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# Sess13 new_1 - Lecture 13 Risk and Return Reading RWJ...

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Fin 3715 - Fall 07 - Kayhan 1 Lecture 13: Risk and Return Reading: RWJ Chapter 12 Outline : Rate of returns Defining risk Estimating risk and return Historical risk and return

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Fin 3715 - Fall 07 - Kayhan 2 Motivation We have by now developed a fairly complete theory of valuation and capital budgeting under certainty. In order to extend this theory to situations involving uncertainty (risk), we need to understand How do we define and measure risk? What is the link between the risk of an investment and its expected rate of return.
Fin 3715 - Fall 07 - Kayhan 3 Rate of Return on Financial Assets The rate of return on a stock at any time t is a random variable: is the price at the beginning of period is the price at the end of period (random variable) is the dividend at the end of period (random variable) is the rate of return earned for investing in the stock over the period. 1 ~ ~ ~ ~ ~ 0 1 1 0 0 1 1 - + = - + = P P D P P P D r 0 P 1 ~ P 1 ~ D r ~

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Fin 3715 - Fall 07 - Kayhan 4 Statistics Reminder: Random Variables A random variable is a variable that can take several possible values. We will denote random variables by the superscript tilde (e.g., ). For simplicity, we consider only discrete random variables that may take on finite number of values. A probability distribution is a list of all possible outcomes and the probability that each will occur. X ~ n j p x X j j ,..., 1 , ) ~ Pr( = = =
Fin 3715 - Fall 07 - Kayhan 5 Example: Rate of Returns The rate of returns over future periods is generally uncertain. For example, the S&P 500 index and Dell stock may have the following returns in different states of the world over the next period: State of the world 1 2 3 Probability 0.2 0.6 0.2 Return on S&P500 -5% 10% 20% Return on Dell stock -10% 10% 40%

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Fin 3715 - Fall 07 - Kayhan 6 Statistics Reminder: Mean Mean : the expected or forecasted value of a random variable. We will denote the mean of a random variable by the superscript bar (e.g., ).
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