The Z-spread, ZSPRD, zero-volatility spread, or yield curve spread of a bond is the parallel shift or spread over the zero-coupon Treasury yield curve required for discounting a pre-determined cash flow schedule to arrive at its present market price. The Z-spread is also widely used in the credit default swap (CDS) market as a measure of credit spread that is relatively insensitive to the particulars of specific corporate or government bonds.
Since the Z-spread uses the entire yield curve to value the individual cash flows of a bond, it provides a more realistic valuation than an interpolated yield spread based on a single point of the curve, such as the bond's final maturity date or weighted-average life. However, the Z-spread does not incorporate variability in cash flows, so a fuller valuation of an interest-rate-dependent security often requires the more realistic (and more complicated) option-adjusted spread (OAS).
The Z-spread of a bond is the number of basis points (bp, or 0.01%) that one needs to add to the Treasury yield curve (or technically to Treasury forward rates) so that the Net present value of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (including accrued interest). The spread is calculated iteratively.
For a mortgage-backed security, a projected prepayment rate tends to be stated; for example, the PSA assumption for a particular MBS might equate a particular group of mortgages to an 8-year amortizing bond with 6% mortality per annum. This gives a single series of nominal cash flows as if the MBS were a riskless bond. If these payments are discounted to net present value (NPV) with a riskless zero-coupon Treasury yield curve, the sum of their values will tend to overestimate the market price of the MBS. This difference arises because the MBS market price incorporates additional factors such as liquidity and credit risk and embedded option cost.
The Z-spread is widely used as the "cash" benchmark for calculating the CDS basis. The CDS basis is commonly the CDS fee minus the Z-spread for a fixed-rate cash bond of the same issuer and maturity. For instance, if a corporation's 10-year CDS is trading at 200 bp and the Z-spread for the corporation's 10-year cash bond is 287 bp, then its 10-year CDS basis is –87 bp.
Assume that on 7/1/2008:
Then the price P of this bond on 7/1/2008 is given by:
where (for simplicity) the calculation has ignored the slight difference between parallel shifts of spot rates and forward rates.
In economics and finance, arbitrage is the practice of taking advantage of a difference in prices in two or more markets – striking a combination of matching deals to capitalise on the difference, the profit being the difference between the market prices at which the unit is traded. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price.
In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.
In finance, a bond is a type of security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to provide cash flow to the creditor. The timing and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds. The interest is usually payable at fixed intervals: semiannual, annual, and less often at other periods. Thus, a bond is a form of loan or IOU. Bonds provide the borrower with external funds to finance long-term investments or, in the case of government bonds, to finance current expenditure.
In finance, the yield on a security is a measure of the ex-ante return to a holder of the security. It is one component of return on an investment, the other component being the change in the market price of the security. It is a measure applied to fixed income securities, common stocks, preferred stocks, convertible stocks and bonds, annuities and real estate investments.
United States Treasury securities, also called Treasuries or Treasurys, are government debt instruments issued by the United States Department of the Treasury to finance government spending in addition to taxation. Since 2012, U.S. government debt has been managed by the Bureau of the Fiscal Service, succeeding the Bureau of the Public Debt.
The yield to maturity (YTM), book yield or redemption yield of a fixed-interest security is an estimate of the total rate of return anticipated to be earned by an investor who buys a bond at a given market price, holds it to maturity, and receives all interest payments and the capital redemption on schedule. It is the (theoretical) internal rate of return : the discount rate at which the present value of all future cash flows from the bond is equal to the current price of the bond. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more often market convention is followed. In a number of major markets the convention is to quote annualized yields with semi-annual compounding ; thus, for example, an annual effective yield of 10.25% would be quoted as 10.00%, because 1.05 × 1.05 = 1.1025 and 2 × 5 = 10.
In finance, the yield curve is a graph which depicts how the yields on debt instruments – such as bonds – vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity.
Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates. In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance. Convexity was based on the work of Hon-Fei Lai and popularized by Stanley Diller.
The current yield, interest yield, income yield, flat yield, market yield, mark to market yield or running yield is a financial term used in reference to bonds and other fixed-interest securities such as gilts. It is the ratio of the annual interest (coupon) payment and the bond's price:
Floating rate notes (FRNs) are bonds that have a variable coupon, equal to a money market reference rate, like SOFR or federal funds rate, plus a quoted spread. The spread is a rate that remains constant. Almost all FRNs have quarterly coupons, i.e. they pay out interest every three months. At the beginning of each coupon period, the coupon is calculated by taking the fixing of the reference rate for that day and adding the spread. A typical coupon would look like 3 months USD SOFR +0.20%.
A corporate bond is a bond issued by a corporation in order to raise financing for a variety of reasons such as to ongoing operations, mergers & acquisitions, or to expand business. The term is usually applied to longer-term debt instruments, with maturity of at least one year. Corporate debt instruments with maturity shorter than one year are referred to as commercial paper.
Fixed-income arbitrage is a group of market-neutral-investment strategies that are designed to take advantage of differences in interest rates between varying fixed-income securities or contracts. Arbitrage in terms of investment strategy, involves buying securities on one market for immediate resale on another market in order to profit from a price discrepancy.
Fixed-income attribution is the process of measuring returns generated by various sources of risk in a fixed income portfolio, particularly when multiple sources of return are active at the same time.
In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps.
In finance, mortgage yield is a measure of yield of mortgage-backed bonds. It is also known as cash flow yield. The mortgage yield, or cash flow yield, of a mortgage-backed bond is the monthly compounded discount rate at which net present value of all future cash flows from the bond will be equal to the present price of the bond.
An asset swap refers to an exchange of tangible for intangible assets, in accountancy, or, in finance, to the exchange of the flow of payments from a given security for a different set of cash flows.
In finance, par yield is the yield on a fixed income security assuming that its market price is equal to par value. Par yield is used to derive the U.S. Treasury’s daily official “Treasury Par Yield Curve Rates”, which are used by investors to price debt securities traded in public markets, and by lenders to set interest rates on many other types of debt, including bank loans and mortgages.
Option-adjusted spread (OAS) is the yield spread which has to be added to a benchmark yield curve to discount a security's payments to match its market price, using a dynamic pricing model that accounts for embedded options. OAS is hence model-dependent. This concept can be applied to a mortgage-backed security (MBS), or another bond with embedded options, or any other interest rate derivative or option. More loosely, the OAS of a security can be interpreted as its "expected outperformance" versus the benchmarks, if the cash flows and the yield curve behave consistently with the valuation model.
