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# Portfolio Variance

## Definition

Portfolio Variance is a measure of the dispersion of returns of a portfolio. It is the average of the squared deviations from the expected return, showing the volatility or risk associated with the chosen portfolio. This allows investors to predict the expected volatility and adjust their investments accordingly.

### Phonetic

Portfolio Variance: /pɔːrˈtfoʊlioʊ ˈveəriəns/

## Key Takeaways

Sure, here are some key takeaways about Portfolio Variance:

1. Portfolio Variance is a measure of dispersion, specifically, it quantifies the total variability in a portfolio’s returns. It is a key part of the process of calculating investment risk, as it elucidates the degree of risk associated with an investment portfolio.
2. It is primarily used in the fields of finance and investing, particularly in Modern Portfolio Theory, where it serves to identify how much an individual’s investment might deviate from the expected return. Lower variance indicates that the portfolio’s returns are more stable and predictable, while higher variance indicates more volatility and risk.
3. Portfolio Variance not only considers the variances of individual securities but also their correlations. It is precisely computed using the variances of each security, the proportions or weights of each security in the portfolio, and the correlations between securities. Thus, diversifying the portfolio to include non-correlated assets can help in reducing the overall portfolio variance and risk.

## Importance

Portfolio variance is an important concept in business and finance as it measures the dispersion of returns of a portfolio. It evaluates the risk associated with a particular portfolio in terms of how much the actual returns can deviate from the expected returns. In other words, it helps in understanding the volatility or risk involved with a specific portfolio. The lower the portfolio variance, the lower the risk, as it indicates that the returns are more consistent and predictable. Conversely, a higher variance signifies a higher level of risk, meaning the returns can drastically fluctuate. Hence, investors and financial analysts use portfolio variance as a crucial tool in investment decision-making and risk management to optimize their investment returns while mitigating potential risks.

## Explanation

Portfolio variance is a critical concept primarily used to measure the dispersion of actual returns of a specific portfolio. Its main purpose is to quantify the volatility or the degree of risk involved in the portfolio. Such risk may arise from various sources including uncertainties in market prices, inflation trends, or sector-specific risks. The concept of portfolio variance enables investors to make informed decisions by providing them with an empirical measure of how their investment might be expected to fluctuate over a certain period. This allows them to further understand the performance of their investments, anticipate potential losses, and consequently adjust their strategy accordingly.At a strategic level, portfolio variance can play an integral role in creating a diversification strategy. Diversification can result in reduction of portfolio variance and consequently risk, as it involves spreading the investment across different assets whose returns do not move exactly in tandem. This way, the poor performance of some investments might be counteracted by the good performance of others. Therefore, understanding and calculating portfolio variance helps investors to choose the right mix of assets, balancing risk and return, and thus maximally reducing the portfolio risk for a given level of expected return.

## Examples

1. Mutual Fund Investments: An individual chooses to invest in a high-risk mutual fund that mostly consists of equities from tech companies, a medium-risk mutual fund that incorporates a balance of equities and bonds, and a low-risk fund focused on government securities. The range of returns between these three different funds would constitute the portfolio variance, as it measures the dispersion of these returns and aids in understanding the total risk the investor has taken on.2. Retirement Savings: Consider an individual who divides her retirement savings across various types of investments types such as stocks, bonds, and real estate. These all come with a variety of risks and potential returns. The portfolio variance in this case would refer to how the potential returns on these varied assets fluctuate from their expected return, indicating the volatility of her retirement portfolio.3. Institution’s Investment Strategy: Suppose an university’s endowment fund is invested across a diverse range of assets, including international equities, commodities, real estate and bonds. Each of these assets would have different rates of return based on the market conditions at a given time. The portfolio variance in this circumstance would provide the university a sense of the risk of their investments in relation to the potential returns. This insight can help in refining the investment strategy to meet the long-term financial goals.

What is Portfolio Variance?

Portfolio Variance is a measure of how the returns of the assets in a portfolio move together over a certain period. It’s a key concept in modern portfolio theory, used to quantify the volatility, or risk, of the portfolio.

How is Portfolio Variance calculated?

Portfolio variance is calculated using the standard deviations of each asset, the proportion of the total portfolio that each asset represents, and the correlations between each pair of assets in the portfolio.

Why is Portfolio Variance important?

Portfolio variance is important because it is used to help investors diversify their portfolio by selecting a mix of assets to minimize variability or risk.

Does a lower Portfolio Variance indicate a better investment?

Not necessarily. A lower portfolio variance indicates less risk in the portfolio, but it does not equate to better investment returns. Risk and return go hand in hand, often higher risk investments can provide higher returns.

Can a Portfolio Variance be negative?

No, Portfolio Variance cannot be negative. Variance, by definition, is squared differences from the mean which makes it impossible to be negative.

Does Portfolio Variance consider individual asset risk?

Yes, Portfolio Variance takes into account the standard deviation (risk) of individual assets and their respective weights in the portfolio, while also considering the correlation between them.

What happens to Portfolio Variance if assets are perfectly correlated?

If the assets are perfectly correlated, they would move in the same direction together, which could increase the portfolio variance, indicating a higher portfolio risk.

How can I use Portfolio Variance to adjust my investment strategy?

You can use Portfolio Variance to identify how diversified your portfolio is. If variance is high, it might indicate that your portfolio is highly concentrated in certain types of investments and you may consider diversifying to spread the risk.

Is it possible to completely eliminate risk using Portfolio Variance?

No, it’s not possible to eliminate all risk, even with a perfectly diversified portfolio. Portfolio variance can help to minimize variability, but there will always be some level of risk inherent in investing.

How does asset correlation impact Portfolio Variance?

The correlation of assets greatly impacts Portfolio Variance. If assets are perfectly positively correlated, variance tends to increase, and the diversification benefit is lost. On the other hand, if assets are negatively correlated, diversification benefits are increased, typically resulting in lower portfolio variance.

## Related Finance Terms

• Asset Allocation: This term refers to the strategic distribution of investments across various types of assets (such as stocks, bonds, real estate, etc.) to balance risk and reward according to an investment strategy.
• Expected Return: It’s the anticipated profit or loss an investor expects on an investment or portfolio over a specific period, expressed as a percentage of the invested amount.
• Diversification: This is a risk management strategy that mixes different kinds of investments within a portfolio. The rationale is that a variety of investments will yield a higher return, and pose a lower risk, than any individual investment found within the portfolio.
• Correlation Coefficient: This statistical measure is used in portfolio theory to identify the degree to which two securities move in relation to each other. It helps in understanding and managing portfolio risk.
• Standard Deviation: In finance, it’s a statistical measure that represents the dispersion of a set of values. In investing, a high standard deviation signals higher volatility, and therefore, a higher degree of risk associated with an investment or portfolio.

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