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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?

The standard deviation of an asset measures risk by looking at the price movement of the asset over time. This can be thought of as measuring risk from a stand-alone basis.

On the other hand, beta measures risk by looking at the price movement of an asset relative to the market. Theoretically, the “market” is all investible assets. In practice, the beta can be relative to any index or benchmark such as the S&P 500. 

This means that beta is a measure of systematic risk, the risk that cannot be diversified away, and tells us the amount of risk the asset adds to an already-diversified portfolio.

Sticking with the statistics

In order to measure the beta of an asset, we need to observe how it’s 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.

The correlation of our asset’s returns with the market’s returns will tell us if they move up and down together. If they are negatively correlated then they will move in opposite directions of each other, and if they are uncorrelated then the movements will be more unrelated.

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). 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.

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

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.

We can use the table below to help interpret this :

 

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. 

 

Disadvantages of beta and standard deviation

These measures of risk are by no means perfect. 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?”.

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?

Lastly, 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, standard deviation and beta give us a way to better understand the risks of investing. They allow us to make more informed future investment decisions and evaluate past performance.

Use beta to better understand and set expectations for the risk of a particular investment. The beta of most investments is calculated for you and easy enough to find on sites like YahooFinance. 

Check out our lesson on diversification to see how beta and standard deviation can be used to show how diversifying our investments impacts the overall risk and return of a portfolio.

Glossary

What is beta?

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

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