Pricing of financial instruments. Josechu Fernández Analistas Financieros Internacionales Universidad Autónoma de Madrid

Tamaño: px
Comenzar la demostración a partir de la página:

Download "Pricing of financial instruments. Josechu Fernández Analistas Financieros Internacionales Universidad Autónoma de Madrid"

Transcripción

1 Pricing of financial instruments Josechu Fernández Analistas Financieros Internacionales Universidad Autónoma de Madrid

2 Financial acousmatics The sect was divided between the akousmatikoi (hearers) and the mathematikoi (learned) Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

3 L acusmatico Leibnitz: calculating machines, calculus notation (practical approach), Probability of 1 head and 1 tail C and C 2. C and X 3. X and X well, hum! 1/3 Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

4 André Weil 1 1 Trinck signifie beuvez dans L Oracle de la Dive Bouteille de la Princesse Babuc à Panurge pour le guérir de ses angoisses (Rabelais : 5 livre). Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

5 Trend of the day Mathematicians becoming acousmatician: computers, (as laboratory) digital era, (everything is 0 s and 1 s) information (informational science), complex systems Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

6 Akusmatika (well, Matematika) in finance Actuarial science Credit [Banks] Insurance [Insurance companies] Risk management Uncertainty about values and cash flows. Companies must have enough capital to be able to sustain a fair proportion of adverse scenarios. Pricing of financial instruments This aspect is the one that originally attracted the interest for/and of mathematicians. It is the one that demands the most advanced acousmatics: Partial differential equations, Stochastic processes, Numerics, Data mining and Pattern recognition Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

7 Data mining Marketing. Credit scoring. Speculation Systems to detect patterns of market behavior. Neural networks and others. Once the trader or speculator has a view, maths helps to design a procedure that would take the greatest advantage of that view as opposed to the market view. Design a bet, if the view is right..., but if the view is wrong... Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

8 From Pattern recognition, by William Gibson. Fully imagined cultural futures were the luxury of another day, one in which now was of some greater duration. For us, of course, things can change so abruptly, so violently, so profoundly, that futures like our grandparents have insufficient now to stand on. We have no future because our present is too volatile.... We have only risk management. The spinning of the given moment s scenarios. Pattern recognition. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

9 Financial instruments The financial system has generated so-called financial instruments to better serve its purposes. A financial instrument is a contract between two parties, these parties promise to each other certain cash-flows at certain times in the future, and agree to a certain price to be paid by one party to the other at inception. Financial instrument: Uncertain cash flows at future times for a price today. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

10 Stocks and corporate bonds and loans Stock options Treasury Bonds Inflation linked bonds Money market instruments Swaps. Caps. Floors Mutual funds, Pension funds Mortgages, loans,... Insurance policies... Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

11 Old, very old, history. Outsmarting Savoranola: The Medicis and the Pope. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

12 Pricing, what s pricing? Quite conceptually. You have a certain universe of financial instruments, let us denote them by I. These instruments promise certain cash flows (which we should consider as uncertain) at specified dates in the future (the dates themselves could be uncertain). A pricer P is a functional that associates to every instrument in I a real number, its price. The price, by the way, could be a negative number. instrument I I price: P(I) R cash flows at future dates equivalent value today We should think of I as a large vector space. A portfolio being the same as a linear combination of financial instruments, itself a financial instrument. Of course, a pricer has to fulfill certain properties. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

13 1. Actuarial pricing This is the origin. You have a large number N of similar individuals exposed to the same specific risk. As a consequence of this risk they may incur in certain damage. Years of experience tells us that the potential damage (moneywise) for individual i during a single year could be represented by a random variable X i, whose distribution is known and common to all of those similar individuals. Denote this common distribution by X. The total potential loss is then N i=1 X i The potential individuals damages are independent (although at this point this is not relevant). Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

14 Mathematics or... Even the stupidest man by some instinct of nature per se and by no previous instruction (this is truly amazing) knows for sure that the more observations...that are taken, the less the danger will be of straying from the mark. Ars Conjectandi and/or in a letter to Leibnitz. Jacob Bernoulli tell us that quite surely the average is quite close to 1 N N i=1 E (X) X i Suddenly, the random nature of the events has disappeared, if you take the aggregate then it becomes a sure thing. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

15 The conclusion is: if each of the persons involved puts down an amount of E (X), we will collect N E (X) which quite surely and very approximately equals N i=1 X i The amount E (X) is the pure prime. It is the fair price of the contract that pays the random amount X i to participant i. Dealing with the quite surely and quite approximately qualifications above requires mathematics, statistics and business knowledge: actuaries. The pricing rule comes from the fact that the law of large numbers (the repetition of a large number of independent instances) allows to replace uncertainty future cash flows by a certain amount of money today. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

16 Retail credit The context of retail credit is very similar to that of insurance: large number of small credits. From the point of view of the bank or the saving and loans, the interesting event now is default. The law of large numbers is the driving principle again. Lets us depict this with a simple example. Suppose you (the bank) have made 1000 loans of 1000 euros. These loans constitute a homogeneous block (they are quite similar in all respects). Scoring. These are clients with similar financial statements, similar age, similar.... Comparison with your data bases of clients and defaults occurring in the path will tell you that the probability of default of these individuals is, say, 1 %. This process of assigning a probability of default is termed (credit) scoring. It uses techniques like discriminant analysis, neural networks, classification tress and other data mining procedures. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

17 Pagan justos por pecadores. That s life! The bank wants to make a return of, say, 5 % on the loans. It charges an interest of 5 % plus a spread, x %. Large numbers: { 990, will pay back 1000 (1 + 5 % + x %) 10, will pay back...0 Total received, quite certainly, (1 + 5 % + x %) and total desired, (1 + 5 %) Equating both totals reads 10 (1 + 5 %) = 990 x % 990 (random) individuals pay extra to cover for 10 (random) who default. Of course, WE all are always going to be part of the 990. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

18 2. Opinions and subjective probabilities Decisions, pricing, etc., are based on subjective assignation of probabilities of potential events to come. Of course, this assignation is not based purely on crystal ball, but based on substantial analysis, fundamental knowledge, careful scrutiny of the past, econometrics and projections, and, well,... some crystal ball... for the final touch. Comparisons to form opinions and reach decisions based on this approach makes perfect good sense. Prices obtained by calculating expectations based on these probabilities, when there is only one instance of the experiment, is ludicrous, but some how unavoidable. Fundamental analysis no real models economic reasoning (bayesian experience) cause effect, with natural models which are not, most of the time, spelled out Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

19 3. Marked to market pricing. Relative pricing. Fair value Hugh Grant. The Englishman Who Went Up a Hill But Came Down a Mountain Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

20 Anson and Garrad have explained they must go and calculate the height. Thomas Twp Too: And how d you know later? Reginald Anson: Well, w-we ve made, um, we ve made measurements with those two hills, and w-we already know the height of Newton Beacon and Whitchurch Hill... Thomas Twp: But how were they measured? Reginald Anson: The same way, by comparing them with other hills. Thomas Twp Too: But who measured the first hill? Rev. Robert Jones: whispering God. God, my boy. God. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

21 Come back to the conceptual introduction. We have the whole universe I of financial instruments. But besides this there are a number of instruments M 1,M 2,...,M n which constitute a market. These instruments are traded regularly, with enough liquidity, and their prices are representative opinions. The point here is that the prices that are quoted of these basic instruments are real prices in the sense that at any given time you can buy or sell them at the quoted (bid or ask) price. Let us denote the prices of these instruments at a given time (valuation date) by: π 1,π 2,...,π n These instruments constitute THE MARKET. All other financial instruments are OTC (over the counter). You can buy or sell them, but have to find a seller or a buyer, and the price is not a public affair. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

22 Basic instruments whose price is transparent: stocks Treasury bonds interest rate swaps, vanilla options caps, floor, swaptions corporate bonds credit options inflation linked bonds an ever growing list Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

23 We wish to develop a technique of pricing according to the market, i.e. the pricing tool P has to interpolate: P(M j )=π j Portfolios of these basic instruments should be considered as market instruments. To avoid arbitrage we should have: P ( ) α j M j = α j π j j Thus the pricer should be linear. The coefficients could be positive and negative. short selling. The pricer is given in the subspace M of I generated by the instruments M 1,M 2,... and should be extended to the whole universe I. j Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

24 Dr. Hahn and Dr. Banach, would you please keep quiet in the back row.... Have you ever heard about arbitrage? Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

25 Whypricetomarket? If all OTC instruments are marked to market (priced accordingly to the market) you get a fair perception of the real value of the portfolio. A good indication of the price you could get if you were to transform the whole portfolio into cash. In this volatile world we live in, it is better accounting than the price you pay ab initio. It gives a good reference point to start trading. One byproduct of the pricing to market is that it reveals the probability distribution that the market is assuming (in prices). Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

26 Arbitrage The main requirement is that pricer should not create arbitrage. An arbitrage opportunity is a trading strategy which requires no initial investment of money but no matter what happens will end up producing positive (or at least non negative) cash flows, surely. Markets are supposed to be so efficient that they do not allow arbitrage. In fact, there are arbitrageurs who are eager to detect arbitrage opportunities and take advantage. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

27 Examples. The price of a call should be less than the price of the underlying stock. Prices of zero coupon bonds should be decreasing with maturity. Call-Put =Stock - Discounted strike Forward on Euribor should be striked at implicit rate. Price of a bond paying annually Eur1Y should be par. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

28 Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

29 So our pricer should not produce arbitrage. Notice: Plenty of rules, plenty of potential strategies. Arbitrage could be: Static If two instruments X and Y, are going to pay in all scenarios the same amounts, then P(X) =P(Y ) Dynamic If trading dynamically with a self-financing strategy based (initially) on a portfolio of M 1,M 2,...,M n (say with weights λ 1,λ 2,...,λ n ) we are able to produce exactly the same cash-flows as a certain instrument X then P(X) = i λ i π i Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

30 Glossary trading dynamically self-financing strategy exactly the same cash-flows (bounds) Technically, those instruments that can be replicated as above could (and do) become part themselves of replicating strategies. Mathematically, this is not a problem, but in practice it places a certain burden of uncertainty in the technology. Let us denote by A those instruments which can be replicated. The pricer P should extend to A without creating arbitrage. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

31 Introducing scenarios. Taming by naming Imagine that we can codify as Ω={ω 1,ω 2,...,ω n } the collection of scenarios that can occur between now and the... future. Our financial instruments have become vectors (columns) in R n, or, if you prefer, as functions from Ω into R. Lets us point out that it is not coincidence that the number of scenarios is the same as the number of basic instruments of reference. This instance would allow us to present in a simple manner the fundamental ideas. M 1 M 2... M n ω 1 M 1 (ω 1 ) M 2 (ω 1 )... M n (ω 1 ) ω 2 M 1 (ω 2 ) M 2 (ω 2 )... M n (ω 2 ) ω n M 1 (ω n ) M 2 (ω n )... M n (ω n ) Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

32 An appropriate change of basis. The Arrow-Debreu securities: AD j. These are given by AD j (ω i )=δ ij AD 1 AD 2... AD n ω ω ω n Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

33 We have X = j X(ω j )AD j No arbitrage tell us: P(X) = j X(ω j )P(AD j ) But no arbitrage tell us also: P(AD j ) > 0 j P(AD j)= 1 1+r =discount=price of the security that pays 1 in any case. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

34 Enters probability Define Observe q j = P(AD j ) (1 + r) q j =1, q j > 0 j Drums! We have a probability Q in ω. And P(X) = 1 1+r } {{ } discount average payoff { }} { E Q (X) Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

35 Bah!, big deal! 1. But, notice. Surely we can write (changing back basis) each AD j = i u i j M i and therefore (pricing rules, no arbitrage) P(AD j )= i u i j P(M i ) and so q j = (1+r) } {{ } market given u i j i π i }{{} market given What! The pricing probability Q is given by prices quoted in the market. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

36 2. The return R X on any instrument X is given by: R X (ω j )= X(ω j) P(X) P(X) and it turns out that E Q (R X )=r = return of money What! To price you should use a probability that makes investing in any instrument equivalent (on average) to have money in the bank. What!, again The odyssey of Black Scholes. What did they do, actually? Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

37 Two recommendations at this point: Library corner Against the Gods. Peter Bernstein Fortune s formula. William Poundstone Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

38 Enters time Instruments can be traded continuously (quite frequently, at least) and have cash flows at certain points in time, not just a single future time in the future. If X t denotes price/value of instrument X at time t, then the pricing probability should verify: 1 ) X t = (1 + r) (s t)e Q (X s F t (Conditional expectations. F t = all information about prices known at time t. Filtration.) Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

39 In other terms: discounted (to present time) prices, i.e must be martingales under Q 1 (1 + r) t X t and viceversa, if discounted prices are martingale there is no arbitrage So, to price instruments (actually only those in A, but never mind), all you have to do is to find a Q so that discounted prices of (actually only) the basic instrument are martingales. In the basic stylized situation we started with, there was only one Q, but that was special. We just need one. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

40 In practice, things proceed as follows. Q, what Q? 1. First, you are given I. There many different I s. All markets (interest rates, stocks, currencies,...) are interconnected, but you may consider some portions of interest as reasonable independent. 2. There are a number of instruments M 1,M 2,...,M n which you may consider basic. There maybe many other transparent but less relevant instruments. 3. Then you propose a model to generate scenarios: usually this is a stochastic process, with some free parameters. 4. Finally you perform some fine tuning (well, bricolage!, actually) so that the M i s appropriately discounted become martingales. 5. Then, finally price the instruments in A by averaging and discounting. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

41 Black-Scholes You have stock and money as basic instruments. Discounted money is constant, so always a martingale. For the stock, postulate (Bachelier, Mandelbrojt, Samuelson,...) ds t = S t (rdt + σdw t ) where W t is brownian process under a certain probability Q. 250 sample of evolutions; r=10%, sigma=40% 200 level of stock time in years Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

42 The deterministic part (and Ito) makes S t e rt a martingale under Q And that is all, no arbitrage possible (within the model) by trading with stock and money. You may price basic (vanilla) stock options, but these are already priced by the market. To be consistent with the market, you choose σ so that this vanilla instruments are correctly priced. And you may price all sorts of derivatives on the stock. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

43 Ito tells that where N is a standard normal variable. A call C with maturity T and strike K pays The price today is: Fortune s formula S T = S 0 e (r σ2 /2)T e σ T N C T =máx ((S T K); 0) ) C 0 = e rt E Q (máx (S T K; 0)) = e rt E Q (máx (S 0 e (r σ2/2)t e σ T N K;0) Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

44 After some algebra this expectation turns out to be: C 0 = Black-Scholes formula = S 0 Φ(d + ) Ke rt Φ(d ) where Φ is the distribution function of the standard normal variable and ln d ± = ( S0 Ke rt σ T ) ± 1 2 σ2 T Probably, the most quoted mathematical formula in history. C 0 = S 0 Φ ( ln ( S0 Ke rt σ T ) σ2 T ) Ke rt Φ ( ln ( S0 Ke rt σ T ) 1 2 σ2 T ) Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

45 Actuarial/Fundamental plus arbitrage gives Black-Scholes Assume that we all believe in geometric brownian motion. As actuaries or as fundamental analists we postulate: ds t = S t (µdt + σdw t ) We know that call-put must be S 0 Ke rt. This is the no-arbitrage bit. But we price (with µ) as call put = e rt ( E((S T K) + (K S T ) +) = e rt (E(S T K)) = e rt (S 0 e µt K) and it should equal S 0 Ke rt. Therefore: µ = r No matter what you think (µ) you should be risk neutral (µ = r) for pricing. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

46 Models for all seasons. Model risk Model risk. Model are interpolation techniques. If the prices obtained are use for hedging, there is risk (uncertainty) involved. And capital needed to cover that potential downturns Rama Cont Uses and needs. Pricing is used for different purpooses and requires different calibrations and tunings to market instruments: Back office Traders Risk Managers Regulators Ethics Model arbitrage. Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

47 Lotteries. Coins People bet on the outcome of a match. Only two possible outcomes of the match, A or B wins. Every bet (ticket) costs 1 euro. There are a million bets. Somebody offers you a contract that pays 4 if A wins and 3 if B wins. We have the following information a) Historically, A have won 60 % of the time (average payoff=1,2) b) 55 % of the bets for A (average payoff=0.85) c) Insider information God is going to decide the winner of the match by tossing a fair coin (average payoff=0,5) Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

48 People is willing to pay.6 for the contract which pays 1 if heads, and pays 0 otherwise. People is willing to pay.4 for the contract which pays 1 if tails, and pays 0 otherwise. The coin is perfect, unbiased, every test confirms that probability of heads and tails, or throw twice many times and only allow CX or XC. Price (fair price, market price,... ) of the contract that pays 1 if heads, 0 if tails?...2 Escuela de Finanzas Aplicadas Todos los derechos reservados. Fecha de elaboración: 21 de septiembre de

Welcome to lesson 2 of the The Spanish Cat Home learning Spanish course.

Welcome to lesson 2 of the The Spanish Cat Home learning Spanish course. Welcome to lesson 2 of the The Spanish Cat Home learning Spanish course. Bienvenidos a la lección dos. The first part of this lesson consists in this audio lesson, and then we have some grammar for you

Más detalles

Forex ebook "My Book of Trading. Forex."

Forex ebook My Book of Trading. Forex. Forex ebook "My Book of Trading. Forex." "Dedicado a todos aquellos que piensan, que la vida es un continuo análisis de riesgo, que hay que ir valorando." "Dedicated to those who think that life is a continuous

Más detalles

PROBLEMAS PARA LA CLASE DEL 20 DE FEBRERO DEL 2008

PROBLEMAS PARA LA CLASE DEL 20 DE FEBRERO DEL 2008 PROBLEMAS PARA LA CLASE DEL 20 DE FEBRERO DEL 2008 Problema 1 Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful,

Más detalles

Lengua adicional al español IV

Lengua adicional al español IV Lengua adicional al español IV Topic 11 Life little lessons Introduction In this lesson you will study: Time clauses are independent clauses. These are the clauses that tell you the specific time when

Más detalles

An explanation by Sr. Jordan

An explanation by Sr. Jordan & An explanation by Sr. Jdan direct object pronouns We usually use Direct Object Pronouns to substitute f it them in a sentence when the it them follows the verb. Because of gender, him and her could also

Más detalles

Qué viva la Gráfica de Cien!

Qué viva la Gráfica de Cien! Qué viva la Gráfica de Cien! La gráfica de cien consiste en números del 1 al 100 ordenados en cuadrilones de diez números en hileras. El resultado es que los estudiantes que utilizan estás gráficas pueden

Más detalles

TOUCH MATH. Students will only use Touch Math on math facts that are not memorized.

TOUCH MATH. Students will only use Touch Math on math facts that are not memorized. TOUCH MATH What is it and why is my child learning this? Memorizing math facts is an important skill for students to learn. Some students have difficulty memorizing these facts, even though they are doing

Más detalles

Connection from School to Home Kindergarten Math Module 2 Topic A. Making 3 with Triangles and Chips

Connection from School to Home Kindergarten Math Module 2 Topic A. Making 3 with Triangles and Chips Connection from School to Home Kindergarten Math Module 2 Topic A Making 3 with Triangles and Chips Here is a simple activity to help your child learn about composing and decomposing the number 3 and analyzing

Más detalles

RDA in BNE. Mar Hernández Agustí Technical Process Department Manager Biblioteca Nacional de España

RDA in BNE. Mar Hernández Agustí Technical Process Department Manager Biblioteca Nacional de España RDA in BNE Mar Hernández Agustí Technical Process Department Manager Biblioteca Nacional de España RDA at the National Library of Spain: BNE preparation for new Cataloguing Rules Since 2007 BNE has been

Más detalles

SIGUIENDO LOS REQUISITOS ESTABLECIDOS EN LA NORMA ISO 14001 Y CONOCIENDO LAS CARACTERISTICAS DE LA EMPRESA CARTONAJES MIGUEL Y MATEO EL ALUMNO DEBERA

SIGUIENDO LOS REQUISITOS ESTABLECIDOS EN LA NORMA ISO 14001 Y CONOCIENDO LAS CARACTERISTICAS DE LA EMPRESA CARTONAJES MIGUEL Y MATEO EL ALUMNO DEBERA SIGUIENDO LOS REQUISITOS ESTABLECIDOS EN LA NORMA ISO 14001 Y CONOCIENDO LAS CARACTERISTICAS DE LA EMPRESA CARTONAJES MIGUEL Y MATEO EL ALUMNO DEBERA ELABORAR LA POLITICA AMBIENTAL PDF File: Siguiendo

Más detalles

Swap Cancellation Letter to Bank

Swap Cancellation Letter to Bank Swap Cancellation Letter to Bank This letter is for people affected by bank swap clauses. Use this letter to notify the bank you will not accept any more charges having to do with this product, and demand

Más detalles

Synergy Spanish Solutions. Día de San Valentín Audio Lessons

Synergy Spanish Solutions. Día de San Valentín Audio Lessons Synergy Spanish Solutions Día de San Valentín Audio Lessons Created by Marcus Santamaria Edited by Elena Chagoya & Claire Boland Copyright 2014 Marcus Santamaria All Rights reserved. No part of this publication

Más detalles

Shortcut to Informal Spanish Conversations Level 2 Lesson 1

Shortcut to Informal Spanish Conversations Level 2 Lesson 1 Shortcut to Informal Spanish Conversations Level 2 Lesson 1 These lessons extend on the ideas from Shortcut to Informal Spanish Conversations Level 1 http://www.informalspanish.com and Shortcut to Spanish

Más detalles

Canutillo Middle School 7311 Bosque, P.O. Box 100 Canutillo, Texas 79835 (915) 877-7900 Fax (915) 877-7919

Canutillo Middle School 7311 Bosque, P.O. Box 100 Canutillo, Texas 79835 (915) 877-7900 Fax (915) 877-7919 Mark Paz August 24, 2015 Dear Parents/Legal Guardian, I would like to start by thanking each and every single one of you for the tremendous help and support we have been receiving. Thank You! Next school

Más detalles

HERRAMIENTA PARA LA OPTIMIZACIÓN DEL PORFOLIO DE PRODUCTOS DE LAS REDES DE VENTAS DE UN LABORATORIO FARMACÉUTICO

HERRAMIENTA PARA LA OPTIMIZACIÓN DEL PORFOLIO DE PRODUCTOS DE LAS REDES DE VENTAS DE UN LABORATORIO FARMACÉUTICO HERRAMIENTA PARA LA OPTIMIZACIÓN DEL PORFOLIO DE PRODUCTOS DE LAS REDES DE VENTAS DE UN LABORATORIO FARMACÉUTICO Autor: Tárano Pastor, Ramón. Director: Moreno Alonso, Pablo. Director: Ruiz del Palacio,

Más detalles

GENERAL INFORMATION Project Description

GENERAL INFORMATION Project Description RESULTADOS! GENERAL INFORMATION Project Description The campaign "Adopt a car " had as its main objective to position Autoplaza, the main automotive selling point of Chile, as a new car sales location

Más detalles

THE 3DSYMPOSIUM CONTEST 2015

THE 3DSYMPOSIUM CONTEST 2015 THE 3DSYMPOSIUM CONTEST 2015 Do you want to work in Miami? Hi everybody, this is Aldo Garcia and I m the organizer of the 3dsymposium event, I m very happy to announce the guide lines for the contest 2015,

Más detalles

Disfruten su verano! Hola estudiantes,

Disfruten su verano! Hola estudiantes, Hola estudiantes, We hope that your experience during Spanish 1 was enjoyable and that you are looking forward to improving your ability to communicate in Spanish. As we all know, it is very difficult

Más detalles

Trading & Investment In Banking

Trading & Investment In Banking Trading & Investment In Banking MÁSTER UNIVERSITARIO EN BANCA Y FINANZAS (Finance & Banking) Universidad de Alcalá Curso Académico 2015/16 GUÍA DOCENTE Nombre de la asignatura: Trading & Investment In

Más detalles

Learning Masters. Fluent: States of Matter

Learning Masters. Fluent: States of Matter Learning Masters Fluent: States of Matter What I Learned List the three most important things you learned in this theme. Tell why you listed each one. 1. 2. 3. 22 States of Matter Learning Masters How

Más detalles

Instructor: Do you remember how to say the verb "to speak"? Instructor: How do you ask a friend Do you speak Spanish?

Instructor: Do you remember how to say the verb to speak? Instructor: How do you ask a friend Do you speak Spanish? Learning Spanish Like Crazy Spoken Spanish Lección Dos. Listen to the following conversation: Male: Hablas inglés? Female: Sí, hablo inglés porque practico todos los días. Male: Dónde? Female: Practico

Más detalles

GUIDE FOR PARENT TEACHER CONFERENCES

GUIDE FOR PARENT TEACHER CONFERENCES GUIDE FOR PARENT TEACHER CONFERENCES A parent-teacher conference is a chance for you and your child s teacher to talk. You can talk about how your child is learning at home and at school. This list will

Más detalles

Agustiniano Ciudad Salitre School Computer Science Support Guide - 2015 Second grade First term

Agustiniano Ciudad Salitre School Computer Science Support Guide - 2015 Second grade First term Agustiniano Ciudad Salitre School Computer Science Support Guide - 2015 Second grade First term UNIDAD TEMATICA: INTERFAZ DE WINDOWS LOGRO: Reconoce la interfaz de Windows para ubicar y acceder a los programas,

Más detalles

Please join us in circle. Please put on a nametag. Por favor, únete a nosotros en ronda. Ponte una etiqueta con su nombre.

Please join us in circle. Please put on a nametag. Por favor, únete a nosotros en ronda. Ponte una etiqueta con su nombre. Welcome! Bienvenido! Please join us in circle. Please put on a nametag. Por favor, únete a nosotros en ronda. Ponte una etiqueta con su nombre. Questions for You to Think About Preguntas para que pienses

Más detalles

Pistas Separadas TÉRMINOS Y CONDICIONES

Pistas Separadas TÉRMINOS Y CONDICIONES Pistas Separadas POETA MUSIC PRODUCTIONS le da un control total sobre lo que se hace con la grabación original. Ahora, usted puede agregar diferentes sonidos voses teclados derivados como desee ( añada

Más detalles

A1 Second level. Timeline. Servicio Nacional de Aprendizaje - SENA. Reservados todos los derechos 2013.

A1 Second level. Timeline. Servicio Nacional de Aprendizaje - SENA. Reservados todos los derechos 2013. A1 Second level Timeline Start UP Welcome Hi! It s great to see you again! It s time to learn how to make a timeline to talk about past events of our lives in a sequential manner. Let s begin! 2 /9 Warm

Más detalles

Welcome to the Leaders Only Invitation!

Welcome to the Leaders Only Invitation! Welcome to the Leaders Only Invitation! Q & A A. Ultimate Cycler is here to stay! UC remains completely intact and is complementary to FreeToolBox. As a matter of fact, Ultimate Cycler is getting a facelift!

Más detalles

MajestaCare Healthy Baby Program

MajestaCare Healthy Baby Program MajestaCare Healthy Baby Program Helping you have a healthy baby Para que tenga un bebé saludable Your baby s provider After your baby becomes a member of MajestaCare health plan, you will get a letter

Más detalles

It is call the clients paradise... MWP2 clients are as partners with the company.

It is call the clients paradise... MWP2 clients are as partners with the company. En español clic aqui Hello, my name is: Arturo Bravo and my email arcangelmi@hotmail.com and has been client of MWP2 since 28/03/2016 05:29 and I am contacting you to let you know the same opportunity

Más detalles

Mi ciudad interesante

Mi ciudad interesante Mi ciudad interesante A WebQuest for 5th Grade Spanish Designed by Jacob Vuiller jvuiller@vt.edu Introducción Tarea Proceso Evaluación Conclusión Créditos Introducción Bienvenidos! Eres alcalde de una

Más detalles

Guide to Health Insurance Part II: How to access your benefits and services.

Guide to Health Insurance Part II: How to access your benefits and services. Guide to Health Insurance Part II: How to access your benefits and services. 1. I applied for health insurance, now what? Medi-Cal Applicants If you applied for Medi-Cal it will take up to 45 days to find

Más detalles

Improving Rates of Colorectal Cancer Screening Among Never Screened Individuals

Improving Rates of Colorectal Cancer Screening Among Never Screened Individuals Improving Rates of Colorectal Cancer Screening Among Never Screened Individuals Northwestern University, Feinberg School of Medicine Contents Patient Letter Included with Mailed FIT... 3 Automated Phone

Más detalles

Learning Masters. Fluent: Wind, Water, and Sunlight

Learning Masters. Fluent: Wind, Water, and Sunlight Learning Masters Fluent: Wind, Water, and Sunlight What I Learned List the three most important things you learned in this theme. Tell why you listed each one. 1. 2. 3. 22 Wind, Water, and Sunlight Learning

Más detalles

Matemáticas Muestra Cuadernillo de Examen

Matemáticas Muestra Cuadernillo de Examen Matemáticas Muestra Cuadernillo de Examen Papel-Lápiz Formato Estudiante Español Versión, Grados 3-5 Mathematics Sample Test Booklet Paper-Pencil Format Student Spanish Version, Grades 3 5 Este cuadernillo

Más detalles

Español. Learn a language your way! Lesson #6 - Por el mismo dinero que la otra, me llevo dos! PDF - Beginner. www.cactuslanguagetraining.

Español. Learn a language your way! Lesson #6 - Por el mismo dinero que la otra, me llevo dos! PDF - Beginner. www.cactuslanguagetraining. Learn a language your way! PDF - Beginner Lesson #6 - Por el mismo dinero que la otra, me llevo dos! www.cactuslanguagetraining.com/hola Lesson Conversation: Escucha la conversación, primero a una velocidad

Más detalles

El desarrollo del mercado ISR: Integración

El desarrollo del mercado ISR: Integración El desarrollo del mercado ISR: Integración III Evento Anual SpainSIF 17 octubre 2012 Amundi, French joint stock company ( Société Anonyme ) with a registered capital of 578 002 350 and approved by the

Más detalles

Puede pagar facturas y gastos periódicos como el alquiler, el gas, la electricidad, el agua y el teléfono y también otros gastos del hogar.

Puede pagar facturas y gastos periódicos como el alquiler, el gas, la electricidad, el agua y el teléfono y también otros gastos del hogar. SPANISH Centrepay Qué es Centrepay? Centrepay es la manera sencilla de pagar sus facturas y gastos. Centrepay es un servicio de pago de facturas voluntario y gratuito para clientes de Centrelink. Utilice

Más detalles

Connection from School to Home Science Grade 5 Unit 1 Living Systems

Connection from School to Home Science Grade 5 Unit 1 Living Systems Connection from School to Home Science Grade 5 Unit 1 Living Systems Here is an activity to help your child understand human body systems. Here is what you do: 1. Look at the pictures of the systems that

Más detalles

IRS DATA RETRIEVAL NOTIFICATION DEPENDENT STUDENT ESTIMATOR

IRS DATA RETRIEVAL NOTIFICATION DEPENDENT STUDENT ESTIMATOR IRS DATA RETRIEVAL NOTIFICATION DEPENDENT STUDENT ESTIMATOR Subject: Important Updates Needed for Your FAFSA Dear [Applicant], When you completed your 2012-2013 Free Application for Federal Student Aid

Más detalles

UPV software for risk models

UPV software for risk models UPV software for risk models Armando Serrano Lombillo arserlom@doctor.upv.es www.edams.upv.es Risk analysis is feasible 1 Contents Introduction Review of previous concepts From influence diagrams to event

Más detalles

ANÁLISIS Y DESARROLLO DE UNA PLATAFORMA BIG DATA

ANÁLISIS Y DESARROLLO DE UNA PLATAFORMA BIG DATA ANÁLISIS Y DESARROLLO DE UNA PLATAFORMA BIG DATA Autor: de la Cierva Perreau de Pinninck, Leticia Director: Sonia García, Mario Tenés Entidad Colaboradora: VASS RESUMEN DEL PROYECTO Tras la realización

Más detalles

Volatilidad: Noviembre 2010 Futuros Frijol de Soya

Volatilidad: Noviembre 2010 Futuros Frijol de Soya Observaciones Junio 09, 2010 1. La volatilidad tiene una tendencia a aumentar de Junio a Julio. 2. Este reporte sugiere que se debería considerar la implementación de estrategias largas con opciones en

Más detalles

Edgar Quiñones. HHRR: Common Sense Does Not Mean Business. Objective

Edgar Quiñones. HHRR: Common Sense Does Not Mean Business. Objective Edgar Quiñones HHRR: Common Sense Does Not Mean Business Objective Share experiences & insight gained in the last two decades in the management consulting business regarding why Common Sense Does Not Mean

Más detalles

Lesson 6. Joke of the week

Lesson 6. Joke of the week Lesson 6 Joke of the week El doctor llama por teléfono a su paciente: Verá, tengo una noticia buena y otra mala. Bueno... dígame primero la buena. Los resultados del análisis indican que le quedan 24 horas

Más detalles

\RESOURCE\ELECTION.S\PROXY.CSP

\RESOURCE\ELECTION.S\PROXY.CSP The following is an explanation of the procedures for calling a special meeting of the shareholders. Enclosed are copies of documents, which you can use for your meeting. If you have any questions about

Más detalles

Some examples. I wash my clothes, I wash the dishes, I wash the car, I wash the windows. I wash my hands, I wash my hair, I wash my face.

Some examples. I wash my clothes, I wash the dishes, I wash the car, I wash the windows. I wash my hands, I wash my hair, I wash my face. Reflexive verbs In this presentation, we are going to look at a special group of verbs called reflexives. Let s start out by thinking of the English verb wash. List several things that you can wash. Some

Más detalles

Economía Ayudantía # 05: Ingreso Nacional e Inflación

Economía Ayudantía # 05: Ingreso Nacional e Inflación Ayudantía # 05: Ingreso Nacional e Inflación Profesor: Carlos R. Pitta 1 1 cpitta@spm.uach.cl PREGUNTAS BREVES Pregunta Corta 01: Explique por qué la renta de una economía debe ser igual a su gasto. RESPUESTA:

Más detalles

Flashcards Series 3 El Aeropuerto

Flashcards Series 3 El Aeropuerto Flashcards Series 3 El Aeropuerto Flashcards are one of the quickest and easiest ways to test yourself on Spanish vocabulary, no matter where you are! Test yourself on just these flashcards at first. Then,

Más detalles

LA RUTINA DIARIA & LOS VERBOS REFLEXIVOS

LA RUTINA DIARIA & LOS VERBOS REFLEXIVOS WHAT IS A REFLEXIVE VERB? LA RUTINA DIARIA & LOS VERBOS REFLEXIVOS Reflexive verbs are verbs that. The person the action also the action. HOW DO YOU KNOW WHEN THE VERB IS REFLEXIVE? When the letters are

Más detalles

RFID TEMPERATURE SENSOR. Autor: Polo Tascón, David. Director: Kramer, Kathleen. Entidad colaboradora: Advantageous Systems LLC.

RFID TEMPERATURE SENSOR. Autor: Polo Tascón, David. Director: Kramer, Kathleen. Entidad colaboradora: Advantageous Systems LLC. RFID TEMPERATURE SENSOR. Autor: Polo Tascón, David. Director: Kramer, Kathleen. Entidad colaboradora: Advantageous Systems LLC. RESUMEN DEL PROYECTO Existen casos en la industria de la tecnología, medicina,

Más detalles

Sistemas de impresión y tamaños mínimos Printing Systems and minimum sizes

Sistemas de impresión y tamaños mínimos Printing Systems and minimum sizes Sistemas de impresión y tamaños mínimos Printing Systems and minimum sizes Para la reproducción del Logotipo, deberán seguirse los lineamientos que se presentan a continuación y que servirán como guía

Más detalles

Creating your Single Sign-On Account for the PowerSchool Parent Portal

Creating your Single Sign-On Account for the PowerSchool Parent Portal Creating your Single Sign-On Account for the PowerSchool Parent Portal Welcome to the Parent Single Sign-On. What does that mean? Parent Single Sign-On offers a number of benefits, including access to

Más detalles

manual de servicio nissan murano z51

manual de servicio nissan murano z51 manual de servicio nissan murano z51 Reference Manual To understand featuring to use and how to totally exploit manual de servicio nissan murano z51 to your great advantage, there are several sources of

Más detalles

SEMINAR 3: COMPOSITION

SEMINAR 3: COMPOSITION SEMINAR 3: FORMAL LETTER COMPOSITION 1 Lengua C I (Inglés) Código 00EM Imagine you were selected as an Erasmus student and you wanted to write to your host university to ask them for information about

Más detalles

SCADA BASADO EN LABVIEW PARA EL LABORATORIO DE CONTROL DE ICAI

SCADA BASADO EN LABVIEW PARA EL LABORATORIO DE CONTROL DE ICAI SCADA BASADO EN LABVIEW PARA EL LABORATORIO DE CONTROL DE ICAI Autor: Otín Marcos, Ana. Directores: Rodríguez Pecharromán, Ramón. Rodríguez Mondéjar, José Antonio. Entidad Colaboradora: ICAI Universidad

Más detalles

Instructor: She just said that she s Puerto Rican. Escucha y repite la palabra Puerto Rican -for a man-.

Instructor: She just said that she s Puerto Rican. Escucha y repite la palabra Puerto Rican -for a man-. Learning Spanish Like Crazy Spoken Spanish Lección once Instructor: Cómo se dice Good afternoon? René: Buenas tardes. Buenas tardes. Instructor: How do you ask a woman if she s Colombian. René: Eres Colombiana?

Más detalles

Resumen de Entrevista: Asociación Mexicana de Agentes de Carga

Resumen de Entrevista: Asociación Mexicana de Agentes de Carga Resumen de Entrevista: Asociación Mexicana de Agentes de Carga 1. In regard to the hiring and payment of international freight services, can you tell me in what percentage of total export transactions

Más detalles

A Member of My Community

A Member of My Community Connection from School to Home Kindergarten Social Studies Unit 1 A Member of My Community Here is an easy activity to help your child learn about what it means to be a member of a community. Here is what

Más detalles

Real Time Systems. Part 2: Cyclic schedulers. Real Time Systems. Francisco Martín Rico. URJC. 2011

Real Time Systems. Part 2: Cyclic schedulers. Real Time Systems. Francisco Martín Rico. URJC. 2011 Real Time Systems Part 2: Cyclic schedulers Scheduling To organise the use resources to guarantee the temporal requirements A scheduling method is composed by: An scheduling algorithm that calculates the

Más detalles

UNIVERSIDAD DE GUAYAQUIL FACULTAD DE ODONTOLOGÍA ESCUELA DE POSTGRADO Dr. José Apolo Pineda

UNIVERSIDAD DE GUAYAQUIL FACULTAD DE ODONTOLOGÍA ESCUELA DE POSTGRADO Dr. José Apolo Pineda UNIVERSIDAD DE GUAYAQUIL FACULTAD DE ODONTOLOGÍA ESCUELA DE POSTGRADO Dr. José Apolo Pineda EVALUACIÓN IN VITRO DE LA FILTRACIÓN APICAL EN RAICES DE DIENTES EXTRAIDOS, UTILIZANDO DOS MÉTODOS DE OBTURACION:

Más detalles

Entrevista: el medio ambiente. A la caza de vocabulario: come se dice en español?

Entrevista: el medio ambiente. A la caza de vocabulario: come se dice en español? A la caza de vocabulario: come se dice en español? Entrevista: el medio ambiente 1. There are a lot of factories 2. The destruction of the ozone layer 3. In our city there is a lot of rubbish 4. Endangered

Más detalles

Learning Masters. Early: Force and Motion

Learning Masters. Early: Force and Motion Learning Masters Early: Force and Motion WhatILearned What important things did you learn in this theme? I learned that I learned that I learned that 22 Force and Motion Learning Masters How I Learned

Más detalles

Los ensayos que se van a desarrollar son los siguientes:

Los ensayos que se van a desarrollar son los siguientes: I Resumen El objetivo principal del proyecto es desarrollar un software que permita analizar unos datos correspondientes a una serie de ensayos militares. Con este objetivo en mente, se ha decidido desarrollar

Más detalles

ADAPTACIÓN DE REAL TIME WORKSHOP AL SISTEMA OPERATIVO LINUX

ADAPTACIÓN DE REAL TIME WORKSHOP AL SISTEMA OPERATIVO LINUX ADAPTACIÓN DE REAL TIME WORKSHOP AL SISTEMA OPERATIVO LINUX Autor: Tomás Murillo, Fernando. Director: Muñoz Frías, José Daniel. Coordinador: Contreras Bárcena, David Entidad Colaboradora: ICAI Universidad

Más detalles

MÁSTER UNIVERSITARIO EN BANCA Y FINANZAS

MÁSTER UNIVERSITARIO EN BANCA Y FINANZAS Corporate Finance MÁSTER UNIVERSITARIO EN BANCA Y FINANZAS (Finance & Banking) Universidad de Alcalá Curso Académico 2015/16 GUÍA DOCENTE Nombre de la asignatura: Corporate Finance Código: 201554 Titulación

Más detalles

iclef-2002 at Universities of Alicante and Jaen University of Alicante (Spain)

iclef-2002 at Universities of Alicante and Jaen University of Alicante (Spain) iclef-2002 at Universities of Alicante and Jaen University of Alicante (Spain) ! Introduction! Passage Retrieval Systems! IR-n system! IR-n system at iclef-2002! Conclusions and Future works ! Introduction!

Más detalles

EMPLOYER & EMPLOYEE RETIREMENT PLAN TAX CREDITS

EMPLOYER & EMPLOYEE RETIREMENT PLAN TAX CREDITS EMPLOYER & EMPLOYEE RETIREMENT PLAN TAX CREDITS For employers who set up and maintain retirement plans, the setup costs, annual administrative costs, and retirement-related employee education costs are

Más detalles

Cómo comprar en la tienda en línea de UDP y cómo inscribirse a los módulos UDP

Cómo comprar en la tienda en línea de UDP y cómo inscribirse a los módulos UDP Cómo comprar en la tienda en línea de UDP y cómo inscribirse a los módulos UDP Sistema de registro y pago Este sistema está dividido en dos etapas diferentes*. Por favor, haga clic en la liga de la etapa

Más detalles

Speak Up! In Spanish. Young s Language Consulting. Young's Language Consulting. Lesson 1 Meeting and Greeting People.

Speak Up! In Spanish. Young s Language Consulting. Young's Language Consulting. Lesson 1 Meeting and Greeting People. Buenos días Good morning Buenos días Good afternoon Buenas tardes Good evening Buenas tardes Good night Buenas noches Sir Señor Ma am/mrs. Señora Miss Señorita Buenas tardes Culture Note: When greeting

Más detalles

Curso Online Vaughan Classroom Temario Completo

Curso Online Vaughan Classroom Temario Completo Curso Online Vaughan Classroom Temario Completo Nivel Principiante El curso principiante tiene como objetivo dotarte de todo lo necesario para dominar las partes más elementales del inglés, pero también

Más detalles

Condiciones y Reglas de la presentación de Declaración Sumaria de Salida (EXS)

Condiciones y Reglas de la presentación de Declaración Sumaria de Salida (EXS) C/ Santa María Magdalena 16, 28016 Madrid ECS Sistema de Control de Exportaciones Condiciones y Reglas de la presentación de Declaración Sumaria de Salida (EXS) Autor: S.G.A.A Fecha: 06/06/2011 Versión:

Más detalles

Vicky Christina Barcelona

Vicky Christina Barcelona Vicky Christina Barcelona by Woody Allen LAFS Scene Study Film Production Course 323.860.0789 Copyrighted material for educational use only Vicki Christina Barcelona 2/12/10 1. INT. S HOUSE/KITCHEN - DAY

Más detalles

Objetivo: You will be able to You will be able to

Objetivo: You will be able to You will be able to Nombre: Fecha: Clase: Hora: Título (slide 1) Las cosas _ Capítulo 2 1 (Chapter Two, First Step) Objetivo: You will be able to You will be able to First look at the other sheet of vocabulary and listen,

Más detalles

High acceptance short term loans Fast Payday Loans - CLICK HERE

High acceptance short term loans Fast Payday Loans - CLICK HERE High acceptance short term loans. Was to have with appealing dollars, tried the book of the best cash advance 10032 personal loan albany ga httpwww. trhyales. czpersonal-loanalbany-ga. High acceptance

Más detalles

Steps to Understand Your Child s Behavior. Customizing the Flyer

Steps to Understand Your Child s Behavior. Customizing the Flyer Steps to Understand Your Child s Behavior Customizing the Flyer Hello! Here is the PDF Form Template for use in advertising Steps to Understanding Your Child s Behavior (HDS Behavior Level 1B). Because

Más detalles

PROGRAMA. Operaciones de Banca y Bolsa SYLLABUS BANKING AND STOCK MARKET OPERATIONS

PROGRAMA. Operaciones de Banca y Bolsa SYLLABUS BANKING AND STOCK MARKET OPERATIONS PROGRAMA 4º Curso. Grado en Administración y Dirección SYLLABUS BANKING AND STOCK MARKET OPERATIONS 4 rd year. Pág. 1 / 8 Colegio Universitario de Estudios Financieros Leonardo Prieto Castro, 2 Tel. +34

Más detalles

Keeping Your Home, Protecting Your Investment. Cómo retener su casa, Cómo proteger su inversión

Keeping Your Home, Protecting Your Investment. Cómo retener su casa, Cómo proteger su inversión Keeping Your Home, Protecting Your Investment Cómo retener su casa, Cómo proteger su inversión Learn The Steps You Can Take Today Aprenda los pasos que puede tomar hoy Don t risk losing your home or jeopardizing

Más detalles

Lump Sum Final Check Contribution to Deferred Compensation

Lump Sum Final Check Contribution to Deferred Compensation Memo To: ERF Members The Employees Retirement Fund has been asked by Deferred Compensation to provide everyone that has signed up to retire with the attached information. Please read the information from

Más detalles

July 2011. Graduations & Learning After High School. Español/Spanish

July 2011. Graduations & Learning After High School. Español/Spanish July 2011 Graduations & Learning After High School Español/Spanish Last month our schools graduated 1,734 students from high school. These are students who met all the graduation standards from the State

Más detalles

DISEÑO DE UN SISTEMA AUTOMÁTICO DE INVERSIÓN EN BOLSA BASADO EN TÉCNICAS DE PREDICCIÓN DE SERIES TEMPORALES

DISEÑO DE UN SISTEMA AUTOMÁTICO DE INVERSIÓN EN BOLSA BASADO EN TÉCNICAS DE PREDICCIÓN DE SERIES TEMPORALES DISEÑO DE UN SISTEMA AUTOMÁTICO DE INVERSIÓN EN BOLSA BASADO EN TÉCNICAS DE PREDICCIÓN DE SERIES TEMPORALES Autor: Astudillo Zulueta, Antón. Directores: Cruz García, Alberto Miguel. Arroyo Gallardo, Javier

Más detalles

Plan de negocio para la explotación de un sistema de alquiler de bicicletas en la Comunidad de Madrid

Plan de negocio para la explotación de un sistema de alquiler de bicicletas en la Comunidad de Madrid Plan de negocio para la explotación de un sistema de alquiler de bicicletas en la Comunidad de Madrid Autor: Directores: Lago Vázquez, Óscar. Ortíz Marcos, Susana. Entidad Colaboradora: ICAI-Universidad

Más detalles

Vermont Mini-Lessons: Leaving A Voicemail

Vermont Mini-Lessons: Leaving A Voicemail Vermont Mini-Lessons: Leaving A Voicemail Leaving a Voice Mail Message Learning Objective 1) When to leave a message 2) How to leave a message Materials: 1) Voice Mail Template blanks & samples 2) Phone

Más detalles

Student Perception Survey

Student Perception Survey Student Perception Survey Grades 6-12 Survey Directions You will be completing a survey that will provide important information about your teacher. A survey is different from a test. On a survey, you are

Más detalles

INNOVACIÓN Tecnologías de información La nueva Era. Javier Cordero Torres Presidente y Director General Oracle México Febrero 27, 2015

INNOVACIÓN Tecnologías de información La nueva Era. Javier Cordero Torres Presidente y Director General Oracle México Febrero 27, 2015 INNOVACIÓN Tecnologías de información La nueva Era Javier Cordero Torres Presidente y Director General Oracle México Febrero 27, 2015 Oracle Confidential Internal/Restricted/Highly Restricted 3 4 OF WORLD

Más detalles

1. Título: 2. Objetivos: 3. Contenidos de la propuesta: 4. Relación con los temas transversales: 5. Sesiones de trabajo: Preventing back injuires.

1. Título: 2. Objetivos: 3. Contenidos de la propuesta: 4. Relación con los temas transversales: 5. Sesiones de trabajo: Preventing back injuires. 1. Título: Preventing back injuires. 2. Objetivos: a) Adquirir vocabulario inglés básico relacionado con la prevención de riesgos por manipulación de cargas. b) Estudiar las formas gramaticales más apropiadas

Más detalles

Propiedades del Mineral en Molinos SAG y AG Ahorrando tiempo y dinero con MetSMART: Probando y Simulando la Dureza del Mineral

Propiedades del Mineral en Molinos SAG y AG Ahorrando tiempo y dinero con MetSMART: Probando y Simulando la Dureza del Mineral Propiedades del Mineral en Molinos SAG y AG Ahorrando tiempo y dinero con MetSMART: Probando y Simulando la Dureza del Mineral Ore Properties in AG/SAG Mill Saving Time and Money with MetSMART: Testing

Más detalles

Asistencia para alimentos de Iowa (Iowa Food Assistance Program) SCRIPT

Asistencia para alimentos de Iowa (Iowa Food Assistance Program) SCRIPT Asistencia para alimentos de Iowa (Iowa Food Assistance Program) http://video.extension.iastate.edu/2011/12/14/asistencia para alimentos de iowa/ Six minute video in Spanish explaining what Food Assistance

Más detalles

REFUERZO EDUCATIVO de INGLÉS. Área/Materia: INGLÉS Curso: 2º ESO Grupo: Número: Curso lectivo: 2013-14 Fecha presentación RE: SEPTIEMBRE 2014

REFUERZO EDUCATIVO de INGLÉS. Área/Materia: INGLÉS Curso: 2º ESO Grupo: Número: Curso lectivo: 2013-14 Fecha presentación RE: SEPTIEMBRE 2014 E. S. O. COLEGIO NSTRA. SRA. DEL RECUERDO Jefatura de Estudios REFUERZO EDUCATIVO de INGLÉS Departamento: INGLÉS Alumno: Área/Materia: INGLÉS Curso: 2º ESO Grupo: Número: Profesor: Tutor/a: Curso lectivo:

Más detalles

Learning Masters. Fluent: Animal Habitats

Learning Masters. Fluent: Animal Habitats Learning Masters Fluent: Animal Habitats What I Learned List the three most important things you learned in this theme. Tell why you listed each one. 1. 2. 3. 22 Animal Habitats Learning Masters How I

Más detalles

Lista 1. Nombre. Lista 5. Lista 4 Lista 3 Lista 2. Lista 1. Lista 10. Lista 9. Lista 8. Lista 7. Lista 6

Lista 1. Nombre. Lista 5. Lista 4 Lista 3 Lista 2. Lista 1. Lista 10. Lista 9. Lista 8. Lista 7. Lista 6 Nombre Lista 1 Lista 10 Lista 9 Lista 8 Lista 7 Lista 6 Lista 5 Lista 4 Lista 3 Lista 2 Lista 1 Yo (I) Y (and) Un (a, an) Una (a-for female) Veo (I see) Mi (my) Tu (you) A (to) Al (to) Así (like this)

Más detalles

STAR/Cross-age Tutoría Frases del Sr. Fry Grupo 1 Práctique leyendo con su niño(a) 5 frases diariamente. Continue con las siguiente 5 frases cuando

STAR/Cross-age Tutoría Frases del Sr. Fry Grupo 1 Práctique leyendo con su niño(a) 5 frases diariamente. Continue con las siguiente 5 frases cuando Grupo 1 1. the little boy el niño pequeño 2. a good boy un buen niño 3. is about me es acerca de mí 4. then you give luego tú das 5. was to come iba a suceder 6. old and new viejo y nuevo 7. what we know

Más detalles

Introduction to accounting

Introduction to accounting Introduction to accounting 1 Welcome to Introduction to accounting I. 2 Let s get started. 3 We want to first begin by defining what accounting is. 4 Accounting is most frequently defined as the language

Más detalles

Daly Elementary. Family Back to School Questionnaire

Daly Elementary. Family Back to School Questionnaire Daly Elementary Family Back to School Questionnaire Dear Parent(s)/Guardian(s), As I stated in the welcome letter you received before the beginning of the school year, I would be sending a questionnaire

Más detalles

Pages: 205. Authors: Dr. Carmen Bestué, Ph. D. Dr. Mariana Orozco Jutoran, Ph. D. Chapters: 6

Pages: 205. Authors: Dr. Carmen Bestué, Ph. D. Dr. Mariana Orozco Jutoran, Ph. D. Chapters: 6 Pages: 205 Authors: Dr. Carmen Bestué, Ph. D. Dr. Mariana Orozco Jutoran, Ph. D. Chapters: 6 1 Course Description and Objectives The aim of this course is to provide an in depth analysis and intensive

Más detalles

DUAL IMMERSION PROGRAM INFORMATION PRESCHOOL PRESENTATION SEPTEMBER 10, 2014 6:30 P.M.

DUAL IMMERSION PROGRAM INFORMATION PRESCHOOL PRESENTATION SEPTEMBER 10, 2014 6:30 P.M. DUAL IMMERSION PROGRAM INFORMATION PRESCHOOL PRESENTATION SEPTEMBER 10, 2014 6:30 P.M. Presented by Dr. Norma R. Delgado, Director of Curriculum & Instruction 1 The United States Government has identified

Más detalles

VALE LA PENA INVERTIR EN TECNOLOGÍAS RENOVABLES?

VALE LA PENA INVERTIR EN TECNOLOGÍAS RENOVABLES? Palabras Clave Conservar renovable invertir proceder maximizar!!! Únete al debate nacional! VALE LA PENA INVERTIR EN TECNOLOGÍAS RENOVABLES? WORD GENERATION Unidad 2.15 Lectura Semanal! El!BigBelly!es!una!papelera!(o!basurero)!

Más detalles

Screener for Peer Supporters

Screener for Peer Supporters Screener for Peer Supporters Primary Recruiter: Secondary Recruiter: Potential Peer Supporter Name: Phone #1: Home/Cell Phone #2: Home/Cell Address: City: Zip: Contact 1: Date: / / Contact 2: Date: / /

Más detalles

V. Appendix V: Experiment 5

V. Appendix V: Experiment 5 V. Appendix V: Experiment 5 171 172 173 Pre-Test Questions (Spanish version used in experiment): Antes de empezar, le pedimos que por favor conteste 5 breves preguntas. Cuál es su ID#? 1. Cuántos años

Más detalles