Measuring financial asset risk using spot regressions

By Jovina Ang

SMU Office of Research & Tech Transfer – Beta is one of the financial metrics that investors use for investing in stocks, bonds, currencies, exchange-traded funds (ETF), mutual funds, crypto or any financial asset that is traded on a daily basis.

Beta indicates the relationship between the financial asset and the broader market. It is often used to measure the systematic risk of assets in relation to broader market indices, such as the Nasdaq 100 or the S&P 500.

For instance, an ETF with a beta of 1.0 is expected to move in line with the market. Say for instance, the NASDAQ index rises by one percent, the ETF is expected to also rise by one percent. If the market falls by one percent, the ETF is expected to do likewise.

As an investor, you might be wooed to invest in assets with high positive betas during a bull market to beat the market. However, high beta assets are more volatile as there will be more price movements compared to the overall market and thus, are purported to have more risk. Hence, to hedge against market-wide risk, you might want to invest in some negative beta assets.

Given that beta is a commonly used metric in investing, it is important to accurately measure it. However, like everything else in financial markets, it is a moving target and hard to catch. This is especially true during extreme market conditions, like what the global market had experienced during the onset of the COVID-19 pandemic.

What is the best way to measure beta? Do we really know the betas of sophisticated financial instruments as we thought? These are the questions Lee Kong Chian Professor of Economics Li Jia wanted to answer when he explained his research to the Office of Research & Tech Transfer.  

The research

To embark on the research, Professor Li collaborated with his former colleague and long-term collaborator, Professor Tim Bollerslev of Duke University, and Yuexuan Ren, who is one of his PhD students at SMU.

The research team focused on three ETFs: the QQQ, TQQQ, and SQQQ, traded on the U.S. stock market. These ETFs are highly popular among institutional and retail investors who are interested in the U.S. tech sector.

The QQQ index fund is explicitly designed to track the Nasdaq 100 stock market index. The leveraged TQQQ fund seeks to generate three times the return on the Nasdaq 100 index whereas the SQQQ fund is designed to yield negative three times the return on the Nasdaq 100 index on any given trading day. The leveraged funds are constructed using sophisticated financial engineering tools. If everything goes in the right way, the beta of the TQQQ should be three and the beta of the SQQQ should be negative three, relative to the baseline QQQ index fund.

To track the actual beta values of the three funds, the research team performed spot regressions using high-frequency transaction data over many short trading sessions within each day – a statistical method shown to yield the most accurate measurement of beta without assuming it to be constant over time, over a period of four years, from 2018 to 2021. This allowed the team to test scientific hypotheses regarding whether the leveraged funds were doing what they were supposed to do.

Insights from the research

Under normal market conditions, the research showed that the two leveraged funds adequately fulfil their designed purpose. Throughout the 6.5 hours of a typical trading day, the beta of the three-time leveraged TQQQ fund is close to three and the beta of the inversed three-time leveraged SQQQ fund is close to negative three.

However, things can go sideways under extreme market conditions. During March 2020, when COVID-19 impacted the U.S. stock market in full force, the betas for the leveraged ETFs significantly deviated from their target values more than 60 percent of the time. This was particularly noticeable in the two weeks from March 9 to March 20, 2020, when the U.S. stock market experienced multiple crashes, the efficacy of the funds was highly compromised.

During the crashes, the TQQQ exhibited severe over-leverage, exposing investors to higher-than-expected systematic risk. The SQQQ showed severe under-leverage, and so, failed to provide enough hedging against downward market-wide movements as investors had intended.

Contributions of research

As an investor, measuring beta values of financial assets is critical to manage one’s exposure to risks.

Professor Li commented: “Previously, most of the research has overlooked the possibility that classical measures of risk, such as beta, can swing quickly under extreme market conditions. This is also partly because it was unclear what would be the best way to conduct measurement in such a challenging scenario. This research provides a definitive answer to this question. Our method is really an incarnation of classical statistical principles in the modern algorithmic trading era.”

“The data is trying to tell us, ‘Financial instruments do not always perform as designed.’ To make things worse, their mechanics tend to break down exactly when they are needed the most, especially during turbulent times. This creates an extra layer of uncertainty for investors. Being aware of this. My advice is: invest with extra caution,” he concluded.