Choosing Efficient Portfolios (Portfolio Theory) A. Portfolios of Risky Securities i. Mean-Variance Analysis ii. The Markowitz Efficient Frontier B. Risky Securities Plus a Risk-Free Asset i. The Tangent Portfolio ii. (Another) Separation Theorem iii. The Capital Market Line (CML) FIN2200 Fall 2014 – Lecture 5 61
3.B.ii Risky Securities Plus a Risk-Free Asset: (Another) Separation Theorem The optimal portfolio choice problem can be separated into two independent tasks : 1. Determining the tangent portfolio • I.e. the portfolio of all risky assets with the highest Sharpe ratio • This is a non-personal choice 2. Mixing the tangent portfolio and risk-free asset to form an investor’s optimal portfolio • This is a personal choice ; depends on the investor’s risk preferences Separation Theorem : In a world with homogeneous expectations, the tangent portfolio is the same for everyone All investors will hold the same risky portfolio ! (I.e. the efficient, tangent portfolio) They can separate their level of risk aversion from their choice of the risky component of their total portfolio An investor’s risk preferences will determine how much to invest in the tangent portfolio versus the risk-free investment • That is, all investors choose a point along the line FIN2200 Fall 2014 – Lecture 5 62
3.B.iii. Risky Securities Plus a Risk-Free Asset: The Capital Market Line The optimal portfolio is a combination of the risk-free asset and tangent portfolio Since the tangent portfolio is same for everyone, it equals the market portfolio When the tangent line goes through the market portfolio , it’s called the capital market line FIN2200 Fall 2014 – Lecture 5 63 σ P E[ R P ] R f Market Portfolio The CML While all investors invest in the market portfolio, the optimal portfolio chosen (on the CML) depends on their level of risk aversion Becomes an issue of asset allocation A risk-averse investor will invest more in the risk-free asset A less risk-averse investor will invest more in the market portfolio An investor may even borrow to buy the market portfolio on margin, this would be an even riskier strategy Riskless borrowing and lending are offset in the aggregate portfolio
To Summarize (Portfolio Theory)… 1. The investment opportunity set is: A point when there is one risky asset A curve when there are two risky assets An area when there are many risky assets 2. When there is a risk-free asset : Given the investment set, find the tangency portfolio by maximizing the Sharpe ratio The line connecting the riskless rate and the tangency portfolio is the CML and any portfolio along this line has the potential to be optimal depending on the investor’s utility function When there is a riskless and only one risky asset , the risky asset is the “tangency portfolio” since it is the only risky portfolio available 3. When there is no risk-free asset : There is no tangency portfolio RSM 330 Winter 2011 - Class 6 64
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