Archimedes Finance

Become a better investor


Measuring risk

Lesson in Course: Portfolio management (advanced, 5min )

I know some assets are riskier than others but how can I quantify that risk?

Since risk can be explained as when something occurs that isn’t planned or expected, the occurrence of such an event will result in a change in the value of the asset (stock, bond, ETF, or any investment). Assets whose prices fluctuate more dramatically are considered riskier since unexpected events have a greater impact on the price.

Bring in the statistics

Prices are quantities that can be tracked regardless of the currency (dollars, pesos, euros, etc.). By following the price movements, we can see how much fluctuation there is over time by looking at what the percent change in price is each day, also known as the daily return. We can visualize these changes on a graph of daily returns.

Apple stock daily returns

This graph shows the daily return of a share of Apple stock over a 5 year period from 4/2/2015 to 4/1/2020. You can see that on any given day, the price could change by less than ±5% except on a few rare occasions where it changed by more than that.

*based on historical daily adjusted closing price sourced from Yahoo Finance
IEF ETF daily returns

This graph shows the daily return of IEF, an ETF that tracks the investment results of an index composed of U.S. Treasury bonds with maturities between seven and ten years, over a 5 year period from 4/2/2015 to 4/1/2015. You can see that on any given day, the price could change by less than ±1% except on a few rare occasions where it changed by more than that.  

*based on historical daily adjusted closing price sourced from Yahoo Finance

Standard deviation

Using these statistics, we can measure the variation, or fluctuation, of the daily returns and then express that in annual terms. This annual amount of variation in the daily returns is known as the volatility or standard deviation.

A higher standard deviation means that the daily returns are more spread out and further from the average daily return; whereas, a lower standard deviation means the daily returns are closer together and closer to the average daily return. 

Since the standard deviation is how we can quantify how large the changes are of an asset’s price, it is how we can measure the risk of that asset.

Comparing risk

By taking the standard deviation of the daily returns, we can compare the relative risk of assets by comparing their standard deviations. Let’s start by comparing the standard deviation of Apple stock and the IEF ETF, which we can use as a proxy for bonds, from the example above.

On any given day, the daily return of APPL typically lies between ±5%; however, the daily return of IEF is usually between ±1%. When we annualize these changes, we get a standard deviation of about 34.0% for APPL and 6.8% for IEF. This means that APPL exhibits more variation, or is more volatile, and therefore considered riskier than IEF. 

All of this math just proves what we may have already been told, that stocks are riskier than bonds.

Looking at how the price of an asset fluctuates over time will help you get a sense of how risky the asset is; however, taking it one step further and finding the standard deviation allows you to compare the level of risk between asset classes and the risk of assets in the same class. 

This can also help you decide how much risk you are comfortable with and which investments are appropriate for a portfolio. For example, a standard deviation of 15% might be too much for some but not others.

Glossary

What is Standard deviation (Volatility)?

Measures how much the price of an investment fluctuates. It's often used to measure the risk of an investment.

At Archimedes, our goal is to make investment literacy accessible and free for everyone.

Join our investment learning hub for more free lessons like this, connect with our trusted community, and get hands-on experience by playing a game!

Sitemap