what is the difference between minimum variance portfolio, minimum correlation portfolio and minimum connectedness portfolio
  Minimum variance, minimum correlation, and minimum connectedness portfolios are different types of portfolio optimization strategies that aim to construct a portfolio with desirable risk-return characteristics. Here are the key differences between them:

1. Minimum Variance Portfolio:
A minimum variance portfolio is constructed by selecting a subset of assets that minimizes the portfolio's variance, or the amount of volatility in the portfolio's returns. The idea behind this approach is that a portfolio with lower variance is likely to experience smaller losses during market downturns and may be less sensitive to market volatility.

Minimum variance portfolios are typically constructed using a Markowitz mean-variance optimization framework, which seeks to minimize the portfolio's risk (measured by variance) for a given expected return. The resulting portfolio will typically have a lower expected return than a portfolio that is more heavily invested in stocks, but will also be less volatile.

2. Minimum Correlation Portfolio:
A minimum correlation portfolio is constructed by selecting a subset of assets that have the lowest possible correlation with each other. The idea behind this approach is that assets with low correlation tend to move independently of each other, which can help to reduce the overall risk of the portfolio.

Minimum correlation portfolios are typically constructed using a correlation-based optimization framework,
These three portfolios are all related to risk minimization in portfolio optimization, but they differ in their approach to measuring and minimizing risk. Here's a brief overview of each:

**1. Minimum Variance Portfolio (MVP)**:
The MVP is a portfolio that minimizes the overall volatility or risk of the portfolio, measured by the variance or standard deviation of the portfolio returns. The goal is to construct a portfolio that has the lowest possible risk, while still achieving a target return. The MVP is often used as a benchmark for other portfolio optimization strategies.

**Key characteristics:**

* Minimizes portfolio variance or standard deviation
* Focuses on individual asset risks and correlations
* Typically leads to a diversified portfolio with a mix of low-risk assets

**2. Minimum Correlation Portfolio (MCP)**:
The MCP is a portfolio that minimizes the average correlation between assets in the portfolio. The idea is to construct a portfolio with assets that are as uncorrelated as possible, which can help reduce overall portfolio risk. This approach is useful when investors want to minimize the impact of any one asset on the overall portfolio.

**Key characteristics:**

* Minimizes average correlation between assets
* Focuses on pairwise correlations between assets
* Can lead to a more diversified portfolio with a mix of assets from different classes or sectors

**3. Minimum Connectedness Portfolio (MConP)**:
The MConP is a portfolio that minimizes the connectedness or systemic risk of the portfolio.