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Motivation Mean Variance Theory Mean Variance Theory

Lecture 2.1: Mean Variance Portfolio TheoryInvestment Analysis

Fall, 2012

Anisha Ghosh

Tepper School of BusinessCarnegie Mellon University

November 8, 2012

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Motivation Mean Variance Theory Mean Variance Theory

Motivation

The process of constructing an investor portfolio consists of a sequence

of two steps:

1 selecting the composition of ones portfolio of risky assets (e.g.,

stocks, long term bonds)2 deciding how much to invest in that risky portfolio versus in a safe

asset (e.g., short-term Treasury bills)

the investor needs to know the risk-return trade-off for the above

risky portfolio

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Motivation Mean Variance Theory Mean Variance Theory

Motivation

The process of constructing an investor portfolio consists of a sequence

of two steps:

1 selecting the composition of ones portfolio of risky assets (e.g.,stocks, long term bonds)

2 deciding how much to invest in that risky portfolio versus in a safe

asset (e.g., short-term Treasury bills)

the investor needs to know the risk-return trade-off for the above

risky portfolio

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CMU-log

Motivation Mean Variance Theory Mean Variance Theory

Motivation

The process of constructing an investor portfolio consists of a sequence

of two steps:

1 selecting the composition of ones portfolio of risky assets (e.g.,stocks, long term bonds)

2 deciding how much to invest in that risky portfolio versus in a safe

asset (e.g., short-term Treasury bills)

the investor needs to know the risk-return trade-off for the above

risky portfolio

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CMU-log

Motivation Mean Variance Theory Mean Variance Theory

Motivation

The process of constructing an investor portfolio consists of a sequence

of two steps:

1 selecting the composition of ones portfolio of risky assets (e.g.,stocks, long term bonds)

2 deciding how much to invest in that risky portfolio versus in a safe

asset (e.g., short-term Treasury bills)

the investor needs to know the risk-return trade-off for the above

risky portfolio

M i i M V i Th M V i Th

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Motivation Mean Variance Theory Mean Variance Theory

Mean Variance Portfolio Theory

A risky asset offers a return that can take any one of a set of possible

values along with their associated probability of occurrence:

Return DistributionReturn Probability

Ri1 Pi1Ri2 Pi2. .

. .

. .

RiM PiM

Mean Variance Portfolio Theory all the relevant information about a

return distribution can be captured by two summary measures:

1 Expected Return: that measures the average value2 Variance: that measures the risk or dispersion around the mean

M ti ti M V i Th M V i Th

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CMU-log

Motivation Mean Variance Theory Mean Variance Theory

Mean Variance Portfolio Theory

A risky asset offers a return that can take any one of a set of possible

values along with their associated probability of occurrence:

Return DistributionReturn Probability

Ri1 Pi1Ri2 Pi2. .

. .

. .

RiM PiM

Mean Variance Portfolio Theory all the relevant information about a

return distribution can be captured by two summary measures:

1 Expected Return: that measures the average value2 Variance: that measures the risk or dispersion around the mean

Motivation Mean Variance Theory Mean Variance Theory

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Motivation Mean Variance Theory Mean Variance Theory

Mean Variance Portfolio Theory contd

Mean-Variance (M-V) or Mean-Standard Deviation criterion

Portfolio A dominates Portfolio B if

E(rA) E(rB)

andA B

Portfolio A is preferable to Portfolio B if its expected return is equal to

or greater than Bs and its standard deviation is equal to or smaller than

Bs in the expected return-standard deviation space, the preferred

direction is northwest, because in this direction we simultaneously

increase the expected return and decrease the variance of the rate of

return

Motivation Mean Variance Theory Mean Variance Theory

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Motivation Mean Variance Theory Mean Variance Theory

Mean Variance Portfolio Theory contd

Mean-Variance (M-V) or Mean-Standard Deviation criterion

Portfolio A dominates Portfolio B if

E(rA) E(rB)

andA B

Portfolio A is preferable to Portfolio B if its expected return is equal to

or greater than Bs and its standard deviation is equal to or smaller than

Bs in the expected return-standard deviation space, the preferred

direction is northwest, because in this direction we simultaneously

increase the expected return and decrease the variance of the rate of

return

Motivation Mean Variance Theory Mean Variance Theory

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Motivation Mean Variance Theory Mean Variance Theory

Mean Variance Portfolio Theory contd

Mean-Variance (M-V) or Mean-Standard Deviation criterion

Portfolio A dominates Portfolio B if

E(rA) E(rB)

andA B

Portfolio A is preferable to Portfolio B if its expected return is equal to

or greater than Bs and its standard deviation is equal to or smaller than

Bs in the expected return-standard deviation space, the preferred

direction is northwest, because in this direction we simultaneously

increase the expected return and decrease the variance of the rate of

return

Motivation Mean Variance Theory Mean Variance Theory

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Motivation Mean Variance Theory Mean Variance Theory

Solution to the Mean Variance Portfolio Problem

Steps:

1 Identification of theEfficient Frontierand the optimal portfolio ofrisky assets

2 Deciding how much to invest in that risky portfolio versus in a safe

asset (e.g., short-term Treasury bills) based on the investors

preferences

Motivation Mean Variance Theory Mean Variance Theory

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Motivation Mean Variance Theory Mean Variance Theory

Solution to the Mean Variance Portfolio Problem

Steps:

1 Identification of theEfficient Frontierand the optimal portfolio ofrisky assets

2 Deciding how much to invest in that risky portfolio versus in a safe

asset (e.g., short-term Treasury bills) based on the investors

preferences