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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
Bond Mathematics 2
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
Bond Mathematics 4
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
Bond Mathematics 5
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
Bond Mathematics 6
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.