VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)Section 1: Sachin in Numbers [Source: espncricinfo.com, RSS] Section 2: Sachin : Some Rare moments & Best Innings Sachin’s 200th Test Sachin’s Best Innings...

## Demystifying Forex Quotes and Triangular Arbitrage

posted by vikram

VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)Quickbits Section: Read & Learn I have always seen that most of the students always find it very difficult to understand bid/ask rate derivation and triangular arbitrage in Forex Market. This is my attempt to give them some tricks which may prove really handy during quick revision for exam. Quote Convention: CFA Institute uses two conventions for Forex Quotes Currency A: Currency B OR Currency A/Currency B . For instance INR:USD will mean INR per unit of USD. Let’s take one more example, In the quotation 1 .2 USD/EUR, the USD is the price currency and the EUR is the base currency. The price of one euro (base currency) is 1 .2 USD (the price currency) so 1.2 is the price of one unit of the base currency in terms of the other. Trick to remember: Try to remember it this way:- if 1.2 USD/EUR is given treat it as 1.2 USD = 1 Euro i.e. just replace ‘:’ sign or ‘/’ sign with ‘=’ sign. You will be amazed to note that in real-life quotes are given exactly the opposite way but for CFA exam purpose you can remember it the way we have discussed. Direct vs Indirect Quotes: In a Direct quote, base currency is always a domestic currency while the opposite case is called Indirect Quote. For instance, in above example 1.2 USD/EUR is Direct Quote for a European trader (Euro being base currency) however it is also an Indirect Quote for US trader. Bid / Ask Rate: Bid Rate is the rate at which TRADER will want to BUY currency FROM YOU. So in other words it is the rate at which YOU will SELL the currency to the TRADER. Ask Rate is the rate at which TRADER will want to SELL currency TO YOU. So in other words it is the rate at which YOU will BUY the currency FROM the TRADER. Trick to remember: Quotes are always given by traders and hence you need to consider them from trader’s point of view. Bid is always less than Ask. Try to remember it this way, if you are a business man (trader) you will buy at lower and sell at higher rate in order to earn profit. Hence Bid = Buy (for Trader) which is always less than Ask = Selling price (for trader). Cross Currency Rates: Cross Rate is the currency exchange rate between two currencies, both of which are not the official currencies of the country in which the exchange rate quote is given in. This phrase is also sometimes used to refer to currency quotes which do not involve the U.S. dollar, regardless of which country the quote is provided in. Conversion from Bid to Ask Cross Rate: Let’s say you are presented with INR/USD quote of 62.50/7. This means that (INR/USD)Bid rate is 62.50 and (INR/USD) ask rate is 62.57. Now if you are asked to quote USD/INR Bid/Ask rate then you need to simply inverse the opposite rates. For instance: USD/INR bid rate = 1/(INR/USD)ask rate and the same way USD/INR ask rate = 1/(INR/USD) bid rate. Hence in this case the quote will be USD/INR = 0.01598/600 Triangular Arbitrage: let’s say you are given three bid-ask quotes as given below 1) a/b 2) b/c 3) a/c (each letter above represents unique currency. Further, suppose even if last one is c/a you can easily convert it to a/c by taking new bid = 1/ask & new ask =1/bid. Remember that finally we should have 1 * 2 = 3 format i.e. a/b * b/c = a/c format) Step-1 Find cross currency rate from 1 & 2 quote. As i have mentioned above if 1 * 2 = 3 then a/c bid-ask quotes are simply bid1 * bid2 – ask1*ask2 Step 2: Now compare your calculated quote (step1) with the given quote (3)....

## Mysterious Primes

posted by vikram

VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)On analysis of prime numbers I found following few unique relationship which I couldn’t find anywhere else. Few Unique Relationship between two Prime Numbers: If both P1 & P2 are prime numbers then: (P1^P2+P2^ P1) MOD P1*P2 = P1+ P2 I had posted this as a question on Yahoo Answers community & following is the proof given by Dannix. Let P1=p and P2=q. Proof: From Fermat’s Little Theorem we have q^p ≡ q (mod p) p^q ≡ p (mod q) Also it is trivial that, q^p ≡ q (mod q) p^q ≡ p (mod p) By the Chinese Remainder Theorem we get q^p ≡ q (mod pq) p^q ≡ p (mod pq) Adding the two congruences yields q^p + p^q ≡ q+p (mod pq) Q.E.D ...

## New way to find Pythagorean Triples...

posted by vikram

VN:F [1.9.22_1171]please wait...Rating: 5.0/5 (1 vote cast)How to find all possible triples from only one side of right angle triangle LOGICAL EXPLANATION My formula is based upon the following equality Hence if D is chosen in such a manner that it is a factor of x2 then we will always have integer values for Pythagorean Triples since D will get canceled from numerator & denominator Moreover D should be such that X2 / D is ‘Odd’ if D is Odd or it is ‘even’ if D is ‘even’ since even +/- even = even & odd +/- odd =even, denominator’s 2 will also get canceled. We should note that D can also be greater than X, since we get negative value in such cases we should take absolute figure. Thus if, First side of triple = X then, Second Side = |(X2 – D2)/2D| Hypotenuses = (X2 + D2)/2D For defining solution set for D, we first have to express X in terms of 2n * y. (where y is an odd number) Let set ‘A’ contain factors of y2 Solution set for D = {21 * all members of set A U 22 * all member of set A U … 2n * all member of set A} (Here ‘U’ stands for union) [Note:- While solving last part (i.e. 2n * all member of set A), one should stop as soon as 2n * any member of A = X and remaining members of A need not be consider since they will give same answer as first half element of that particular subset.] Examples: 1) if X = 35 then it means X = 20 * 35 hence y = 35. Hence set A will contain factors of 352 i.e. {1,5,7,25,35,49,175,245,1225} However Solution set for D will be {1,5,7,25} [as 20*5th element of set = 35 we need to consider only till 4th element]. Hence there will be 4 triples having 35 as one of the sides. Triples in this case will be (35,612,613),(35,120,125),(35,84,91),(35,12,37) 2) if X = 24 then it means X = 23 * 3 hence y = 3....

## Denmark Kangaroo Orange Trick & Mathematical vs Real Life Probability...

posted by vikram

VN:F [1.9.22_1171]please wait...Rating: 3.9/5 (9 votes cast)A Brain Teaser which is very popular on net goes as below: 1. pick a number between 2 and 9 2. multiply it by 9 3. add the two digits in the new number not counting their place values 4. minus 5 from that answer 5. every number stands for a letter 1 – A, 2 – B, 3 – C, find your letter 6. think of a country that starts with that letter 7. take the last letter of that country and think of an animal 8. take the last letter of that animal and think of a fruit Now let’s analyze the problem step by step: First part: Guess a number and Multiply it with 9, then add its digits and reduce 5 from it. This part is just a simple distraction to make you feel you are doing something complex. As many of you may know multiplying any number by 9 and adding its digits till you get a single digit will always result in 9. (visit http://mathforum.org/library/drmath/view/67061.html for more information) Now when you remove 5 from 9, you are always left with 4 and Fourth letter of alphabet is “D”, As you may know: (1) You have four countries starting with “D” (a) Denmark (b) Djibouti (c) Dominica (d) Dominican Republic Hence Mathematically you will agree that you have 1/4 chances of selecting Denmark (2) Now If you have selected Denmark then what is the chance that you will select Kangaroo in the next round? Well you have following choices (a) Kangaroo (b) Kaffir cat (c) Kafue flats lechwe (d) Kelp gull (e) Killer whale (f) Kinkajou (g) Kirk’s dik dik (h) Klipspringer (i) Koala (j) Komodo dragon (k) Kongoni (l) Kudu So you have...