# What is Portfolio Risk and how is it calculated?

## Definition of Portfolio Risk

Portfolio Risk can be defined as the probability of the assets or units of stock that the company holds to sink, thereby causing a significant loss to the company in terms of their investment being lost.

A portfolio is defined as the combination or the collection of stocks or investment channels within the company.

Within the portfolio, there are different investment stocks that the investor holds, and all of them individually have different risk assessments.

However, when they all combine in form of a portfolio, then the risk is diversified, and is then different for a portfolio of the existing different stocks.

## Formula of Portfolio Risk

Portfolio Risk is measured by calculating the standard deviation of the portfolio. In this regard, standard deviation alone is not sufficient to calculate the portfolio risk.

There is a need to ensure that all the different standard deviations are accounted for with their weights as well as the existing covariance and correlation between the existing assets.

In this regard, covariance can simply be defined as the extent to which stocks move in the same direction.

In other words, it is a measure of the extent to which both the stocks act responds similarly, to market trends and other macroeconomic factors.

For example, if two stocks have a correlation of +1, this implies that they either will increase or decrease hand in hand. On the other hand, if two stocks have a correlation of -1, it implies that if one stock generates a positive return, the other stock is unlikely to generate a positive return too.

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Therefore, portfolio risk calculation includes three main variables: the weightage of the respective assets in the portfolio, the standard deviation of those assets, as well as the covariance of those assets. Using these three variables, the following formula is used to calculate portfolio risk:

Portfolio risk = Sqrt [(weight of Asset A) ^2 * (SD of Asset A) ^2) + (weight of Asset B)^2 * (SD of Asset B)^2) + 2(weight of Asset A*Weight of Asset B*Correlation between Asset A and Asset B *SD Asset A * SD Asset B)]

## Example of Calculating Portfolio Risk

In order to further understand and explain how portfolio risk is calculated, the following example is given:

ABC Co. has invested in 2 stocks, Alpha and Beta. They have purchased 40,000 shares (\$1 each) of Alpha, and 60,000 shares (\$1 each of Beta). The standard deviation of both the stocks is 1.5 and 2 each. In the same manner, the correlation coefficient of both the stocks is -1.

In the example given above, portfolio risk is simply calculated by using the following formula:

Portfolio risk = Sqrt [(weight of Asset A) ^2 * (SD of Asset A) ^2) + (weight of Asset B)^2 * (SD of Asset B)^2) + 2(weight of Asset A*Weight of Asset B*Correlation between Asset A and Asset B *SD Asset A * SD Asset B)]

Portfolio Risk = sqrt [(0.42*1.52) + (0.62*22) + 2(0.4*0.6*1.5*20*-1)]

Portfolio Risk = sqrt (0.36)

Portfolio Risk = 0.6

This implies that the portfolio risk is 0.6, or 60%. This normally lies in the medium high risk, and it means the risk profile is described to be relatively high.

## Importance of calculating Portfolio Risk

Portfolio Risk management is described as one of the most important elements from the perspective of the company.

In this regard, it is highly important to ensure that companies are able to realize the inherent risk that they undertake when designing their portfolio.

Keeping the risk-return principle in mind, a lot of organizations are often risk averse, and they do not prefer taking projects with higher risks.

Therefore, calculating portfolio risk can help them realize, and duly craft their portfolios so that the risk strategy of the portfolio matches the risk profile they want to maintain.

Calculating portfolio risk can also help them realize their potentials, and ensure that they are able to predict the outcome of their investment.

For example, if they have invested a chunk of their investments in a risky stock, they can then try to balance that off by purchasing a stock that is not very risky.

## Limitations of Portfolio Risk

Regardless of the fact that it is considered to be a very good practice to have a general understanding of the portfolio risks, yet it can be seen that there are certain limitations that need to be accounted for too. Portfolio Risk is not always correct and dependable.

Therefore, it cannot be identified as a single true source of investment from the perspective of the company. As a matter of fact, a number of other decisions also need to be accounted for when it comes to organizations deciding on where to invest and how to invest.

In the same manner, it can also be seen that calculating portfolio risk is a challenging task. In a typical portfolio, there are numerous different stocks that are included.