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Malkiel's theorems summarize the relationship between bond prices, yields, coupons, and maturity. Malkiel's Theorems paraphrased (see text for exact wording); all theorems are ceteris paribus:
· Bond prices move inversely with interest rates.
· The longer the maturity of a bond, the more sensitive is its price to a change in interest rates.
· The price sensitivity of any bond increases with its maturity, but the increase occurs at a decreasing rate.
· The lower the coupon rate on a bond, the more sensitive is its price to a change in interest rates.
· For a given bond, the volatility of a bond is not symmetrical, i.e., a decrease in interest rates raises bond prices more than a corresponding increase in interest rates lower prices.
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What are basic mathematical assumptions called?
Theorems
Congruence theorems for right triangles?
LL , La , HL and Ha
What is an axiomatic system in mathematics?
An axiomatic system in mathematics is a system of axioms that can be used together to derive a theorem. Axiomatic systems help prove theorems in mathematics.
What is the definition for angle side angle?
In the context of congruent triangle theorems, it means that a pair of angles in corresponding locations in two triangles, and the sides that are included between them, are congruent. That being the case, the two triangles are congruent.
Do theorems need to be proved?
By definition, a theorem is a proven statement- until a proof is made for a statement, it is not a theorem but rather a conjecture. Whether you need to be able to reproduce the proof of a known theorem is another matter. If you trust the prover, I think you can make use of a theorem without knowing the proof. However, studying the proof can give you valuable insights into what the theorem really means and how it might be used. Also, reading proofs made by other people can help you prove you own theorems and write them up coherently.
