo; for the party

on the other end of the transaction, (buying the security

and agreeing to sell in the future) it is a reverse

repurchase agreement.

Bond Mathematics 25

Wholesale Debt Market

NSE accounts for nearly 70 % of the market share in capital market and 98 % market share in

the derivatives market.

The Wholesale Debt Market segment provides the trading platform for trading of a

wide range of debt securities. Its product, which is now disseminated jointly with

FIMMDA, the FIMMDA NSE MIBID/MIBOR is used as a benchmark rate for majority of

deals struck for Interest Rate Swaps, Forwards Rate Agreements, Floating Rate Debentures

and Term Deposits in the country. Its ‗Zero Coupon Yield Curve‘ as well as NSE-VaR for

Fixed Income Securities have also become very popular for valuation of sovereign securities

across all maturities irrespective of its liquidity and facilitated the pricing of corporate papers

and GOI Bond Index.

Figure 2.3

NSEs Capital Market segment offers a fully automated screen based trading system, known

as the National Exchange for Automated Trading (NEAT) system, which operates on a strict

price/time priority. It enables members from across the country to trade simultaneously with

enormous ease and efficiency. Its Futures & Options segment provides trading of a wide

range of derivatives like Index Futures, Index Options, Stock Options and Stock Futures.

The Wholesale Debt Market segment deals in fixed income securities and is fast gaining

ground in an environment that has largely focussed on equities. The Wholesale Debt Market

(WDM) segment of the Exchange commenced operations on June 30, 1994. This provided

the first formal screen-based trading facility for the debt market in the country.

This segment provides trading facilities for a variety of debt instruments including

Government Securities, Treasury Bills and Bonds issued by Public Sector Undertakings/

Corporates/ Banks like Floating Rate Bonds, Zero Coupon Bonds, Commercial Papers,

Certificate of Deposits, Corporate Debentures, State Government loans, SLR and Non-SLR

Bonds issued by Financial Institutions, Units of Mutual Funds and Securitized debt by banks,

financial institutions, corporate bodies, trusts and others. Large investors and a high average

trade value characterize this segment. Till recently, the market was purely an informal market

with most of the trades directly negotiated and struck between various participants. The

commencement of this segment by NSE has brought about transparency and efficiency to the

debt market, along with effective monitoring and surveillance to the market.

Bond Mathematics 26

Retail Debt Market

Netting factor (%) Figure 2.4

With a view to encouraging wider participation of all classes of investors across the country

(including retail investors) in government securities, the Government, RBI and SEBI have

introduced trading in government securities for retail investors. Trading in this retail debt

market segment (RDM) on NSE has been introduced w.e.f. January 16, 2003.

Main participants in the retail debt market include mutual funds, provident funds, pension

funds, private trusts, state-level and district-level co-operative banks, housing finance

companies, NBFCs and RNBCs, corporate treasuries, Hindu Undivided Families (HUFs), and

individual investors.

The reasons why the retail debt market boomed were: 1995-96 saw the worst ever liquidity

crunch. The stock market plunged to its nadir, financial institutions were unable to disburse

sanctioned amounts, and the GDR route failed to bring in enough funds. To raise money,

industry needed a new instrument. It found one in retail debt. The old retail finance culture

tilted towards equity is poised to give way to a more equitable debt-equity ratio dictated by

financial prudence and market forces.

Conclusion:

The securities markets in India have witnessed several policy initiatives, which have refined

the market micro-structure, modernised operations and broadened investment choices for the

investors. The irregularities in the securities transactions in the last quarter of 2000-01,

hastened the introduction and implementation of several reforms. While a Joint Parliamentary

Committee was constituted to go into the irregularities and manipulations in all their

ramifications in all transactions relating to securities, decisions were taken to complete the

process of demutualisation and corporatisation of stock exchanges to separate ownership,

funds (%)

0

20

40

60

80

100

funds (%)

securities (%)

Bond Mathematics 27

management and trading rights on stock exchanges and to effect legislative changes for

investor protection, and to enhance the effectiveness of SEBI as the capital market regulator.

T+5 basis: introduced from July 2, 2001

T+3 basis: introduced from April 1, 2002

T+2 basis: introduced from April 1, 2003

All deferral products: banned from july2, 2002

1381 companies listed at NSE: March 2008

Derivative trading at NSE: June 12, 2000

Trading in index options: June 4, 2001

Trading in individual securities: July 2, 2001

Short term S&P CNX Nifty were introduced: January, 2008

long term S&P CNX Nifty were introduced: March 3, 2008

Due to rapid changes in volatility in the securities market from time to time, there was a need

felt for a measure of market volatility in the form of an index that would help the market

participants. NSE launched the India VIX, a volatility index based on the S&P CNX Nifty

Index Option prices. Volatility Index is a measure of market‘s expectation of volatility over

the near term.

SEBI allowed the direct market access (DMA): April 3, 2008.

Short sell and the facility for securities lending and borrowing scheme: April 21, 2008.

The Debt markets in India have also witnessed a series of reforms, beginning in the year

2001-02 which was quite eventful for debt markets in India, with implementation of several

important decisions like setting up of a clearing corporation for government securities, a

negotiated dealing system to facilitate transparent electronic bidding in auctions and

secondary market transactions on a real time basis and dematerialisation of debt instruments.

Further,

Adoption of modified Delivery-versus-Payment mode of settlement: March 2004

Securities was standardized to T+1 cycle: May 11, 2005

Order matching trading platform (NDS-OM) was introduced: August 2005

Short sale was permitted in G-secs: 2006

‗When issued‘ (WI) trading in Central Government Securities was introduced: 2006

Ensures safe settlement with Straight through Processing (STP)

Bond Mathematics 28

Bond basic concepts

Features:

Nominal, principal or face

amount — the amount on which

the issuer pays interest, and which,

most commonly, has to be repaid at

the end. Some structured bonds can

have a redemption amount which is

different to the face amount and

can be linked to performance of

particular assets such as a stock or

commodity index, foreign

exchange rate or a fund. This can

result in an investor receiving less

or more than his original

investment at maturity.

Issue price — the price at which

investors buy the bonds when they

are first issued, which will

typically be approximately equal to

the nominal amount. The net

proceeds that the issuer receives

are thus the issue price, less

issuance fees.

Maturity date — the date on

which the issuer has to repay the

nominal amount. As long as all

payments have been made, the

issuer has no more obligation to the

bond holders after the maturity

date. The length of time until the

maturity date is often referred to as

the term or tenor or maturity of a

bond. The maturity can be any

length of time, although debt

securities with a term of less than

one year are generally designated

money market instruments rather

than bonds. Most bonds have a

term of up to thirty years. Some

bonds have been issued with

maturities of up to one hundred

years, and some even do not

mature at all. In early 2005, a

market developed in euros for

bonds with a maturity of fifty

years. In the market for U.S.

Treasury securities, there are three

groups of bond maturities:

o short term (bills): maturities

up to one year;

o medium term (notes):

maturities between one and

ten years;

o long term (bonds):

maturities greater than ten

years.

Coupon — the interest rate that the

issuer pays to the bond holders.

Usually this rate is fixed

throughout the life of the bond. It

can also vary with a money market

index, such as LIBOR, or it can be

even more exotic. The name

coupon originates from the fact that

in the past, physical bonds were

issued which had coupons attached

to them. On coupon dates the bond

holder would give the coupon to a

bank in exchange for the interest

payment.

• Tax free bonds – public sector

companies in India are sometimes

permitted to issue bonds with tax-

free interest. In this case bond-

holder pays no tax on the interest

• Trustee – when a debenture issue

is made, a trustee is appointed

(usually an FI / bank). The trustee

is responsible to ensure that the

company fulfils its contractual

obligations

• Trust (bond) indenture or

Debenture trust deed – a complex

and lengthy legal agreement

between the company and the

debenture trustee, stating the

conditions under which a bond has

been issued, rights of debenture

holders, rights of the issuing

company, and responsibilities of

the trustee.

Bond Mathematics 29

• Debenture Redemption Reserve (DRR) – has to be created for the

redemption of all debentures with a

maturity period exceeding 18

months. The DRR must be equal to

atleast 50% of the amount of

redemption

Table 3.1

Kinds of bonds:

The following descriptions are not mutually exclusive, and more than one of them may apply

to a particular bond.

Zero-coupon bonds pay no regular interest. They are issued at a substantial discount

to par value, so that the interest is effectively rolled up to maturity (and usually taxed

as such). The bondholder receives the full principal amount on the redemption date.

An example of zero coupon bonds is Series E savings bonds issued by the U.S.

government. Zero-coupon bonds may be created from fixed rate bonds by a financial

institution separating "stripping off" the coupons from the principal. In other words,

MODIFIABLE INTOPARAMETERSCLASSIFICATION

BONDS

coupon

zero coupon

treasury strips

floating rate bonds

other variations

maturity

callable bonds

puttable bonds

convertible bonds

principalamortising

sinking fundasset based securities

Bond Mathematics 30

the separated coupons and the final principal payment of the bond may be traded

separately. See IO (Interest Only) and PO (Principal Only).

Strip bonds - Zero coupon bonds have a duration equal to the bond's time to

maturity, which makes them sensitive to any changes in the interest rates. Investment

banks or dealers may separate coupons from the principal of coupon bonds, which is

known as the residue, so that different investors may receive the principal and each of

the coupon payments. This creates a supply of new zero coupon bonds.

The coupons and residue are sold separately to investors. Each of these investments

then pays a single lump sum. This method of creating zero coupon bonds is known as

stripping and the contracts are known as strip bonds. "STRIPS" stands for Separate

Trading of Registered Interest and Principal Securities.

Fixed rate bonds have a coupon that remains constant throughout the life of the

bond.

Floating rate notes (FRNs) have a variable coupon that is linked to a reference rate

of interest, such as LIBOR or Euribor. For example the coupon may be defined as

three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically,

typically every one or three months.

Inflation linked bonds in which the principal amount and the interest payments are

indexed to inflation. The interest rate is normally lower than for fixed rate bonds with

a comparable maturity. However, as the principal amount grows, the payments

increase with inflation. The United Kingdom was the first sovereign issuer to issue

inflation linked Gilts in the 1980s. Treasury Inflation-Protected Securities (TIPS) and

I-bonds are examples of inflation linked bonds issued by the U.S. government.

Other indexed bonds, for example equity-linked notes and bonds indexed on a

business indicator (income, added value) or on a country's GDP.

Callable bonds: A bond which the issuer has the right to redeem prior to its maturity

date, under certain conditions. When issued, the bond will explain when it can be

redeemed and what the price will be. In most cases, the price will be slightly above

the par value for the bond and will increase the earlier the bond is called. A company

will often call a bond if it is paying a higher coupon than the current market interest

rates. Basically, the company can reissue the same bonds at a lower interest rate,

saving them some amount on all the coupon payments; this process is called

"refunding." Unfortunately, these are also the same circumstances in which the bonds

have the highest price; interest rates have decreased since the bonds were issued,

increasing the price. In many cases, the company will have the right to call the bonds

at a lower price than the market price. If a bond is called, the bondholder will be

notified by mail and have no choice in the matter. The bond will stop paying interest

shortly after the bond is called, so there is no reason to hold on to it. Companies also

typically advertise in major financial publications to notify bondholders. Generally,

callable bonds will carry something called call protection. This means that there is

some period of time during which the bond cannot be called. It is also called

redeemable bond, opposite of irredeemable bond or non-callable bond.

Bond Mathematics 31

Puttable bond or put bond is a combination of straight bond and embedded put

option. The holder of the puttable bond has the right, but not the obligation, to

demand early repayment of the principal. The put option is usually exercisable on

specified dates.

This type of bond protects investors: if interest rates rise after bond purchase, the

future value of coupon payments will become less valuable. Therefore, investors sell

bonds back to the issuer and may lend proceeds elsewhere at a higher rate.

Bondholders are ready to pay for such protection by accepting a lower yield relative

to that of a straight bond.

Of course, if an issuer has a severe liquidity crisis, it may be incapable of paying for

the bonds when the investors wish. The investors also cannot sell back the bond at any

time, rather specified dates. However, they would still be ahead of holders of non-

puttable bonds, who may have no more right than 'timely payment of interest and

principal' (which could perhaps be many years to get all their money back).

The price behaviour of puttable bonds is the opposite of that of a callable bond. Since

call option and put option are not mutually exclusive, a bond may have both options

embedded.

A debenture in corporate finance is a medium- to long-term debt instrument used by

large companies to borrow money. In some countries the term is used interchangeably

with bond, loan stock or note. Debentures are generally freely transferable by the

debenture holder. Debenture holders have no voting rights and the interest paid to

them is a charge against profit in the company's financial statements. In the United

States, debenture refers specifically to an unsecured corporate bond. However, in the

United Kingdom a debenture is usually secured. In Asia, if repayment is secured by a

charge over land, the loan document is called a mortgage; where repayment is secured

by a charge against other assets of the company, the document is called a debenture;

and where no security is involved, the document is called a note or 'unsecured deposit

note'.

Types:

1. Convertible debentures, which are convertible bonds or bonds that can be converted

into equity shares of the issuing company after a predetermined period of time.

"Convertibility" is a feature that corporations may add to the bonds they issue to make

them more attractive to buyers. In other words, it is a special feature that a corporate

bond may carry. As a result of the advantage a buyer gets from the ability to convert;

convertible bonds typically have lower interest rates than non-convertible corporate

bonds.

2. Non-convertible debentures, which are simply regular debentures, cannot be

converted into equity shares of the liable company. They are debentures without the

convertibility feature attached to them. As a result, they usually carry higher interest

rates than their convertible counterparts.

Call and Put Provision – provides an option to the issuing company to redeem the

debentures at a specified price before maturity. Call price may be more than the par /

face value, and this difference is called the Call Premium (In India, generally 5%). Put

Bond Mathematics 32

option is an option to the debenture holder to seek redemption at a specified time at a

specified price

Sinking fund provision is just a pool of money set aside by a corporation to help

repay a bond issue. Typically, bond agreements (called indentures) require a company

to make periodic interest payments to bondholders throughout the life of the bond,

and then repay the principal amount of the bond at the end of the bond's lifespan.

Amortising: Charges made against the interest received on a debt in order to offset a

premium paid for the debt. Thus, with each periodic payment, a debtor is not only

paying back interest, but also part of his or her premium. This leads to higher periodic

payments than in the case when only interest is paid out. However, a payment

schedule which includes premium amortization makes debt management easier,

especially if the principal is large. While paying just the interest each period will lead

to a low outflow of cash each month, the debtor might not save enough to pay the

principal. Thus, amortizing the premium each period also reduces the credit risk of the

debt, since the creditor gets some part of the principal each time period, as opposed to

allowing a debtor to forfeit on all of it at the maturity of the loan. Amortization of

premium is a common feature in cases when a person or company takes on a large

amount of debt at one time, such as a mortgage.

Asset-backed securities are bonds whose interest and principal payments are backed

by underlying cash flows from other assets. Examples of asset-backed securities are

mortgage-backed securities (MBS's), collateralized mortgage obligations (CMOs) and

collateralized debt obligations (CDOs).

Subordinated bonds are those that have a lower priority than other bonds of the

issuer in case of liquidation. In case of bankruptcy, there is a hierarchy of creditors.

First the liquidator is paid, then government taxes, etc. The first bond holders in line

to be paid are those holding what is called senior bonds. After they have been paid,

the subordinated bond holders are paid. As a result, the risk is higher. Therefore,

subordinated bonds usually have a lower credit rating than senior bonds. The main

examples of subordinated bonds can be found in bonds issued by banks, and asset-

backed securities. The latter are often issued in tranches. The senior tranches get paid

back first, the subordinated tranches later.

Perpetual bonds are also often called perpetuities or 'Perps'. They have no maturity

date. The most famous of these are the UK Consols, which are also known as

Treasury Annuities or Undated Treasuries. Some of these were issued back in 1888

and still trade today, although the amounts are now insignificant. Some ultra-long-

term bonds (sometimes a bond can last centuries: West Shore Railroad issued a bond

which matures in 2361 (i.e. 24th century)) are virtually perpetuities from a financial

point of view, with the current value of principal near zero.

Successive bonds are those where sureties are discharged and new sureties are taken,

the two sets of sureties become jointly liable for a breach of the bond which accrued

before discharge, and the right of contribution exists as between co-sureties. The new

bond relates back, and the two sets of sureties are jointly liable for a breach

committed prior to the second execution.

Bond Mathematics 33

Pricing factors

Interest rates change over time, based on a variety of factors, particularly base rates set by

central bank. If the coupon on the bond is lower than the prevailing interest rate, then this

pushes the price down, and conversely, high interest rates reduce the attractiveness of a given

coupon, and so reduce the price.

In buying a bond, one is in effect buying a set of cash flows, which are discounted according

to the buyers perception of how interest and exchange rates will move over its life.

Price determination in the debt markets The price of a bond in the markets is determined by the forces of demand and supply, as is

the case in any market. The price of a bond also depends on the changes in:

Economic conditions

General money market conditions, including the state of money supply in the

economy

Interest rates prevalent in the market and the rates of new issues

Future Interest Rate Expectations

Credit quality of the issuer

Note: There is, however, a theoretical underpinning to the determination of the price of the

bond based on the measure of the yield of the security.

Supply and demand affect prices, especially in the case of market participants which are

constrained in the set of investments they make. Insurance companies often have long term

liabilities that they wish to hedge, which requires low risk, predictable cash flows, such as

long dated government bonds.

Bond pricing

The cash flow of a fixed income product generally consists of several coupon payments over

the period of the bond's life, and repayment of the principal at the time of maturity. Since

these cash flows occur at several times in the future, the "Time Value of Money" approach is

used to find the "Present Value" of each cash flow. The sum of all the present values of the

bonds cash inflows of the bond is its theoretical value.

Price–Discounted present value of debt service on an individual maturity. Debt service is

calculated using the coupon and discounted at the yield.

As a result, price and yield move in opposite directions.

Bond Mathematics 34

• Yield – two types:

– Current yield: ratio of the annual interest payment to the CMP eg. If the

market price of a 12% Rs 1000 FV debenture is Rs 750, then current yield is

120/750 ie. 16%

– Yield to Maturity: takes into account the payments of interest and principal

over the life of the debenture. So it is the internal rate of return of the

debenture

Par bonds:

Coupon equals yield

Purchase price equals

principal amount

Discount bonds:

Coupon less than yield

Purchase price less than

principal amount

Premium bonds:

Coupon greater than yield

Purchase price greater than

principal amount

Bond Mathematics 35

Pricing a bond

The price of a bond is the present value of its expected cash flow(s).

The present value will be lower than the future value, as holding Rs100 next week is worth

less than holding Rs100 now. There are a number of possible reasons for this:

If inflation is high, the value will have eroded by the following week; if it remains in another

person‘s possession for a further week, there is a potential credit risk; and there is no

opportunity to invest the money until the following week, and therefore any potential return

is delayed.

The arithmetic assumes no credit risk or other (e.g. liquidity, tax) effects. It calculates the

price of a risk-free bond, and therefore would need to be adjusted for other factors.

Single Cash Flow

Calculating the future value of an investment: -

Starting from the simplest example, investing Rs100 for one period at 8% would give the

following return:

Return = 100 (1 + 8/100) = Rs108

In other words:-

FV = PV (1 + r)

where FV is the future value (i.e. cash flow expected in the future)

PV is the present value

r is the rate of return

Assuming the same rate of return, if the investment is made for two periods, then:-

FV = 100 (1 + 8/100)(1 + 8/100)

In other words:-

FV = PV (1 + r)2

And in general:

FV = PV (1 + r)n

where n is the number of periods invested, at a rate of return, r.If we want to calculate the

price (i.e present value) of a bond as a function of its future value, we can rearrange this

equation:- P = F/ (1+ r)n

where P is the price of the bond and is the same as the ‗present value‘. The future value is the

expected cash flow i.e. the payment at redemption n periods ahead.

Discount Rate

r is also referred to as the discount rate, i.e the rate of discount applied to the future payment

in order to ascertain the current price.

1/ (1+ r)n is the value of the discount function at period n. Multiplying the discount

function at period n by the cash flow expected at period n gives the value of the cash flow

today.

Relationship between discount rate and coupon rate: Discount rate less than the coupon

rate implies that the security is traded at a premium. Discount rate greater than the coupon

Bond Mathematics 36

rate implies that the security is traded at a discount. Discount rate equal to the coupon rate

implies that the security is traded at a par.

Multiple Cash Flow

In practice, most bonds have more than one cash flow and therefore each cash flow needs to

be discounted in order to find the present value (current price). This can be seen with another

simple example - a conventional bond, paying an annual coupon and the face value at

maturity. The price at issue is given as follows:

Where P = ‗dirty price‘

c = annual coupon

r i = % rate of return which is used in the ith period to discount the cash flow (in this

example, each period is one year)

R = redemption payment at time n

The above example shows that a different discount rate is used for each period (r r etc 1, 2, ).

Whilst this seems sensible, the more common practice in bond markets is to discount using a

redemption yield and discount all cash flows using this rate. In theory, each investor will

have a slightly different view of the rate of return required, as the opportunity cost of not

holding money now will be different, as will their views on, for example, future inflation,

appetite for risk, nature of liabilities, investment time horizon etc. The required yield should,

therefore, reflect these considerations. In practice, investors will determine what they

consider to be a fair yield for their own circumstances. They can then compute the

corresponding price and compare this to the market price before deciding whether – and how

much – to buy or sell.

Pricing a bond with a semi annual coupon follows the same principles as that of an annual

coupon. A ten year bond with semi annual coupons will have 20 periods (each of six months

maturity); and the price equation will be:

where c = coupon

y = Redemption Yield (in % on an annualised basis)

In general, the bond maths notation for expressing the price of a bond is given by:-

Where PV ( cf t) is the present value of the cash flow at time t

Bond Mathematics 37

Dirty prices and clean prices

When a bond is bought or sold midway through a coupon period, a certain amount of coupon

interest will have accrued. The coupon payment is always received by the person holding the

bond at the time of the coupon payment (as the bond will then be registered in his name).

Because he may not have held the bond throughout the coupon period, he will need to pay the

previous holder some ‗compensation‘ for the amount of interest which accrued during his

ownership. In order to calculate the accrued interest, we need to know the number of days in

the accrued interest period, the number of days in the coupon period, and the money amount

of the coupon payment. In most bond markets, accrued interest is calculated on the following

basis:-

Coupon interest x no. of days that have passed in coupon period

total no of days in the coupon period

Prices in the market are usually quoted on a clean basis (i.e. without accrued) but settled on a

dirty basis (i.e. with accrued).

Relationship between price and yield

There is a direct relationship between the price of a bond and its yield. The price is the

amount the investor will pay for the future cash flows; the yield is a measure of return o n

those future cash flows. Hence price will change in the opposite direction to the change in the

required yield. There are a number of different formulae for the relationship between price

and yield.

Looking at the price-yield relationship of a standard i.e. non-callable bond, the shape such as

below is seen: Figure 3.1

As the required yield increases,

the factor by which future cash

flows are discounted also

increases and therefore the

present value of the cash flow

decreases. Hence the price

decreases as yield increases.

Bond Mathematics 38

Money market yields

Money market yields are quoted on a different basis and therefore in order to compare short-

term bonds and money market instruments it is necessary to look at them on a comparable

basis.

Uses of Yield Curves and Yield Curve Theories

A yield curve is a graphical representation of the term structure of yields for a given market.

It attempts to show, for a set of bonds that have differing maturities but otherwise similar

characteristics, how the yield on a bond varies with its maturity.

Yield curves are therefore constructed from (as far as possible) a homogeneous group of

bonds: we would not construct a yield curve using both government and corporate securities,

given the different categories of risk.

Yield curves are used for a number of different purposes. For example, government

securities‘ yield curves demonstrate the tightness (and expected tightness) of monetary

policy; allow cross-country comparisons; assist pricing of new issues; assess relative value

between bonds; allow one to derive implied forward rates; and help traders/investors

understand risk. As there are a number of different types of yield curve that can be

constructed, different ones are used for different purposes.

There are various theories of the yield curve, which attempt to explain the shape of the curve,

depending on, inter alia, investors‘ preferences/views:

Preferred Habitat (again investors have a maturity preference, but will shift from their

preferred maturity if the increase in yield is deemed sufficient compensation to do so). These

are all demand-based; supply-based factors include government policy (fiscal position, views

on risk, views on optimal portfolio etc).

• risk premia increase with time so, other things being equal, one would expect to see a rising yield curve

Liquidity Preference Theory

• forward rates govern the curve - these are simply expectations of future spot rates and do not take into account risk premia

Pure Expectations Hypothesis

• the yield curve depends on supply and demand in different sectors and each sector of the yield curve is only loosely connected to others

Segmented Markets Hypothesis

Bond Mathematics 39

Flat Yield

This is the simplest measure of yield (also known as current yield, interest yield, income

yield or running yield). It is given by:-

Flat yield = Coupon rate (%) x 100

Clean price

This is a very crude measure. It does not take into account accrued interest; nor does it take

into account capital gain/loss (i.e. it assumes prices will not change over the holding period);

nor does it recognise the time value of money. It can only sensibly be used as a measure of

value when the term to maturity is very long (as coupon income will be more dominant in the

total return than capital gain/loss).

Simple Yield

This is a slightly more sophisticated measure of return than flat yield, which takes into

account capital gain, although it assumes that it accrues in a linear fashion over the life of the

bond. However, it does not allow for compounding of interest; nor does it take into account

accrued interest as it uses the clean price in the calculation.

Simple Yield = [Coupon Rate + (100 - clean price) x 100] x clean price

Years to maturity

Obviously a bond in its final coupon period is, in terms of its cash flows, directly comparable

with a money market instrument. In this case simple interest yield calculations are used (ie no

need to discount at a compounded rate).

Redemption Yield (Yield to Maturity)

A redemption yield is that rate of interest at which the total discounted values of future

payments of income and capital equate to its price in the market.

Where P = dirty price (ie including accrued interest)

c = coupon

R = redemption payment

n = no of periods

y = redemption yield

It is also referred to as the Internal Rate of Return or the Yield to Maturity.

When quoting a yield for a bond, it is the redemption yield that is normally used, as all the

factors contributing to the return can be captured in a single number. The redemption yield

takes into account the time value of money by using the discount function: each cash flow is

discounted to give its net present value. Obviously a near coupon is worth more than a far

coupon because it can be reinvested but also, in nearly all cases (except for negative interest

rates), the real coupon amount will be greater the sooner it is received.

Bond Mathematics 40

However, this measure gives only the potential return. The limitations of using the

redemption yield to discount future cash flows are:

The redemption yield assumes that a bond is held to maturity. (i.e. the redemption

yield is only achieved if a bond is held to maturity);

It discounts each cash flow at the same rate;

It assumes a bondholder can reinvest all coupons received at the same rate i.e. the

redemption yield rate (i.e. assumes a flat yield curve), whereas in reality coupons will

be reinvested at the market rate prevailing at the time they are received;

The discount rate used for a cash flow in, say, three years‘ time from a 5 year bond

will be different from the rate used to discount the three year payment on a 10 year

bond.

The redemption yield curve suffers from these limitations. The curve is used for simple

analysis, and can also be used when there are insufficient bonds available to construct a more

sophisticated yield curve.

Net redemption yields

The above equation has looked at gross returns, but bond investors are likely to be subject to

tax: possibly both on income and capital gain.

The net redemption yield, if taxed on both coupon and redemption payments, is given by:-

P = Dirty price

c = Coupon

R = Redemption payment

r net = net redemption yield

This is a simple example. In practice, if withholding tax is imposed the equation is not so

simple as a percentage of tax will be imposed at source with the remainder being accounted

for after the payment has been received. As tax rules can materially affect the price of bonds,

their effects need to be taken into account in any yield curve modelling process in order to

avoid distortions in the estimated yield curve.

Spot rate:

Each spot rate is the specific zero coupon yield related to that maturity and therefore gives a

more accurate rate of discount at that maturity than the redemption yield. It also means that

assumptions on reinvestment rates are not necessary. Spot rates take into account current spot

rates, expectations of future spot rates, expected inflation, liquidity premia and risk premia.

Bond Mathematics 41

Various curves

Zero

coupon

curve

Forward

zero

coupon

yield

Par yield

P = Price (dirty)

c = Coupons

n = Number of periods

f i = ith period forward rate for one further period (i.e. the one-year rate in i years‘ time)

y is the par yield

z i is the rate of return at maturity i (i.e. the spot rates at maturity i)

R is the redemption payment

zero coupon curve

•The curve resulting from the zero coupon (spot) rates is often referred to as the ‘Term Structure of Interest Rates’; the plot of spot rates of varying maturities against those maturities. This curve gives an unambiguous relationship between yield and maturity.

•advantages: 1.finding relatively misvalued bonds, valuing swap portfolios and valuing new bonds at auction. 2. it discounts all payments at the appropriate rate, provides accurate present values and does not need to make reinvestment rate assumptions.

forward zero coupon yield

•the forward rate is such that an investor will be indifferent to investing for two years or investing for one year and then rolling over the proceeds for a further year.

•(1+r1)(1+f1,2)=(1+r2)2

•advantages: 1. the implied forward rate equals the spot rate that prevails in the future. 2. the liquidity premium hypothesis suggests that the implied forward rate equals the expected future spot rate plus a risk premium.

•real implied forward rates: (1+ nominal forward) = (1+ real forward)[(1+ inflation forward)]

•Nominal forward = real forward + inflation forward

par yield

•The par yield is a hypothetical yield. It is the coupon that a bond would have in order to be priced at par, using the zero coupon rates in the discount function. This can be seen from the following equation.

Bond Mathematics 42

Relationship between curves

The par, zero and forward curves are related. Figure 3.2

In an environment of upward sloping yield curves, the zero curve will sit above the par curve

because the yield on a coupon bearing bond is affected by the fact that some income is

received before the maturity date, and the rate used to discount these payments will be lower

than the rate used to discount the payment at maturity. Also, as the forward curve gives

marginal rates derived from the zero curve, it will be above the zero curve. The opposite is

true in a downward sloping yield curve environment.

Bond Mathematics 43

Debt management products (calculations)

Treasury bill

Treasury bills are short term discount instruments (usually of less than one year maturity) and

therefore are useful funding instruments in the early stages of a debt market when investors

do not want to lock in to long maturities. They are issued at a discount to their face value and

have one payment on redemption. The advantages of Treasury bills are that they are simple,

tradeable in the secondary market and are government credit risk.

However, because of their short maturities they need to be rolled over frequently, meaning

that the future cost of debt servicing is uncertain. Also, shorter maturities result in a very

short government yield curve: a longer yield curve is obviously beneficial to developing

financial markets as it provides information and allows pricing of new products.

There are a number of issues to take into account before issuing Treasury bills. For example,

how will they be issued and to whom? If the government wishes to reach a wide range of

investors, including the retail sector, then this could mean that the government is a competitor

to the banking system, which could actually stifle market development (although this will, of

course, provide the private sector with a benchmark). Also, if issuing to the retail investor, an

auction process may prove difficult to understand and to price correctly. The government

may need to think of other distribution channels (e.g. banks themselves, although they may

charge a fee for this, making issuance expensive). A further consideration is minimum

denomination (smaller if the retail investor is to be attracted) and whether to set a minimum

price.

In more developed countries, Treasury bills are also used for monetary management

purposes. The increase (decrease) of Treasury bill issuance will affect the liquidity position of

banks by withdrawing (increasing) liquidity from the market.

Calculation of Treasury bill yield/price

The discount rate is described as the return on a discount instrument compared with its

redemption value (also referred to as par or face value) in the future. It is given by the

following formula:

Treasury

bills

Conventi

onal

bonds

Converti

ble

bonds

Floating

rate

bonds

Zero

coupon

bonds &

strips

Bond Mathematics 44

For the yield and price on a treasury bill, the following formulae are used:

Or, simply, face value minus discount. It is important to note that the discount rate (often

referred to as the rate of interest) and the yield on a Treasury bill are not the same. The

discount rate is a market convention. Using the discount rate gave an easy calculation from

rate to price and a fairly close approximation to true yield.

Conventional bonds

A 'conventional' bond is one that has a series of fixed coupons and a redemption payment at

maturity. Coupons are usually paid annually or semi-annually.

A conventional bond, e.g. ‗6% 2005‘, is a bond that has a 6% coupon and a repayment date in

2005. The prospectus will detail the terms and conditions applied to the bond, including the

dates of the coupon payments and the final maturity of the bond. For example, if the above

bond has semi-annual coupon payments, then for each Rs100 of the bond purchased, the

holder will receive Rs3 coupon payment every six months up to the maturity of the bond.

This is a ‗standard‘ bond issued by governments, although it does not necessarily suit all

investors, not least because the receipt of regular coupon payments introduces reinvestment

risk, as coupons need to be re-invested at rates of interest that are uncertain at the time of

purchasing the bond.

The conventional bond can be thought of as offering a nominal yield that takes into account

the real yield and anticipated inflation. The real yield required can be thought of as the sum of

two components: a real return and a risk premium reflecting the uncertainty of inflation12.

This can be written as:

where N is the nominal return

R is the real yield

Pe is the expected inflation rate over the period the bond is held

RP is the risk premium

The risk premium is the amount the market demands for unanticipated inflation. It is difficult

to exactly price the risk premium, but if we know the market‘s view of inflation expectations

then it is possible to have some idea of the size of the risk premium, by looking at the

difference between nominal and real rates in the market.

Obviously in countries with high inflation, the risk premium will be greater, given the

uncertainty. But the very act of issuing index-linked debt (suggesting that the government is

confident of reducing inflation) may help reduce the risk premium built into conventional

debt. In countries where inflation has been low and stable, investors will feel more certain

that the value of their investment will not be eroded and therefore will demand a lower risk

premium.

Bond Mathematics 45

Floating Rate Bonds

A floating rate bond (―floater‖) has a coupon linked to some short-term reference rate e.g. an

interbank rate. It is usually issued at a margin (or spread) above this reference rate. This

ensures that the investor gets a current rate of return, whilst (usually) locking in his

investment for a longer period than this. The price of a floater depends on the spread above or

below the reference rate and any restrictions that may be imposed on the resetting of the

coupon (e.g. if it has caps or floors) plus the usual credit and liquidity considerations.

The rate is usually a market rate.

An obvious measure of value to the issuer is the return given above or below the market

index or benchmark rate (i.e. LIBID, in the UK‘s case). These margin values (if below

market norm) indicate the better credit quality of government issuance.

Corporates also issue floaters and may pay a small margin over a reference rate, depending

on their credit quality.

Because the value of the coupon in the future is not known, it is not possible to determine the

future cash flows. This means that a redemption yield measure cannot be calculated for a

floating-rate bond.

simple margin

The simple margin uses a comparison withthe 'index' and calculates it throughout thelife of the bond. However, it does not takeinto account the current yield effect on theprice of the floater, since coupon paymentsreceived are given the same weight if theprice is above or below par. Also, thediscount/premium of the bond is amortisedto par in a straight line over the life of thefloater rather than discounted at aconstantly compounded rate. To overcomethese drawbacks, one can use a discountedmargin.

discount margin

This measure attempts to discount allcash flows and to therefore give someidea of the Net Present Value of eachcash flow. However, it makes anassumption that LIBOR will remain thesame throughout the life of the bond. Amore sophisticated technique would beto construct a projected LIBOR curve,and therefore discount at a moreaccurate rate. However, as the maturityof the floater is usually short term (andthat this method also necessitatessome form of assumption) it is notusually employed.

Bond Mathematics 46

Convertible bonds

Some governments have issued convertible bonds. These normally offer the investor the

option of converting from one type of security to another, e.g. short to long-term or vice

versa, fixed to floating or indexed. In issuing them the government hopes that the investor

will pay a premium for the option, and that this premium will more than offset the cost to the

government if the option is exercised.

Equity-convertible bonds may be useful if the government is planning to privatise certain

assets, such as state-owned enterprises, and wishes to obtain some of the value of the

privatisation proceeds early. For instance, a security convertible into an equity could be sold

for 100, redeemable in 2 years time or convertible at the investor‘s option into, say, 10 shares

of a certain enterprise which is to be privatised. If the estimated market value of that

enterprise rises during the period, the investor will exercise his option and convert; and if its

value has risen much faster than expected, the opportunity cost to the government - through

selling the option to buy at a fixed price - may outweigh the premium received for selling the

option. If the enterprise‘s estimated value falls, the investor will buy the shares more cheaply

in the market and not exercise the option. If it turns out, for whatever reason, that the

enterprise is not privatised, some compensation may need to be paid to the investor.

Zero coupon bonds and strips

A zero coupon bond has only one (redemption) payment and is sold at a discount to its face

value. In pricing the bond, it will be discounted at its spot rate i.e. the rate of discount specific

to that maturity.

The price of a zero coupon bond is therefore given by:-

Where R is the redemption payment

Zi is the spot rate relating to period i: (the maturity of the bond)

The discount rate used (Zi ) can be thought as the redemption yield of a zero-coupon bond.

The zero coupon bond has a number of advantages over its conventional counterpart. The

zero coupon bond consists of a single point cash flow and therefore, by purchasing a selection

of such bonds, the investor can build up the cash flows he wants, rather than receiving - and

possibly needing to reinvest - frequent coupons.

This allows far more efficient asset/liability management and eliminates reinvestment risk.

Zero coupon bonds can therefore be used as building blocks from which to construct financial

instruments such as annuities or deferred payment bonds.

A zero coupon bond also has greater duration (for the same maturity) and greater convexity

(for the same duration) than coupon bonds. This makes them potentially attractive to a large

part of the market; for example, traders, who trade on risk and are looking for increased

volatility; investors who want long duration assets; fund managers who are seeking to match

the duration of their portfolios and have, for example, long duration pension liabilities.

Bond Mathematics 47

Strips

A strip is a zero coupon bond, derived from separating a standard coupon-bearing bond into

its constituent interest and principal payments that can then be separately held or traded as

zero-coupon bonds22. For example, a 5-year bond with an annual coupon could be separated

into six zero-coupon bonds, five representing the cash flows arising from coupons and one

relating to the principal repayment. For Rs100 nominal worth of this bond with, say, a 6%

coupon paying on 1 June each year the following cash flow would result from stripping:- Figure 3.3

Thus, stripping would leave five zero coupon bonds of Rs6.00 (nominal), maturing on 1 June

each year and one zero coupon bond of Rs100 (nominal) maturing on 1 June in five years

time.

As most strip markets trade on yield rather than price, it follows that a standard yield formula

should be used to calculate settlement value, to avoid any disputes.

where: P = Price per Rs100 nominal of the strip

y = Gross redemption yield (decimal) ie if the yield is 8% then y = 0.08

r = Exact number of days from the settlement/issue date to the next quasi coupon date

(the quasi coupon date is a date on which a coupon would be due were the bond

coupon bearing than the shortest strip)

s = Exact number of days in the quasi-coupon period in which the settlement date falls

n = Number of remaining quasi-coupon period after the current period

So far we have seen the relationship between various factors for determination of the bond

price. These factors plat eminent role in decision making process of bond management.

The Objective of the project ―Effective bond management‖ requires us to have basic concept

of the above discussed aspects to understand its impact on the bond prices thereby the

effective bond management.

Bond Mathematics 48

Measures of risk and return

Duration

Duration is a measure of:

Duration is a measure of interest rate risk exposure of a financial asset and it measures

the sensitivity of a security‘s price to interest rate.

It is the approximate percentage change in the value of a fixed income security that

will result from a 1% change in interest rates.

There were various ways of measuring the ‗riskiness‘ of the bond, and perhaps the

most common was the time to maturity. All other things being equal, the longer the

bond the greater the volatility of its price (risk). However, this measure only takes into

account the final payment (not any other cash flows), does not take into account the

time value of money and therefore does not give an accurate comparison of relative

‗riskiness‘ across bonds.

Duration is a weighted average of the maturity of all the income streams from a bond

or portfolio of bonds. It allows us to compare the riskiness of bonds with different

maturities, coupons etc.

Investors use duration to measure the volatility of the bond. The higher the duration

(the longer an investor needs to wait for the bulk of the payments), the more its price

will drop as interest rates go up.

It can be said that duration is how long it would take for you to get your money back

if a rise in interest rates causes your bond portfolio to drop in value.

A zero coupon bond duration equals maturity. When there are interim payments,

duration will be less than maturity. For a deep discount bond, a point is reached at

which duration actually decreases as maturity increases.

a• the approximate sensitivity of a bond's value to interest rate changes

b• a bond's lifetime that accounts for the entire pattern of cash flows over the life of the bond

(i.e the weighted average time to recovery of all interest payemnts plus principal)

c• the number of years needed to fully recover the purchase price of a bond given the present

value of its cash flows

d• the price volatility of a zero coupon bond with that number of years to maturity

e• the number for each bond that summarizes 3 key factorsthat affect the sensitivity of a

bond's price to a change in interest rates: maturity, coupon and YTM

Bond Mathematics 49

In mathematical terms, this is expressed as:-

Macauley Duration =

Where D= duration of the bond

CF= interest or principal payment at time t

t= time period in which principal or coupon interest is paid

n= number of periods to maturity

i= the yield to maturity (market rate interest rate)

Modified duration

For a 5-year bond with a 10% annual coupon, imagine that the shaded area represents the net

present value of each cash flow; and that the shaded areas are weights along a seesaw. The

Macauley duration is the point at which the seesaw balances.

The relation between Macauley duration, price

and yield is given by: (1)

Where,

ΔP / Δy = Proportional change in price with respect to change in yield

P = price

y/fc = yield/frequency of coupon payments per annum

D = Macauley duration

From Macauley duration, we can express Modified Duration, which is a measure of the price

sensitivity of a bond:

Substituting Modified Duration into equation (1) above and slightly rearranging gives:-

Figure 4.1

Bond Mathematics 50

Modified Duration describes the sensitivity of a price of a bond to small changes in its yield –

and is often referred to as the volatility of the bond. It captures, in a single number, how a

bond‘s maturity and coupon affect its exposure to interest rate risk. It provides a measure of

percentage price volatility, not absolute price volatility and is a measure of the percentage

price volatility of the full (i.e. dirty) price. For any small change in yield, the resulting

percentage change in price can be found by multiplying yield change by Modified Duration

as shown below:-

% change in price = - (Modified Duration) x yield change (in basis points) (3)

The negative sign in the equation is, of course, necessary as price moves in the opposite

direction to yield. Figure 4.2

However, there are limitations in using Modified

Duration in predicting the price/yield

relationship. It is only valid for small changes in

yield; for parallel shifts in the yield curve; and

for small time horizons. The reasons for these

limitations can be more clearly seen from the

graph below. The price/yield relationship

estimated from the Modified Duration of a bond

is linear (shown by the tangent to the curve at Po)

whilst the actual price/yield relationship is a

curve. There is therefore an error when using

Modified Duration to estimate price movements

Duration is used as a way to ensure that a goal to be met in the future will not be affected by

interest rate changes. The ―duration gap‖ is a well respected subject among banks.

DG = DA – (MVL/MVA)* DL

DG = duration gap (which you want it to be zero if you are duration matching)

DA = duration of the assets

MVL = market value of the liabilities

MVA = market value of the assets

DL = duration of the liabilities

Bond Mathematics 51

Table 4.1

Convexity

duration α1/coupon

• higher coupon lead to quicker recovery of the bond's value, resulting inshorter duration

duration α 1/YTM

• higher yields produce lower present values of cash receipts received far out in time, thereby diminishing their relative value

duration αmaturity

• duration expands with time to maturity but at a decreasing rate

percentage price change

• the percentage change in a bond's price is approximately equal to negative modified duration times the change in yield

price change

• the change in a bond's price is approximately equal to percentage change in prices times the original price

estimated price

• the estimated bond's price is approximately equal to percentage changes in prices times original price plus the original price

a• Convexity is a measure of the sensitivity of a bond‘s price to changes in

yield.

b•It is also a measure of the degree to which a bond‘s price-yield curve departs from a straight line. This characteristic affects the estimates of a bond‘s price volatility.

c

•Modified Duration indicates how the price of a bond varies for small changes in yield. However, for large changes in yield, two bonds that have the same yield and the same Modified Duration can behave quite differently. This is due to the ‗error‘ in using modified duration. This error is explained by convexity

d•It is the second derivative of a bond‘s price with respect to yield. The convexity of a bond is a measure of the curvature of its price/yield relationship.

Bond Mathematics 52

where,

C= cash flow at time t

t= period when the cash flow is expected to be received

T= number of periods until maturity

m= number of periods per year

r= discount rate per period

The approximate percentage price change due to convexity is:-

% price change = ½ x convexity x (percentage yield change)2

Figure 4.3

The diagram shows the modified duration line relating to bonds AB and CD (i.e. a tangent to

the price/yield curve at point P1). The price/yield curve for bond CD is clearly more convex

than that for bond AB.

This means that, at this point, for any given change of yield, bond CD will outperform AB.

However, over time, the price yield curves will shift and therefore bond CD will not always

outperform. Table 4.2

convexity α1/coupon

• the curvature relationship betwen yield and prices is greater for lower yields

convexity α 1/YTM

• the curavture is flatter for higher coupon bonds than lower coupon bonds

convexity αduration

• the curavture is greater for longer maturity bonds and therefore for long duration bonds

Bond Mathematics 53

Comparison of two bonds Figure 4.4

Bond 1 is more convex than Bond 2

Price falls at a slower rate as yield increases

Bond Convexity is defined formally as the degree to which the duration changes

when the yield to maturity changes. It can be used to account for the inaccuracies

of the Modified Duration approximation. On top of that, if we assume two bonds

will provide the same duration and yield then the bond with the greater convexity

will be less affected by interest rate change. This can be easily visualized from the

diagram above where the greater the "curvature", the lesser the price drop when

interest rate increase.

But at the same time, if the interest rate increases, the expected yield increases and

it can be observed in the above diagram that higher the convexity higher the price

increases than the lesser convexity.

This shows that convexity has double advantage because when interest rates fall,

bond prices rise very high comparatively when interest rates rise, the prices fall

less.

percentage price change

•the percentage change in a bond's price associated with the convexity is approximately equal to the product of negative modified duration and change in yield plus the product of 1/2, convexity and change in yield

price change

• the change in a bond's price is approximately equal to percentage change in prices times price for both duration and convexity

estimated price

• the change in a bond's price is approximately equal to percentage change in prices times price for both duration and convexity plus original price

Bond 1 _________

Bond 2 ------------

Bond Mathematics 54

Immunization

It is the strategy of protecting a portfolio against interest rate risk (i.e both price and

reinvestment risk).

Zero coupon bond immunization: buy zero coupon bonds that match the desired

future cash flows. (prefect immunization)

Coupon bond immunization: the process of balancing bond holdings such that price

and reinvestment risks cancel out. (approximate immunization)

Components of interest rate risk

Price risk: risk resulting from the inverse relationship between bond prices and

required rates of return

Reinvestment rate risk: risk resulting from the uncertainty about the rate at which

future coupon income can be reinvested.

The two components of interest rate risk move in opposite directions. Hence, the strategy

would be to purchase a bond with duration equal to the investment horizon.

Bond Mathematics 55

Exposure of bonds to HPCL

Background of bonds in HPCL

HPCL issues NCD‘s (Debentures) and receives oil bonds. Bonds is a way to finance long

term money requirements for the new projects. It is obligatory for HPCL to receive oil bonds

from the government. As government subsidises oil prices, public sector companies have to

face losses. Instead of paying back the losses to the company in cash, government issues oil

bonds.

Now, it is the company‘s task to manage these bonds for profits ( selling and issueing). Also

called management of baond portfolio. This can be done in a very efficeint manner by

implementing a tool called bond mathematics (which we have studied so far).

Balance sheet 2008 – 2009

Table 5.1

Bond Mathematics 56

As seen from the above investments, the modes of investments of HPCL are coupon bonds,

convertible debentures, equity shares and NCDs. HPCL received 3 oil special bonds of

8108.35 Cr from the government of India which are mandatory.

It bought convertible debenture from Prize Petroleum Co. Limited of 15 Cr. Also bought

debentures from Shell MRPL Aviation Fuels and from Petronet India ltd of 18.54 Cr.

As seen in the current investments, HPCL has been continuously been compensated by oil

bonds in form of subsidy financing by GOI. In the year 2008-09 total outstanding oil bonds in

hand of HPCL stood at 4594.64 Cr against 10 special oil bonds of 5682.39 Cr in year 2007-

08. This shows that the oil prices in 2009 have been sold by HPCL in the market to manage

working capital requirement. All these bonds in this year have been discussed in detail below.

But as an overall picture, HPCL has made huge investments of 12827.38 Cr in 2009 as

against 5869.17 Cr in 2008. Most of their investments are bond based which are secured and

gives fixed income. They are playing safe and hence their returns might be low due to low

risk but their volumes are high this year comparitively.

Bond Mathematics 57

Analysis

MTM statement of oil bonds issued by govt. Of India as on 01-June -2009

7.47 % Oil Marketing Companies' GOI Special Bonds, 2012

Face

value

Issue

date Maturity date coupon rate Yield Year to maturity

100

07-Mar-

2006 07-Mar-12 7.74% 7.5648% 6

All these calculations have been performed on HPCL. Yield, price, duration of the bonds can

be calculated directly on excel. It has inbuilt formulae:

PRICE(seetlement, maturity, rate, yld, redemption, frequency, [basis]);

YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis]);

DURATION(settlement, maturity, coupon, yld,frequency, [basis]);

But for calculation of convexity, there is no inbuilt formula, hence the following method as

the formula for convexity is 1/(P(1+y)2) ∑ [CF/(1+y)

2 (t

2+t)]

A B

Period CF

Discounted

flows t^2 + t a*b

1

7.74 3.72 2 7.45

2

7.74 3.86 6 23.18

3

7.74 3.86 12 46.43

4

7.74 3.86 20 77.39

5

7.74 3.86 30 116.09

6

107.74 53.86 42 2262.53

Sum 2533.12

1/(P((1+y)^2)) 0.0086

Convexity 21.89

Duration 4.91

% change in bond price

6.03

for 1% change in yield

Bond Mathematics 58

The percentage change in bond price is calculated by (-D x Δy) + (o.5 x convexity x Δy2).

The rupee change in bond price can be calculate by multiplying current bond price with the

percentage change in bond price.

As seen from the above bond, the yield is just above coupon rate, hence the bond price is

trading at discount price of Rs99.75. The curve has less curvature which indicates less

sensitivity in the bond prices due to the yield changes. Hence the observed convexity and the

duration is also less. There is only 6.03% change in prices for 1% change in yield. This is

obvious as the time to maturity is just 6 years which is the major factor for price volatility.

0

50

100

150

0 5 10 15

price yield curve

price yield curve

Bond Mathematics 59

7.61 % Oil Marketing Companies' GOI Special Bonds, 2015

Face

value

Issue

date Maturity date coupon rate Yield time to maturity

100

07-Mar-

2006 07-Mar-15 7.61% 8.1467% 9

A B

Period CF

Discounted

flows t^2 + t a*b

1

7.61 3.65

2 7.31

2

7.61 3.79

6 22.79

3

7.61 3.80

12 45.65

4

7.61 3.80

20 76.09

5

7.61 3.80

30 114.14

6

7.61 3.80

42 159.80

7

7.61 3.80 56 213.08

8

7.61 3.80 72 273.96

9

107.61 53.80 90 4842.45

sum 5755.31

% change in bond price

17.97

for 1% change in yield

1/(P((1+y)^2))

0.0086

convexity

49.21

Duration 6.62

0

50

100

150

200

0 5 10 15

price yield curve

price yield curve

Bond Mathematics 60

The above bond is better than the previous bond in terms of yield or returns, hence the bond

is traded at a discount price of Rs 97.55. The good curvature to the price yield curve, average

duration and moderate convexity. For 1% change in yield, the price of this bond fluctuates to

17.97%.

Bond Mathematics 61

6.35 % Oil Marketing Companies' GOI Special Bonds, 2024

Face

value

Issue

date Maturity date coupon rate Yield time to maturity

100

23-Dec-

2008 07-Mar-15 6.35% 6.3495% 16

A B

Period CF

Discounted

flows t^2 + t a*b

1

6.35 3.07 2 6.15

2

6.35 3.17 6 19.03

3

6.35 3.17 12 38.09

4

6.35 3.17 20 63.49

5

6.35 3.17 30 95.24

6

6.35 3.17 42 133.34

7

6.35 3.175 56 177.8

8

6.35 3.175 72 228.6

9

6.35 3.175 90 285.75

10

6.35 3.175 110 349.25

11

6.35 3.175 132 419.1

12

6.35 3.175 156 495.3

13

6.35 3.175 182 577.85

14

6.35 3.175 210 666.75

15

6.35 3.175 240 762

16

106.35 53.175 272 14463.6

Sum 18781.38

Bond Mathematics 62

1/(P((1+y)^2))

0.0088

convexity

166.06

duration 5.13

This bond has maturity of 16 years but its yield being almost equal to the coupon rate, the

price in the market remains same. The curavture is less and but its duration convexity is high

and hence for 1% change in yield there is 77.9% change in prices.

0

50

100

150

0 5 10 15

price yield curve

price yield curve

% change in bond price

77.90

for 1% change in yield

Bond Mathematics 63

a b

Period CF

Discounted

flows t^2 + t a*b

1

6.90 3.33 2 6.66

2

6.90 3.44 6 20.67

3

6.90 3.44 12 41.39

4

6.90 3.44 20 68.99

5

6.90 3.44 30 103.49

6

6.90 3.44 42 144.89

7

6.90 3.45 56 193.2

8 6.90 3.45 72 248.4

9

6.90 3.45 90 310.5

10

6.90 3.45 110 379.5

11

6.90 3.45 132 455.4

12

6.90 3.45 156 538.2

13

6.90 3.45 182 627.9

14

6.90 3.45 210 724.5

15

6.90 3.45 240 828

16

6.90 3.45 272 938.4

17

106.90 53.45 306 16355.7

sum 21985.84

6.90 % Oil Marketing Companies' GOI Special Bonds, 2026

Face

value

Issue

date Maturity date coupon rate Yield time to maturity

100

04-Feb-

2009 04-Feb-26 6.90% 6.8986% 17

Bond Mathematics 64

1/(P((1+y)^2))

0.0088

convexity

192.40

duration 10.26

This bond has very good curvature and time to maturity and hence has high duration and

convexity. Therefore, the change in yield by 1%, has 85.94% change in its prices. It is very

sensitive.

0

50

100

150

200

250

0 5 10 15

price yield curve

price yield curve

% change in bond price

85.94

for 1% change in yield

Bond Mathematics 65

8.00 % Oil Marketing Companies' GOI Special Bonds, 2026

Face

value

Issue

date Maturity date coupon rate Yield time to maturity

100

23-Mar-

2009 23-Mar-26 8.00% 7.9980% 17

a b

Period CF

Discounted

flows t^2 + t a*b

1

8.00 3.84 2 7.69

2

8.00 3.99 6 23.96

3

8.00 3.99 12 47.99

4

8.00 3.99 20 79.99

5

8.00 3.99 30 119.99

6

8.00 3.99 42 167.99

7

8.00 3.99 56 224

8

8.00 4 72 288

9

8.00 4 90 360

10

8.00 4 110 440

11

8.00 4 132 528

12

8.00 4 156 624

13

8.00 4 182 728

14 8.00 4 210 840

15

8.00 4 240 960

16

8.00 4 272 1088

17

108.00 54 306 16524

sum 23051.65

Bond Mathematics 66

1/(P((1+y)^2))

0.0086

Convexity

197.64

Duration 9.57

This bond too has high curvature and high time to maturity due to which its convexity and

duration are high making it sensitive. Change in yield by 1% has impact on prices by 89.24%.

As on June 1. 2009, the yield being equal to the coupon rate, the bond price remains same as

the face value.

0

50

100

150

200

250

0 5 10 15

price yield curve

price yield curve

% change in bond price

89.24

for 1% change in yield

Bond Mathematics 67

8.20 % Oil Marketing Companies' GOI Special Bonds, 2024

Face

value

Issue

date Maturity date coupon rate Yield time to maturity

100

15-Sep-

2009 15-Sep-24 8.20% 8.1977% 15

a b

Period CF

Discounted

flows t^2 + t a*b

1

8.20 3.93 2 7.87

2

8.20 4.09 6 24.55

3

8.20 4.09 12 49.19

4

8.20 4.09 20 81.99

5

8.20 4.09 30 122.99

6

8.20 4.09 42 172.19

7

8.20 4.09 56 229.6

8

8.20 4.1 72 295.2

9

8.20 4.1 90 369

10

8.20 4.1 110 451

11

8.20 4.1 132 541.2

12

8.20 4.1 156 639.6

13

8.20 4.1 182 746.2

14

8.20 4.1 210 861

15

108.20 54.1 240 12984

sum 17575.63

Bond Mathematics 68

This bond too has good curvature and time to maturity and hence good convexity and

duration. It is sensitive for about 66.17% in prices for a change in 1% of yield. The yield on

june 1, 2009 remains the same as coupon, hence the bond price is neither discounted nor

premium.

Convexity of all bonds

Figure 5.1

Comparing convexity of all the bonds, it can be said that bonds with coupon rates 6.9%, 8%

and 8.2% have high curavature indicating high sensitivity. In these bonds, if the yield

decreases, the prices increase highly but at the same time if the yield increases, the prices

decrease less comparitively. HPCL being the investor, this is an advantage to it.

0

50

100

150

200

250

0 5 10 15

price yield curve

price yield curve

0

25

50

75

100

125

150

175

200

225

0 5 10 15

7.47%, 2012

7.61%, 2015

6.35%, 2024

6.9%, 2026

8%, 2026

8.2%, 2024

% change in bond price

66.17

for 1% change in yield

1/(P((1+y)^2))

0.0085

Convexity

150.13

Duration 8.89

Bond Mathematics 69

HPCL has lately started issuing NCDs in the market. The present bonds in the market are

discussed below:

HINDUSTAN PETROLEUM

CORP LTD N/A S&P 12-Apr-2010 ISIN:INE094A07038, LOCAL CODE:PTHPCL137.70%

Oil and Gas - Oil and Gas Fixed:Plain Vanilla Fixed Coupon

Issuance Details Bond Issued

Issue Date / Price / Yield 12-Apr-2010

Issue Spread: -- (--)

Original Issue Amount: 10,00,00,00,000 INR

Total Issue Amount: 10,00,00,00,000 INR

Total Price to Public:

INR

Announcement Date: 12-Apr-2010

Auction Date: --

MTN: No

Underwriters:

Name Type Amount

CITIBANK NA Joint Lead Manager

AXIS BANK LTD Joint Lead Manager

SBI CAPITAL MARKETS LTD Joint Lead Manager

STANDARD CHARTERED BANK (INDIA BRANCH) Joint Lead Manager

Principal / Coupon Information

Maturity Date: 12-Apr-2013 100

Principal / Coupon Currency: INR / INR

Amount Outstanding: 10,000,000,000 INR

Coupon Type / Frequency: Fixed:Plain Vanilla Fixed Coupon / Annually

Current Coupon / Next Pay Date: 7.7000 12-Apr-2011

Coupon Formula: --

Dated / First / Final Coupon: 12-Apr-2010 12-Apr-2011 12-Apr-2012

Irregular Coupon: None

Cumulative Dividend: --

Ratings

Rating Source Date Rating Watch Code

Credit Information Svce of India 12-Apr-2010 AAA --

Moody's Long-term Issue Credit

Rating 12-Apr-2010 N/A --

Standard & Poor's 12-Apr-2010 N/A --

7.7 % fixed plain vanilla bond, HPCL 2013

Bond Mathematics 70

Face value Issue date Maturity date coupon rate Yield Year to maturity

100 12-Apr-2010 12-Apr-13 7.70% 7.5333% 3

A B

Period CF

Discounted

flows t^2 + t a*b

1

7.70 3.71 2 7.42

2

7.70 3.84 6 23.06

3

107.70 53.84 12 646.16

Sum 676.65

1/(P((1+y)^2)) 0.0086

Convexity 5.85

Duration 2.73

As seen the yield is 7.533, less than the coupon rate 7.7. It is an advantage to HPCL as it has

to pay less interest rate to the receiver of the bond. The time to maturity is just 3 years and

hence its duration and convexity are low. For a change in yield by 1%, there is only 0.19%

change in price. Hence an advantage as an issuer.

0

20

40

60

80

100

120

140

0 5 10 15

price yield curve

price yield curve

% change in bond

price

0.19

for 1% change in

yield

Bond Mathematics 71

7.35 % fixed plain vanilla bond, HPCL 2012

HINDUSTAN PETROLEUM

CORP LTD N/A S&P 04-Dec-2009 ISIN:INE094A07020, LOCAL CODE:PTHPCL127.35

Oil and Gas - Oil and Gas Fixed:Plain Vanilla Fixed Coupon

Issuance Details Asset Backed Security Issued

Issue Date / Price / Yield 04-Dec-2009

Issue Spread: -- (--)

Original Issue Amount: 5,00,00,00,000 INR

Total Issue Amount: 5,00,00,00,000 INR

Total Price to Public:

INR

Announcement Date: --

Auction Date: --

MTN: No

Underwriters:

Name Type Amount

CITIBANK NA Lead Underwriter or Manager

SBI CAPITAL MARKETS LTD Joint Lead Manager

STANDARD CHARTERED BANK (INDIA BRANCH) Bookrunner

Principal / Coupon Information

Maturity Date: 04-Dec-2012 100

Principal / Coupon Currency: INR / INR

Amount Outstanding: 5,000,000,000 INR

Coupon Type / Frequency: Fixed:Plain Vanilla Fixed Coupon / Semiannually

Current Coupon / Next Pay Date: 7.3500

Coupon Formula: --

Dated / First / Final Coupon: 04-Dec-2009 04-Jun-2010 04-Jun-2011

Irregular Coupon: Last

Cumulative Dividend: --

Ratings

Rating Source Date Rating Watch Code

Credit Information Svce of India 04-Dec-2009 AAA --

Moody's Long-term Issue Credit

Rating 04-Dec-2009 N/A --

Standard & Poor's 04-Dec-2009 N/A --

Face value Issue date Maturity date coupon rate Yield Year to maturity

100 04-Dec-2009 04-Dec-12 7.35% 7.2454% 3

Bond Mathematics 72

A B

Period CF

Discounted

flows t^2 + t a*b

1

7.35 3.54 2 7.09

2

7.35 3.67 6 22.02

3

107.35 53.67 12 644.06

Sum 673.18

1/(P((1+y)^2)) 0.0087

convexity 5.85

duration 2.74

Even this NCD has low yield of 7.2454 adding an advantage to the issuer. The curvature is

less depicting less convexity. Duration is ought to be low as the time to maturity is just 3

years.

0

20

40

60

80

100

120

140

0 5 10 15

price yield curve

price yield curve

% change in bond

price

0.18

for 1% change in

yield

Bond Mathematics 73

Study of yield: for NCD/ Oil bond

We have seen oil bonds and NCDs have 3 basic elements, irrespective of the issuer and the

investor. i.e

1. Coupon

2. Tenor

3. Face value

To consider the appriopriate time of sale and issuance, the issuer has to understand the

relation between above three components. The price of bond (oil bond) from the side of

issuer depends on the yield expectation of the market. So, to ensure appriopriate time for sale

of oil bond , the study of yield takes utmost importance. The yields are determined by similar

government securities of same tenor and relevant spreads are added as per the market appetite

and interest.

For the study of appriopriate timing for sale of oil bond and its yield discovery, we have

taken following bond:

8.00 % Oil Marketing Companies' GOI Special Bonds, 2026

Face

value

Issue

date Maturity date coupon rate Yield time to maturity

100

23-Mar-

2009 23-Mar-26 8.00%

17

Indicative yields of G-secs

14 years G-sec with maturity of 22-jun-2024 with yield of 8.265

15 years G-sec with maturity of 02-aug-2027 with yield of 8.232

Interpolating the above G-sec: 8.265+ (8.232-8.265)/38* 22= 8.246

so we have derived equivalent yield from the relevant benchmark and considering the market

expectations spreads are added to the benchmark yield to get the price. For similar bond,

spread cn be presumed at 50 basis point. So effective yield becomes 8.746.

To ensure accurate timing of the sale, we have to predict the movement of benchmarks. The

recent movement of benchmarks is as shown below:

Bond Mathematics 74

Figure5.2

Based on our above study the price of above bond comes to Rs96.39. Studying the graph and

selling the same at appriopriate time at a yield of 7.4%, the price should come to Rs99.87.

The technical analysis shows that it has an upward but has a tendency to fall due to following

reasons. During this quarter, 7.4% seems to be dropped the least and this area has to be

tapped for good profits. As seen, the maximum peaks touched are 8.2%, 8% and 7.8% in the

recent quarter. So keeping this in mind, we can estimate that yields would not rise too high

unless extreme market conditions. 7.4% is the best yield for the sale of bond only for this

quarter. According to me, this is not the right time for sale, HPCL should wait for the next

quarter as the yields might fall further to make the necessary decision.

Bond Mathematics 75

Determination of Benchmark

Table 5.2

Observing the indicative yields of the above G- sec, the following yields of the bonds can be

predicted:

Table 5.3

Description of Oil Bonds Issue Date Maturity

Date

Nearest G-

sec

considered

Interpolation Benchm

ark

7.47 % Oil Marketing

Companies' GOI Special

Bonds, 2012

07-Mar-2006

07-Mar-12

2 jun, 11 :

5.699

3 sep, 12:

6.816

5.699 + (6.816-

5.699)/14*9

6.417

7.61 % Oil Marketing

Companies' GOI Special

Bonds, 2015

07-Mar-2006

07-Mar-15

20 oct, 14:

7.166

14 jun, 15:

7.37

7.166 + (7.37-

7.166)/8*5

7.2935

6.35 % Oil Marketing

Companies' GOI Special

Bonds, 2024

23-Dec-2008

23-Dec-24

22 jun, 24:

8.265

02 aug, 27:

8.232

8.265 + (8.232-

8.265)/38*22

8.246

6.90 % Oil Marketing

Companies' GOI Special

Bonds, 2026

04-Feb-2009

04-Feb-26

22 jun, 24:

8.265

02 aug, 27:

8.232

8.265 + (8.232-

8.265)/38*22

8.246

8.00 % Oil Marketing

Companies' GOI Special

Bonds, 2026

23-Mar-2009

23-Mar-26

22 jun, 24:

8.265

02 aug, 27:

8.232

8.265 + (8.232-

8.265)/38*22

8.246

8.20 % Oil Marketing

Companies' GOI Special

Bonds, 2024

15-Sep-2009

15-Sep-24

22 jun, 24:

8.265

02 aug, 27:

8.232

8.265 + (8.232-

8.265)/38*22

8.246

Bond Mathematics 76

We have seen all oil bonds are benchmarked to G- secs for determination of its yield. Since,

the maturity of G- secs are not same as of oil bonds, we use mathematical tools to interpolate

G- secs of nearer maturity to get benchmark for similar oil bonds. Specimen of the

benchmark of government securities as on 19-07-10 is shown in table 5.2. Based on the same

principle we have calculated the indicative yiled for al ol bonds. Spread factors are market

determined and to be considered based on the market indications.

Conclusion

We have seen HPCL, a fortune 500 company has wide presence in bond market in form of

Oil Bonds and Non Convertible debentures. The investments of HPCL have major impact on

the financials of the corporation. Hence it is of top most priority to manage the fixed

income securities effectively.

As seen, bonds play a major role in funding projects and a good source of income. Hence,

most of the companies opt for bond portfolios and its management. HPCL is no different and

it has also entered into bond management. Managing, analysing and predicting bonds is not a

difficult task. Bonds can be very well managed with the tool ‗bond mathematics‘.

Mathematics is one of the keys to understanding the bond market. Grasping the concepts that

underlie the bond market is the crucial task. Bond market maths can be reduced to a few key

concepts: compounding and discounting; accrued interest; running yields; redemption yields;

and spreads. Armed with knowledge of these concept and hefty amount of common sense,

finding an undervalued bond in which to invest becomes less of a lottery.

Studying bond yields, maturity, duration and convexity gives a clearer picture whether to buy

that particular bond or not. At same time, what is the appropriate timing for the sale of bonds

and the price at which it should be sold can also be determined. Such factors are crucial to

make profits and to gain smart income.

Research Methodology: An in-depth investigation of the industry conventions for calculating

price and yield applied to plain vanilla bonds, including the exploration of implicit

assumptions and interpretation of resulting numbers.

We have further seen that bonds are sensitive to various market factors and its effective

management can increase the profitability of the corporations. The advanced mathematical

tools provide effective methods to systematically analyse the bonds and times its sale or

issuance in the primary as well as secondary market.