07 Fin 301 Risk and return I Ulearn

07 Fin 301 Risk and return I Ulearn - Risk and Return What...

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1 Risk and Return What goes in the denominator? 2 Expected Return on TD Stock = ? What is an expectation (expected value)? A likely or representative outcome: Midterm Score ( Z i ) Probability ( p i ) 100 p 1 95 p 2 80 p 3 70 p 4 60 p 5 3 What is an expectation? What if all equally likely? Expected score: E ( Z i ) = (100 + 95 + 80 + 70 + 60) 5 = 81 What if the probabilities are: { p 1 , p 2 , p 3 , p 4 , p 5 } = {0.1, 0.1, 0.5, 0.2, 0.1} ? Expected score: E ( Z i )= 0.1 100 + 0.1 95 + 0.5 80 + 0.2 70 + 0.1 60 = 79.5
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2 4 Probability Weighted Average of Possible Outcomes  n i i i Z p Z E 1 5 Great Expectations: TD Bank Oct 31: 71.35 Nov 30: 75.00 6 Expected v.s. realized return Ex post – what actually happened Paid $71.35, received $75, no dividend One month return: % 12 . 5 0512 . 0 35 71 35 71 00 75 . . . R TD NOV Ex ante –w h a t w e e x p e c t Is 5.12% good or bad – what do investors expect? What is the probability distribution of TD returns?
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3 7 Possible outcomes Are stock returns discrete random variables? U.S. banks stay out high return: 5.0% U.S. banks enter market low return: 0.5% More like: –4% –3% –2% –1% 0% 1% 2 3% 4% 5% 6% 8 Which One Is Riskier? 6 – 4 – 3 – 2 – 1 012345   n i i i Z E Z p Z Z 1 2 2 A B Standard Deviation: 9 Annual returns fall between – 6.63% and 27.09% with approximately 2/3 probability Return on Large Company Stocks
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4 10 Assets in a portfolio   Y E Y Z E Z p i n i i i Y Z 1 , We need to measure how much asset returns move together Invest in TD Bank and Bank of Montreal Invest in TD Bank and Research in Motion (RIM) Covariance: 11 Positive Covariance E[Z] E[Y] 0 Z E Z i 0 Y E Y i 0 Y E Y i 0
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07 Fin 301 Risk and return I Ulearn - Risk and Return What...

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