Lecture6_6x1 - Why Is This Important Investors and...

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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 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 diFerent 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 bene±ts of diversi±cation 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 More Coin Tossing: St. Petersburg Paradox I I will toss a coin repeatedly until tails appear I I will put $1 in the payoF pot if the ±rst toss is heads and then double the pot every time heads appear I WhenItossata i l ,youwa lkawayw ithwhateverisinthepot 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 payoF is 1 2 · 1+ 1 4 · 2+ 1 8 · 4+ 1 16 · 8+ ... = 1 2 + 1 2 + 1 2 + 1 2 + ... = ± n =1 1 2 = I How much will you be willing to pay to play such a game with an in±nite expected payoF? 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 ±nance: 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 Measuring Returns I Returns can either be ex post , meaning returns were already realized ,o r ex ante , which means they are expected I Let’s ±rst look at ex post returns I Holding period return if you bought a stock at time t 1and 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 456 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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Measuring Realized (Ex Post) Returns I Holding period return realized over two years is 1 . 15 · 1 . 0727 1=23 . 36% I Holding period return per year is (1 . 15 · 1 . 0727) 1 / 2 1=11 . 07% I
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Lecture6_6x1 - Why Is This Important Investors and...

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