# Risk of portfolio

Risk of portfolio |
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See also |

**Portfolio risk** is the potential for losses that arise from a combination of investments in a portfolio. It is the risk that the returns from a portfolio will be lower than expected due to the inherent risks of its holdings. Portfolio risk is a measure of the amount of uncertainty associated with the expected return of a portfolio. It is a measure of the sensitivity of the portfolio returns to changes in the market environment that the portfolio is exposed to. As such, it requires a thorough understanding of the market environment, the portfolio's asset mix, and the correlations between the assets.

## Example of risk of portfolio

**Equity Risk**: Equity risk is the risk associated with investing in stocks or equity-based investments. This type of risk is related to the volatility of the stock market, which can cause the value of the investments to rise and fall. Equity risk can be mitigated by diversifying investments across different sectors and industries, as well as diversifying across different countries.**Credit Risk**: Credit risk is the risk of losses caused by a borrower's inability to make payments on debt. This type of risk is particularly relevant in fixed income investments, such as bonds and other debt instruments. Credit risk can be mitigated by diversifying across different debt issuers and investing only in high-quality debt instruments.**Interest Rate Risk**: Interest rate risk is the risk that changes in interest rates will adversely affect the value of a portfolio. This type of risk is particularly relevant in investments such as bonds, which are sensitive to changes in interest rates. Interest rate risk can be mitigated by investing in short-term bonds or by using derivative instruments such as options or futures to hedge against interest rate volatility.

## Formula of risk of portfolio

Portfolio risk can be measured using a variety of methods, but one of the most popular is the portfolio variance formula. This formula can be used to calculate the overall risk of a portfolio.

The portfolio variance formula is given as:

$$\sigma^2_p = \sum_{i=1}^n w_i^2\sigma_i^2 + 2\sum_{i=1}^{n-1}\sum_{j=i+1}^nw_iw_j\sigma_{ij} $$

Where:

$$\sigma^2_p$$ = Portfolio Variance

$$w_i$$ = weight of asset i

$$\sigma_i^2$$ = Variance of asset i

$$\sigma_{ij}$$ = Covariance between assets i and j

The formula can be interpreted as follows: the portfolio variance is equal to the sum of the weight of an asset squared multiplied by its variance, plus the sum of the product of the weights of two assets multiplied by their covariance. This formula takes into account both the individual risks of the assets in the portfolio, as well as the correlations between them.

This formula can be used to calculate the overall risk of a portfolio, and can be used to assess the potential for losses that arise from a combination of investments in a portfolio. By understanding the risks of the individual assets in the portfolio, as well as the correlations between them, investors can better understand the overall risk of their portfolio.

## Types of risk of portfolio

Portfolio risk is a measure of the amount of uncertainty associated with the expected return of a portfolio. There are several types of risk that must be considered when constructing a portfolio, including:

**Market Risk**: This is the risk that the overall market, or a specific sector or asset class, will move against the portfolio’s positions.**Interest Rate Risk**: This is the risk that interest rates will move against the portfolio’s positions.**Credit Risk**: This is the risk that a borrower or issuer will default on their obligations.**Liquidity Risk**: This is the risk that a portfolio will be unable to sell its holdings at a desired price or within a desired timeframe.**Operational Risk**: This is the risk that a portfolio will suffer losses due to an inability to execute trades or manage its positions effectively.**Currency Risk**: This is the risk that the value of a currency will shift against the portfolio’s positions.**Regulatory Risk**: This is the risk that a portfolio will be affected by changes in regulations or laws.**Political Risk**: This is the risk that a portfolio will be affected by political instability or events.

## Limitations of risk of portfolio

Portfolio risk has several limitations that should be considered when constructing a portfolio. These limitations include:

**Lack of diversification**: As the portfolio contains a limited number of assets, it is likely to be exposed to a greater degree of risk than a more diversified portfolio.**Limited asset coverage**: If a portfolio has limited coverage of asset classes, it may not be able to benefit from any positive performance of those asset classes that are not included in the portfolio.**Market risk**: A portfolio may be exposed to market risk due to the correlation of the assets in the portfolio, as well as external factors such as economic conditions, political events, and other market forces.**Concentration risk**: A portfolio that is concentrated in one or a few asset classes may be highly exposed to the risk associated with those asset classes.**Short-term volatility**: A portfolio may experience short-term volatility due to the daily movements of the markets, which can lead to losses if the portfolio is not managed properly.**Illiquidity risk**: A portfolio may be exposed to the risk that it is unable to liquidate its assets due to a lack of liquidity in the markets.

Portfolio risk can be approached in many different ways, including:

**Diversification**: Diversification is the process of spreading investments across different asset classes in order to reduce the risk associated with any one asset class. By diversifying, investors spread their risk across multiple assets and can help to reduce their potential losses.**Asset Allocation**: Asset allocation is the process of dividing a portfolio among different asset classes, such as stocks, bonds, cash, and commodities, in order to maximize returns and minimize risk.**Risk Management**: Risk management is the process of identifying, measuring, and controlling risks in order to achieve a desired level of risk and return.**Risk Tolerance**: Risk tolerance is an individual investor’s ability and willingness to accept volatility in their portfolio returns.**Rebalancing**: Rebalancing is the process of periodically adjusting the portfolio's asset allocation in order to maintain the desired level of risk.

In summary, portfolio risk can be approached in a variety of ways, including diversification, asset allocation, risk management, risk tolerance, and rebalancing. Each of these approaches can help to reduce portfolio risk and maximize returns.

## Suggested literature

- Gaivoronski, A. A., & Pflug, G. (2005).
*Value-at-risk in portfolio optimization: properties and computational approach*. Journal of risk, 7(2), 1-31.