Characterizing_Risk_and_Return_TRNS

Characterizing_Risk_and_Return_TRNS - Characterizing Risk...

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Characterizing Risk and Return Professor Gideon Saar Johnson School Cornell University Johnson School, Cornell University Outline Risky securities: random variables. Reward: expected return. Risk: – Variance and standard deviation. » Pros and Cons. – Shortfall probability. – Semivariance. – Value-at-Risk. It f i k d t Copyright 2009, Prof. Gideon Saar, All rights reserved/Characterizing Risk and Return Investors’ preferences over risk and return: – Mean-Variance Preferences. – Dominance rules. – Indifference curves.
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Realized Return Definition of Realized Return: –P e =End of period price. P Bii f i di eo o PPC r P – P o =Beginning of period price. – C=Cash flow received (e.g., dividends). IBM: – Price (Dec. 31, 2007)=$108.10 – Price (Dec. 31, 2008)=$84.16 – Dividends: $0.40, $0.50, $0.50, $0.50 r=(84 16 108 10+0 40+0 50+0 50+0 50)/108 10= 20 39% Copyright 2009, Prof. Gideon Saar, All rights reserved/Characterizing Risk and Return – r=(84.16-108.10+0.40+0.50+0.50+0.50)/108.10= -20.39% Could you have used this information when you considered IBM as an investment on January 1, 2008? Return Distribution How would you evaluate return at the beginning of the period? IBM example: r s Probability (p s ) Event s -15% 0.20 (20%) Credit crunch causes a long worldwide recession; price war in computer industry. 3% 0.20 (20%) Credit crunch causes a long worldwide recession, but no price war. 14% 0.35 (35%) Recession ends 3 rd quarter of 2009; price war in computer industry. 40% 0.25 (25%) Recession ends 3 rd quarter of 2009; no price war. Copyright 2009, Prof. Gideon Saar, All rights reserved/Characterizing Risk and Return The return of a stock at the beginning of the period is a random variable with values that are the possible realized returns and probabilities that are associated with the values.
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Measure of Reward: Expected Return E( )=Mathematical Expectations. – A summary statistic for the value of a random variable. Th f th ibl li d l lti li d b th – The sum of the possible realized values multiplied by the probability of each value. – Should be read “the expected value of” the variable inside ( ). Formula for Expected Return: () * s s s Er r p Copyright 2009, Prof. Gideon Saar, All rights reserved/Characterizing Risk and Return –r s =Realized return if event s occurs. –p s =Probability of event s. =Notation for summation over all s events. The Expected Return is also called Mean Return. s Meaning of Expected Return IBM example: – E(r)=sum(r s *p s )= 0 15*0 2+0 03*0 20+0 14*0 35+0 40*0 25 0 125 12 5% -0.15*0.2+0.03*0.20+0.14*0.35+0.40*0.25=0.125 or 12.5% Is the expected return the most likely return? Frequency or “statistical” interpretation: – Repeat the “experiment” (same period with the same return distrib tion) man times Copyright 2009, Prof. Gideon Saar, All rights reserved/Characterizing Risk and Return distribution) many times.
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This note was uploaded on 09/16/2009 for the course NBA 5420 taught by Professor Saar,gideon during the Spring '09 term at Cornell.

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Characterizing_Risk_and_Return_TRNS - Characterizing Risk...

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