We can now consider portfolios that are combinations of the risk-free security, denoted with the subscript f and risky portfolios along the Efficient Frontier. E[R] σ P R f
58 A+Lending The riskfree asset: riskless lending and borrowing Consider combinations of the risk-free asset with a portfolio, A, on the Efficient Frontier. With a risk-free asset available, taking a long f position (positive portfolio weight in f ) gives us risk- free lending combined with A. Taking a short f position (negative portfolio weight in f ) gives us risk-free borrowing combined with A. σ P E[R] R f A+Borro wing Portfolio A
59 The riskfree asset: riskless lending and borrowing Which combination of f and portfolios on the Efficient Frontier is best? Portfolios along the line tangent to the Efficient Frontier dominate everything else. Now, the only efficient risky portfolio on the Markowitz Efficient Frontier is Portfolio M. σ P E[R] R f What is the optimal strategy for every investor? M
60 M: The Market Portfolio The combination of f and portfolios on the Efficient Frontier that are best are… combinations of f and M. All investors choose a point along the line… each point is some combination of the risk-free asset, f , and the market portfolio M . In a world with homogeneous expectations, M is the same for all investors. σ P E[R] R f CML stands for the Capital Market Line M CML
61 A new separation theorem This separation theorem states that the market portfolio, M, is the same for all investors. They can separate their level of risk aversion from their choice of the risky component of their total portfolio. All investors should have the same risky component, M! σ P E[R] R f M CML
62 Given Separation, what does an investor choose? While all investors will choose M for the risky part of their portfolio, the point on the CML chosen depends on their level of risk aversion. A very risk-averse investor will choose a point closer to R f (i.e., a higher weight for f and a lower weight for M). A less risk averse investor will choose a greater weight in M. σ P E[R] R f M CML An investor may even borrow to invest more in M, this would be an even riskier strategy.
63 7. The Capital Market Line (CML) The CML equation can be written as follows: Where EP i = efficient portfolio i (a portfolio on the CML composed of the risk-free asset, f , and M) E[ ] is the expectation operator R = return σ = standard deviation of return f denotes the risk-free asset M denotes the market portfolio E R EP i R f EP i E R M R f M Note: the CML is our first formal relationship between risk and expected return. Unfortunately it is limited in its use as it only works for perfectly efficient portfolios: composed of f and M.
64 8. The Capital Asset Pricing Model (CAPM) If investors hold the market portfolio, M, then the risk of any asset, j, that is important is not its total risk, but the risk that it contributes to M.
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