Lecture5 - Chapter 6 07/15/11 20:30 Uncertainty, Default,...

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Uncertainty, Default, and Risk • We continue to assume perfect markets , including: 1. No differences in opinion. 2. No taxes. 3. No transaction costs. 4. No big sellers/buyers But we now allow uncertainty. So, we do not know in advance exactly what will happen in the future. We now need to predict the future. For this, we need (just a little!) statistics . 07/15/11 20:30 References Corporate Finance: An Introduction (Welch, 2009, Prentice Hall) Chapter 6
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2 A Few Statistical Concepts • I will only cover a few basic concepts, enough to begin understanding risk. For more, take a (mathematical) stats course. • In particular, we will use the following concepts: State of the world : a possible outcome of the future Random variable : a variable which takes different outcomes in different states of world. Can be cash flow or rate of return Expected value : a method for taking the “average” of different possible outcomes in the future • In a later lecture, we will learn standard deviation, a common measure of risk in finance. We won't need it today. 6-1
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3 States of the World • From now on, we no longer know the future with certainty. But, we can write down a list of possible future outcomes – Of course, in reality many things can happen in future. For simplicity, we pretend there are only a few outcomes. • Ex. 1. States of world for tomorrow's weather: – Sunny, Cloudy, Rain, Snow, Hail • Ex. 2. States of world for 2014 World Cup winner: – Spain, Germany, Italy, Holland, Brazil, Argentina, Other • Ex. 3. States of world for U.S. GDP growth next year: – 5% or better, 2 to 5%, 0 to 2%, -2 to 0%, worse than -2% 6-1
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4 States of World for Facebook Q1: Social networking is new phenomenon, with uncertainty about how it will evolve. With your classmates, come up with a handful of possible states of world for Facebook in near future. (It is fine to disagree about likelihood of what will happen!) 6-1B
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5 Random Variables • An ordinary variable is something with a particular value. You often use algebra to solve for this value. – The value does not depend on what will happen in future • A random variable is not an ordinary variable. It can take a different value in each state of world in future. – Notation: often denoted with a tilde (~) above it – It can take on a whole range of possibilities. These can often be drawn in a histogram. • Some examples of random variables: – Outcome of coin flip (heads or tails) – Face of card drawn from deck (ace, king, queen, jack) – Wages next year (0 if fired, higher if promoted) – Google's stock return next year (-100% to infinity) 6-1
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6 Statistics and Random Variables • In many applications, we know the histogram of a random variable, but not the actual outcome. – A coin flip has two outcomes with 50% probability each
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Lecture5 - Chapter 6 07/15/11 20:30 Uncertainty, Default,...

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