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Lecture7_6x1

# Lecture7_6x1 - Why Is This Important Lecture 7 Portfolio...

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Lecture 7: Portfolio Theory RSM 332 Capital Market Theory Rotman School of Management University of Toronto Mike Simutin October 26/27, 2011 Portfolio Theory RSM 332, 1/21 Why Is This Important? We as investors want to achieve the highest possible expected return for a given level of risk Modern Portfolio Theory (MPT) allows us to find the optimal way to allocate our money to achieve this goal Whether you are managing your own or someone else’s money, MPT tells you how to build the ‘best’ portfolio MPT and its offsprings are still widely studied and used MPT is a stepping stone to the very popular asset pricing models such as the CAPM Portfolio Theory RSM 332, 2/21 Intuition Behind MPT Investing is a trade-off between risk and return Rather than selecting assets on their own merits, we should consider how returns of every asset correlate with returns of every other asset in the portfolio We can combine assets to achieve the highest possible expected return for a given level of risk Or alternatively, we can combine the assets to achieve the lowest possible level of risk for a given level of expected return MPT can be thought of as a form of diversification: minimizing risk without hurting expected return Portfolio Theory RSM 332, 3/21 Modern Portfolio Theory We will consider three cases Two risky assets N risky assets N risky assets and a risk-free asset Caveat : MPT relies on a number of assumptions, including: Returns follow a normal distribution Investors only care about mean and variance of returns Correlations between returns of different assets are predictable Markets are eﬃcient Investors are rational There are no transaction costs Assets are infinitely divisible Portfolio Theory RSM 332, 4/21 Two-Stock Case Let’s start with just two risky assets (stocks), A and B Define expected return and variance of each stock i = A , B as E ( R i ) and Var ( R i ) = σ 2 i Define covariance and correlation between the returns of stocks A and B as σ AB and ρ AB , respectively If we invest a fraction w A of our money in stock A and the remaining fraction w B = 1 w A in B , expected return and variance of such portfolio P will be E ( R P ) = w A E ( R A ) + w B E ( R B ) σ 2 P = w 2 A σ 2 A + w 2 B σ 2 B + 2 w A w B σ AB = w 2 A σ 2 A + w 2 B σ 2 B + 2 w A w B σ A σ B ρ AB We can vary weights w A and w B and plot the expected return and standard deviation of returns of the resulting portfolios Risk of the portfolios we obtain this way will importantly depend on correlation ρ AB Portfolio Theory RSM 332, 5/21 Two-Stock Case Expected Return, Percent 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 Standard Deviation, Percent 0 1 2 3 4 5 6 7 8 9 10 11 Stock A: E(R)=1%, =5% Stock B: E(R)=1.5%, =10% Portfolio Theory RSM 332, 6/21

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Lecture7_6x1 - Why Is This Important Lecture 7 Portfolio...

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