Standard Deviation
Standard Deviation in Investing:
How to Measure Portfolio Volatility
By VizMetrics. Figures cover the 20 years ending August 31, 2026.
Standard Deviation is the most common measure of portfolio risk. It shows, as a percentage, how far a portfolio's returns typically swing above or below its average. This page explains what the number means, what counts as a good one, and how to calculate it.
What is Standard Deviation?
Standard Deviation is a percentage showing how much a portfolio's returns swing up and down compared to its average return. In other words, it measures how spread out the returns are around the average.
RecipeInvesting.com calculates Standard Deviation from monthly returns and reports it as an annualized percentage.
What does the Standard Deviation tell you?
The Standard Deviation tells you a portfolio's typical move up or down from its average, which gives you a snapshot of its overall volatility. It helps you understand the range of results to expect in a normal year.
For example, suppose a portfolio averages 8% a year with a Standard Deviation of 10%. If its returns follow a bell-curve pattern, about two years out of three will land between −2% and +18%. Markets produce extreme years more often than a bell curve predicts, so treat that range as a guide rather than a limit.
Why is the Standard Deviation important?
- It measures risk. A low Standard Deviation means steadier, more predictable returns. A high Standard Deviation means returns swing widely, which is higher risk.
- It measures consistency. Two investments can end up with the same average return, one steadily and the other erratically. Standard Deviation shows which is which.
What is a good Standard Deviation?
Lower is better, as long as the return is still worth having. You want steady growth without wild swings.
Two reference points help. Over the 20 years ending August 31, 2026, an S&P 500 fund (SPY) had a Standard Deviation of 17.1%. A balanced portfolio of 60% stocks and 40% bonds had 10.9%.
A low number is only half the picture, because cutting risk usually cuts return too. It does not always. Over the same 20 years, Adaptive Asset Allocation F (t.aaaf), a tactical Portfolio Recipe, had a lower Standard Deviation than the S&P 500 fund (12.5% vs. 17.1%) and a higher annualized return (14.5% vs. 11.3%). The tradeoff is upkeep. Its target allocation is reviewed every month, so it needs more attention than a buy-and-hold fund.
Figures are historical and based on monthly total returns. Past performance does not guarantee future results.
What is a typical range for the Standard Deviation?
These are the lowest and highest Standard Deviation values tracked by RecipeInvesting.com for the 20 years ending August 31, 2026, among portfolios with a full 20-year history.
| Group | Lowest | Highest |
|---|---|---|
| Portfolio Recipes (investable model portfolios) | 3.4% for Arbitrage Fund (ARBNX) | 43.7% for Quartile Sector Rotation (t.srqr) |
| Portfolio Ingredients (asset class ETFs) | 1.5% for iShares 1-3 Year Treasury Bond (SHY) | 36.2% for iShares MSCI Brazil ETF (EWZ) |
What do specific Standard Deviation values mean?
- 1%: very low risk, gentle fluctuations (for example, short-term government bonds)
- 5%: low risk, tolerable variation (for example, a bond fund)
- 10%: moderate risk, with notable variation (for example, a balanced fund)
- 15%: high risk, with potential large swings (for example, a broad stock index fund)
- 20%: very high risk, with significant variation (for example, a technology-heavy stock fund)
What is the Standard Deviation for example portfolios?
Standard Deviation and annualized return for the 20 years ending August 31, 2026.
| Portfolio | Risk level | Standard Deviation | Annualized return |
|---|---|---|---|
| 1-3 Year Treasury Bond fund (SHY)Short-term bond fund | Very low | 1.5% | 1.9% |
| Total Bond Market fund (BND)Aggregate bond fund | Low | 4.6% | 3.1% |
| Balanced Portfolio (s.6040)60% stocks, 40% bonds | Medium | 10.9% | 8.2% |
| Adaptive Asset Allocation F (t.aaaf)Tactical Portfolio Recipe | Medium | 12.5% | 14.5% |
| S&P 500 fund (SPY)Large company stocks | High (market risk) | 17.1% | 11.3% |
| Nasdaq 100 Index fund (QQQ)Technology-heavy, large company stocks | Very high | 21.9% | 16.6% |
See the full lists: Standard Deviation for every Portfolio Recipe and Standard Deviation for every Portfolio Ingredient.
What is the formula for the Standard Deviation?
$$ \text{Standard Deviation} = \sqrt{\frac{\sum(R - R_{\text{mean}})^2}{\text{n}}} $$
Where:
- R = the portfolio's return in one period
- Rmean = the mean (average) of all the portfolio's returns
- Σ = the sum of the terms
- n = the total number of observations
This is the population form, which divides by n. Some spreadsheet functions, such as Excel's STDEV.S, divide by n − 1 instead and give a slightly higher figure. Excel's STDEV.P matches the formula above.
How do you calculate Standard Deviation?
You might expect the calculation to be an average difference: find each year's difference from the average return, then average those differences. That does not work. The ups and downs cancel each other out, so the result is always zero.
A second idea is to drop the minus signs before averaging, so that −5% counts as 5%. This calculation exists. It is called the Mean Absolute Deviation (MAD).
Standard Deviation squares the differences instead, averages the squares, and then takes the square root. Squaring has two advantages:
- Big differences count for more. This helps investors because it penalizes extreme volatility. For example, a portfolio with annual returns of +5%, +50%, −5% and −50% has a MAD of 27.5% and a Standard Deviation of 35.5%. The higher figure is often more meaningful to an investor who saw the portfolio's value cut in half.
- The math fits with other risk measures. Variance, covariance and correlation are easier to calculate from squared differences.
Step-by-step calculation
Using 10 years of annual returns as an example:
- Get each year's total return (for example, −4.3% or +5.0%).
- Calculate the average (mean) return over the 10 years.
- Calculate each year's difference from that average.
- Square each difference, then calculate the average of those squares. This emphasizes the larger swings.
- Take the square root of that average. This converts the number back into a percentage, which is easier to understand and compare.
Can you explain Standard Deviation graphically?
Here is the same calculation in pictures. The example uses the annual returns of Adaptive Asset Allocation F (t.aaaf) for the 10 years from 2016 to 2025.
Step 1. Get the total return for each year (the blue bars) and calculate the average return (the orange line).
Step 2. Find each year's difference from the average (the green and red arrows).
Step 3. Square each difference (the yellow squares).
Step 4. Find the square whose area is the average of the 10 squares above.
Step 5. The side length of this average square is the Standard Deviation, the typical annual deviation from the average. In this example, the Standard Deviation is 11.6%.
RecipeInvesting.com's published figures use monthly returns, so they differ slightly from this annual example.
What’s the difference between the Standard Deviation and the Downside Deviation?
- Standard Deviation measures total volatility. It counts moves above the average return as well as moves below it.
- Downside Deviation measures only negative volatility. It counts the returns that fall below a minimum acceptable return, typically zero or a target return.
The Sharpe Ratio compares return to Standard Deviation. The Sortino Ratio compares return to Downside Deviation.