## Definition of Portfolio Risk

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

A portfolio is a combination or 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, the risk is diversified and then different for a portfolio of the existing different stocks.

## The formula for Portfolio Risk

*Portfolio Risk is measured by calculating the standard deviation of the portfolio. In this regard, standard deviation alone cannot calculate the portfolio risk. *

There is a need to ensure that all the different standard deviations are accounted for with their weights and 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 measures the extent to which the stocks act and respond similarly to market trends and other macroeconomic factors.

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

Therefore, portfolio risk calculation includes three main variables: the weightage of the respective assets in the portfolio, the standard deviation of those assets, and 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

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 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 [(0.4^{2}*1.5^{2}) + (0.6^{2}*2^{2}) + 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, meaning the risk profile is relatively high.

## Importance of calculating Portfolio Risk

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

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

Keeping the risk-return principle in mind, many organizations are often risk-averse and 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 potential, and ensure that they can 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

Even though it is considered very good practice to have a general understanding of the portfolio risks, it can be seen that certain limitations also need to be accounted for. Portfolio Risk is not always correct and dependable.

Therefore, it cannot be identified as a single true source of investment from the company’s perspective.

Several 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, numerous different stocks are included.

Ensuring that accurate portfolio risk is calculated is subject to available figures for the stocks, like standard deviation, and the correlation between the assets.