Lecture 5 - Lecture5:Outline...

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Lecture 5: Outline • Topic 4:  Portfolio Theory (Chapters 10 and 11) – Capital Allocation Line (CAL) – Sharpe ratio – Diversification – Efficient Frontier – Mean-Variance Optimization – CAPM and Beta – Single index model and diversification
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The Capital Allocation Line (CAL) The  Capital Allocation Line  (CAL) represents all possible  combinations of risk (standard deviation) and expected return that can  be generated by holding a portfolio of the risky asset and the risk free  asset.  If we invest a fraction “w” in the risky asset then we have, for the  portfolio: A p A p f A p σ σ σ r w) - (1 ) r ~ E( w ) r ~ E( = = + = w + = + = A f A p f f A p A A p p σ r - ) r ~ E( σ r r σ σ - 1 ) r ~ E( σ σ ) r ~ E( × + = Risk Reward Risk rate free Risk return Expected
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The Capital Allocation Line (CAL) Quiz: how do  you get here? Investing in a risky  asset and a risk free  asset Portfolio P: 50-50 weights
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Sharpe ratio The slope of the CAL, called the  Sharpe ratio  (or reward-to-risk  ratio), equals the increase in expected return that can be obtained  per unit of additional standard deviation.  It is a measure of the  risk-return trade-off (extra return per extra risk), and is given by: Thus,  the  Sharpe  ratio  is  a  ratio  of  risk  premium  to  standard  deviation All points on the CAL have the same Sharpe ratio ( 29 p f p r r E S σ - =
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CAL: example • Suppose IBM has a standard deviation of 75%, and an  expected return of 25%. The risk free rate is 3%.  Construct a portfolio of IBM and the risk free asset that  has a standard deviation of 50%. What are the expected  return and Sharpe ratio of the portfolio?
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Diversification: introduction Diversification:  spreading  one’s  wealth  across  different  risky  assets Diversification can increase Sharpe ratios Intuitively, the more dissimilar the return patterns of a group of  assets, the greater the portfolio risk reduction that is achievable  by combining these assets in a portfolio The return variations offset one another, at least to some extent,  provided the individual asset returns are not perfectly positively  correlated
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Flip a coin once. Referencing that one coin flip: Lottery A: pays $1M if heads, $0 if tails Lottery B:  pays $1M if tails, $0 if heads Note: Lottery A and B are perfectly negatively correlated Each lottery has expected payoff of $500,000 Each lottery is individually risky. But ½ lottery A + ½ lottery B has sure payoff of $500,000
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This note was uploaded on 08/31/2010 for the course MANAGEMENT MGCR 341 taught by Professor Jassim during the Summer '09 term at McGill.

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Lecture 5 - Lecture5:Outline...

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