LN2_ModelingUncertainty - annotated

LN2_ModelingUncertainty - annotated - Investments and...

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FIN 320, Lecture Notes, Korniotis Page 1 Investments and Security Markets (Lecture Notes) George Korniotis 514J Jenkins Building University of Miami Coral Gables, FL 33124 Email Phone: (305) 284-5728. Fall 2011

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FIN 320, Lecture Notes, Korniotis Page 2 Lecture Notes 2 MODELING UNCERTAINTY Main Topics Part A: 1. Return Distributions 2. Event Tree Representation of Return Distributions 3. Several Examples Part B: 4. Basic Statistical Concepts 5. Computing Statistics using the Event Tree Representation Note: These notes cover material from Chapter 5 Recommended problems from Chapter 5: 7, 9, CFA3, CFA4, and CFA5
FIN 320, Lecture Notes, Korniotis Page 3 PART A: Return Distributions Earlier, we had talked about the fundamental goals of investment. The 3 main goals are: (i) Max Portfolio Return (ii) Min Portfolio Risk (iii) Match Portfolio Risk with your own risk tolerance. In sum, the goal is to MAXIMIZE Return/Risk ratio. Before we can make these ideas operational, we need to define measures of return, risk, and risk- aversion (opposite of risk tolerance). Using these measures, we will develop tools that would allow us to examine the risk-return characteristics of portfolios. Knowing the risk-return characteristics of a portfolio is a crucial step in portfolio selection that take the following steps: 1. Choose assets to include in a portfolio 2. Uncover the range of values for the asset’s returns and the probability distribution of these returns 3. Simplify the probability distribution 4. Determine the portfolio weights 5. Determine the portfolio payoffs 6. Compare portfolios using summary statistics 7. Conditional on investor risk tolerance, choose a portfolio

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FIN 320, Lecture Notes, Korniotis Page 4 In the first step of portfolio selection we need to choose the assets that we are interested. More importantly, we need to quantify the risk and return characteristics of each individual asset. To do so, we assume that: Stock price or return is a random variable , i.e., future values of stock prices or returns are unknown A random variable is defined using a probability distribution , i.e., future values are uncertain but we can assign probabilities to them
FIN 320, Lecture Notes, Korniotis Page 5 UNDERSTANT THE PROPERTIES OF THE ASSET Example: IBM Stock Prices Suppose you know the IBM’s closing price today (say, \$100). What would be the closing price of IBM tomorrow? Given that it is not a deterministic variable, it is hard to provide a precise estimate. However, you can make a reasonable guess. First, we determine the range of potential prices, and then we assign probabilities 0-20 20-40 40-60 60-80 Distribution of 80-100 IBM stock 100-120 prices (or returns). 120-140 140-160 160-180 180-200 Stock Price Range Probability Note : The range for a stock price is [0, + ], the range for stock returns is [-100, + ].

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LN2_ModelingUncertainty - annotated - Investments and...

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