# Portfolio risk

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**Portfolio risk** refers to the potential loss or uncertainty of an investment portfolio's value. It can be measured by calculating the volatility of the portfolio's returns, or the potential deviation of actual returns from expected returns. Diversifying investments across different asset classes and sectors can help to reduce portfolio risk.

## Portfolio risk formula

There are several ways to measure portfolio risk, but one common method is to calculate the volatility of the portfolio's returns. The most popular measure of volatility is the standard deviation, which is a statistical measure of the dispersion of a set of data points. The formula for calculating the standard deviation of a portfolio's returns is:

**σp = √(Σ(wi^2)σi^2 + 2ΣΣwiwjσiσjcorr(i,j))**

Where:

- σp is the standard deviation of the portfolio returns
- wi is the weight of the ith asset in the portfolio
- σi is the standard deviation of the ith asset's returns
- corr(i,j) is the correlation coefficient between the returns of the ith and jth assets

This formula takes into account both the volatility of individual assets as well as the correlation between their returns, which can be especially important for portfolios that contain assets that tend to move in opposite directions (i.e. negative correlation).

Another measure is Value at Risk(VaR) which gives the maximum loss of portfolio over a given confidence level and time horizon. Also, expected shortfall(ES) is another measure which is the expected loss given that the VaR has been breached.

## Methods of portfolio risk management

There are several methods used in portfolio risk management, including:

**Diversification**: spreading investments across different asset classes, sectors, and geographical regions to reduce the impact of any one investment on the overall portfolio.**Asset allocation**: determining the appropriate mix of different asset classes (e.g. stocks, bonds, cash) based on the investor's risk tolerance and investment goals.**Risk budgeting**: allocating a portion of the portfolio to higher-risk investments while also setting limits on potential losses.**Hedging**: using financial instruments such as options or futures contracts to offset potential losses in the portfolio.**Regular monitoring and rebalancing**: regularly monitoring the portfolio's performance and making adjustments as necessary to maintain the desired level of risk.- Using Value at Risk(VaR) and Expected Shortfall(ES) to measure and monitor portfolio risk.
- Using Risk Parity and Risk Factor approaches for portfolio allocation.

These methods are not mutually exclusive and can be used in combination to effectively manage portfolio risk.

## References

- Teller, J., & Kock, A. (2013).
*An empirical investigation on how portfolio risk management influences project portfolio success*. International Journal of Project Management, 31(6), 817-829. - Jacques, K., & Nigro, P. (1997).
*Risk-based capital, portfolio risk, and bank capital: A simultaneous equations approach*. Journal of Economics and business, 49(6), 533-547. - Corter, J. E., & Chen, Y. J. (2006).
*Do investment risk tolerance attitudes predict portfolio risk?*. Journal of business and psychology, 20(3), 369-381.