Thread starter
#1

In the mean variance framework what is the mathematical expression for the market portfolio?

- Thread starter sumitmaan19
- Start date

Thread starter
#1

In the mean variance framework what is the mathematical expression for the market portfolio?

Thread starter
#2

This is the question I was asked in an interview.

What I know about the market portfolio is the following:

1) it is the portfolio of all the risky assets available in the market with weights equal to the proportion of their market capitalisation.

2) it is the point at which the ray from the risk free asset is tangent to the efficient frontier.

3) it is the point on the efficient frontier so that the slope of the CAL or the sharpe ratio (Rm-Rf)/σm is maximum.

But I don't know how to express the market portfolio mathematically. So it will be great if someone can please help.

What I know about the market portfolio is the following:

1) it is the portfolio of all the risky assets available in the market with weights equal to the proportion of their market capitalisation.

2) it is the point at which the ray from the risk free asset is tangent to the efficient frontier.

3) it is the point on the efficient frontier so that the slope of the CAL or the sharpe ratio (Rm-Rf)/σm is maximum.

But I don't know how to express the market portfolio mathematically. So it will be great if someone can please help.

- T1-7 How the portfolio possibilities curve (PPC) illustrates the benefit of diversification https://www.bionicturtle.com/forum/...strates-the-benefit-of-diversification.21442/
- T1-8 Capital market line (CML) versus security market line (SML) https://www.bionicturtle.com/forum/...ne-cml-versus-security-market-line-sml.21443/
- T1-9 Capital asset pricing model (CAPM) https://www.bionicturtle.com/forum/threads/t1-9-capital-asset-pricing-model-capm.21445/

Thread starter
#4

Thanks for the detailed response and that definitely was really helpful particularly the maths. So, theoretically the market portfolio is a portfolio on the efficient frontier in which the fraction invested in any asset is equal to the market value of that asset divided by the market value of all risky assets (or our approximated set of investable assets) and the CML passes through it when we add the risk free asset in the scenario. But mathematically it can simply be considered as an optimization problem (with the assumptions of returns, volatilities and correlations) and solving for the weights for the maximum Sharpe ratio.

## Stay connected