Characteristics and Pricing of Government Bonds
Government bonds are fixed income securities issued by the Government of India
(GOI). Government bonds have the following characteristics:
Face Value, maturity date, coupon, coupon frequency and coupon dates. An example of a GOI bond
is given below.
Nomenclature: 8.40% 2024 GOI
Maturity date: 28-Jul-2024
Issue date: 28-Jul-2014
Coupon: 8.40%
Coupon frequency: Semi annual
Coupon dates: 28th November, 28th July every year until maturity.
The bonds are dematerialized and can be held in Demat form or as a book entry in the SGL
(Securities General Ledger).
Government bonds have maturities ranging from one year to 30 years. The coupon is predominantly
fixed i.e. the coupon rate is fixed for the entire tenure of the bonds. There are also floating rate
bonds where the coupon rate changes along with change in the benchmark interest rate, which is
usually the yield on the 364 days Treasury bill.
Pricing of Government Bonds
Government bond are priced on the present value of future cash flows basis. The points to note on
pricing the government bonds are that the basis of calculating accrued interest is 30/360 and
interest is semi annual.
Example 1: What is the price of 8.40% 2024 bond that is trading at a semi annual yield of 8.25%?
The price of a bond is equal to the present value of future cash flows. The price of 8.79% 2021 bond
is
P= (8.40/2)/ ((1+8.25/2)) ^ (1) + (8.40/2)/ ((1+8.25/2)) ^ (2) + ............- (8.40/2)/ ((1+8.25/2)) ^ (20).
Solving the equation above gives the answer of Rs 101.00.
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P is the price of the bond, 8.40/2 is the half yearly interest paid on the bond (8.40% on face value
of Rs 100), 8.25/2 is the yield on the bond quoted in semi-annual terms, (1,2 to 20) is the time period
for discounting the cash flows.
Example 2: What is the yield at which the 8.40% 2024 bond is trading when the price is Rs 98?
The same equation in example 1 is used for calculating the yield.
98= (8.40/2)/ ((1+r/2)) ^ (1) + (8.40/2)/ ((1+r/2)) ^ (2) + .........(8.40/2)/ ((1+r/2)) ^ (20).
Solving for r in the equation above gives the answer of 8.7035%.
Excel Functions
The following excel functions are used for calculating the price and yield of GOI bonds.
Yield= Yield (settlement, maturity, rate, price, redemption, frequency, basis).
Price= Price (settlement, maturity, rate, yield, redemption, frequency, basis).
Settlement value is the date of payment for purchase or sale, maturity is the maturity date of the
bond, rate is the coupon rate, price/yield is the market price/yield, redemption value is Rs 100,
frequency is 2 and basis is 0.
Example 3: What is the yield of the 8.40% 2024 bond, maturing on the 28th July 2024, trading at a
price of Rs 104 with a settlement date of 8thof September 2014? Use yield function to solve.
=Yield (8th September 2014, 28th July 2024, 8.40%, 104,100,2,0) = 7.81%.
Settlement of Bond Purchase/Sales
Government bonds are traded actively in the secondary market and the settlement dates for trades
are on a T+1 basis i.e. settlements take place the next working day. Settlements fall between coupon
payment dates that are semi annual and given this in-between coupon payment dates settlements,
the buyer has to pay the seller accrued interest.
Accrued Interest
Nomenclature: 8.40% 2024 GOI
Maturity date: 28-Jul-2024
Issue date: 28-Jul-2014
Coupon: 8.40%
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Registered Office: 13/701 NRI Complex, Nerul, Navi Mumbai - 400706. Mobile: +919819770641 E-mail: [email protected]
Coupon frequency: Semi annual
Coupon dates: 28th January, 28th July every year until maturity.
Government bonds are traded everyday and settlement is on a T+1 basis i.e bonds bought or sold
today will be settled the next working day. We learnt about bond pricing in the last tutorial and in
this tutorial we will learn about the settlement process by taking an example of a transaction in a
government bond.
Settlement of Government Bond Transaction
Bank A sells GOI 8.40% 2024 bond to Bank B on the 23rd of August 2014. One bond was sold at a
yield of 8.20% or price of Rs 101.33 and the face value of the bond sold was Rs 100. What will Bank
B pay to Bank A for the bond on the settlement date.
Transaction: Bank A sells 8.40% 2021 GOI to Bank B
Transaction date: 23/8/2014
Face Value: Rs 100
Number of bonds sold: 1
Transaction yield: 8.25%
Transaction Price: Rs 101.33
Settlement date: 24/8/2014
Transaction value
Bank B has to pay Bank A the following.
Purchase price of Rs 101.33 for 1 bond of face value Rs 100 = Rs 101.33 = (1*101.33 ).
Accrued Interest From The Last Interest Payment Date:
8.40% 2024 Bond is issued on 28th July 2014 then The number of days elapsed between 28th July
2014 to 23rd August 2014 is as follows- using a 30/360 day count convention.
August: 2 days ( Number of days between 30th July and 28th July). A 30/360 day count convention
implies that all months of the year have 30 days irrespective of the actual number of days in a
month. August: 23 (Number of days between August 23rd and August 1st).
Total number of days for calculating accrued interest = 2+23= 25.
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Registered Office: 13/701 NRI Complex, Nerul, Navi Mumbai - 400706. Mobile: +919819770641 E-mail: [email protected]
Accrued interest payable at 8.40% for 25 days for 1 bond of face value of Rs 100=
8.40%*100*(25/360)= Rs 0.5833
Total consideration = Purchase price plus accrued interest= Rs 101.33+ Rs 0.5833 = Rs 101.9133.
The purchase price is the clean price and the purchase price plus accrued interest is the dirty price in
bond terminology.
Accrued Interest Can Also Be Calculated Using Excel Formula Which Is As Follows:
ACCRINT (Issue, First Interest, Settlement, Rate, Par, Frequency, Basis)
Issue: 28th July 2014(issue date of bond)
First Interest: 28th January 2015 (first interest payment date)
Settlement: 24th August 2014
Rate: 8.40% (coupon rate)
Par: 100 (face value)
Frequency: 2 (semi annual)
Basis: 0 (day count convention is 30/360)
How to use G-sec calculator
Zephyr Financial Publishers Pvt Ltd.
Registered Office: 13/701 NRI Complex, Nerul, Navi Mumbai - 400706. Mobile: +919819770641 E-mail: [email protected]
Consider image given above.First enter government security data given in row number 1 (Security
specification),2 (Coupon) and 3 (Maturity date),16 (Settlement date) .
Calculation of Yield of bond:
To calculate yield of bond, enter given price in row number 6 and row 7 will give you the yield
corresponding to the price. Please look at red circular region. Here given price is 104.062 and yield
calculated is 7.7959%. The bond details have to be input to get the required yield.
Calculation of Price of bond:
To calculate price of bond, enter given yield in row number 12 and row 13 will give you the
corresponding calculated price. Please look at black circular region. Here given yield is 7.4521 and
price calculated is 106.482. The bond details have to be input to get the required price.
Zephyr Financial Publishers Pvt Ltd.
Registered Office: 13/701 NRI Complex, Nerul, Navi Mumbai - 400706. Mobile: +919819770641 E-mail: [email protected]