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Acquisition Date
A user-supplied value, this is the date on which a security was purchased.
Acquisition Price
A user-supplied value, this is the price at which a security was originally purchased.
Amortized Cost
See Book Price.
Accrued Interest
The amount which the buyer of a fixed-income security must pay the seller of the security to compensate the seller for holding the security between the last coupon payment date and settlement date. The accrued interest, added to the instrument's dollar price, constitutes the net amount, net proceeds or invoice amount. How this accrued interest is calculated varies from security to security. Depending on the type of bond, the accrued interest calculation uses one of several day count conventions for calculating the difference between two dates. The most common day count conventions are Actual/Actual, 30/360, and 30/360 European.
Average Coupon
The weighted average coupon of a bond.
Average Life
The weighted average time to receipt of principal payments (including scheduled paydowns and repayments).
Average Maturity
The market value weighted average maturity of the bonds in a portfolio, where maturity is defined as Stated Final for bullet maturity bonds and Average Life for amortizing instruments, including mortgage pass-throughs, CMOs, amortizing asset-backed securities and ARMs.
Average Yield
The market value weighted average Yield to Maturity/Option a bond. If the bond is trading to the call or put date, the yield to the option date is used. If the bond is trading to the maturity date, the YTM is used.
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Banker's Acceptances
Banker's acceptances (BAs) are short-term interest at maturity notes. These notes do not bear interest but are sold at a discount and redeemed for full face value by the accepting bank at maturity. Both the issuer and the accepting bank guarantee the BA.
Most BAs are issued out of foreign trade transactions. In place of an immediate cash payment, a transacting party may request his bank to issue a letter of credit. Upon receipt of this letter of credit, the party at the other end of the deal draws a time draft from that bank and discounts this draft at its own local bank. The local bank then sends back the draft to the first bank. By "accepting" it, the bank guarantees payment on the draft. The resulting BA may then be immediately cashed in or held as an investment.
Today, major investors in BAs include the accepting banks themselves, foreign central banks, money market funds, corporations and other domestic and foreign institutional investors. Dealers in the secondary market create sufficient liquidity for these instruments to continually attract investors.
Book Price
The amortized carrying cost of the security as of the pricing date. For Treasuries, Agencies, Corporates, ABS and Municipals, the Scientific (Constant Yield) amortization method is used. Securities which are trading to call/(put) as of the Acquisition Date are amortized to the nearest call/(put) date and price.
Bond Equivalent Yield
Discount securities, like Treasury bills, are quoted on a bank discount basis. But the discount basis is not a yield, and so cannot be compared to yields of other instruments. The bond equivalent yield converts the price implied by the discount basis into a yield which is directly comparable to that of other investments.
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Call
The right of the bond issuer to redeem a bond before its maturity date.
Call Price, Call Date, and Yield to Call
Some bonds may be callable before maturity by the issuer, typically on coupon payment dates. Frequently, these issues pay par plus a premium over par on the call date for the right to call the bonds prior to maturity. This is referred to as a non-par call.
Call provisions (i.e. the call premium and the applicable dates) in conjunction with current market conditions will affect the expected cash flow of the bond. Market participants frequently evaluate these securities by calculating yields to these call dates, especially if there is a strong likelihood that the issuer will exercise these rights. The lowest of the yields, under all scenarios, is called the "yield to worst" (we will leave aside the affects of sinking fund provisions on the "yield to worst", at this time). The yield to worst can become the effective yield measure used by the market to price the issue.
It is a "Street" convention to price par-callable bonds using their next call date if they are trading above par, and to price them to maturity if trading at, or below, par.
CD Equivalent Yield
The CD equivalent yield is a measure that makes the yield on a discount security comparable to yields on money market instruments that pay interest on a 360-day basis. Unlike the yield quoted on a bank discount basis, this measure considers the price one pays for the security rather than its face value. It is also known as the money market equivalent yield.
Commercial Paper
Commercial paper is an unsecured promissory note issued for a specified amount. This security may carry a maturity of up to 270 days. However, the bulk of the issues mature within 30 days or shorter. Among the entities that issue commercial paper are industrial and manufacturing firms, most especially those with good credit ratings. While these firms can readily turn to banks to finance their short-term capital needs, they sometimes choose to sell paper, an alternative and cheaper source of funds. These firms together with finance companies, bank holding companies, municipalities, and municipal authorities have become the major issuers of commercial paper. Through the years, foreign entities such as sovereigns and corporations have joined this list as well.
Typically, issuers cannot raise sufficient funds quick enough to pay back maturing paper. To get around this problem, they normally roll over the paper. They sell new paper to pay off the others.
The rates offered on commercial paper depend on several factors: the credit rating of the issuer, the paper's maturity, the total amount of money sought by the issuer, and the general level of interest rates. To provide the potential borrowers an idea of how much credit risk is involved with each issue, rating agencies such as Standard & Poor's and Moody's rate almost all paper. Top credit ratings, however, do not preclude the possibility of default. Hence, to compensate investors for this risk, yields on commercial paper are generally higher than on government securities of similar maturities and most issuers today back their paper with lines of credit from banks.
Convexity
The convexity of a bond measures the curvature of the price/yield relationship of a bond's cash flows. The larger the convexity, the steeper the curvature of the price/yield curve. This behavior is more evident for large changes in yield.
High convexity is frequently a desired characteristic because for a given percentage change in yield, up or down, the bond's percentage price gain will be greater than its percentage price loss. Another way of looking at this is to compare two bonds, one with high convexity and one with low convexity. The highly convex bond will become shorter faster than the low convexity bond for a given rise in rates, and will become longer faster than the low convexity bond for a given fall in rates.
In mathematical terms, convexity is related to the second derivative of price with respect to yield. Whereas modified duration may be used to calculate price changes for small changes in yield, duration and convexity together allow you to estimate price changes for large yield movements according to the following relationship:
dP= -Duration*Price*dY+0.5*Convexity*Price*dYsqrd.
where
dP = change in price ("delta P")
dY = change in yield ("delta Y")
Convexity, in conjunction with modified duration, is used to immunize portfolios for large movements in interest rates (see Immunization).
Coupon
The coupon rate is the annual rate of interest on the bond's face value that the issuer agrees to pay the holder until maturity.
The term "coupon" comes from the manner by which bonds were redeemed historically. Attached to older bond certificates were a series of coupons, one for each coupon payment date stipulated in the bond's indenture. At each coupon payment date, the bondholder would clip the appropriate coupon, and present it for payment. Such issues were known as "coupon" or "bearer" bonds. Today, most issuers no longer issue bearer bonds. Instead, almost all bonds are now offered in book-entry registered form.
Most U.S. bonds pay interest on a semi-annual basis. For example, the Treasury 8 1/8% due 5/15/2021 will pay coupons of 4.0625% of face value on 5/15 and 11/15 of each year until maturity. Most non-US domestic bond issues pay annual coupons. Exceptions are Japanese Government Bonds, UK Gilts, Canadian bonds, and Australian bonds, which pay coupons semi-annually.
In addition to bonds, many money market instruments pay coupons. But unlike bonds, they typically pay a single coupon which occurs at maturity. Short dated Certificates of Deposit (CD's) are an example of these one-coupon securities.
CPR (Constant Prepayment Rate)
This method describes the percentage of the remaining loan balance which is expected to prepay (or has prepaid), above and beyond the scheduled amortization of principal, using a single, unchanging rate. Home equity loan prepayments are often described using a CPR%, and speeds can cover a fairly broad range, e.g. 4% to 25%, depending upon the combination of voluntary prepayments and defaults in the collateral pool.
Credit Risk
Credit risk is the risk that an issuer of a debt security or a borrower may default on its obligations. In a slightly different context, it is also defined as the risk that payment may not be made on the sale of a negotiable instrument (i.e. counter-party risk).
Current Yield
The current yield of a bond is the annual coupon divided by the market price of the bond. It is an inadequate measure of yield because it takes into account neither the entire amount nor the timing of the cash flows of a bond.
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Day Count Basis
In the capital markets, there are a number of ways that days between dates are computed for interest rate calculations. Many of these conventions were developed before the wide spread introduction of computers. The historical rationale for many of these calculations was to simplify the math involved in performing normally complex financial calculations. And as in most industries with a long history, many of these conventions have stayed with us despite considerable advances in computers and computational methods.
The day count basis indicates the manner by which the days in a month and the days in a year are to be counted. The notation utilized to indicate the day count basis is (days in month)/(days in year).
For example, 30/360 assumes that each of the twelve months in a year consists of exactly 30 days. On the other hand, Actual/Actual considers the actual number of days in a month and the actual number of days in a year. Other types of day count basis are Actual/360, Actual/365, and 30/360 European. The 30/360 European day count basis differs from 30/360 basis in the algorithm used to handle the end of the month.
The five basic day count basis are the following:
- Actual/360
- Actual/365
- Actual/Actual
- 30/360
- 30/360 European
Each of these are explained in their own section.
Actual/360
This calculates the actual number of days between two dates and assumes the year has 360 days. Many money market calculations with less than a year to maturity use this day count basis.
For example, a $1MM six month CD issued on 4/15/92 and maturing on 10/15/92, with an 8% coupon would pay an interest payment of:
Actual days between 4/15/92 to 10/15/92 = 183 days
Interest = 0.08 x 1,000,000 x (183/360) = $40,666.67
Actual/365
This calculates the actual number of days between two dates and assumes the year has 365 days.
Using an Actual/365 day count basis, a $1MM six month CD issued on 4/15/92 and maturing on 10/15/92, with an 8% coupon would pay an interest payment of:
Actual days between 4/15/92 to 10/15/92 = 183 days
Interest = 0.08 x 1,000,000 x (183/365) = $40,109.59
Actual/Actual
This day count basis calculates the actual number of days between two dates and assumes the year has either 365 or 366 days depending on whether the year is a leap year. More accurately, if the range of the date calculation includes February 29 (the leap day), the divisor is 366, otherwise the divisor is 365.
Again using our CD example, the interest payment would be:
Actual days between 4/15/92 to 10/15/92 = 183 days
Interest = 0.08 x 1,000,000 x (183/365) = $40,109.59
Notice that even though 1992 is a leap year, the denominator used for this calculation was 365 because February 29, 1992 does not fall into the date range of the calculation. If the issue date was before February 29, the divisor would have been 366 instead.
30/360
This day count convention assumes that each month has 30 days and the total number of days in the year is 360 (12 months x 30 days per month). There are adjustments for February and months with 31 days.
The formula for the 30/360 day calculation is as follows:
Assume Date 1 is of the form M1/D1/Y1 and Date 2 is of the form M2/D2/Y2. Let Date 2 be later than Date 1.
Then:
If D1 = 31, change D1 to 30
If D2 = 31 and D1 = 30, change D2 to 30
Days between dates = (Y2-Y1) x 360 + (M2-M1) x 30 + (D2-D1)
30/360 European
The 30/360 day count basis is different outside of the United States. They further simplified this calculation. The formula for the 30/360 European day calculation follows:
Assume Date 1 is of the form M1/D1/Y1 and Date 2 is of the form M2/D2/Y2. Let Date 2 be later than Date 1.
Then:
If D1 = 31, change D1 to 30
If D2 = 31, change D2 to 30
Days between dates = (Y2-Y1) x 360 + (M2-M1) x 30 + (D2-D1)
Discount Basis
Discount basis refers to the practice of quoting a security in terms of a discount from its par value. For example, a discount of 5% means 100% - 5% = 95%. In this case 95 would be the quoted dollar price of this discount security. Discount securities are non-interest-bearing money market instruments that are issued and traded on a discount basis. They are quoted using either an Actual/360 or an Actual/365 day count convention. Discount securities include U.S. Treasury bills, commercial paper, and banker's acceptances (BA's).
Dollar Duration
Essentially a tool for calculating the hedge ratio (see Swap Hedge Ratio) between different securities, this measurement of duration is defined to be the product of the modified duration of the bond and its full price (dollar price + accrued interest). It has various disguises and aliases, some of the more well-known being dPdY, risk, POPs, etc. It is the preferred method of weighting a swap or arbitrage when one wishes to confine "risk" to that of a change in yield spread between the bond(s) being sold and the bond(s) being purchased.
Mathematically, it is the derivative of price with respect to yield; the main difference between it and modified duration is that the latter is always stated in percentage terms, whereas dollar duration is expressed in units of dollar price.
Dollar Price
The unit in which the market quotes a fixed-income security, usually stated as a percentage of the security's face value, the fractional component of which may be quoted in terms of decimals, 8ths, 32nds, or 64ths. The dollar price does not include accrued interest.
dPdY and Risk
In mathematical terms, dPdY (which is the same thing as dollar duration), is the derivative of price with respect to yield. In simpler terms, dPdY measures the impact of a small change in a security's yield on the security's price.
The higher the dPdY value, the more sensitive the security is to interest rate changes. For example, a security with a dollar duration of 8.0 will be twice as sensitive to the same change in yield as a security with one of 4.0.
dPdY is used to calculate other frequently used bond analytics. For example, the yield value of a 32nd (YV32) basically measures the effect on yield of a 1/32nd change in price. This can be easily calculated from dPdY as follows:
YV32=(1/32)/(dPdY)
Similarly, the price value of an 01 change in yield, PV01, quoted in 32nds may be calculated as follows:
PV01=32*dPdY*0.01
Risk is also related to modified duration by the following equation:
dPdY=Modified Duration*Invoice Price
Duration
The common objective behind the different definitions of duration is to measure the price sensitivity (and, therefore market risk) of a fixed-income security to changes in its yield. In general, one can distinguish between the following duration or duration-related concepts:
- Macaulay's duration
- Modified duration
- Dollar duration, dPdY, or "risk"
- Price value of an 01
- Yield value of a 32nd
Macaulay's Duration
If a bond is viewed as a series of cash flows, this concept measures sensitivity (in years) as the present value-weighted average of the cash flows of the bond. As such, it is a good measure for ranking different bonds as to their price sensitivity, and for constructing portfolios which will fully defease a future series of cash flows (see Immunization).
Modified Duration
The exact measurement of the price sensitivity of a fixed-income security to a very small change in yield, expressed as a % change in price to a 1% change in yield. Since the price/yield relationship is not linear, the calculation is only exact for very small changes around the initial yield.
Dollar Duration, dPdY, or Risk
Essentially a tool for calculating the hedge ratio between different securities, this measurement of duration is defined to be the product of the modified duration of the bond and its full price (dollar price plus accrued interest).
Price value of an 01, Yield value of a 32nd
The concept of duration is frequently used by market participants to "immunize" portfolios (see Immunization). Since many institutional investors have liabilities that must be met on schedule with the proceeds of a bond portfolio, immunization attempts to ensure that regardless of what happens to interest rate levels between the present and the due date of one's liabilities, enough cash will be available to meet them.
Duration and convexity are risk estimation tools which allow the manager to structure the portfolio so as to offset the two counterbalancing risks in the fixed-income world: market risk, whereby prices and yields move inversely in proportion to "longness"; and reinvestment risk, whereby as prices rally securities sold and new cash flows are reinvested at lower yield levels, and conversely.
Duration (Macaulay's)
If a bond is viewed as a series of cash flows, this concept of duration measures price sensitivity (in years) as the present value-weighted average of the cash flows of the bond, according to the formula:
DurMac = ( Formula to be represented at a later date)
where
N = total number of compounding periods to maturity
P$ = dollar price of the bond
As such, it is a good measure for ranking different bonds as to their price sensitivity, and for constructing portfolios which will fully defease a future series of cash flows (see Immunization).
Duration (Modified)
The exact measurement of the price sensitivity of a fixed-income security to a very small change in yield, expressed as a % change in price to a 1% change in yield. Since the price/yield relationship is not linear, the calculation is only exact for very small changes around the initial yield.
The main difference between modified duration and dollar duration, dPdY or risk lies in that modified duration is expressed as a percentage, whereas the modified duration is expressed in terms of actual dollar price values.
Its relationship to Macaulay's duration (DurMac) can be stated as follows:
DurMod=(-DurMac)/(1+(Yield/2))
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Effective Margin
The coupon rate for a floating-rate security periodically changes based on a predetermined index such as the prime rate or the three-month Treasury bill. Given this uncertainty, the true value of the cash flows cannot be determined, and hence, yield to maturity cannot be calculated.
A security's effective margin measures the potential return for a floating-rate security. It measures the average spread or margin over the underlying index that an investor can earn over the life of the security.
While this measure has its merits, it nevertheless overlooks two important aspects that may affect the potential return from investing in a floating-rate security. First, effective margin assumes that the index will remain constant. Second, this measure does not take into account the cap or floor on the security, if any exists.
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Face Value/Par Amount
The face amount, or face value, of a security is the amount the issuer pays the holder at maturity. Different security types have different face value denominations. Most bonds are quoted in multiples of $1,000 face value. For example, 50 bonds would be equivalent to holding $50,000 face value of a bond.
First Coupon Date
The first coupon date is the date on which the first cash coupon payment will be made. Since most bond issues in the US pay semi-annually, normally their first coupons are paid exactly 6 months after they are issued. Such issues are said to have normal first coupons.
Sometimes, however, the amount of the first coupon is not equal to 1/2 the issue's coupon rate, because for some reason the bonds were issued before or after the date 6 months prior to the first coupon date. Such issues are said to have "short" (first coupon < normal coupon) or "long" (first coupon > normal coupon) first coupon periods.
For example, the U.S. Treasury 7 3/4% due 3/31/96 were originally 5-year notes with a short first coupon. The Federal Reserve would have normally issued the note on 3/31/91. But, since 3/31/91 was a Sunday, the actual issue date was 4/1/91. Therefore, the first coupon was less than the normal 3.875% since the first coupon period was one day less than a normal coupon period.
In order to calculate the odd first coupon correctly, both the issue date and the first coupon date must be specified (the first coupon date may be deduced). However, if the settlement date (or valuation date) is beyond the first coupon date, both the issue date and the first coupon date become irrelevant for analytical purposes, since all remaining coupons will be normal.
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Governments
Securities issued by the U.S. Government such as Treasuries. Debt issues of federal agencies.
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Horizon Analysis
Horizon analysis is a method of analyzing the cash flows and total return of a security before maturity using user-supplied assumptions, with the intention of assessing relative values. In what follows, "security" can be replaced with "portfolio", since the same principles apply.
The basic form of the analysis is as follows: The security is priced on the valuation date (which is used for settlement date in the calculations). We will assume that its full price is X. The analyst chooses a date in the future which will be the horizon date, and determines the horizon period, N. Any coupon payments or repayments of principal are assumed to be reinvested at a user-specified reinvestment rate until the horizon date. At the horizon date, the security is again priced. We will assume an ending value of Y. The horizon return is the effective return of these cash flows assuming semi-annual compounding such that following identity is maintained:
Y= ( Formula to be represented at a later date )
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IRR
The "internal rate of return" is the discount rate which equates the present value of the future cash flows of an investment to the cost of the investment. Hence, the net present values of cash outflows and cash inflows equal zero when IRR is used as the discount rate. The yield to maturity in an IRR.
Immunization
Immunization is the structuring of a portfolio in such a way that any changes in the general level of interest rates will not negatively affect the total expected return from a bond or bond portfolio. There are some important assumptions underlying immunization through duration, chief among which are that when the general level of rates changes, all rates change in a parallel fashion, and that such changes will be "moderate". The latter assumption is necessary when convexity is not used, since duration is only accurate for relatively small changes around the status quo.
Immunization is an approach to interest-rate risk, not credit risk. It addresses the other two principal sources of risk in a bond portfolio: market risk and reinvestment risk. Briefly, the duration of a bond, or of a portfolio, measures exactly that investment horizon where market risk and reinvestment risk offset one another. Hence, it represents that time frame over which the currently available total return is assured.
Interest Rate Risk
Risk associated with fluctuations of bond prices in response to the general movement of the interest rates and to changes in investor perceptions of government monetary policy and economic data.
Invoice Price
The invoice price of a security is its quoted price plus any accrued interest on the next coupon, where the interest is accrued to the valuation date.
Issue Date
The issue date is the first day a fixed income security begins accruing interest. Most issues have issue dates that occur on a six month anniversary date of maturity. But some bonds are issued on odd dates. These odd-first coupon bonds pay a different coupon amount during their first coupon period. See First Coupon Date.
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Jumbos
CD's denominated at a $100000 minimum, usually bought and sold by large financial institutions.
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Liquidity
The ability to convert a security or asset quickly into cash. A much desired quality in investing.
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Market Risk
Market risk is synonymous to the classic price/yield behavior of bonds. As yields fall, bond prices rise; as yields rise, bond prices fall. In some contexts, this phenomenon may be called "interest rate risk" or "price risk".
Maturity
The maturity of a security is the date the issuer makes the final payment to the security holder. After maturity, no further obligations or rights exist between the two parties. Typically, at maturity the issuer pays the redemption value to the holder, along with the final coupon payment.
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Net Amount
The amount which appears on a trade confirmation is the amount the buyer has to pay, or equivalently, the amount the seller has to receive. It is computed as the follows:
Net Amount = Par Amount * Dollar Price + Accrued Interest
Synonyms for net amount include net proceeds and invoice price.
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Odd Lot
Bonds traded at the less than normal trading units.
Option Adjusted Spread (OAS)
The spread over the Treasury spot curve which equates the present value of a bond's cashflows to its market price, incorporating the fact that the bond's cashflows may change under different interest rate environments. For corporate bonds with embedded options, the OAS is derived using a "finite difference grid" to examine the impact of option features on cashflows across interest rates and through time. For mortgage-backed securities (pass-throughs, CMOs and ARMs), OAS is derived using a Monte Carlo simulation which generates cashflows along various interest rate paths, using the appropriate prepayment model. The spread over the initial Treasury spot curve which equates the average present value of the cashflows across these various paths to the market price of the security is the OAS.
Option Adjusted Yield (OAY)
For corporate bonds, this is calculated by adding/(subtracting) the value of a call option/(put option) to the bond's market price to obtain the price of an otherwise equivalent but option-free bond. The yield which equates this new higher/(lower) price to the bond's cashflows to maturity is the Option Adjusted Yield. For mortgage-backed securities (pass-throughs and CMOs), this is calculated by first generating the cashflows produced by the vector of single monthly mortality rates (SMMs) based on today's forward curve. These cashflows, which may be thought of as the cashflows which exclude the time value of the prepayment option, are discounted by today's spot curve plus the bonds OAS to derive a theoretical option-adjusted price. The single IRR which equates the SMM cashflows to this theoretical price is the Option Adjusted Yield.
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Price
The price of a security is typically quoted as a percentage of face value. It is also sometimes referred to as the "clean price". The actual payment that is exchanged between two parties may be different from the quoted price. For example, bonds between coupon payments accrue interest that is proportional to the coupon period. Therefore, the buyer has to pay the seller the quoted price of the security plus any accrued interest. This sum is known as the invoice price of the bond.
Most securities are quoted as a percent in decimal. For example, a corporate bond quoted as 101.125 is equal to 101 and 1/8th percent. Almost all foreign-denominated securities are quoted in decimal.
Treasury and federal agency securities are quoted in 32nds and halves of a 32nd. For example, a price of 101-12 is equal to 101 and 12/32nds percent. As a convention, many market participants use a "+" (plus sign) to denote 1/2 of 1/32nd or 1/64th percent. For example, a price of 101-12+ implies a price of 101 + 12/32nds + 1/64ths percent.
Recently, due to increased competitive pressures in the marketplace, another convention has been adopted for instruments trading in 32nds. The two places to the right of the decimal point remain in 32nds. A third decimal place was added to represent 1/8ths of a 32nd or 1/256th. For example, a price of 101.126 implies a price of 101 + 12/32nds + 6/256ths percent.
Though these conventions seem confusing, most market participants are familiar with the quoting conventions of securities they frequently trade.
Exercise caution when trading across market sectors. There is a big difference between 101.16 quoted in 32nds and 101.16 quoted in decimal. This warning holds true for day count conventions as well. As a general rule, verify the conventions in use when in doubt.
Price Convention Units
By convention, the markets quote certain types of bonds in 32nds of 1 point, others in 8ths of 1 point, and others in decimals or decimals derived from yield quotes. For consistency, references to prices such as price value of an 01 are usually quoted in these price convention units as well, although strictly speaking, they are just prices quotes in different bases.
Price Risk
Price risk is the risk that a debt security's price may change due to a rise or fall in the prevailing level of interest rates. For a related definition, see Market Risk.
Price Value of an 01
The price value of an 01 is the change in price of a security based on a 0.01% change in yield. It is usually quoted in the price convention units of the security (i.e., 32nds for Treasuries, decimals for corporates). It is also known as dollar value of an 01.
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Quoted Price
The price at which the last sale and purchase of a security took place.
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Redemption Value
Most securities pay 100% of face value (par) at maturity. Some may pay more or less at redemption, depending upon call and put terms for the issue. These amounts would be paid on corresponding call and/or put dates. Redemption value is that amount which is paid to redeem the securities.
Reinvestment Rate
The reinvestment rate is the rate at which intermediate income will be invested. Many securities like bonds make intermediate payments between the settlement date (or valuation date) and some horizon date. To analyze the return of all these cash flows, the intermediate payments are assumed to be reinvested at a user-defined reinvestment rate until the investment horizon date.
Reinvestment Risk
Reinvestment risk refers to the risk that a bondholder may only be able to reinvest his coupons at a lower rate than originally planned. If yields fall, his reinvestment income and consequently his total return from holding the bond will fall relative to the original yield. Conversely, if yields rise, total return will also rise.
The time to maturity and the coupon rate determine the degree of reinvestment risk. For a given yield to maturity and a given coupon rate, the longer the maturity, the greater the reinvestment risk. A long maturity implies that the bond's total return is heavily dependent on interest earned on coupon payments in order to realize the yield to maturity at the time of purchase. Likewise, for a given maturity and a given yield to maturity, higher coupon payments translate to greater reinvestment risk.
Risk-Free Rate
This refers to the return on a risk-free investment, with risk taken to mean "credit risk". An example is the yield on the three-month Treasury bill. Given that this security carries the explicit backing of the U.S. Government and that its term is short enough to minimize the risks of inflation and market interest rate changes, the yield on this T-Bill may be considered risk-free.
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Settlement Date
Settlement date is the date when a security and the payment for it are actually exchanged between buyer and seller. It is also commonly known as the valuation date.
Settlement date is sometimes confused with trade date. The latter is the date on which the buyer and seller agree to the amount, price, and other terms of the trade, while settlement is the date on which the terms of the transaction are executed. Historically, settlement date occurred several days after the trade date, thus allowing for physical delivery and payment of the agreed upon transaction. As technology improved and bonds were registered in book entry form, this time delay has been shortened.
Most bonds settle with either next day settlement or five business day settlement. Holidays and weekends are excluded from the count. Five day settlement is frequently called "corporate settlement", since most corporate bonds still settle this way. Occasionally, especially among dealers, some securities can be traded for same day settlement, known as "cash settlement". Book entry registration and payment occur electronically on trade date.
Swap Hedge Ratios
A swap hedge ratio answers the question: "If I sell Bond A, how much of Bond B should I buy to achieve my swap objectives?" While there have been various weighting schemes over the years, and while there may be good reasons for using such schemes as "$ for $ swap", the "dollar duration"-based approaches are the ones which answer the above question most appropriately for most investors.
$ for $ Swap
A bond swap in which the weighting is established by dividing the net proceeds of the "sell" security by the net proceeds of the "buy" security, rounding down to the nearest number of whole "buy" bonds. Note that you may purchase more or less of the second bond depending on the bonds' respective invoice prices. For example, when you sell 1,000M face value of the first bond at 110.00%, your proceeds amount to $1,100M (assuming no accrued interest is due). With this, you may purchase 1,100M of bonds trading at par.
Par for Par Swap
A bond swap in which the investor replaces the par value of the bonds sold with exactly the same par amount of bonds purchased. This only makes sense if the swap represents a trade between two bonds which are virtually substitutes for one another.
Yield Value of a 32nd Swap
A bond swap in which the weighting of the two bonds is made according to the respective values of the yield values of a 32nd. This weighting will be very close to weighting the trade according to a duration scheme.
Dollar duration, dPdY, or "risk" Swap
A bond swap in which the weighting of the two bonds is made according to their respective measures of $ duration, defined to be the product of the modified duration of the bond and its full price (dollar price plus accrued interest).
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Tom Next
Tom next or "tomorrow next" refers to a transaction in the interbank market in Eurodollar deposits and the foreign exchange market with a next business day value or delivery date.
Total Return Analysis
Total return calculates the effective return of a security (or portfolio of securities) over a specified holding period, taking into account all scheduled payments, beginning and ending securities values, and reinvestment income earned from investing the cash flows generated within the holding period.
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Underwrite
To assume the risk of buying a new security issue from a corporate or federal entity, and profiting or losing by reselling at a spread between a fluctuating public offering price and the purchase price.
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Volatility
A relative measure of how rapidly the price of a security falls or rises within a short period of time.
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WAC (Weighted Average Coupon)
An arithmetic mean of the coupon rate of the underlying mortgage loans or pools that serve as collateral for a security.
WAC is calculated by (1) Multiplying the purchased unpaid principal balance of each mortgage by its coupon rate (resulting in a "product" for each mortgage) (2) Adding the products for all of the mortgages (3) Dividing the sum by the aggregate purchased unpaid principal balance of all the mortgages in the group.
WALA (Weighted Average Loan Age)
The weighted average number of months since the date of note origination of the mortgages in the Participation Certificate pool.
WAM (Weighted Average Maturity)
An arithmetic mean of the remaining term to maturity of the underlying mortgage loans that collateralize a security.
WARM (Weighted Average Remaining Maturity)
The WARM of any group of mortgages is calculated by (1) Multiplying the unpaid principal balance of each mortgage by the number of months remaining to maturity (resulting in a "product" for each mortgage), (2) Adding the products for all of the mortgages, (3) Dividing the sum by the aggregate unpaid principal balance of all the mortgages in the group.
When Issued
Term for a Treasury bond transaction conditionally made because the bond, although authorized, has not yet been issued.
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Yield
Also known as "yield to maturity", yield is defined as the internal rate of return of a security's cash flows. It is that discount rate which equates a bond's invoice price (principal + accrued interest) with the present value of its coupon and principal payments.
For most securities, this rate is quoted in terms of the compounding convention of the security. Money market instruments quote yield on a simple interest basis, whereas bonds are quoted on a semi-annual, compounded basis.
Except in the case of zero-coupon instruments, "yield" is not an assured rate. In addition, it suffers from the inherent limitations of any internal rate of return (see IRR). This is one of the reasons why there exist other frameworks within which to compare securities.
Yield to Call
The yield to call is the interest rate that will make the present value of the cash flows equal to the price paid for the bond if it is held to its first call date.
Yield to call is computed in the same manner as yield to maturity, except that the maturity date is replaced by the first call date and that the redemption value at maturity is replaced by the call price.
Yield to Maturity
Yield to maturity (YTM) is the internal rate of return of a bond. In calculating YTM, coupon income, redemption value, interest earned on interest, as well as the timing of each cash flow, are all taken into account from settlement to maturity. All intermediate cash flows are reinvested at the YTM itself. The YTM may only be realized when the bond is held to maturity and all cash flows are reinvested at exactly the YTM rate.
Yield Value of a 32nd
The yield value of an 32nd measures the amount by which the yield on a security would change if its price moved by 1/32. This is a price sensitivity measurement.
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Zero Coupon Bond
A bond that pays no periodic interest and sold at a deep discount from the face value. Buyer's rate of return comes from the gradual appreciation of the bond.
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