Modern Portfolio Theory Portfolio choice Chapter 6 By ding zhaoyong
Modern Portfolio Theory Portfolio Choice Chapter 6 By Ding zhaoyong
Main contents The efficient set theorem Concavity of the efficient set The market model Diversification and market risk Allowing for riskfree lending Allowing for risk free borrowing Allowing for both riskfree borrowing and lending
Main Contents • The efficient set theorem • Concavity of the efficient set • The market Model • Diversification and market risk • Allowing for riskfree lending • Allowing for risk free borrowing • Allowing for both riskfree borrowing and lending
How to make portfolio choice How can Markowitz's approach be used to select portfolio once it is recognized that there are an infinite number of portfolio available for investment? What happens when the investor considers investing in a set of securities, one of which is riskless? What happens if the investor is allowed to buy securities on margin?
How to make portfolio choice • How can Markowitz’s approach be used to select portfolio once it is recognized that there are an infinite number of portfolio available for investment? • What happens when the investor considers investing in a set of securities, one of which is riskless? • What happens if the investor is allowed to buy securities on margin?
The efficient set Theorem The efficient set theorem can be stated An investor will choose his or her optimal portfolio from the set of portfolios that 1. Offer maximum expected return for varying levels of risks, and 2. Offer minimum risk for varying levels of expected returns
• The efficient set theorem can be stated: An investor will choose his or her optimal portfolio from the set of portfolios that 1. Offer maximum expected return for varying levels of risks, and 2. Offer minimum risk for varying levels of expected returns. The Efficient Set Theorem
The efficient set Theorem The feasible set The feasible set is also called for the opportunity set, which represents all portfolios that could be formed from a group ofn securities. All possible portfolios that could be formed fromn securities lie either on or within the boundary of the feasible set, which has a umbrella-type shape
The Efficient Set Theorem • The feasible set – The feasible set is also called for the opportunity set, which represents all portfolios that could be formed from a group of N securities. – All possible portfolios that could be formed from N securities lie either on or within the boundary of the feasible set, which has a umbrella-type shape
The efficient set Theorem E(P)Efficient frontier H Feasible E se G
E(rP ) s H Feasible E set G The Efficient Set Theorem Efficient frontier
The efficient set Theorem The efficient frontier The efficient frontier or efficient set is a set of portfolio which meets both conditions of the efficient set theorem It is from this set of efficient portfolios that the investor will find his or her optimal one All the other feasible portfolios are inefficient portfolio and can be ignored
The Efficient Set Theorem • The efficient frontier – The efficient frontier or efficient set is a set of portfolio which meets both conditions of the efficient set theorem. – It is from this set of efficient portfolios that the investor will find his or her optimal one. – All the other feasible portfolios are inefficient portfolio and can be ignored
The efficient set Theorem The optimal portfolio The optimal portfolio correspond to the point where an indifference curve is just tangent to the efficient set (WHY?) There will be only one tangency point between the investors indifference curves and the eficient set (WHy?)
The Efficient Set Theorem • The optimal portfolio – The optimal portfolio correspond to the point where an indifference curve is just tangent to the efficient set. (WHY?) – There will be only one tangency point between the investor’s indifference curves and the efficient set. (WHY?)
The efficient set Theorem E(P) H Feasible set
The Efficient Set Theorem I3 I2 E(rP ) I1 S H O* Feasible E set G
Portfolio With Two Risky Assets The two risky securities Security 1: E(r1=5%, 01=20% Security2:E(r2)=15%,2=40% The bounds on the location of portfolio by calculating the expected returns and standard deviations of the portfolios under different correlation and weights. Diversification leads to risk reduction
Portfolio With Two Risky Assets • The two risky securities Security 1: E(r1)=5%, 1=20% Security 2: E(r2)=15%, 2=40% • The bounds on the location of portfolio by calculating the expected returns and standard deviations of the portfolios under different correlation and weights. • Diversification leads to risk reduction
