Lecture6 - Lecture 6: Risk and Return RSM 332 Capital...

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Lecture 6: Risk and Return RSM 332 Capital Market Theory Rotman School of Management University of Toronto Mike Simutin October 19/20, 2011 Risk and Return RSM 332, 1/26

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Why Is This Important? I Investors and investment professionals want to measure performance of investment strategies and account for their risk I This allows us to distinguish between diﬀerent investment alternatives I It also permits us to evaluate mutual fund and other money managers I Investors and investment professionals would like to construct portfolios that maximize expected return without taking on unnecessary risk I Understanding and taking advantage of the beneﬁts of diversiﬁcation helps improve portfolio performance I Understanding risk and return forms the basis of understanding Modern Portfolio Theory, which dominates today’s investment philosophy Risk and Return RSM 332, 2/26
A Couple Coin-Tossing Games Game 1 I I’ll toss a fair coin, and if either heads or tails come up, I’ll give you a \$100 I How much will you be willing to pay to play this game? Game 2 I Now I’ll toss the same coin, and if it comes up heads, I’ll give you \$1,000,200 I But if it comes up tails, you’ll have to pay me \$1,000,000 I How much will you be willing to pay to play this game? Risk and Return RSM 332, 3/26

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More Coin Tossing: St. Petersburg Paradox I I will toss a coin repeatedly until tails appear I I will put \$1 in the payoﬀ pot if the ﬁrst toss is heads and then double the pot every time heads appear I When I toss a tail, you walk away with whatever is in the pot I So if I toss four straight heads and then a tail, I’ll pay you 1 · 2 · 2 · 2 = \$2 3 = \$8 I If I toss n straight heads and then a tail, I’ll pay you \$2 n - 1 I Your expected payoﬀ is 1 2 · 1+ 1 4 · 2+ 1 8 · 4+ 1 16 · 8+ ... = 1 2 + 1 2 + 1 2 + 1 2 + ... = X n =1 1 2 = I How much will you be willing to pay to play such a game with an inﬁnite expected payoﬀ? Risk and Return RSM 332, 4/26
Risk and Return I Investors dislike risk: they are risk averse I Returns on investment vary with risk: you should require more return if you take on more risk I So returns is only half the story in ﬁnance: we also need to take into account risk I Discount rates should therefore reﬂect not only the time value of money, but also the riskiness of the underlying security I How should we measure returns and risk? Risk and Return RSM 332, 5/26

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Measuring Returns I Returns can either be ex post , meaning returns were already realized , or ex ante , which means they are expected I Let’s ﬁrst look at ex post returns I Holding period return if you bought a stock at time t - 1 and sold it at time t is R t = P t + D t - P t - 1 P t - 1 = P t + D t P t - 1 - 1 Year 0 Year 1 Year 2 Dividends at year-end, D t 4 5 6 Price at year-end, P t 100 110 112 I Return during year 1 is R 1 = 110 + 5 - 100 100 = 15% I Return during year 2 is R 2 = 112 + 6 - 110 110 = 7 . 27% Risk and Return RSM 332, 6/26
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This note was uploaded on 10/22/2011 for the course RSM 332 taught by Professor Raymondkan during the Spring '08 term at University of Toronto- Toronto.

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Lecture6 - Lecture 6: Risk and Return RSM 332 Capital...

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