QP model

To adapt the model developed in Chapter 2 to the new way of looking at the problem, we need to make the following changes:

New objective function: mean variance instead of total return.
The risk-related constraint disappears.
Addition of a new constraint: target yield.

The new objective function is the mean variance of the portfolio, namely:

∑_{s,t ∈ SHARES} VAR_st·frac_s ·frac_t

where VAR_st is the variance/covariance matrix of all shares. This is a quadratic objective function (an objective function becomes quadratic either when a variable is squared, e.g., frac₁², or when two variables are multiplied together, e.g., frac₁ · frac₂).

The target yield constraint can be written as follows:

∑_{s ∈ SHARES} RET_s·frac_s ≥ 9

The limit on the North-American shares as well as the requirement to spend all the money, and the upper bounds on the fraction invested into every share are retained. We therefore obtain the following complete mathematical model formulation:

minimize ∑_{s,t ∈ SHARES} VAR_st·frac_s ·frac_t
∑_{s ∈ NA} frac_s ≥ 0.5
∑_{s ∈ SHARES} frac_s = 1
∑_{s ∈ SHARES} RET_s·frac_s ≥ 9
∀ s ∈ SHARES: 0 ≤ frac_s ≤ 0.3

Contents

Index

Glossary

Search Results

QP model