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Risks to Consider: Although closely correlated stock pairs generally come back into sync with each other after diverging, there is no rule that says this has to happen. Stock pairs can stay out of sync for a substantial period of time, depending on the underlying circumstances. Always use stops and position size properly.
In addition, the idea is not just limited to two stocks. The same idea can be applied to groups of three or more correlated names. However, special software is often employed to manage multiple-issue statistical arbitrage.
For example, let's say Coca-Cola started rapidly climbing higher than Pepsico. Savvy statistical arbitrage traders would short Coca-Colashares in anticipation of its price falling back into the historic correlation.
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An important fact concerning cellularity is the Erdos-Tarski theorem: if the cellularity of a BA is a singular cardinal, then there actually is a set of disjoint elements of that size; for cellularity regular limit (inaccessible), there are counterexamples. Every infinite complete BA has an independent subset of the same size as the algebra. Every infinite BA A has an irredundant incomparable subset whose size is the π-weight of A. Every interval algebra has countable independence. A superatomic algebra does not even have an infinite independent subset. Every tree algebra can be embedded in an interval algebra. A BA with only the identity automorphism is called rigid. There exist rigid complete BAs, also rigid interval algebras and rigid tree algebras.
These laws are better understood in terms of the basic example of a BA, consisting of a collection A of subsets of a set X closed under the operations of union, intersection, complementation with respect to X, with members ∅ and X. One can easily derive many elementary laws from these axioms, keeping in mind this example for motivation. Any BA has a natural partial order ≤ defined upon it by saying that x ≤ y if and only if x + y = y. This corresponds in our main example to ⊆. Of special importance is the two-element BA, formed by taking the set X to have just one element. The two-element BA shows the direct connection with elementary logic. The two members, 0 and 1, correspond to falsity and truth respectively. The Boolean operations then express the ordinary truth tables for disjunction (with +), conjunction (with ·) and negation (with −). An important elementary result is that an equation holds in all BAs if and only if it holds in the two-element BA. Next, we define x ⊕ y = (x · −y) + (y · −x). Then A together with ⊕ and ·, along with 0 and 1, forms a ring with identity in which every element is idempotent. Conversely, given such a ring, with addition ⊕ and multiplication, define x + y = x ⊕ y ⊕ (x · y) and −x = 1 ⊕ x. This makes the ring into a BA. These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent. This puts the theory of BAs into a standard object of research in algebra. An atom in a BA is a nonzero element a such that there is no element b with 0 < b < a. A BA is atomic if every nonzero element of the BA is above an atom. Finite BAs are atomic, but so are many infinite BAs. Under the partial order ≤ above, x + y is the least upper bound of x and y, and x · y is the greatest lower bound of x and y. We can generalize this: ΣX is the least upper bound of a set X of elements, and ΠX is the greatest lower bound of a set X of elements. These do not exist for all sets in all Boolean algebras; if they do always exist, the Boolean algebra is said to be complete.
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A Boolean algebra (BA) is a set A together with binary operations + and · and a unary operation −, and elements 0, 1 of A such that the following laws hold: commutative and associative laws for addition and multiplication, distributive laws both for multiplication over addition and for addition over multiplication, and the following special laws:
The B-valued universe is the proper class V(B) which is the union of all of these Vs. Next, one defines by a rather complicated transfinite recursion over well-founded sets the value of a set-theoretic formula with elements of the Boolean valued universe assigned to its free variables
Every BA is isomorphic to a Lindenbaum-Tarski algebra. However, one of the most important uses of these classical Lindenbaum-Tarski algebras is to describe them for important theories (usually decidable theories). For countable languages this can be done by describing their isomorphic interval algebras. Generally this gives a thorough knowledge of the theory. Some examples are:
A basic result of Tarski is that the elementary theory of Boolean algebras is decidable. Even the theory of Boolean algebras with a distinguished ideal is decidable. On the other hand, the theory of a Boolean algebra with a distinguished subalgebra is undecidable. Both the decidability results and undecidablity results extend in various ways to Boolean algebras in extensions of first-order logic.
Create a Forecast from the Deseasonalized DataYou can now use any of the straight-line forecasting tools on the deseasonalized data. (I covered four methods of straight-line forecasting during the Webcast. This article will show only one method. You can use any of the desired methods.)
CFO contributor Bill Jelen is the author of 32 books on Excel, including Pivot Table Data Crunching. You have the chance to win a copy of one of his books by posting a question to the Community Center on the right. If Bill selects your question as the topic of a future column, we’ll send you a book as a thank-you. Bill’s next MrExcel Webcast, on consolidating data for financial reporting, is Thursday, July 14, at 2:00 Eastern Time.
1. Start with sales data by month for several years. It is important that the historical data contain a multiple of 12 months. I used five years of history in this example. The data could run from January 2006 through December 2010, or it could run from July 2007 through June 2011. The important part is that every month is represented by the same number of annual data points. If you have five Decembers, then you should have five Junes. Having five of some month and six of other months will skew the seasonal indices.
IS it possible to send a copy of the actual excel file of this example. I want to test this but do not have all the data available as all year’s data is not displayed in the example?
You will now have a pivot table that shows the seasonal index for each month. If the average monthly sales is 100%, then the value in each month shows how that month compares to the average. In Figure 5, you can see that January is 54.8% of the average month and December is 256.19% of the average month.