What is Mean Variance Portfolio Theory
First developed by Harry Markowitz in the paper titled "Portfolio Selection" in 1952, we have the following names:
- Modern Portfolio Theory
- MPT
- Mean-Variance Portfolio Theory
- MVPT
MVPT is a mathematical framework for assembling a portfolio of assets that:
- maximises return for a given level of risk
- minimises risk for a given level of return <fn>https://en.wikipedia.org/wiki/Modern_portfolio_theory</fn>
Two parts to presenting the framework:
- defining available portfolios - the opportunity set
- choosing from the opportunity set
Defining the opportunity set
We need the following information:
- expected return for each asset
- variance covariance matrix for eash asset
The opportunity set is the possible expected return and standard deviation pairs of all portfolios that can be constructed from a given set of assets.
<we need to start inserting diagrams at this point>
Choosing from the opportunity set
Key Tenets
<fn>https://en.wikipedia.org/wiki/Modern_portfolio_theory</fn>:
- an asset's risk and return should be assessed by how it contributes to a portfolio's overall risk and return
- variance is a proxy for risk
Assumptions of MVPT
- investors select portfolios on basis of
- expected return
- variance
- variance is a proxy for risk
- Investor behaviour is such that
- investors prefer higher return to lower one
- investors dislike risk
- more specifically, for same expected return, investors prefer asset with less variance
(so far... i would say these are fairly reasonable assumptions)
When is MVPT valid
Mean–variance efficiency rests is valid if either <fn>Portfolio Construction and Risk Budgeting By Bernd Scherer</fn>
- investors exhibit quadratic utility (i.e. ignore non normality of investment returns)
- or returns are multivariate normal (utlity functions are irrelevant)
In reality<fn>Portfolio Construction and Risk Budgeting By Bernd Scherer</fn>,
- returns are not multivariate normal distributed
- investors do not exhibit quadratic utility and they do not live in a one-period world
Optimal Portfolio Determined by MVPT
text...
Benefits of MVPT
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Key Mathematical Results
Expected return or the portfolio
$E[R_{p}]=\sum_{i}^{}w_{i}E[R_{i}]$