# Inverse Variance

Learn more about Inverse Variance Strategy

In portfolio management, the inverse variance weighting strategy employs the covariance matrix, and more specifically its diagonal, to allocate weights to assets. This strategy aims to minimize the overall variance of the portfolio by assigning greater weight to assets with lower variances, thereby adjusting the portfolio according to the stability of each asset. It is a method that inherently leans towards a more conservative investment stance, by favoring assets that have demonstrated less fluctuation in their returns over time.

Imagine architects allocating budgets for construction projects. They first identify plots of land with the least seismic risk. On these safer plots, they invest more heavily, knowing that the risk of damage is lower. Similarly, in our strategy, assets with a lower variance, signifying less risk, are allocated a larger portion of the investment budget, reflecting increased confidence in their stable performance. This prudent approach to budget allocation in construction mirrors the inverse variance weighting in portfolio management, where investments are skewed towards assets deemed more stable and less likely to fluctuate unpredictably.

La pondération par inverse de la variance alloue les poids sur la base de l'élément diagonal de la matrice de covariance de chaque actif, qui représente sa propre variance au sein du portefeuille. Les actifs les moins volatils se voient attribuer des poids plus élevés, reflétant une plus grande confiance dans leur stabilité relative.

**The portfolio weighting is calculated using the following formula : **

$w_i = \frac{\sum {} ^{-1}}{\sum ^N _{j=1} (\sum_{j, j}) ^{-1}}$

Here, $wi$ is the weight of the ith asset, $σi2$ is the variance of the ith asset (represented by the diagonal element of the covariance matrix for the ith asset), and $N$ is the total number of assets in the portfolio.

**Summary **

**Summary**

Dubbed as * quadratic risk utility*, this method integrates both portfolio return and risk into its objective function, aiming to minimize risk while simultaneously maximizing return based on the investor's risk tolerance. The risk aversion parameter is instrumental in this process, delineating the investor's willingness to engage with risk. A higher parameter value indicates a prioritization of risk mitigation over return, whereas a lower value underscores a focus on maximizing returns, even at the cost of increased risk exposure. This strategy empowers investors to sculpt a portfolio that resonates with their individual risk preferences, blending the art of maximizing returns with the science of minimizing volatility.

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