Fixed Income Knowledge Series 2. Characteristics and Pricing of Government Bonds

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1 Fixed Income Knowledge Series 2 Characteristics and Pricing of Government Bonds Government bonds are fixed income securities issued by the Government of India (GOI). The total outstanding bonds issued by the government as of 31st March 2012 is Rs 27 lakh crores. 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: 8.79% 2021 GOI Maturity date: 8th November 2021 Issue date: 8th November 2011 Coupon: 8.79% Coupon frequency: Semi annual Coupon dates: 8th November, 8th May 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. 1

2 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 semiannual. Example 1: What is the price of 8.79% 2021 bond that is trading at a semiannual yield of 8.60%? The price of a bond is equal to the present value of future cash flows. The price of 8.79% 2021 bond is P= (8.79/2)/ ((1+8.6/2)) ^ (1) + (8.79/2)/ ((1+8.6/2)) ^ (2) + - (8.79/2)/ ((1+8.6/2)) ^ (20). Solving the equation above gives the answer of Rs P is the price of the bond, 8.79/2 is the half yearly interest paid on the bond (8.79% on face value of Rs 100), 8.6/2 is the yield on the bond quoted in semiannual terms, (1, 2 42) is the time period for discounting the cash flows. Example 2: What is the yield at which the 8.79% 2021 bond is trading when the price is Rs 98? The same equation in example 1 is used for calculating the yield. 98= (8.79/2)/ ((1+r/2)) ^ (1) + (8.79/2)/ ((1+r/2)) ^ (2) + (8.79/2)/ ((1+r/2)) ^ (20). Solving for r in the equation above gives the answer of 8.96%. Excel Functions 2

3 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 8.79% 2021 bond, maturing on the 8th of November 2021, trading at a price of Rs 104 with a settlement date of 8th of May 2021? Use yield function to solve. =Yield (8th May 2012, 8th Nov 2021, 8.79%, 104, 100, 2, 0) = 8.45%. 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 semiannual and given this in-between coupon payment dates settlements, the buyer has to pay the seller accrued interest. Accrued Interest Nomenclature: 8.79% 2021 GOI Maturity date: 8th November 2021 Issue date: 8th November

4 Coupon: 8.79% Coupon frequency: Semi annual Coupon dates: 8th November, 8th May every year until maturity. Government bonds are traded every day 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 8.79% 2021 bond to Bank B on the 23rd of June One bond was sold at a yield of 8% or price of Rs 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 8.79% 2021 GOI to Bank B Transaction date: 23/6/2012 Face Value: Rs 100 Number of bonds sold: 1 Transaction yield: 8% Transaction Price: Rs Settlement date: 24/6/2012 Transaction value 4

5 Bank B has to pay Bank A the following. Purchase price of Rs for 1 bond of face value Rs 100 = Rs (1*105.13). Accrued Interest From The Last Interest Payment Date: The last interest payment date was on the 8th of May The number of days elapsed between 8th May 2012 to 23rd June 2012 is as follows- using a 30/360 day count convention. May: 22 days (Number of days between 30th May and 8th May). A 30/365 day count convention implies that all months of the year have 30 days irrespective of the actual number of days in a month. June: 23 (Number of days between June 23rd and June 1st). Total number of days for calculating accrued interest = 22+23= 55. Accrued interest payable at 8.79% for 55 days for 1 bond of face value of Rs 100= 8.79%*100*(55/365)= Rs 1.34 Total consideration = Purchase price plus accrued interest= Rs Rs 1.34 = Rs 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: 5

6 ACCRINT (Issue, First Interest, Settlement, Rate, Par, Frequency, Basis) Issue: 8th November 2011(issue date of bond) First Interest: 8th May 2012 (first interest payment date) Settlement: 24th June 2012 Rate: 8.79% (coupon rate) Par: 100 (face value) Frequency: 2 (semiannual) Basis: 0 (day count convention is 30/360) 6

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