Lecture 10- Portfolio theory 4 - efficient and optimal portfolios with multiple risky assets.pdf

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Fundamental of Finance L10 1 Portfolio Selection with a Riskless Security Investor Preferences Outline Fundamental of Finance L10 2 1. Portfolio selection with a risk free and 1 risky security. 2. Portfolio selection with a risk free and 2 risky securities. 3. Portfolio selection with a risk free and many risky securities. Systematic and idiosyncratic risk The Single Index Model > last class > today Outline Fundamental of Finance L10 3 Investment opportunity set With many risky assets (3 to…) With many risky assets and a risk free security Optimal portfolio choice and two fund separation Diversifiable and non diversifiable risk (systematic risk)
Three risky assets – Intuition Fundamental of Finance L10 4 Efficient Set AB Efficient Set BC Three Assets Example Fundamental of Finance L10 5 Source: G. Saar Three Assets Example Fundamental of Finance L10 6 Source: G. Saar
Three Assets Example Fundamental of Finance L10 7 Source: G. Saar Three Assets Example Fundamental of Finance L10 8 Source: G. Saar Investment Opportunity Set with Many Assets Fundamental of Finance L10 9 Expected return Standard deviation Global Minimum Variance Portfolio Individual Assets Inefficient Frontier Efficient Frontier Handout 13 explains how to construct the EF – It’s optional.
Step 3B: Optimal Portfolio Selection with Many Risky Assets and a Risk Free Asset (on board) 1. Create the set of possible mean s.d. combinations from different portfolios of risky assets 2. Find the “tangency portfolio,” i.e. the portfolio with the highest Sharpe ratio: 3. Choose the combination of the tangency portfolio and the risk free asset to suit your risk return preferences. Fundamental of Finance L10 10 i f i i R ] E[R SR Optimal Portfolio Selection with Many Risky Assets and a Risk Free Asset Fundamental of Finance L10 11 Two Fund Separation All investors hold combinations of the same two “mutual funds”: The risk free asset The tangency portfolio An investor’s risk aversion determines the fraction of wealth invested in the risk free asset.

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