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? I We as investors want to achieve the highest possible expected return for a given level of risk I Modern Portfolio Theory (MPT) allows us to Fnd the optimal way to allocate our money to achieve this goal I Whether you are managing your own or someone else’s money, MPT tells you how to build the ‘best’ portfolio I MPT and its o±springs are still widely studied and used I 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 I Investing is a trade-o± between risk and return I 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 I We can combine assets to achieve the highest possible expected return for a given level of risk I Or alternatively, we can combine the assets to achieve the lowest possible level of risk for a given level of expected return I MPT can be thought of as a form of diversiFcation: minimizing risk without hurting expected return Portfolio Theory RSM 332, 3/21 Modern Portfolio Theory I We will consider three cases I Two risky assets I N risky assets I N risky assets and a risk-free asset I Caveat : MPT relies on a number of assumptions, including: I Returns follow a normal distribution I Investors only care about mean and variance of returns I Correlations between returns of di±erent assets are predictable I Markets are efficient I Investors are rational I There are no transaction costs I Assets are inFnitely divisible Portfolio Theory RSM 332, 4/21 Two-Stock Case I Let’s start with just two risky assets (stocks), A and B I DeFne expected return and variance of each stock i = A , B as E ( R i )and Var ( R i )= σ 2 i I DeFne covariance and correlation between the returns of stocks A and B as σ AB and ρ AB , respectively I 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 w A w B σ A σ B ρ AB I We can vary weights w A and w B and plot the expected return and standard deviation of returns of the resulting portfolios I 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 01234567891 0 1 1 Stock A: E(R)=1%, =5% Stock B: E(R)=1.5%, =10% Portfolio Theory RSM 332, 6/21
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This note was uploaded on 12/20/2011 for the course RSM 332 taught by Professor Raymondkan during the Fall '08 term at University of Toronto- Toronto.

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

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