Bond value calculation based on a desired Rate of interest

Interest Rates and Bond Yields
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Video transcript - [Instructor] Let's say that you agree to lend me some money.

Bond Valuation

And you say, no, no, you want some interest. And I say, how much interest? This is how much I'm going to have to pay back. Let me write this down. This is borrow. This is what I'm going to have to pay back. And so this interest rate, that just the face value of how much more I'm gonna have to pay back, this is known as the nominal interest rate. Nominal interest rate. And we can compare this to the real interest rate. And you might say, why do we need some other type of interest rate?

And you might guess why that is the case. Because of inflation. Within the shorter maturity range say years , it would be safer to buy securities which are liquid, that is, securities which trade in relatively larger volumes in the market. The coupon rate of the security is equally important for the investor as it affects the total return from the security.

Where and Whom to buy from- In terms of transparent pricing, the NDS-OM is the safest because it is a live and anonymous platform where the trades are disseminated as they are struck and where counterparties to the trades are not revealed. In case, the trades are conducted on the telephone market, it would be safe to trade directly with a bank or a PD. Wherever a broker is used, the settlement should not happen through the broker. Trades should not be directly executed with any counterparties other than a bank, PD or a financial institution, to minimize the risk of getting adverse prices.

To be sure of prices, only liquid securities may be chosen for purchase. A safer alternative for investors with small requirements is to buy under the primary auctions conducted by RBI through the non-competitive route. Since there are bond auctions almost every week, purchases can be considered to coincide with the auctions. Please see question 14 for details on ascertaining the prices of the G-Secs. The price of a G-Sec, like other financial instruments, keeps fluctuating in the secondary market.

The price is determined by demand and supply of the securities. Specifically, the prices of G-Secs are influenced by the level and changes in interest rates in the economy and other macro-economic factors, such as, expected rate of inflation, liquidity in the market, etc. Developments in other markets like money, foreign exchange, credit and capital markets also affect the price of the G-Secs.

Policy actions by RBI e. This will show a screen containing the details of the latest trades undertaken in the market along with the prices. On this page, the list of securities and the summary of trades is displayed. The total traded amount TTA on that day is shown against each security. Typically liquid securities are those with the largest amount of TTA. Pricing in these securities is efficient and hence UCBs can choose these securities for their transactions.

Since the prices are available on the screen they can invest in these securities at the current prices through their custodians. The screenshots of the above webpage are given below:. Reporting on NDS-OM is a two stage process wherein both the seller and buyer of the security have to report their leg of the trade. System validates all the parameters like reporting time, price, security etc.

The securities leg of these trades settle in the CSGL account of the custodian. The system, in turn, will match the orders based on price and time priority. That is, it matches bids and offers of the same prices with time priority. It may be noted that bid and offer of the same entity do not match i. The NDS-OM platform is an anonymous platform wherein the participants will not know the counterparty to the trade. Once an order is matched, the deal ticket gets generated automatically and the trade details flow to the CCIL. The settlement cycle for auctions of all kind of G-Secs i.

On the settlement date, the fund accounts of the participants are debited by their respective consideration amounts and their securities accounts SGL accounts are credited with the amount of securities allotted to them. The securities and funds are settled on a net basis i. CCIL guarantees settlement of trades on the settlement date by becoming a central counter-party CCP to every trade through the process of novation, i. During the period under shut, no trading of the security which is under shut is allowed.

The main purpose of having a shut period is to facilitate finalizing of the payment of maturity redemption proceeds and to avoid any change in ownership of securities during this process. Currently, the shut period for the securities held in SGL accounts is one day. Delivery versus Payment DvP is the mode of settlement of securities wherein the transfer of securities and funds happen simultaneously.

This ensures that unless the funds are paid, the securities are not delivered and vice versa. DvP settlement eliminates the settlement risk in transactions. There are three types of DvP settlements, viz. DvP I — The securities and funds legs of the transactions are settled on a gross basis, that is, the settlements occur transaction by transaction without netting the payables and receivables of the participant.

DvP II — In this method, the securities are settled on gross basis whereas the funds are settled on a net basis, that is, the funds payable and receivable of all transactions of a party are netted to arrive at the final payable or receivable position which is settled. DvP III — In this method, both the securities and the funds legs are settled on a net basis and only the final net position of all transactions undertaken by a participant is settled. Liquidity requirement in a gross mode is higher than that of a net mode since the payables and receivables are set off against each other in the net mode.

In effect, during settlement, the CCP becomes the seller to the buyer and buyer to the seller of the actual transaction. Once CCIL receives the trade information, it works out participant-wise net obligations on both the securities and the funds leg. All "WI " transactions are on an "if" basis, to be settled if and when the security is actually issued. WI market helps in price discovery of the securities being auctioned as well as better distribution of the auction stock. Short Sale is defined as sale of securities one does not own.

Certain Urban Cooperative Banks specifically permitted by the Department of Cooperative Bank Supervision for the purpose, can also undertake intra-day short sale of Government securities subject to adherence to the short sale limits, reporting and other risk management requirements prescribed for eligible entities by RBI from time to time. What are the basic mathematical concepts one should know for calculations involved in bond prices and yields?

An outline of the same with illustrations is provided in Box II below. The concept of time value of money is based on the premise that an investor prefers to receive a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal. In particular, if one receives the payment today, one can then earn interest on the money until that specified future date. Further, in an inflationary environment, a Rupee today will have greater purchasing power than after a year. It is a standard method for using the time value of money to appraise long-term projects.

Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value PV terms, once financing charges are met. Then they are summed. Where t - the time of the cash flow N - the total time of the project r - the discount rate the rate of return that could be earned on an investment in the financial markets with similar risk. C t - the net cash flow the amount of cash at time t for educational purposes, C 0 is commonly placed to the left of the sum to emphasize its role as the initial investment.

How is the Price of a bond calculated? What is the total consideration amount of a trade and what is accrued interest? The price of a bond is nothing but the sum of present value of all future cash flows of the bond. The interest rate used for discounting the cash flows is the Yield to Maturity YTM explained in detail in question no. Accrued interest is the interest calculated for the broken period from the last coupon day till a day prior to the settlement date of the trade.

Since the seller of the security is holding the security for the period up to the day prior to the settlement date of the trade, he is entitled to receive the coupon for the period held. The last coupon date being Nov 25, , the number of days in broken period till Jan 29, one day prior to settlement date i. In the instant case, it is If market interest rate levels rise, the price of a bond falls.

Conversely, if interest rates or market yields decline, the price of the bond rises. In other words, the yield of a bond is inversely related to its price. The relationship between yield to maturity and coupon rate of bond may be stated as follows:. When the market price of the bond is less than the face value, i. When the market price of the bond is more than its face value, i. When the market price of the bond is equal to its face value, i. The three yield measures commonly used by investors to measure the potential return from investing in a bond are briefly described below:. Coupon yield refers to nominal interest payable on a fixed income security like G-Sec.

This is the fixed return the Government i. Coupon yield thus does not reflect the impact of interest rate movement and inflation on the nominal interest that the Government pays. Illustration: Coupon: 8.

Why is IRR important?

The current yield does not take into account the reinvestment of the interest income received periodically. The current yield for a 10 year 8. The price of a bond is simply the sum of the present values of all its remaining cash flows. Present value is calculated by discounting each cash flow at a rate; this rate is the YTM. Thus YTM is the discount rate which equates the present value of the future cash flows from a bond to its current market price.

In other words, it is the internal rate of return on the bond. The calculation of YTM involves a trial-and-error procedure. YTM could be calculated manually as well as using functions in any standard spread sheet like MS Excel. Manual or trial and error method is complicated because G-Secs have many cash flows running into future. This is explained by taking an example below. In the MS Excel programme, the following function could be used for calculating the yield of periodically coupon paying securities, given the price. Settlement is the security's settlement date. The security settlement date is the date on which the security and funds are exchanged.

Step 1: Turning on the Calculator

Maturity is the security's maturity date. The maturity date is the date when the security expires. Basis is the type of day count basis to use. What are the day count conventions used in calculating bond yields? Day count convention refers to the method used for arriving at the holding period number of days of a bond to calculate the accrued interest.

As the use of different day count conventions can result in different accrued interest amounts, it is appropriate that all the participants in the market follow a uniform day count convention. Hence, in the case of T-Bills, which are essentially money market instruments, money market convention is followed. Hence the convention changes in different countries and in different markets within the same country eg.

Money market convention is different than the bond market convention in India. In simplest form, duration refers to the payback period of a bond to break even, i. Duration is expressed in number of years. A step by step approach for working out duration is given in the Box IV below. First, each of the future cash flows is discounted to its respective present value for each period. Since the coupons are paid out every six months, a single period is equal to six months and a bond with two years maturity will have four time periods.

Second, the present values of future cash flows are multiplied with their respective time periods these are the weights. That is the PV of the first coupon is multiplied by 1, PV of second coupon by 2 and so on. Third, the above weighted PVs of all cash flows is added and the sum is divided by the current price total of the PVs in step 1 of the bond.

The resultant value is the duration in no. Since one period equals to six months, to get the duration in no. This is the time period within which the bond is expected to pay back its own value if held till maturity. The weighted average term time from now to payment of a bond's cash flows or of any series of linked cash flows. The higher the coupon rate of a bond, the shorter the duration if the term of the bond is kept constant. Duration is useful primarily as a measure of the sensitivity of a bond's market price to interest rate i.

It is approximately equal to the percentage change in price for a given change in yield. In other words, duration is the elasticity of the bond's price with respect to interest rates. It refers to the change in value of the security to one per cent change in interest rates Yield. The formula is. It is the present value impact of 1 basis point 0. It is often used as a price alternative to duration a time measure. Higher the PV01, the higher would be the volatility sensitivity of price to change in yield.

From the modified duration given in the illustration under In value terms that is equal to 1. Thus, if the yield of a bond with a Modified Duration of 1. This is because the relationship between bond price and yield is not strictly linear i. Over large variations in prices, the relationship is curvilinear i. This is measured by a concept called convexity, which is the change in duration of a bond per unit change in the yield of the bond. The book value of individual securities in AFS and HFT categories would not undergo any change after marking to market.

Prices of all Central G-Secs are given out everyday. Currently, a spread of 25 basis points 0. An illustration of valuation taking a State Government bond is given in the Box V below. Illustration for valuation of State Government Bonds Security — 9. Since valuation is being done on Jan 27, , we need to find out the number of years from this date to the maturity date of the security i. Jan 1, to get the residual maturity of the security. This could be done manually by counting the number of years and months and days.

However, an easier method will be to use MS. This gives us the residual maturity of 9. To find the Central Government yield for 9. The yield for the 9. Here we are finding the yield difference for 0. Also notice that the yield has to be used in decimal form e. Having found the Central Government yield for the particular residual maturity, we have to now load the appropriate spread to get the yield of the security to be valued. Since the security is State G-Sec, the applicable spread is 25 basis points 0. Hence the yield would be 8. Here, we specify the valuation date as Jan 27, , maturity date as Jan 1, , rate as 9.

The only difference is the spread that need to be added to the corresponding yield on central G-Sec will be higher instead of the fixed 25 bps for State G-Secs , as published by the FIMMDA from time to time. What are the risks involved in holding G-Secs? What are the techniques for mitigating such risks? G-Secs are generally referred to as risk free instruments as sovereigns generally never default on their payments.

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However, as is the case with any financial instrument, there are risks associated with holding the G-Secs. Hence, it is important to identify and understand such risks and take appropriate measures for mitigation of the same. The following are the major risks associated with holding G-Secs:. This will result in booking losses on marking to market or realizing a loss if the securities are sold at adverse prices.

Small investors, to some extent, can mitigate market risk by holding the bonds till maturity so that they can realize the yield at which the securities were actually bought. These cash flows need to be reinvested whenever they are paid. Hence there is a risk that the investor may not be able to reinvest these proceeds at profitable rates due to changes in interest rate scenario prevailing at the time of receipt of cash flows by investors.

Liquidity risk refers to the inability of an investor to liquidate sell his holdings due to non-availability of buyers for the security, i. Usually, when a liquid bond of fixed maturity is bought, its tenor gets reduced due to time decay. For example, a 10 year security will become 8 year security after 2 years due to which it may become illiquid. The bonds also become illiquid when there are no frequent reissuances by the issuer RBI in those bonds. Bonds are generally reissued till a sizeable amount becomes outstanding under that bond.

However, issuer and sovereign has to ensure that there is no excess burden on Government at the time of maturity of the bond as very large amount maturing on a single day may affect the fiscal position of Government. Hence, generally reissuances under any security are stopped after outstanding under that bond touches a particular limit. This alleviates any question concerning whether to conduct cost—benefit analysis in terms of constant or nominal prices.

The Fisher equation has important implications in the trading of inflation-indexed bonds , where changes in coupon payments are a result of changes in break-even inflation, real interest rates and nominal interest rates. The Fisher equation plays a key role in the Fisher hypothesis , which asserts that the real interest rate is unaffected by monetary policy and hence unaffected by the expected inflation rate. With a fixed real interest rate, a given percent change in the expected inflation rate will, according to the equation, necessarily be met with an equal percent change in the nominal interest rate in the same direction.

From Wikipedia, the free encyclopedia.

This article is about an equation from financial mathematics. For the unrelated partial differential equation, see Fisher's equation. Water Resources Research.

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