1 EXAMPLE: PORTFOLIO RISK & RETURN

2 PORTFOLIO RISK

3 PORTFOLIO RISK: EXAMPLE

4 Return and Risk for Portfolios

5 SUPPOSE EXPECTED RETURNS ARE AS FOLLOWS:

6 EXAMPLE:INTERNATIONAL PORTFOLIO SELECTION

7 CORRELATIONS BETWEEN RETURNS ON DIFFERENT MARKETS

8 EFFICIENT PORTFOLIOS

9 Security Market Line (SML)

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11 Capital Market Line (CML) Equilibrium relationship between E(R p ) and σ p for efficient portfolios Linear efficient set of CAPM by combining Market portfolio with risk free (r f ) borrowing and lending CML only permits to well-diversified portfolios; portfolios not employing M, the market portfolio, will plot below the CML Equation of CML: E(R p )=r f + [(E(R M )-R f ) / σ M ] σ(R p ) Slope of CML: price of risk {E(R M ) – R f }/ σ M Price of time: R f

12 Capital Asset Pricing Model (CAPM) Developed by Sharpe, Treynor, Lintner and Mossin An equilibrium theory of how to price and measure risk of portfolios as well as individual security Concerning decomposition of risk into two components: systematic (market, non-diversifiable) and unsystematic (unique, diversifiable) Stating that required return on any investment is the risk free return plus a risk premium measured by its systematic risk E(r i )=r f +[E(r m )-r f ]β where β = covariance risk of security i E(r m )-r f = market risk premium

13 Expected portfolio Return K p Risk, σ p E D C B A Feasible, or Attainable, Set Feasible Set of Risky Portfolios

14 Expected portfolio Return K p Risk, σ p E D C B A Optimal Portfolio Selection Optimal Portfolio Investor B Optimal Portfolio Investor A

15 Expected portfolio Return K p Risk, σ p E D C B A Efficient Frontier with Risk-Free Asset rmrm k RF M KMKM Z new efficient portfolio Y=mx+b K i =K rf +σ i /σ m (K m -K rf ) b = intercept m = slope = K m -K rf /σ m