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:

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.

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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)

 

sorry the red ones are not written yet

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

$E[R_{p}]=\sum_{i}^{}w_{i}E[R_{i}]$

Criticisms of Modern Portfolio Theory

Used for asset allocation decisions

Links