The e ffi cient frontier lies to the north west of

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The E ffi cient Frontier lies to the north-west of the individual assets. Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Markowitz Frontier Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Markowitz Frontier Note that the curve below the Global Minimum Variance Portfolio is ine ffi cient . Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Constraints Clients may have the following constraints No Short Sales Invest in only AAA rated securities Socially Responsible Investing Liquidity constraints such as trading costs, depth of market, etc. Tax incentives Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Constraints Constraints will lower the Sharpe ratio of the combined (overall) portfolio Unconstrained maximization will always lead to a higher Sharpe Ratio than constrained maximization. Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Markowitz Frontier The return on the risk-free asset determines the CAL. Portfolio P maximizes the Sharpe ratio given the risk-free rate. Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Markowitz Frontier – An Alternative Approach An alternative to calculate the CAL immediately rather than the E ffi cient Frontier. Introduce the risk-free asset immediately and maximize the Sharpe Ratio to find the e ffi cient portfolio P . Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Markowitz Frontier – An Alternative Approach Find the minimum variance portfolio, G . Construct a portfolio with zero covariance (correlation) to the e ffi cient portfolio P . Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Markowitz Frontier – An Alternative Approach This is the Z portfolio. Find it by maximizing the Sharpe ratio subject to having a covariance (correlation) of zero with the e ffi cient portfolio P . Robert J. McKeown (U of T) ECO358 Week Three
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Generalizing to Many Risky Assets: Security Selection and the Markowitz Frontier (E ffi cient Frontier) Markowitz Frontier – An Alternative Approach We can now “sketch” out the e ffi cient frontier.
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  • Summer '14
  • ATAMAZAHERI
  • Modern portfolio theory, Robert J. McKeown

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