Uncertainty and Risk in Finance

Uncertainty and Risk in Finance - SCHOOL OF BUSINESS...

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S CHOOL OF B USINESS A DMINISTRATION U NIVERSITY OF C ALIFORNIA AT R IVERSIDE BUS 106 Winter 2011 Avinash Verma U NCERTAINTY AND R ISK IN F INANCE This handout is intended to be a brief preview of the statistics that we shall be using in the course. Most of this material will also be covered in class, some in greater detail than here. Throughout this note, key words and concepts are identified by bold font. Our goal in this part of the course is twofold: F IRST , we would like to measure or quantify the risk associated with future values of financial variables, such as cash flows, prices, and returns. S ECOND , we want to be able to factor that risk into the rate of discount. In other words, having measured the risk, we’d like to price it. That is to say, we are interested in working out the appropriate reward per unit of measured risk that investors expect to receive. This note deals only with the first goal. Capital Asset Pricing Model [CAPM], to be discussed in class later, deals with the second goal. 1. There is uncertainty about the future value of most financial variables , such as prices, cash flows, returns, dividends, exchange and interest rates, etc. In Finance, we deal with a situation of uncertainty by turning it into a situation of risk. This is accomplished by imposing a probability distribution on the future values that financial variables can assume. When we do that, we treat these financial variables as random variables . 2. A random variable is a variable that takes on different values based on the outcome of a random or a chance event. These different values are called realizations of the random variable. For example, if we bet $1 on the event that toss of an unbiased coin will result in “heads up,” then the amount we win at the end of a single toss, denoted ~ X , is a random variable that can assume two possible values. The first possible realization of ~ X , denoted X 1 , occurs if we win, and is equal to $1. The other possible realization of ~ X , denoted X 2 , equals 1 $ - , and occurs if we lose. Randomness of a variable is often denoted by putting a tilde (~) on top of the symbol for the variable. Of course, once the outcome is known, there is no further uncertainty. Therefore, the realizations are not random, which is the reason why there is no tilde above the symbols used to denote them. Uncertainty and Risk in Finance 1
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S CHOOL OF B USINESS A DMINISTRATION U NIVERSITY OF C ALIFORNIA AT R IVERSIDE BUS 106 Winter 2011 Avinash Verma 3. Imposing a probability distribution involves two tasks: Making a mutually exclusive and collectively exhaustive list of events that can occur in future. The fact that events in the list are mutually exclusive means that no two events can occur at the same time. And if taken together or collectively, the events in the list exhaust all future possibilities, then, clearly, at least one event from the list must occur. Associating a
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Uncertainty and Risk in Finance - SCHOOL OF BUSINESS...

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