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Matthew Will
Chapter 8
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Markowitz Portfolio Theory
Markowitz was the first person to observe that there are no securities that are perfectly positively or negatively correlated.
Thus, all stocks fall in the middle range and the risk of a PF will always be less than the simple weighted average of the individual risks of the stocks in the PF.
Correlation coefficients make this possible.
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Efficient Frontier
Standard Deviation
Expected Return (%)
Each half egg shell represents the possible weighted combinations for two stocks.
The composite of all stock sets constitutes the efficient frontier.
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The efficient frontier represents the set of portfolios that will give you the highest return at each level of risk. Portfolios on the efficient frontier are efficient in that there is no other combination of stocks that offer that high a return for the risk taken.
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ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
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ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Let’s Add stock New Corp to the portfolio
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Portfolio 28.1 50% 17.4%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
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Portfolio 28.1 50% 17.4%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
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Irwin/McGraw Hill
Portfolio 28.1 50% 17.4%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that?
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Portfolio 28.1 50% 17.4%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION
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WHY?
ABN
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So far, we assume that all the securities on the efficient set are risky. Alternatively, an investor could easily combine a risky investment with an investment in a riskless security.
The combination of the riskless asset and the risky asset produces a liner risk/return line.
The introduction of a risk-free asset changes the Markowitz efficient frontier into a straight line (Capital Market Line). That is, CML can be viewed as the efficient set of all assets, both risky and riskless.
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With riskless borrowing and lending, the PF of risky assets held by any investor would always be point A. Regardless of the investor’s tolerance for risk, he would never choose any other point on the efficient set of risk assets nor any point in the interior of the feasible region.
Rather, he would combine the securities of A with the riskless assets if he had high aversion to risk.
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Notice that the standard deviation of returns is on the X-axis of the CML graph. Is this the relevant measure of risk?
The standard deviation of expected returns measures a stock’s total risk. However, the risk that can be easily diversified should not be compensated for.
If you want to plot return again risk, the risk measure must be the measure of risk influencing return. So, the proper relationship is return vs. systematic risk.
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The relationship between expected return and beta can be represented by the capital asset pricing model.
Expected return on a security = rf + Beta of the security * [E(Rm)-rf ]
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