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Basis
Basis is a term used in mathematics, finance, science, and other contexts to refer to foundational concepts, valuation measures, or organizational names; here, it may refer to: Finance and accounting * Adjusted basis, the net cost of an asset after adjusting for various tax-related items * Basis point, 0.01%, often used in the context of interest rates * Basis swap, an interest rate swap * Cost basis, in income tax law, the original cost of property adjusted for factors such as depreciation * Tax basis, cost of an asset Securities markets and trading strategies * Basis trading, a trading strategy consisting of the purchase of a security and the sale of a similar security Fixed income markets: * Treasury basis trade, a leveraged arbitrage strategy exploiting price differences between Treasury securities and futures contracts * Index arbitrage, a strategy that exploits price differences between a stock index and its futures contract Commodities and physical assets: * Commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis (linear Algebra)
In mathematics, a Set (mathematics), set of elements of a vector space is called a basis (: bases) if every element of can be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to . The elements of a basis are called . Equivalently, a set is a basis if its elements are linearly independent and every element of is a linear combination of elements of . In other words, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the dimension (vector space), dimension of the vector space. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces. Basis vectors find applications in the study of crystal structures and frame of reference, frames of reference. De ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis (options)
Basis trading is a financial strategy involving offsetting positions in a spot (cash) asset and a related derivative—most commonly a futures contract – aimed to profit from price convergence over time. The price difference is known as the basis. Basis trading is used across multiple asset classes, including commodities, fixed income, equities, and digital assets. Definition of basis In finance, the basis typically refers to the difference between the spot price of an asset and the price of a related futures contract: :Basis = Spot price − Futures price The basis reflects various factors including storage costs interest rates, expected dividends (''see Dividend yield''), and time to maturity (see '' Bond''). The concept is used in assessing arbitrage opportunities and in designing hedging strategies. Types of basis trading Basis trading strategies are employed across multiple markets: Treasury basis trade: Refers to a position established through the sale of a T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Trading
Basis trading is a financial strategy involving offsetting positions in a spot (cash) asset and a related derivative—most commonly a futures contract – aimed to profit from price convergence over time. The price difference is known as the basis. Basis trading is used across multiple asset classes, including commodities, fixed income, equities, and digital assets. Definition of basis In finance, the basis typically refers to the difference between the spot price of an asset and the price of a related futures contract: :Basis = Spot price − Futures price The basis reflects various factors including storage costs interest rates, expected dividends (''see Dividend yield''), and time to maturity (see ''Bond (finance), Bond''). The concept is used in assessing arbitrage opportunities and in designing hedging strategies. Types of basis trading Basis trading strategies are employed across multiple markets: Treasury basis trade: Refers to a position established through the sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treasury Basis Trade
Treasury basis trading is a financial strategy that involves taking offsetting positions in a cash market instrument (typically a U.S. Treasury bond) and its related derivative, such as a Treasury futures contract. The strategy seeks to exploit pricing discrepancies between the two instruments, which are expected to converge over time. It is a specialized form of basis trading applied to U.S. government securities. Mechanics of the trade In a typical Treasury basis trade, a trader: * Buys a Treasury bond in the cash market (often financing the purchase via repurchase agreements, or repos), and * Sells short a corresponding Treasury futures contract. The expectation is that the price differential (or "basis") between the cash bond and the futures contract will narrow favorably before the futures contract expires. The trade becomes profitable if the bond price, plus coupon income and financing costs, is lower than the futures delivery price at expiration. Definition of basis "Basis" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjusted Basis
In tax accounting, adjusted basis is the net cost of an asset after adjusting for various tax-related items. Adjusted Basis or Adjusted Tax Basis refers to the original cost or other basis of property, reduced by depreciation deductions and increased by capital expenditures. Example: Michael buys a lot for $100,000. He then erects a retail facility for $600,000, then depreciates the improvements for tax purposes at the rate of $15,000 per year. After three years his adjusted tax basis is $655,000 = $100,000 + $600,000 - (3 x $15,000). Adjusted basis is one of two variables in the formula used to compute gains and losses when determining gross income for tax purposes. The Amount Realized – Adjusted Basis tells the amount of Realized Gain (if positive) or Realized Loss (if negative). Statutory definition Section 1012 of the Internal Revenue Code defines “basis” as a taxpayer's cost in acquiring property, except as provided in Sections 1001–1092. There is also an exceptio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cost Basis
Basis (or cost basis), as used in United States tax law, is the original cost of property, adjusted for factors such as depreciation. When a property is sold, the taxpayer pays/(saves) taxes on a capital gain/(loss) that equals the amount realized on the sale minus the sold property's basis. Cost basis is needed because tax is due based on the gain in value of an asset. For example, if a person buys a rock for $20, and sells the same rock for $20, there is no tax, since there is no profit. If, however, that person buys a rock for $20 and then sells the same rock for $25, then there is a capital gain on the rock of $5, which is thus taxable. The purchase price of $20 is analogous to cost of sales. Typically, capital gains tax is due only when an asset is sold. However, the rules for this are very complicated. If tax is paid because the value has increased, the new value will be the cost basis for any future tax. Internal Revenue Service (IRS) Publication 551 contains the IRS's d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Swap
A basis swap is an interest rate swap which involves the exchange of two floating rate financial instruments. A basis swap functions as a floating-floating interest rate swap under which the floating rate payments are referenced to different bases. The existence of a basis arises from demand and supply imbalances and where, for example, a basis is due for a borrower seeking dollars, this is indicative of a synthetic dollar interest rate in the FX market pricing higher than the direct dollar interest rate. The existence of the basis is a violation of the covered interest rate parity (CIP) condition. Usage of basis swaps for hedging Basis risk occurs for positions that have at least one paying and one receiving stream of cash flows that are driven by different factors and the correlation between those factors is less than one. Entering into a Basis Swap may offset the effect of gains or losses resulting from changes in the basis, thus reducing basis risk. # against exposure to curr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gröbner Basis
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K _1,\ldots,x_n/math> over a field K. A Gröbner basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite. Gröbner basis computation is one of the main practical tools for solving systems of polynomial equations and computing the images of algebraic varieties under projections or rational maps. Gröbner basis computation can be seen as a multivariate, non-linear generalization of both Euclid's algorithm for computing polynomial greatest common divisors, and Gaussian elimination for linear systems. Gröbner bases were introduced by Bruno Buchberger in his 1965 Ph.D. thesis, which also included an algorithm to compute them ( Buchberger's alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthonormal Basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite Dimension (linear algebra), dimension is a Basis (linear algebra), basis for V whose vectors are orthonormal, that is, they are all unit vectors and Orthogonality_(mathematics), orthogonal to each other. For example, the standard basis for a Euclidean space \R^n is an orthonormal basis, where the relevant inner product is the dot product of vectors. The Image (mathematics), image of the standard basis under a Rotation (mathematics), rotation or Reflection (mathematics), reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for \R^n arises in this fashion. An orthonormal basis can be derived from an orthogonal basis via Normalize (linear algebra), normalization. The choice of an origin (mathematics), origin and an orthonormal basis forms a coordinate frame known as an ''orthonormal frame''. For a general inner product space V, an orthono ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Basis
In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimension of V), the dual set of B is a set B^* of vectors in the dual space V^* with the same index set I such that B and B^* form a biorthogonal system. The dual set is always linearly independent but does not necessarily span V^*. If it does span V^*, then B^* is called the dual basis or reciprocal basis for the basis B. Denoting the indexed vector sets as B = \_ and B^ = \_, being biorthogonal means that the elements pair to have an inner product equal to 1 if the indexes are equal, and equal to 0 otherwise. Symbolically, evaluating a dual vector in V^* on a vector in the original space V: : v^i\cdot v_j = \delta^i_j = \begin 1 & \text i = j\\ 0 & \text i \ne j\text \end where \delta^i_j is the Kronecker delta symbol. Introduction To perform operations with a vector, we must have a straightforward method of calculating its components. In a Cartesia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Point
A basis point (often abbreviated as bp, often pronounced as "bip" or "beep") is one hundredth of 1 percentage point. Changes of interest rates are often stated in basis points. For example, if an existing interest rate of 10 percent is increased by 1 basis point, the new interest rate would be 10.01 percent. The related term '' permyriad'' means one part per ten thousand. Definition :1 basis point (bp) = 0.01%, 10−4, , or 0.0001. :10 bp = 0.1%, 10−3, , or 0.001. :100 bp = 1%, 10−2, , or 0.01. Basis points are used as a convenient unit of measurement in contexts where percentage differences of less than 1% are discussed. The most common example is interest rates, where differences in interest rates of less than 1% per year are usually meaningful to talk about. For example, a difference of 0.10 percentage points is equivalent to a change of 10 basis points (e.g., a 4.67% rate increases by 10 basis points to 4.77%). In other words, an increase of 100 basis points means a ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Function
In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors. In numerical analysis and approximation theory, basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points). Examples Monomial basis for ''Cω'' The monomial basis for the vector space of analytic functions is given by \. This basis is used in Taylor series, amongst others. Monomial basis for polynomials The monomial basis also forms a basis for the vector space of polynomials. After all, every polynomial can be written as a_0 + a_1x^1 + a_2x^2 + \cdots + a_n x^n for some n \in \mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
