• Public market • Exchange • Securities Bond market • Bond valuation • Corporate bond • Fixed income • Government bond • High-yield debt • Municipal bond Stock market • Common stock • Preferred stock • Registered share • Stock • Stock certificate • Stock exchange • Voting shareDerivatives market • Credit derivative • Futures exchange • Hybrid security • SecuritizationOver-the-counter • Forwards • Options • Spot market • SwapsForeign exchange
• Currency • Exchange rate Other markets • Commodity market • Money market • Reinsurance market • Real estate market Practical trading • Clearing house • Financial market participants • Financial regulation Finance series • Banks and banking • Corporate finance • Personal finance • Public finance • v • t • eBond valuation is the determination of the fair price of a bond. As with any security orcapital investment, the theoretical fair value of a bond is the present value of the streamof cash flows it is expected to generate. Hence, the value of a bond is obtained bydiscounting the bonds expected cash flows to the present using an appropriate discountrate. In practice, this discount rate is often determined by reference to similar instruments,provided that such instruments exist. Various related yield-measures are calculated forthe given price.If the bond includes embedded options, the valuation is more difficult and combinesoption pricing with discounting. Depending on the type of option, the option price ascalculated is either added to or subtracted from the price of the "straight" portion. Seefurther under Bond option. This total is then the value of the bond.Contents
• 1 Bond valuation o 1.1 Present value approach o 1.2 Relative price approach o 1.3 Arbitrage-free pricing approach o 1.4 Stochastic calculus approach • 2 Clean and dirty price • 3 Yield and price relationships o 3.1 Yield to Maturity o 3.2 Coupon yield o 3.3 Current yield o 3.4 Relationship • 4 Price sensitivity • 5 Accounting treatment • 6 See also • 7 References and external linksBond valuation As above, the fair price of a "straight bond" (a bond with no embedded options; seeBond (finance)# Features) is usually determined by discounting its expected cash flows atthe appropriate discount rate. The formula commonly applied is discussed initially.Although this present value relationship reflects the theoretical approach to determiningthe value of a bond, in practice its price is (usually) determined with reference to other,more liquid instruments. The two main approaches, Relative pricing and Arbitrage-freepricing, are discussed next. Finally, where it is important to recognise that future interestrates are uncertain and that the discount rate is not adequately represented by a singlefixed number - for example when an option is written on the bond in question - stochasticcalculus may be employed.Where the market price of bond is less than its face value (par value), the bond is sellingat a discount. Conversely, if the market price of bond is greater than its face value, thebond is selling at a premium. For this and other relationships relating price and yield,see below.Present value approachBelow is the formula for calculating a bonds price, which uses the basic present value(PV) formula for a given discount rate: (This formula assumes that a coupon paymenthas just been made; see below for adjustments on other dates.)
where: F = face value iF = contractual interest rate C = F * iF = coupon payment (periodic interest payment) N = number of payments i = market interest rate, or required yield, or observed / appropriate yield to maturity (see below) M = value at maturity, usually equals face value P = market price of bond.Relative price approachUnder this approach - an extension of the above - the bond will be priced relative to abenchmark, usually a government security; see Relative valuation. Here, the yield tomaturity on the bond is determined based on the bonds Credit rating relative to agovernment security with similar maturity or duration; see Credit spread (bond). Thebetter the quality of the bond, the smaller the spread between its required return and theYTM of the benchmark. This required return is then used to discount the bond cashflows, replacing in the formula above, to obtain the price.Arbitrage-free pricing approach See: Rational pricing: Fixed income securities.As distinct from the two related approaches above, a bond may be thought of as a"package of cash flows" - coupon or face - with each cash flow viewed as a zero-couponinstrument maturing on the date it will be received. Thus, rather than using a singlediscount rate, one should use multiple discount rates, discounting each cash flow at itsown rate. Here, each cash flow is separately discounted at the same rate as a zero-coupon bond corresponding to the coupon date, and of equivalent credit worthiness (ifpossible, from the same issuer as the bond being valued, or if not, with the appropriatecredit spread).Under this approach, the bond price should reflect its "arbitrage-free" price, as anydeviation from this price will be exploited and the bond will then quickly reprice to itscorrect level. Here, we apply the rational pricing logic relating to "Assets with identicalcash flows". In detail: (1) the bonds coupon dates and coupon amounts are known with
certainty. Therefore (2) some multiple (or fraction) of zero-coupon bonds, eachcorresponding to the bonds coupon dates, can be specified so as to produce identical cashflows to the bond. Thus (3) the bond price today must be equal to the sum of each of itscash flows discounted at the discount rate implied by the value of the correspondingZCB. Were this not the case, (4) the abitrageur could finance his purchase of whicheverof the bond or the sum of the various ZCBs was cheaper, by short selling the other, andmeeting his cash flow commitments using the coupons or maturing zeroes as appropriate.Then (5) his "risk free", arbitrage profit would be the difference between the two values.Stochastic calculus approachWhen modelling a bond option, or other interest rate derivative (IRD), it is important torecognize that future interest rates are uncertain, and therefore, the discount rate(s)referred to above, under all three cases - i.e. whether for all coupons or for eachindividual coupon - is not adequately represented by a fixed (deterministic) number. Insuch cases, stochastic calculus is employed.The following is a partial differential equation (PDE) in stochastic calculus which issatisfied by any zero-coupon bond.The solution to the PDE - given in  - is: where is the expectation with respect to risk-neutral probabilities, and is a random variable representing the discount rate; see also Martingale pricing.To actually determine the bond price, the analyst must choose the specific short ratemodel to be employed. The approaches commonly used are: • the CIR model • the Black-Derman-Toy model • the Hull-White model • the HJM framework • the Chen model.Note that depending on the model selected, a closed-form solution may not be available,and a lattice- or simulation-based implementation of the model in question is thenemployed. See also Jamshidians trick.
Clean and dirty priceMain articles: Clean price and Dirty priceWhen the bond is not valued precisely on a coupon date, the calculated price, using themethods above, will incorporate accrued interest: i.e. any interest due to the owner of thebond since the previous coupon date; see day count convention. The price of a bondwhich includes this accrued interest is known as the "dirty price" (or "full price" or "all inprice" or "Cash price"). The "clean price" is the price excluding any interest that hasaccrued. Clean prices are generally more stable over time than dirty prices. This isbecause the dirty price will drop suddenly when the bond goes "ex interest" and thepurchaser is no longer entitled to receive the next coupon payment. In many markets, it ismarket practice to quote bonds on a clean-price basis. When a purchase is settled, theaccrued interest is added to the quoted clean price to arrive at the actual amount to bepaid.Yield and price relationshipsOnce the price or value has been calculated, various yields relating the price of the bondto its coupons can then be determined.Yield to MaturityThe yield to maturity is the discount rate which returns the market price of the bond; it isidentical to (required return) in the above equation. YTM is thus the internal rate ofreturn of an investment in the bond made at the observed price. Since YTM can be usedto price a bond, bond prices are often quoted in terms of YTM.To achieve a return equal to YTM, i.e. where it is the required return on the bond, thebond owner must: • buy the bond at price P0, • hold the bond until maturity, and • redeem the bond at par.Coupon yieldThe coupon yield is simply the coupon payment (C) as a percentage of the face value (F). Coupon yield = C / FCoupon yield is also called nominal yield.Current yield
The current yield is simply the coupon payment (C) as a percentage of the (current) bondprice (P). Current yield =RelationshipThe concept of current yield is closely related to other bond concepts, including yield tomaturity, and coupon yield. The relationship between yield to maturity and the couponrate 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 yieldPrice sensitivityMain articles: Bond duration and Bond convexityThe sensitivity of a bonds market price to interest rate (i.e. yield) movements ismeasured by its duration, and, additionally, by its convexity.Duration is a linear measure of how the price of a bond changes in response to interestrate changes. It is approximately equal to the percentage change in price for a givenchange in yield, and may be thought of as the elasticity of the bonds price with respect todiscount rates. For example, for small interest rate changes, the duration is theapproximate percentage by which the value of the bond will fall for a 1% per annumincrease in market interest rate. So the market price of a 17-year bond with a duration of7 would fall about 7% if the market interest rate (or more precisely the correspondingforce of interest) increased by 1% per annum.Convexity is a measure of the "curvature" of price changes. It is needed because the priceis not a linear function of the discount rate, but rather a convex function of the discountrate. Specifically, duration can be formulated as the first derivative of the price withrespect to the interest rate, and convexity as the second derivative (see: Bond durationclosed-form formula; Bond convexity closed-form formula). Continuing the aboveexample, for a more accurate estimate of sensitivity, the convexity score would bemultiplied by the square of the change in interest rate, and the result added to the valuederived by the above linear formula.Accounting treatmentIn accounting for liabilities, any bond discount or premium must be amortized over thelife of bond. A number of methods may be used for this depending on applicable
accounting rules. One possibility is that amortization amount in each period is calculatedfrom the following formula: = amortization amount in period number "n+1"Bond Discount or Bond Premium = =Bond Discount or Bond Premium = The 4 Primary Types of BondsThere are millions of different bond issues, but there are only a few types of bonds. Infact, the large majority of bonds fall into one of the 4 categories outlined below. As youcan see from the links in each section, we have lots of information on all the differenttypes of bonds here at Learn Bonds, so enjoy!1. US Government Bonds (Treasuries)When people talk about the US debit being over $16 trillion, what they are really sayingis the US Government has over $16 trillion worth of outstanding debt. Much of this
outstanding debt is in the form of bonds they have issued, called treasuries. Treasuriesare different from all other types of bonds, because they are issued by the USgovernment, and are therefore considered free of credit risk. For this reason, the yields ofall other types of bonds are compared to the yield on a treasury with the same maturity.Here are some of our more popular articles on Treasury bonds.An introduction to treasury bonds – In this article and video we talk about the differenttypes of treasury bonds, and how treasuries differ from other types of bonds.Treasury Auctions 101 – Here we discuss how treasury bonds are sold after they areissued, and how individuals can buy treasuries through the auction commission free.Treasury inflation protected securities – TIPS are a special type of treasury bond that isdesigned to protect investors from inflation. Learn more here.The Safety of US Treasuries – With the US debt level rising at a rapid pace, some arestarting to question just how safe US Treasuries really are. Here are the facts.2. Agency Bonds (Agencies)Agency bonds are bonds issued by institutions that were originally created by the USGovernment to perform important functions such as fostering home ownership, andproviding student loans. The primary government agencies are Fannie Mae, FreddieMac, Ginnie Mae and Sallie Mae. While these agencies technically operate in a similarmanner to a corporation, they are thought to be implicitly backed by the US government.You can learn more about Agency bonds here.3. Municipal Bonds (Munis)State and local governments often borrow money by issuing bonds, similar to the USGovernment, but on a smaller scale. Municipal bonds fund a wide variety of projects andgovernment functions ranging from police and fire departments to bridges and toll roads. Municipal bonds are popular among individual investors because they provide taxadvantages that other types of bonds do not. Most municipal bonds are free from federalincome taxes. If you buy a municipal bond in the state where you reside then it is oftenfree from state and local income taxes as well.Here are some of our more popular articles on Municipal Bonds:An Introduction to Municipal Bonds – The different types of municipal bonds, how tobuy municipal bonds, what you should consider before investing and more.
Municipal Bond Safety - There has been lots of talk about a coming wave of defaults inthe municipal bond market, however the facts show otherwise.5 Tips for Municipal Bond Investors – Our interview with Peter Hayes, one of the topmunicipal bond fund managers in the world.How to buy municipal bonds – If you are considering buying individual municipal bonds,you may want to consider doing so through what is known as the retail order period. Learn more here.4. Corporate Bonds (Corporates)And last but certainly not least are corporations, who often choose the bond market toraise capital as well. A corporation can issue bonds for many reasons, including payingdividends to shareholders, purchasing another company, funding an operating loss, orexpansion. Corporate bonds differ from other types of bonds because they are almostalways taxable at both the federal and state level. As a group, corporate bonds also havemuch more credit risk than the other types of bonds outlined above.Here are some of our more popular articles on corporate bonds.An introduction to corporate bonds – More on how corporate bonds differ from othertypes of bonds, where to find corporate bond prices, callable bonds, bond covenants andmore.Junk Bonds – Feeling adventurous and willing to take on much more risk than with othertypes of bonds for a potentially higher payout? Then junk bonds may be for you.Corporate bond defaults – Ever wonder what happens after a corporation defaults on itsbonds? This article gives you all the details.This lesson is part of our free guide to The Basics of Investing in Bonds. To continue tothe next lesson go here.Financial market efficiencyFrom Wikipedia, the free encyclopediaJump to: navigation, search It has been suggested that Efficient-market hypothesis be merged into this article or section. (Discuss) Proposed since April 2012. Financial markets
• Public market • Exchange • Securities Bond market • Bond valuation • Corporate bond • Fixed income • Government bond • High-yield debt • Municipal bond Stock market • Common stock • Preferred stock • Registered share • Stock • Stock certificate • Stock exchange • Voting shareDerivatives market • Credit derivative • Futures exchange • Hybrid security • SecuritizationOver-the-counter • Forwards
• Options • Spot market • Swaps Foreign exchange • Currency • Exchange rate Other markets • Commodity market • Money market • Reinsurance market • Real estate market Practical trading • Clearing house • Financial market participants • Financial regulation Finance series • Banks and banking • Corporate finance • Personal finance • Public finance • v • t • eIn the 1970s Eugene Fama defined an efficient financial market as "one in which pricesalways fully reflect available information”.The most common type of efficiency referred to in financial markets is the allocativeefficiency, or the efficiency of allocating resources. This includes producing the rightgoods for the right people at the right price.
A trait of allocatively efficient financial market is that it channels funds from the ultimatelenders to the ultimate borrowers in a way that the funds are used in the most sociallyuseful manner.Contents • 1 Market efficiency levels • 2 Efficient Market Hypothesis (EMH) o 2.1 Random Walk theory 2.1.1 Evidence 18.104.22.168 Evidence of Financial Market Efficiency 22.214.171.124 Evidence of Financial Market In-Efficiency • 3 Market efficiency types • 4 Conclusion • 5 References • 6 BibliographyMarket efficiency levelsEugene Fama identified three levels of market efficiency:1. Weak-form efficiencyPrices of the securities instantly and fully reflect all information of the past prices. Thismeans future price movements cannot be predicted by using past prices. It is simply tosay that, past data on stock prices are of no use in predicting future stock price changes.Everything is random. In this kind of market, should simply use a "buy-and-hold"strategy.2. Semi-strong efficiencyAsset prices fully reflect all of the publicly available information. Therefore, onlyinvestors with additional inside information could have advantage on the market. Anyprice anomalies are quickly found out and the stock market adjusts.3. Strong-form efficiencyAsset prices fully reflect all of the public and inside information available. Therefore, noone can have advantage on the market in predicting prices since there is no data thatwould provide any additional value to the investors.Efficient Market Hypothesis (EMH)
Fama also created the Efficient Market Hypothesis (EMH) theory, which states that inany given time, the prices on the market already reflect all known information, and alsochange fast to reflect new information.Therefore, no one could outperform the market by using the same information that isalready available to all investors, except through luck.Random Walk theoryAnother theory related to the efficient market hypothesis created by Louis Bachelier isthe “random walk” theory, which states that the prices in the financial markets evolverandomly and are not connected, they are independent of each other.Therefore, identifying trends or patterns of price changes in a market couldn’t be used topredict the future value of financial instruments.EvidenceEvidence of Financial Market Efficiency • Predicting future asset prices is not always accurate (represents weak efficiency form) • Asset prices always reflect all new available information quickly (represents semi-strong efficiency form) • Investors cant outperform on the market often (represents strong efficiency form)Evidence of Financial Market In-Efficiency • January effect (repeating and predictable price movements and patterns occur on the market) • Stock market crashes, Asset Bubbles, and Credit Bubbles • Investors that often outperform on the market such as Warren Buffett, institutional investors, and corporations trading in their own stock • Certain consumer credit market prices dont adjust to legal changes that affect future losses Market efficiency typesJames Tobin identified four efficiency types that could be present in a financial market:1. Information arbitrage efficiency
Asset prices fully reflect all of the privately available information (the least demandingrequirement for efficient market, since arbitrage includes realizable, risk freetransactions)Arbitrage involves taking advantage of price similarities of financial instruments between2 or more markets by trading to generate losses.It involves only risk-free transactions and the information used for trading is obtained atno cost. Therefore, the profit opportunities are not fully exploited, and it can be said thatarbitrage is a result of market inefficiency.This reflects the weak-information efficiency model.2. Fundamental valuation efficiencyAsset prices reflect the expected past flows of payments associated with holding theassets (profit forecasts are correct, they attract investors)Fundamental valuation involves lower risks and less profit opportunities. It refers to theaccuracy of the predicted return on the investment.Financial markets are characterized by predictability and inconsistent misalignments thatforce the prices to always deviate from their fundamental valuations.This reflects the semi-strong information efficiency model.3. Full insurance efficiencyIt ensures the continuous delivery of goods and services in all contingencies.4. Functional/Operational efficiencyThe products and services available at the financial markets are provided for the least costand are directly useful to the participants.Every financial market will contain a unique mixture of the identified efficiencytypes.ConclusionFinancial market efficiency is an important topic in the world of Finance. While mostfinanciers believe the markets are neither 100% efficient, nor 100% inefficient, manydisagree where on the efficiency line the worlds markets fall.It can be concluded that in reality a financial market can’t be considered to be extremelyefficient, or completely inefficient.
The financial markets are a mixture of both, sometimes the market will provide fairreturns on the investment for everyone, while at other times certain investors willgenerate above average returns on their investment. MARKET EFFICIENCY - DEFINITION AND TESTS What is an efficient market? • Efficient market is one where the market price is an unbiased estimate of the true value of the investment. • Implicit in this derivation are several key concepts -(a) Market efficiency does not require that the market price be equal to true value atevery point in time. All it requires is that errors in the market price be unbiased, i.e., thatprices can be greater than or less than true value, as long as these deviations are random.(b) The fact that the deviations from true value are random implies, in a rough sense, thatthere is an equal chance that stocks are under or over valued at any point in time, andthat these deviations are uncorrelated with any observable variable. For instance, in anefficient market, stocks with lower PE ratios should be no more or less likely to undervalued than stocks with high PE ratios.(c) If the deviations of market price from true value are random, it follows that no groupof investors should be able to consistently find under or over valued stocks using anyinvestment strategy. Market Efficiency for Investor Groups • Definitions of market efficiency have to be specific not only about the market that is being considered but also the investor group that is covered. o It is extremely unlikely that all markets are efficient to all investors, but it is entirely possible that a particular market (for instance, the New York Stock Exchange) is efficient with respect to the average investor. o It is also possible that some markets are efficient while others are not, and that a market is efficient with respect to some investors and not to others. This is a direct consequence of differential tax rates and transactions costs, which confer advantages on some investors relative to others. • Definitions of market efficiency are also linked up with assumptions about what information is available to investors and reflected in the price. For instance, a strict definition of market efficiency that assumes that all information, public as well as private, is reflected in market prices would imply that even investors with precise inside information will be unable to beat the market.Classifications
• Strong versus Weak Form Efficiency:- Under weak form efficiency, the current price reflects the information contained in allpast prices, suggesting that charts and technical analyses that use past prices alone wouldnot be useful in finding under valued stocks.- Under semi-strong form efficiency, the current price reflects the information containednot only in past prices but all public information (including financial statements andnews reports) and no approach that was predicated on using and massaging thisinformation would be useful in finding under valued stocks.- Under strong form efficiency, the current price reflects all information, public as wellas private, and no investors will be able to consistently find under valued stocks. Implications of market efficiency • An immediate and direct implication of an efficient market is that no group of investors should be able to consistently beat the market using a common investment strategy. • An efficient market would also carry very negative implications for many investment strategies and actions that are taken for granted -(a) In an efficient market, equity research and valuation would be a costly task thatprovided no benefits. The odds of finding an undervalued stock should be random(50/50). At best, the benefits from information collection and equity research wouldcover the costs of doing the research.(b) In an efficient market, a strategy of randomly diversifying across stocks orindexing to the market, carrying little or no information cost and minimal executioncosts, would be superior to any other strategy, that created larger information andexecution costs. There would be no value added by portfolio managers and investmentstrategists.(c) In an efficient market, a strategy of minimizing trading, i.e., creating a portfolio andnot trading unless cash was needed, would be superior to a strategy that required frequenttrading. What market efficiency does not imply:An efficient market does not imply that -(a) stock prices cannot deviate from true value; in fact, there can be large deviationsfrom true value. The only requirement is that the deviations be random.
(b) no investor will beat the market in any time period. To the contrary,approximately half of all investors, prior to transactions costs, should beat the market inany period.(c) no group of investors will beat the market in the long term. Given the number ofinvestors in financial markets, the laws of probability would suggest that a fairly largenumber are going to beat the market consistently over long periods, not because of theirinvestment strategies but because they are lucky. It would not, however, be consistent if adisproportionately large number of these investors used the same investment strategy. • In an efficient market, the expected returns from any investment will be consistent with the risk of that investment over the long term, though there may be deviations from these expected returns in the short term.Necessary conditions for market efficiency • Markets do not become efficient automatically. It is the actions of investors, sensing bargains and putting into effect schemes to beat the market, that make markets efficient. • The necessary conditions for a market inefficiency to be eliminated are as follows -(1) The market inefficiency should provide the basis for a scheme to beat the market andearn excess returns. For this to hold true -(a) The asset (or assets) which is the source of the inefficiency has to be traded.(b) The transactions costs of executing the scheme have to be smaller than the expectedprofits from the scheme.(2) There should be profit maximizing investors who(a) recognize the potential for excess return(b) can replicate the beat the market scheme that earns the excess return(c) have the resources to trade on the stock until the inefficiency disappears Efficient Markets and Profit-seeking investors: The Internal Contradiction • There is an internal contradiction in claiming that there is no possibility of beating the market in an efficient market and then requiring profit-maximizing investors to constantly seek out ways of beating the market and thus making it efficient. • If markets were, in fact, efficient, investors would stop looking for inefficiencies, which would lead to markets becoming inefficient again.
• It makes sense to think about an efficient market as a self-correcting mechanism, where inefficiencies appear at regular intervals but disappear almost instantaneously as investors find them and trade on them. Propositions about market efficiencyProposition 1: The probability of finding inefficiencies in an asset market decreases asthe ease of trading on the asset increases. To the extent that investors have difficultytrading on a stock, either because open markets do not exist or there are significantbarriers to trading, inefficiencies in pricing can continue for long periods. • Example: • Stocks versus real estate • NYSE vs NASDAQProposition 2: The probability of finding an inefficiency in an asset marketincreases as the transactions and information cost of exploiting the inefficiencyincreases. The cost of collecting information and trading varies widely across marketsand even across investments in the same markets. As these costs increase, it pays less andless to try to exploit these inefficiencies.Example:Initial Public Offerings: IPOs supposedly make excess returns, on average.Emerging Market Stocks: Do they make excess returns?Investing in loser stocks, i.e., stocks that have done very badly in some prior timeperiod should yields excess returns. Transactions costs are likely to be much higher forthese stocks since-(a) they then to be low priced stocks, leading to higher brokerage commissions andexpenses(b) the bid-ask becomes a much higher fraction of the total price paid.(c) trading is often thin on these stocks, and small trades can cause prices to move.Corollary 1: Investors who can estabish a cost advantage (either in informationcollection or transactions costs) will be more able to exploit small inefficiencies thanother investors who do not possess this advantage.
• Example: Block trades effect on stock prices & specialists on the Floor of the Exchange • Establishing a cost advantage, especially in relation to information, may be able to generate excess returns on the basis of these advantages. Thus a John Templeton, who started investing in Japanese and othe Asian markets well before other portfolio managers, might have been able to exploit the informational advantages he had over his peers to make excess returns on his portfolio.Proposition 3: The speed with which an inefficiency is resolved will be directlyrelated to how easily the scheme to exploit the ineffficiency can be replicated byother investors. The ease with which a scheme can be replicated itselft is inverselyrelated to the time, resouces and information needed to execute it. Since very fewinvestors single-handedly possess the resources to eliminate an inefficiency throughtrading, it is much more likely that an inefficiency will disappear quickly if the schemeused to exploit the inefficiency is transparent and can be copied by other investors. • Example: Investing on stock splits versus Index Arbitrage