Measuring relative risk

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

If beta is another way I can quantify the risk of an investment, how is it different from the standard deviation? Is one measure of risk better than another?


What it's about: Beta is a calculation for the amount of systematic risk we are taking.

Why it's important: As markets change, we need to understand how the risks of our investment also change.

Key takeaway: A beta larger than 1 means we are taking more risk compared to the market. We should thus be paid more for taking this risk.

Volatility is an easy statistic for us to understand the overall risk of an asset. We can manage this risk by buying lower volatility assets when we want to reduce risk or buying higher volatility assets when we want to increase risk. However, how do we pick between different asset classes with very different volatility? We can make a decision by looking at the risk measured by beta.

What is Beta?

Beta measures risk by looking at the price movement of an asset relative to the market.

The beta calculation is used to help investors understand whether an asset moves in the same direction as the rest of the market. It also provides insights into how risky an asset is relative to the rest of the market. In theory, the “market” should represent all investible assets. In practice, it would take a tremendous amount of time to gather the data of every investible asset to make beta practical. Instead, the beta is usually set relative to an index or benchmark such as the S&P 500. 

Sticking with the statistics

In order to measure the beta of an asset, we need to observe how its price moves relative to the market. The way we quantify this movement is by calculating the correlation between the two price movements relative to one another.

What is Correlation?

Correlation is a statistical measure that determines how assets move in relation to each other.

The correlation of our asset’s returns with the market’s returns will tell us if they move up and down together. 

Inversely correlated returns act like seesaws.

If our investment is negatively correlated to the market, then the price will move up when the overall market drops and vice versa. If the returns are uncorrelated, then the movements will be completely unrelated. Let's step through an example comparing $AAPL and $IEF.

Visualizing Correlation

This graph shows the monthly returns over a 5 year period from 4/2/2015 to 4/1/2020 of the S&P 500, $AAPL stock, and $IEF (an ETF that tracks the investment results of an index composed of U.S. Treasury bonds with maturities of 7-10 years).

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

We can see that, for the most part, the returns for $AAPL increase and decrease when the S&P 500 increases or decreases; whereas, the returns for $IEF do not follow the S&P 500 the same way. In fact, there are periods in which they move in opposite directions.

Interpreting beta

A positive beta means that the returns of the asset and the market should move in the same direction relative to one another. If the markets are moving up, then you can expect the value of the asset to move up as well. Depending on the value of beta, we can discover a bit more. The table below is included to help us.

Beta's outcome

There aren’t many assets that would have a negative beta but it implies that the price of an asset would decrease if the value of the market increased. Gold is often considered to have a negative beta relative to the stock market because the price typically rises when markets decline.


In addition to directional movement, beta also tells us how risky the investment is compared to the market. The volatility of a bond could be 15%, and it would look like the bond is a much less risky investment than a stock with a volatility of 20%. However, if the overall bond market has an average volatility of 6% and the average stock market has an average of 17%, we would expect much higher beta for the bond than for the stock.

Beta helps tell us how risky an asset is compared to the market

In that case, we might think twice before we buy the bond. Beta, as a measurement of risk, is by no means perfect. 

The major caveats

  1. Both beta and standard deviation rely on historical price movements so we are often faced with the question, “to what extent is this rear-view mirror perspective predictive of the future?”.
  2. They also do not explicitly factor in qualitative information. By only using prices, we have to assume that the prices properly reflect all other known information. Is this a reasonable assumption?
  3. The calculations are dependent on the data used. For example, the beta or standard deviation based on one year of historical data will be different than if ten years of historical prices are used. Even using daily, weekly, or monthly prices can impact the results. This also means that these measures will change over time.

Risk is both qualitatively conceptual and quantitatively measurable. While not perfect, beta gives us a way to better understand the risks of investing. It allows us to make more informed future investment decisions and evaluate past performance.

Actionable ideas

Use beta to better understand and set expectations for the risk of a particular investment. The beta of most investments is calculated for us and easy enough to find on sites like YahooFinance. For newer asset classes like crypto, there isn't often enough data for these calculations to be meaningful yet.

Beta, while more helpful than volatility, is meant to be used in conjunction with alpha for us to make actionable decisions.



What is Beta?

Beta measures the risk of an investment relative to the market or an index.

What is Correlation?

Correlation is a statistical measure that determines how assets move in relation to each other.