Portfolio

Question 1

The portfolio selection model of Markowitz (1959) requires that
at least one of the following two assumptions hold: i) agents
have quadratic utility functions, ii) return distributions are fully
described by their first and second moments (Normal
Distribution).

Answer 1

When at least one of the following assumptions holds:

Quadratic utility function – utility depends only on mean and variance.

Normally distributed returns – the return distribution is fully described by mean and variance.

If neither holds, mean-variance optimization may not reflect investor preferences.

Question 2

Why do normally distributed returns justify mean-variance optimization even without quadratic utility?

Answer 2

For normal distributions, all relevant information is in μ (mean) and σ² (variance).

Even non-quadratic, concave utility functions depend only on μ and σ² when returns are normal.

So expected utility maximization reduces to mean-variance optimization.

Question 3

What happens if neither quadratic utility nor normal return distribution holds?

Answer 3

Mean and variance may not fully capture investor preferences.

Higher moments like skewness and kurtosis matter.

Must use expected utility theory directly (not MPT).