How to Calculate Portfolio Risk

How to Calculate Portfolio Risk
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Financial investors well understand, or, at least, they should, that the prices of their assets fluctuate over time. This represents the risk inherent to investing. So, the magnitude of variation gives a measure of the risk involved with any given financial purchase. Of course, most investors do not put all their chips in one asset. Diversifying is a tried-and-true method of optimizing earnings and mitigating risk.

How, then, can a prudent money manager evaluate the hazards and potential gains represented by an entire financial portfolio? Rest assured, there are ways to determine the dimension of risk.

First, Count the Positives

Investors should look at each financial holding to determine its rate of return, i.e. using a fixed period of time to measure gains and losses in terms of percentage. This means subtracting the initial value of the asset from its value at the period's end, dividing that difference by the initial value and then multiplying that quotient by ​100​. An assumption is called for here: that the fluctuations of the past will be repeated in the future.

Another given is that not all securities in a portfolio are equally weighted. By dividing the value of each security by the total portfolio value, you can see which holdings carry more weight. After all, losses in "lighter" holdings can be more than offset by gains in those of higher value. Multiplying the return percentage by an asset's weight, and then adding the products on each holding together, yields the expected return on the portfolio.

Understanding Standard Deviation

While the expected return forecasts an amount of wealth a portfolio may generate, the standard deviation represents how much this amount diverges from the average, or mean, of probable investment outcomes. The larger a standard deviation, the greater the distance between the value of an asset or portfolio and its high/low values (data points).

The portfolio variance formula begins with calculating the mean value, adding the data points within the range of values and then dividing them by the actual number of data points. Then, subtract the mean value from that of each data point. What is left are variances, each of which is squared and then those values are totaled. The total sum is then divided by the number of data points minus one; taking the square root of the resulting quotient produces the standard deviation.

This figure is helpful in order to evaluate price volatility and forecast stock performance. Mutual funds may be called conservative because the standard deviation is low. On the other hand, growth funds that are dubbed "aggressive" will likely show higher standard deviations. Thus, a portfolio risk formula must include standard deviation as a factor.

A conservative investment strategy, focused on wealth preservation but seeking safe vehicles of growth, will strive for a portfolio with more assets of low standard deviation. An aggressive strategy will have more holdings with higher volatility.

What Does This Mean for Portfolio Risk?

A stock, commodity or other instrument that is performing demonstrably well in terms of rate of return should have that performance measured against its standard deviation to see if reliability can be expected. A portfolio of financial assets is no different. A large standard deviation signals greater possibilities of gain, to be sure. Yet it also portends higher risk.

A good portfolio risk example would be one that included stocks for Adobe Systems. Enjoying very good returns in early ​2021​, this stock nevertheless shows high volatility over ​five years​. Taking this into account, investors may hold Adobe for the short term.