How to Calculate Portfolio Standard Deviation

How to Calculate Portfolio Standard Deviation

When you invest, one of your strategies might be picking investments with the highest potential return with the lowest potential risk. More risk usually means higher returns, but, it can also mean bigger losses if you do not sell in time. To help minimize your risk and still maximize returns, you should calculate your portfolio standard deviation.

By analyzing the most recent return history of a fund, you can calculate how risky a hypothetical investment is and if it complements your existing investment strategy and risk tolerance.

Calculating the standard deviation for individual funds you already own is also another way to compare your current level of risk to the target level of risk for your portfolio.


What does portfolio standard
deviation mean?

portfolio deviation

Portfolio standard deviation is one of the most common ways to determine the risk of an investment & the consistency of future returns.

  • A low standard deviation means you can expect to receive the same rate of return each year like money market funds.
  • High standard deviations indicate more volatile investments with unstable rates of returns like penny stocks.

In most cases, the standard deviation of a fund is calculated by measuring the fluctuation from the average return for the most recent 36 months.

So, if a fund has a standard deviation of 5 and an average return rate of 15%, the average monthly return was usually between 10% & 20% for each month and the future average rate of return is projected to fall within that same range.

Even if a fund had a negative return rate, let’s use -5% and a standard deviation of 3, the average monthly return would fall between -2% & -8%.

Finally, a fund with a standard deviation of 0 would have the same average monthly return, whether that was -3%, 0%, 1%, or 55%.


Using Standard Deviation in
Your Research

Portfolio standard deviation isn’t necessarily one of those investment terms that advisors and brokerages talk about on a regular basis like the P/E ratio, dividend yields, and expense ratios.

This doesn’t mean it’s not an important factor and standard deviation has probably played more of a factor in some of your previous investing decisions than you realized.

If you have ever researched mutual funds, most brokerages include two gauges that indicate the levels of historic return and historic risk.

Standard deviation is one calculation they use to determine the historic risk of a particular investment or your portfolio.

While your primary focus might be analyzing the historic rate of return for two funds, also looking at the standard deviation can help show you which fund has more long-term stability.

As an example, let’s compare the performance of two different investments:

Investment A Average Rate of Return: 10%Standard Deviation: 5%

Investment B Average Rate of Return: 10%Standard Deviation: 12%

Both investment options have the same rate of return, but, Investment B has a significantly higher standard deviation meaning you could earn 22% this year & lose 2% next year.

If Investment B had a higher historic rate of return, the additional volatility might be acceptable, but, since it has the same rate of return, you might most likely decide to choose Investment A because you can expect similar results with less risk.


How to calculate portfolio standard deviation: Step-by-step guide

While most brokerages will tell you the standard deviation for a mutual fund or ETF for the most recent three-year (36 months) period, you still might wish to calculate your overall portfolio standard deviation by factoring the standard deviation of your holdings.

In the steps below, you will find out how you can calculate your portfolio standard deviation when comparing two different stocks that you currently own or might potentially buy.

The step-by-step guide will show you how to find the standard deviation for an individual investment and also for your portfolio.

If you already know the standard deviation of your stocks, you can skip to step #4.

Step #1:
Find the Standard Deviation of Both Stocks

For this exercise, we are going to find the standard deviation of two different investments. First, we will calculate their average return for the last 5 years.

Investment A: (11.53% + 0.75% + 12.75% + 32.67% + 15.77%)/5 = 14.69%

Investment B: (4.13% + 3.86% + {-0.32%} + 11.27% + 21.63%)/5= 9.71%


Step #2:
Calculate the Variance of Each Stock

Since standard deviation is the square root of variance, we must first find the variance of each investment.

This is a two-part process with for each investment. You first find the individual variance for each year & square the sums.

Then, you divide the sum of the squares from the first step by the 1 less the number of years (∑/n-1). For this example, we will divide the sum of the squares by 4 since we found the average return for 5 years in Step #1.

Investment A: (11.53%-14.69%)² + (0.75%-14.69%)² + (12.75%-14.69%)² + (32.67%-14.69%)² + (15.77%-14.69%)²= 0.052/4=.013

Investment B: (4.13%-9.71%)² + (3.85%-9.71%)² + (-0.32%-9.71%)² + (11.27%-9.71%)² + (21.63%-9.71%)²= 0.032/4=.008


Step #3:
Find the Standard Deviation of Each Stock

The standard deviation of each stock or portfolio is the square root of the variance we calculated in the previous step.

Investment A: √.013= 11.4%

Investment B: √.008= 8.94%


Step #4:
List the Standard Deviation of Each Fund in Your Portfolio

For this exercise, we will use a sample portfolio that holds two funds, Investment A and Investment B, to see what the overall standard deviation is for owning these two funds.

From the previous step, we found out that the standard deviation was 11.4% for Investment A and 8.94% for Investment B.


Step #5:
Weight Each Investment Held

Next, you need to determine the weighted of both funds in the portfolio by comparing the size of the investment to the total size of the portfolio.

Here’s what we know:

Total Portfolio Value: $7,500

Value of Investment A: $6,000 ($6000/$7500=80% of total portfolio value)

Value of Investment B: $1,500 ($1500/$7500=20% of total portfolio value)


Step #6:
Find the Correlation Between Both Funds

The next step is finding the correlation between the two funds. It will range between -1 & 1.

A positive correlation means both funds react the same and go up or down together.

A negative correlation means if one goes up, the other goes down while a correlation of 0 means the performance of one fund has no effect on the other’s performance.

For this example, the correlation is .8030, which means both stocks act very similar.


Step #7:
Calculate the Variance

Now we are going to find the portfolio variance with the formula below.

(.80²)(0.114²)+(.20²)(.0894²)+2*.80*.20*.114*.0894*.8030=.011

Portfolio Variance=.011


Step #8: 
Find Portfolio Standard Deviation

This is the last step to finding your portfolio standard deviation.

All we have to do is calculate the square root of the portfolio variance!

√.011=.1048=10.48%

Portfolio Standard Deviation=10.48%

With a weighted portfolio standard deviation of 10.48, you can expect your return to be 10 points higher or lower than the average when you hold these two investments.

Now, we can compare the portfolio standard deviation of 10.48 to that of the two funds, 11.4 & 8.94. By holding Investment B, your overall volatility is lower than only owning Investment A.

To reduce the volatility further you could consider buying more of Investment B because it has a smaller standard deviation rate.


Summary

Finding portfolio standard deviation is an excellent way to determine if your current investments are too risky, too conservative, or just right for your current investing strategy.

It’s also a good way to calculate your future portfolio risk level when you plan to trade investments and compare it to your current risk level.

With this additional measurement tool, you can make more informed investing decisions.

Andrew
 

My name is Andrew and I run Slick Bucks to help folks learn to manage money cleverly, and how that clever management can make you wealthier.

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