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Chapter 6 Efficient Diversification Two-Security Portfolio Return E(rp) = W1r1 + W2r2 W1 = 0.6 Wi = % of total money W2 = 0.4 invested in security i r1 = 9.28% r2 = 11.97% E(rp) = 0.6(9.28%) + 0.4(11.97%) = 10.36% Easy 6-2 Portfolio Variance and Standard Deviation: Hard! • • • • Consider something simple first instead is always in the range __________ inclusive. Consider 1, 0, -1 benchmarks, ranges in between Which value is ideal for diversification? (use logic, or math formula of portfolio variance in your book) • Again Chapter 11 in FINC301 6-3 Summary: Portfolio Risk/Return Two Security Portfolio • Amount of risk reduction depends critically or covariances on correlations _________________________. <1 • Adding securities with correlations _____ will result in risk reduction. • If risk is reduced by more than expected return, what happens to the return per unit of risk (the Sharpe ratio)? 6-4 Extending Concepts to All Securities • Consider all possible combinations of securities, with all possible different weightings and keep track of combinations that provide more return for less risk or the least risk for a given level of return and graph the result. • The set of portfolios that provide the optimal trade-offs are described as the efficient frontier. • The efficient frontier portfolios are dominant or the best diversified possible combinations. All investors should want a portfolio on the efficient frontier. … Until we add the riskless asset 6-5 6.3 The Optimal Risky Portfolio With A Risk-Free Asset 6.4 Efficient Diversification With Many Risky Assets 6-6 Including Riskless Investments • The optimal combination becomes linear • A single combination of risky and riskless assets will dominate 6-7 Dominant CAL with a Risk-Free Investment (F) • CAL(P) = Capital Market Line or CML dominates other lines because it has the the largest slope • Slope = (E(rp) - rf) / sp (CML maximizes the slope or the return per unit of risk or it equivalently maximizes the Sharpe ratio) • Regardless of risk preferences some combinations of P & F dominate 6-8 Practical Implications o The analyst or planner should identify what they believe will be the best performing well diversified portfolio, call it P. P may include funds, stocks, bonds, international and other alternative investments. o This portfolio will serve as the starting point for all their clients. o The planner will then change the asset allocation between the risky portfolio and “near cash” investments according to risk tolerance of client. o The risky portfolio P may have to be adjusted for individual clients for tax and liquidity concerns if relevant and for the client’s opinions. 6-9 6.5 A Single Index Model: CAPM • Systematic risk arises from events that effect the entire economy such as a change in interest rates or GDP or a financial crisis such as occurred in 2007and 2008. • If a well diversified portfolio has no unsystematic risk then any risk that remains must be systematic. • That is, the variation in returns of a well diversified portfolio must be due to changes in systematic factors • Tremendous computational advantage makes it practical! 6-10 Sharpe Ratios and alphas • When ranking portfolios and security performance we must consider both return & risk • “Well performing” diversified portfolios provide high Sharpe ratios: – Sharpe = (rp – rf) / sp • You can also use the Sharpe ratio to evaluate an individual stock if the investor does not diversify 6-11 Sharpe Ratios and alphas • “Well performing” individual stocks held in diversified portfolios can be evaluated by the stock’s alpha in relation to the stock’s unsystematic risk. Seeking Positive Alphas 6-12 6.6 Risk of Long-Term Investments Are Stock Returns Less Risky in the Long Run? 6-13