Mean-Variance Analysis
8 important questions on Mean-Variance Analysis
What is the expected utility of wealth?
The rationality of the EU model of choice under risk is based on axioms underlying (the derivation of) expected utility maximization as the optimal rule.
Define preferences linked with risk aversion.
All else equal, there is a preference for the alternative with the lowest risk (subjective tradeoff between risk and return): investor's willingness to accept greater risk in order to generate higher proceeds.
Describe two possible justifications for MV analysis.
- Returns obey a normal distribution (or another so-called elliptical distribution) then E(R) and Sigma(R) describe the entire distribution. I.e. there is no skewness, not fat tails in practice: this assumption is very restrictive
- The utility function is a quadratic function: then investors care only about E(R) and Sigma(R). There exists empirical support for its approximative value over the relevant range
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How are investment decisions are made?
Choosing from the possibilities set in the Sigma(R) and E(R) space the portfolio with maximal expected utility.
What is the market portfolio M? (Rm)
A value weighted portfolio of all shares of all stocks and securities in the market.
Describe the correlation between returns RA and RB.
The correlation measures the degree to which returns tend to move together, i.e. share common risk.
- P = +1 --> perfect positive correlation, common risk is at a maximum
- P = 0 --> returns are uncorrelated, independent returns: no common risk
- P= -1 --> perfect negative correlation, returns move in exact opposition of one another: risk is cancelled out
What is a portfolio weight?
The different individual investments between which we have divided our money/welath constitute a portfolio: portfolio weights.
Portfolio weight = the fraction of the total investment in the portfolio held in an individual investment i in the portfolio
What is a long position?
A positive investment in a security
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