...content and the hum of the threshing machine sounding from the farm. "What did I come in here for? What did I want to find?" My hands were empty. "Perhaps its upstairs then?" The apples were in the loft. And so down again, the garden still as ever, only the book had slipped into the grass. But they had found it in the drawing room. Not that one could ever see them. The windowpanes reflected apples, reflected roses; all the leaves were green in the glass. If they moved in the drawing room, the apple only turned its yellow side. Yet, the moment after, if the door was opened, spread about the floor, hung upon the walls, pendant from the ceiling--what? My hands were empty. The shadow of a thrush crossed the carpet; from the deepest wells of silence the wood pigeon drew its bubble of sound. "Safe, safe, safe" the pulse of the house beat softly. "The treasure buried; the room . . ." the pulse stopped short. Oh, was that the buried treasure? A moment later the light had faded. Out in the garden then? But the trees spun darkness for a wandering beam of sun. So fine, so rare, coolly sunk beneath the...
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...guilty, yet helpless man. Doesn’t this sound familiar? Don’t our lives seem, sometimes, the result of a game of dice being played by someone/something bigger than ourselves, even bigger than life itself? Just the fact that we are who we are is nothing but a result of chance. This statement, beyond its recklessness appearance, has an explanation consisting of three moments of existences that are determined by the roulette. The first one goes back to before we’re born. Have you ever thought of how many billions of chances were there when your parents’ genetic material mixed to create you? I, for instance, could’ve been blond, tall and smart. Or short and dumb. Or anything. But, somehow, I turned out to be me, out of what appear to be infinite chances of who I could’ve been. And this process follows no logic or intervention from our part: is the work of randomness. The second moment, chronologically, involves our environment. Where we’re born, who our parents are, and the rest of conditions that welcome us to this world are the sort of aspects I include in this side of this pyramidal die. The third and final moment is composed of the things that are choices in our lives. This is also a consequence of luck because the construction of ourselves is the outcome of the decisions we make, which have a luck component. That...
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...CAPM essay In the second scenario BBBY would use its $400 million in excess cash and borrow the remaining funds until Question 2 a) We will need to calculate the debt-to GDP ratio for each year separately in order to compute the total accumulation. The following equations and variables are used in question a) ∆b=g-t+r-y* b g-t=2 i=3 π=1 r=i-π=3-1=2 y=1 b=0,9 (=90%) Year 1 ∆b=2+2-1* 0,9=2,9 byear 1=90+2,9=92,9 Year 2 ∆b=2+2-1* 0,929=2,929 byear 2=92,9+2,929=95,829 Year 3 ∆b=2+2-1* 0,95829=2,95829 byear 3=95,829+2,95829=98,78729 Year 4 ∆b=2+2-1* 0,9878729=2,9878729 byear 4=98,78729+2,9878729=101,7751629 Year 5 ∆b=2+2-1* 1,017751629=3,017751629 byear 5=101,7751629+3,017751629=104,792914529 Therefore, after 5 years the debt-to-GDP ratio will be equal to 104,8 % (rounded to one decimal) b) The debt is not sustainable. The criteria to test whether debt is sustainable is as follows: ∆b=g-t+r-y* b=0 Plotting in the known variables results in the following: ∆b=2+2-1* b=2+b= 0 Solving for b gives the following: b= -2 Therefore, the initial debt should be -200% (so surplus) in order to maintain a sustainable debt. c) If the nominal interest rate rises to 10%, it would imply that the real interest rate is as follows: r=i-π=10-π Therefore, we know that: ∆b=g-t+r-y* b=2+10-π-1*0,9=2+9-π*0,9 The criteria to maintain a sustainable debt is as follows: ∆b=0 This implies that ∆b= 2+9-π*0,9=0 Solving for inflation results in the...
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...Tutorial 6 Questions Question One What is a probability and how can we relate it to share returns? Question Two Define the terms expected value and standard deviation. In providing your answer, show how these terms relate to share prices. Question Three What do we mean when we say an investor is risk averse? Question Four You are given the following information about the possible returns from an investment: |Return (%) |Probability | |12% |0.15 | |10% |0.65 | |5% |0.20 | Given this information, calculate: 1. The expected return on the investment; 2. The variance of the return on the investment; 3. The standard deviation of the return on the investment; and, 4. The probability that the return on the investment is equal to or less than 8%. Question Five You are a market analyst and have identified 4 different market conditions together with the probability that these market conditions will occur. The information contained in the table below relates to the return on 3 shares under each market condition: |Market Condition |Probability...
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...Formulas to Know for the Exam Although we do not suggest you memorize a lot of information to prepare for the exam, the following formulas are some of the items you do need to memorize, as well as understand. There will not be a lot of questions requiring you to use these formulas, but it will be helpful to be able to apply these at a moment’s notice. If you are not comfortable with math, you should be happy to hear that you can know none of these formulas and still pass the exam! The most important formulas are those relating to earned value, as earned value is a key component of monitoring and controlling. Formulas to Know for the Exam Title PMP® Exam Prep Chapter Reference Formula Present Value (PV) PV = FV (1 + r)n Integration Management Expected Activity Duration (Triangular Distribution)* P+M+O 3 Time Management Expected Activity Duration (Beta Distribution)* P + 4M + O 6 Time Management P−O 6 Time Management Beta EAD +/− SD Time Management LS − ES, or LF − EF Time Management Cost Variance (CV) EV − AC Cost Management Schedule Variance (SV) EV − PV Cost Management Cost Performance Index (CPI), or Cumulative CPI (CPIC) EV EVC or AC ACC Cost Management Schedule Performance Index (SPI) EV PV Cost Management Estimate at Completion (EAC) AC + Bottom-up ETC Cost Management Estimate at Completion (EAC) BAC CPIC Cost Management Estimate at Completion...
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...Week 1 homework chapter 1 1. we have: Cf= 55000, cv= 8, p= 21; v= 10 000 a. Total cost TC = cf + v*cv TC= 55000+ 10000*8 TC= $135000 Total revenue TR= v*p TR= 10000*21 TR=$ 21000 Profit Profit= TR-TC Profit= TR-TC P= 21000-135000 P= $ -114 000 b.Break even volume, V= cf/ (p- cv) V= 55000/ (21- 8) V= 4230.77 recap tires, 2. monthly break even volume V= cf/ (p- cv) We have Cf= 30000, cv= 0.16, p= 0.40 V= 30000/ (0.4- 0.16) V= 125000 units 3. If the new price is p= 0.60, Then the break even volume will decrease. We don’t need to sell as much units as before to break even. Proof: V= 30000/ (0.6- 0.16) V= 68181.81 units 4. If we increase advertising, that means CF increases, then the Break even volume will increase, because the cost of the production increased. Proof; V= 30000+ 14000/ (0.6- 0.16) V= 100000 units 5.we have Cf= 5600, cv= 0.35, p= ?; v= 2000 (note: Cf= 2500+3100; Cf= $5600) a.What price should be charged to break even? Break even means Profit = 0, then TR=TC Meaning V*P= cf+ V*cv, then P= (cf+ V*cv)/ V P= (5600+ 2000*0.35)/ 2000 P= $3.15 b. If during the season, there are less guest than expected, to break even, she needs to increase the prices. 6. we have Cf= 360000, cv= 12000, p= 17000; a. determine V , V= cf/ (p-...
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...I sat in a passenger seat of an old rental van with five of my closest friends, who just happen to be my band mates, staring off into the distance watching the lights fly by the window one by one. The view of the surrounding landscape turned suddenly into a completely unfamiliar area as if teleported to a new world. The unknown street names and buildings took over the area around us. Everything hit me all at once so unexpectedly, like the sound of a first lighting strike in the beginning of a storm. At that moment, nothing else mattered. This is finally happening. Andrew asked, “Do you think we will find a place to sleep every night?” Andrew was always the worried one of the bunch, but he played bass on stage he moved around like a madman. “3 weeks are a long time so probably not,” my vocalist Brandon chuckled out, “but I mean a majority of even the popular bands that go on a tour can not find a place to sleep every night so we can always just crash out in a Wal-Mart parking lot.” From my viewpoint, I could see my band member’s faces in the reflection of the rear view mirror as they all spoke about what they wanted to do at the upcoming shows; their eyes getting bigger than the cities we headed to in excitement. I still just sat there; having this profound realization in my mind while a smile slowly sprouted across my face. Over the course of 4 years, I spent more time alone in my room, sitting in an old desk chair wrapped up in duct tape to keep it from falling apart...
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...Lecture 3 Supplement Annoying Proof of a Useful Result Proof1 that E(ea+bx̃) = ea+b+½Var(x̃) I. The Normal Distribution The probability density function of a normal distribution is 1 2 v 1 y e 2 v 2 which has the property, for any y and v, that 1 2 v 1 y e 2 v 2 dy 1 II. Fun with Completing the Square! Now suppose a b~ is distributed N a b , b 2 2 . x Let’s find the because a bx a b bx expected value of e E e a bx a b~ x . a b~ a b 2 x 1 2 b ~ 1 2 b e a b~ x e dx 2 1 a b e 2 b e a b ~ e bx e bx 1 2 b dx 2 1 2 b 1 bx b ~ 2 x e 2b e b 2b 2 2 2 2 dx 1 e a b 2 b 1 b 2 x 2 2b x b 2 2 2 2 e 2b dx Larger view Ee a b~ x 1 e a b 2 b 1 b 2 x 2 2b x b 2 2 2b 2 2 e dx 1 Why? We use this result a lot in finance. Let’s show that it is true. 1 MSF 501 – Math with Financial Applications Lecture 3 Supplement Annoying Proof of a Useful Result We know that p q 2 p 2 2 pq q 2 . We can see that the expression in the { } could be expressed as...
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...A Good Man is Hard to Find. The grandmother focuses of showing that she cares nothing about the family by concerning herself with her hat. She builds a setting in her head that if she dies she will look like a lady without any concern for her family's well being. This idea that her hat, which makes her look like a lady in her mind, is more important than her family shows selfishness. Her mistaken ethics are aware from the beginning as the hat is the symbol for this negligence to her family. When they did indeed have a car wreck the grandmother was curled up under the dashboard with her hat still attached to her head. The hat represents that goal of still being a lady no matter the cost. While her grand children are in shock and shaking she is complaining that she thinks she has a hurt organ. The symbol of the brim of her hat smashed as she says “But nobody’s killed” in a frustrated tone shows her reluctance to give up that she was wrong. She will not give up this attempt at being a lady no matter what happens to her or grand children. As she confronts the Misfit her self assurance and idea that she is a lady slowly disintegrates away as she becomes more humble that she will most likely die. The symbolism of these disintegration is when her brim actually falls off of her hat and it realization that she is not a lady by any means. The symbolism of the hat to her concept of doing anything by any means necessary to be a considered a lady by everyone including herself is quite...
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...Making sense of . . . LogNormal stock-price models in Exams MFE/3 and C/4 James W. Daniel Austin Actuarial Seminars http://www.actuarialseminars.com June 26, 2008 c Copyright 2007 by James W. Daniel; reproduction in whole or in part without the express permission of the author is forbidden. Foreword This document briefly describes the ideas behind the use of LogNormal models for stock prices in some of the material for Exams MFE and C of the Society of Actuaries and Exams 3 and 4 of the Casualty Actuarial Society. Not a traditional exam-prep study manual, it concentrates on explaining key ideas so that you can then understand the details presented in the textbooks or study manuals. It can be especially useful to anyone taking Exam C/4 without having studied the material for Exam MFE/3. 2 Chapter 1 LogNormal stock-price models 1.1 Why LogNormal models? Why learn about and use LogNormal models for stock prices? I could answer “Because it’s on the exam syllabi” or “Why not?”, but that wouldn’t be helpful. Instead, I’ll take a little space to motivate this. Suppose that the price of a stock or other asset at time 0 is known to be S(0) and we want to model its future price S(10) at time 10—note that some texts use the notation S0 and S10 instead. Let’s break the time interval from 0 to 10 into 10,000 pieces of length 0.001, and let’s let Sk stand for S(0.001k), the price at time 0.001k. I know the price S0 = S(0) and want to model the price S10000 = S(10)....
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...Midterm Practice Problems From Review Session: 11/9/2012 Ch 8 From Chapter 8, I went over problems 8.7, 8.9 (Answers in back of the book) and problems 8.16, 8.17, which you have answers from Homework solutions. Make sure you know the duration and convexity equations, and how the bond price changes due to a change in yield/ ___________________________________________________________________________________ Ch 9 From Chapter 9, I went over problems 9.6, 9.9, 9.10 (Answers in the back of the book) and 9.13. VaR problems in my mind break down into three parts: Normally distributed, the “stair cummulative dist function”, and the autoregressive model. Be familiar with how to solve all three. 9.13. Suppose that daily changes for a portfolio have first-order correlation with correlation parameter 0.12. The 10-day VaR, calculated by multiplying the one-day VaR by , is $2 million. What is a better estimate of the VaR that takes account of autocorrelation? The correct multiplier for the variance is 10 + 2 × 9 × 0.12 + 2 × 8 × 0.122 + 2 × 7 × 0.123 + . . . + 2 × 0.129 = 10.417 The estimate of VaR should be increased to = 2.229 _________________________________________________________________________________ Ch 10 From Chapter 10, I went over 10.11, 10.12 (Answers in Book). While many of the formulas here look complicated, when it comes down to it, many parts of these questions in the book are just “plug-and-chug” questions. Here is 10.21 in case you tried it out for...
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...Extension of the Snow Fun Ski Resort Problem Suppose that the operating cost of the snowmaking equipment is actually 30% higher than the owner had estimated, that is, $13,000 if the snowfall is heavy, $65,000 if it is moderate, and $117,000 if it is light. How will the increased operating cost affect the owner’s optimal decision? As shown above, the best decision now is to let the larger hotel run the ski resort and the profit is $45,000 Calculate the EVPI, and determine that maximum amount that could be paid for a perfect forecast. If the snowfall is more than 40”, the owner should operate the resort without a snowmaker (profit=$120,000, probability=40%). If the snowfall is between 20 to 40 inches or if it is less than 20 inches, the owner should let the larger hotel run the resort (profit=$45,000, probability=20%+40%=60%). EVPI = $120,000*0.40 + $45,000*0.60 = $75,000 Since the optimal profit without perfect information is $45,000, the maximum amount the owner can pay for perfect information is $75,000 - $45,000 = $30,000 1 Decision Tree Final Problem The NC Airport Authority is trying to solve a difficult problem with the over-crowded RaleighDurham airport. There are three options to consider: A. The airport could be totally redesigned and rebuilt at a cost of $8.2 million. The present value of increased revenue from a new airport is in question. There is a 70% chance this present value would be $11 million, a 20% chance present value would be $5 million, and a 10%...
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...in front of hundreds of other people. My father helped me write my speech. Ironically I was going to talk about confidence building. When the date of speech came nearer I panicked and kept forgetting my lines. My teacher guided me to practice before a mirror, it helped but not enough to calm my nerves. After days of practicing before my parents and the mirror I was still not ready. My thoughts were focused upon how my voice would tremble and I would lose feeling in my legs. It was not till I was on stage and I started speaking that I paid attention to what I was saying. I had given the preparation my best effort and if my voice is going to tremble it did not matter anymore. With this thought in my I found my voice strengthen. This was a moment of revelation for me, I was realizing for the first time that I can do this. When I stopped avoiding looking at the audience I realized that I was not afraid anymore. I can give my best or worst performance and it will still be over either way, with this thought I gave it all my effort. The applause I got at the...
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...10/24/2011 Introduction The Sample Mean The Central Limit Theorem The Sample Variance Sampling Distribution from The Normal Distribution Sampling from A Finite Population ◦ Distribution of The Sample Mean ◦ Joint Distribution of X and S2 ◦ Approximate Distribution of The Sample Mean ◦ How Large A Sample Is Needed 2 1 10/24/2011 Recall definitions of: ◦ ◦ ◦ ◦ ◦ ◦ ◦ Population Sample Inferential statistics Sampling Random sampling Parameter Statistic 3 If X1, . . . , Xn are independent random variables having a common distribution F, g , then we say that they constitute a sample (sometimes called a random sample) from the distribution F. 4 2 10/24/2011 Parametric inference problem: Problems in which the form of the underlying distribution is specified up to a set of unknown parameters, eg: Nonparametric inference problem: problems in hi h i which nothing is assumed about the form thi i d b t th f of F ◦ F was assumed as a normal distribution function having an unknown mean and variance 5 µ: population mean, σ2:population variance Let X1, X2, . . . , Xn be a sample of values from this population. The sample mean is defined by 6 3 10/24/2011 X is also a random variable 7 X is also centered about the population mean μ, but its spread becomes more and more reduced as the sample size increases. 8 4 10/24/2011 9 ◦ Distribution of The Sample Mean 10 5 10/24/2011 Let X1, X2, . . . , Xn...
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...Tribute speech Although, I’m not the first born son or daughter; there is a unique bond shared between my father and I. Even though it has never been said, it’s just known that I am his favorite! I have always been told it is because I am the baby of the family: daddys little girl. But as he recalls, I was his good luck charm starting from the moment I was conceived. You see my father faced numerous hardships and struggled his way to get to where he is now. He was raised with 10 other siblings from one of the poorest towns in Pakistan. He would tell me how growing up, he would always aspire to come to America because back home that meant you would be somebody. And he did just that! In 1970, he finished his bachelors at the top of his class in Pakistan and from there he applied for a Student Visa to complete his masters in the US. He had begged his parents to pay for his plane ticket, promising them he would return double the amount as he reaches America; the land of opportunity. However as he set forth to explore his new home he quickly realized it wasn’t an easy ride to success. There were various obstacles he would have to overcome which the average American wouldn’t have to. He continues telling me how he came from a 3rd world country with literally $30 in his pocket, no family or friends near and his biggest disadvantage being the language barrier. Wanting to fulfill the promise he made to his parents, he set out on his journey. Juggling an education...
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