Bond valuation is the process of determining the fair price of a bond. In Economics, a financial market is a mechanism that allows people to easily buy and sell ( Trade) financial Securities (such as stocks and bonds The bond market (also known as the debt, credit, or fixed income market) is a Financial market where participants buy and sell Debt Fixed income refers to any type of Investment that yields a regular (or fixed return A Corporate Bond is a bond issued by a Corporation. The term is usually applied to longer-term debt instruments generally with a maturity date falling at least a A government bond is a bond issued by a national government denominated in the country's own Currency. In the United States, a municipal bond (or muni) is a bond issued by a city or other local government or their agencies In Finance, a high yield bond ( non-investment grade bond, speculative grade bond or junk bond) is a bond that is rated below A stock market, or (equity market is a private or public market for the trading of company Stock and derivatives of company Software for Fixed assets management and Stock control developed in 2004. Preferred stock, also called preferred shares or preference shares, is typically a higher ranking stock than Voting shares, and its terms are negotiated A voting share (also called common stock or ordinary share) is a share of Stock giving the Stockholder the right to vote on matters A Registered share is a Stock that is registered on the name of the exact owner A voting share (also called common stock or ordinary share) is a share of Stock giving the Stockholder the right to vote on matters A stock exchange, share market or bourse is a Corporation or Mutual organization which provides "trading" facilities for Stock The foreign exchange ( currency or forex or FX) market refers to the market for currencies. The derivatives markets are the Financial markets for derivatives The market can be divided into two that for exchange traded derivatives and that for In Finance, a credit derivative is a derivative whose value derives from the Credit risk on an underlying bond loan or other financial asset '"Hybrid securities"' often referred as "hybrids" are a broad group of securities that combine the elements of the two broader groups of securities Debt and Options are financial instruments that convey the right but not the obligation to engage in a future transaction on some Underlying security, or in a Futures In Finance, a futures contract is a standardized Contract, traded on a Futures exchange, to buy or sell a certain Underlying instrument A forward contract is an agreement between two parties to buy or sell an asset at a specified point of time in the future For the Thoroughbred horse racing champion see Swaps (horse. In finance a swap is a derivative in which two counterparties Commodity markets are markets where raw or primary products are exchanged In Finance, the money market is the global Financial market for short-term borrowing and lending Over-the-counter ( OTC) trading is to Trade Financial instruments such as Stocks bonds, commodities or derivatives Real estate is a legal term (in some jurisdictions notably in the USA, United Kingdom The spot market or cash market is a Commodities or Securities market in which goods are sold for Cash and delivered immediately The field of finance refers to the concepts of Time, Money and Risk and how they are interrelated In Economics, a financial market is a mechanism that allows people to easily buy and sell ( Trade) financial Securities (such as stocks and bonds There are two basic financial market participant categories Investor vs Corporate finance is an area of Finance dealing with the financial decisions Corporations make and the tools and analysis used to make these decisions Personal finance is the application of the principles of Finance to the monetary decisions of an individual or family unit Public finance is a field of economics concerned with paying for collective or governmental activities and with the administration and design of those activities A banker or bank is a Financial institution whose primary activity is to act as a payment agent for customers and to borrow and lend money Financial regulations are a form of Regulation or supervision which subjects Financial institutions to certain requirements restrictions and guidelines aiming to Fair value, also called fair price, is a concept used in Finance and Economics, defined as a rational and unbiased Estimate of the potential In Finance, a bond is a Debt security, in which the authorized issuer owes the holders a debt and is obliged to repay the principal and Interest As with any security or capital investment, the fair value of a bond is the present value of the stream of cash flows it is expected to generate. Present value is the value on a given date of a future payment or series of future payments discounted to reflect the Time value of money and other factors such as Investment Hence, the price or value of a bond is determined by discounting the bond's expected cash flows to the present using the appropriate discount rate. For the interest rate charged to Banks for borrowing short-term funds directly from the Federal Reserve, see Discount window.
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General relationships
The present value relationship
The fair price of a straight bond (a bond with no embedded option; see Callable bond) is determined by discounting the expected cash flows:
- Cash flows:
- the periodic coupon payments C, each of which is made n times (n is usually 2) every year
- the par or face value F, which is payable at maturity of the bond after T years. In Finance, a bond is a Debt security, in which the authorized issuer owes the holders a debt and is obliged to repay the principal and Interest Options are financial instruments that convey the right but not the obligation to engage in a future transaction on some Underlying security, or in a Futures Callable bond is a type of bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches the date of maturity (NB final year payments will include the par value plus the coupon payments for the year)
- Discount rate: the required (annually compounded) yield or rate of return r
- r is the market interest rate for bonds with similar terms and risk ratings
- m is the number of coupons to be paid over the remaining lifetime of the bond, ie n times T. (It is assumed that the previous coupon has just been paid. )
- u is (1+r)^(1/n) ie an interest accumulation factor over one coupon period
- Bond Price =
Because the price is the present value of the cash flows, there is an inverse relationship between price and discount rate: the higher the discount rate the lower the value of the bond (and vice versa). A bond trading below its face value is trading at a discount, a bond trading above its face value is at a premium.
Coupon yield
The coupon yield is simply the coupon payment (C) as a percentage of the face value (F). The coupon or coupon rate of a bond is the amount of interest paid per year expressed as a percentage of the face value of the bond
- Coupon yield = C / F
Coupon yield is also called nominal yield. Nominal yield is the coupon rate of a Fixed income security, which is a fixed percentage of the par value
Current yield
The current yield is simply the coupon payment (C) as a percentage of the bond price (P). The current yield, interest yield, income yield, flat yield or running yield is a financial term used in reference to bonds
- Current yield = C / P0.
Yield to Maturity
The yield to maturity (YTM) is the discount rate which returns the market price of the bond. The Yield to maturity ( YTM) or redemption yield is the yield promised to the bondholder on the assumption that the bond or other fixed-interest Market price is an economic concept with commonplace familiarity it is the price that a good or service is offered at or will fetch in the marketplace it is of interest mainly in the It is thus the internal rate of return of an investment in the bond made at the observed price. The internal rate of return (IRR is a Capital budgeting metric used by firms to decide whether they should make Investments It is an indicator of the efficiency YTM can also be used to price a bond, where it is used as the required return on the bond.
In other words, it is identical to r in the above equation.
To achieve a return equal to YTM, the bond owner must:
- buy the bond at price P0,
- hold the bond until maturity, and
- redeem the bond at par.
The concept of current yield is closely related to other bond concepts, including yield to maturity, and coupon yield. The relationship between yield to maturity and coupon rate is as follows:
- When a bond sells at a discount, YTM > current yield > coupon yield.
- When a bond sells at a premium, coupon yield > current yield > YTM.
- When a bond sells at par, YTM = current yield = coupon yield.
Bond pricing
Relative price approach
Here the bond will be priced relative to a benchmark, usually a government security. The yield to maturity on the bond is determined based on the bond's rating relative to a government security with similar maturity or duration. In Finance, the duration of a financial asset measures the sensitivity of the asset's price to Interest rate movements expressed as a number of years The better the quality of the bond, the smaller the spread between its required return and the YTM of the benchmark. This required return is then used to discount the bond cash flows as above to obtain the price.
Arbitrage free pricing approach
In this approach, the bond price will reflect its arbitrage free price (arbitrage=practice of taking advantage of a state of imbalance between two or more markets). In Economics and Finance, arbitrage is the practice of taking advantage of a price differential between two or more Markets striking a combination of matching Here, each cash flow is priced separately and is discounted at the same rate as the corresponding government issue Zero coupon bond. A Zero coupon bond (also called a discount bond or deep discount bond) is a bond bought at a price lower than its Face value, with the face value (Some multiple of the bond (or the security) will produce an identical cash flow to the government security (or the bond in question). ) Since each bond cash flow is known with certainty, the bond price today must be equal to the sum of each of its cash flows discounted at the corresponding risk free rate - i. The risk-free interest rate is the Interest rate that it is assumed can be obtained by investing in Financial instruments with no Default risk e. the corresponding government security. Were this not the case, arbitrage would be possible - see rational pricing. Rational pricing is the assumption in Financial economics that asset prices (and hence asset pricing models will reflect the Arbitrage-free price of the asset as
See also
External links
Discussion
- Bond Price Volatility Investment Analysts Society of South Africa
- Duration and convexity Investment Analysts Society of South Africa
- Course material Fixed Income Analytics
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