# Minimum Variance Portfolio Definition and Examples

Do you know what it means to have a minimum variance portfolio? It may sound complex, but this portfolio structuring model can help you maximize returns while minimizing risk, which is the ultimate goal of the smartest and most successful investors. Best of all, it's not difficult to apply if you know how it works. If you can construct a minimum variance portfolio, you may achieve the optimal results without taking too much risk. It's kind of a "have your cake and eat it too" strategy in the investment world.

### What Is a Minimum Variance Portfolio?

A minimum variance portfolio is a portfolio of securities that combine to minimize the price volatility of the overall portfolio. Volatility, which is a term more commonly used instead of a variance in the investment community, is a statistical measure of a particular security's price movement (ups and downs).

The volatility of an investment is also interchangeable in meaning with its market risk. Therefore, the greater the volatility of an investment (the wider the swings up and down in price), the higher the market risk. So, if an investor wants to minimize risk, they are also wanting to minimize the ups and downs.

### How to Build a Minimum Variance Portfolio

A portfolio, in the investment world, generally describes a set of investment securities held in one account or a combination of securities and accounts held by one investor. So, to build a minimum variance portfolio, an investor would need to have a combination of low volatility investments or a combination of volatile investments with low correlation to each other. The latter portfolio is common in relation to building minimum variance portfolios.

Investments that have low correlation could be described as those that perform differently (or at least not too similar) given the same market and economic environment. It is a prime example of diversification. When an investor diversifies a portfolio, they are essentially seeking to reduce volatility, and this is the basis of the minimum variance portfolio—a diversified portfolio of securities.

### Examples

Perhaps the most simple example of a minimum variance portfolio is a combination of a stock mutual fund and a bond mutual fund. When stock prices are rising, bond prices may be flat to slightly negative; whereas, when stock prices are falling, bond prices are often rising.

Stocks and bonds don't often move in opposite directions, but they have a very low correlation in terms of performance. Using the minimum variance portfolio strategy to its fullest extent, an investor can combine risky assets or investment types together and still achieve high relative returns without taking a high relative risk.

For example, if an investor considers holding three different investment types, such as U.S. large-cap stocks, U.S. small-cap stocks, and emerging markets stocks, each of which have high relative risk and histories of volatile price fluctuations, they each have relatively low correlation to each other, which over time can create lower volatility compared to a portfolio consisting of 100 percent of any one of those three investment types.

A specific statistical measure that is used to express a particular investment's correlation with another investment is called R-squared or R2. Most often, the R-squared is based upon correlation to a major benchmark index, such as the S&P 500.

For example, if an investment's R-squared is 0.97, it means 97 percent of its price movement (ups and downs in performance) is explained by movements in the index. To reduce the volatility of a portfolio, or to minimize variance through diversification, an investor holding an S&P 500 index mutual fund would want to hold additional investments with a low R2, or not highly correlated to that index.

In summary, a minimum variance portfolio can hold investment types that are volatile when holding them individually, but when holding together, they create a diversified portfolio that has lower volatility than any of the individual parts. The optimal minimum variance portfolio will decrease overall volatility with each investment added to it, even if the individual investments are volatile in nature.

### Model

A good overall model to follow in constructing a minimum variance portfolio can be demonstrated by using mutual fund categories that have a relatively low correlation with each other. This particular example follows the core and satellite portfolio structure:

- 40 Percent S&P 500 Index Fund
- 20 Percent Emerging Markets Stock Fund
- 10 Percent Small-Cap Stock Fund
- 30 Percent Bond Index Fund

The first three fund categories are relatively volatile, but all four have a relatively low correlation to each other. With the exception of the bond index fund, the combination of all four together has lower volatility than anyone on an individual basis.

*Disclaimer: The information on this site is provided for discussion purposes only, and should not be misconstrued as investment advice. Under no circumstances does this information represent a recommendation to buy or sell securities.*