Mar 13, 2021
Low Volatility Anomaly in the Stock Market
by Po-Yu Liu
Financial observers may have noticed that the stock price of Tesla grew by four times in the past year, and the cost of Bitcoin increased by five times in the past year. A more recent example, the stock price of GameStop, grew by eight times within a week from $43 on Jan. 21, 2021, to $347 on Jan. 27. These stocks can be risky, and their prices are volatile. For example, GameStop fell from $225 to $90 in just one day on Feb. 2. Investors in GameStop lost more than 50% of their wealth in a single day.
Simultaneously, some investors are placing their bets in more stable and safer companies such as utility or telecommunications companies, earning barely 5% each year. If we invest $1000 in AT&T, the largest telecommunication company in the U.S., ten years ago, we will only have $1700 now, which is a lot less than what we would have earned if we invested in Bitcoin or Tesla. However, these stocks are safe: even in the worst financial crisis, we can still retain more than half of our wealth.
These investments may make novice stock investors rush towards a conclusion: to earn higher returns, investors must bear the risk of potentially huge losses and tolerate volatile price movement. After all, an investment with zero risks should not double our wealth in just a year, or this will be a free lunch. So it is natural for investors to infer that, in general, one must bear high risks to earn high returns.
However, I argue that the concept “one must bear high risks to earn high returns” is not necessarily true. In reality, we can earn roughly the same returns, if not higher, by investing in safe stocks rather than investing in risky stocks. This phenomenon that sounds like a free lunch, that you can earn the same returns with lower risks, is called low volatility anomaly.
For instance, observe the historical compound returns of low-beta and high-beta stocks from the 1960s to the present. If we split $1 into many pieces and invest an equal amount in each of the safest 20% of stocks, wealth would perform like the blue line. However, if we invest in the riskiest 20% of stocks, wealth will behave like the red line. Low-risk stocks exhibit less volatile price movement, lower losses during the financial crises of 2000 and 2008 but result in higher compound returns.
As counterintuitive as it sounds, low volatility anomaly has sound theoretical foundations, and researchers have identified several potential reasons why this seemingly “free lunch” exists. It challenges the traditional understanding of “investment with high returns must come with high risks, “ leading to some of the probable reasons behind the low volatility anomaly.
“High Returns Must Come with High Risks”
Risk has been defined differently in different financial settings, and the most important definition is how much, on average, does a stock rise when the total stock market also rises, and how much does a stock drop when the total stock market also drops. When the total market goes down by 10%, a safe stock such as Walmart is expected to drop by only 5%. On the other hand, a risky stock such as Tesla is expected to drop by 20%. Risk roughly measures the potential downward losses a stock might face.
As most people buy insurance such as health, life, car, or real estate, it is safe to assume that most people are risk-averse. Generally, investors do not prefer risky stocks; they are only willing to buy risky stocks at a lower price, which results in higher growth potential. This pattern can be further illustrated in the following coin-toss thought experiment.
Suppose we have to pay to play the following two fair coin-toss games:
- “Safe Game”: If we toss head, we win $4. If we toss tail, we lose $2.
- “Risky Game”: If we toss head, we win $10. If we toss tail, we lose $8.
If we play the “Safe Game”, we will win $1 on average each time we play. If we play the “Risky Game”, we also win $1 on average each time we play. These two games win us the same money on average, but the “Risky Game” is riskier as we can lose four times than the “Safe Game” if we lose.
If we need to pay money to play the two games, we are only willing to spend less, say $0.6, to play the Risky Game, while being willing to pay more, say $0.8, to play the Safe Game. We win $1 on average in both games, so the average financial return will be higher in the Risky Game since we pay less to play.
We can draw an analogy between the Risky Game and risky stocks. Then we realise that risky stocks should offer us higher returns if we dislike risky stocks in general. This line of reasoning underlies the traditional thinking behind “high return investment must come with high risk”.
Big Investors, Small Investors
As seen from the given examples, low volatility anomaly exists, which goes against the coin-toss thought experiment. What is amiss in the coin-toss experiment? It turns out that investors, in general, do not hate the Risky Game or analogously risky stocks that much. In reality, investors pay a similar amount to play both the Risky Game and the Safe Game, leading both games to offer the same expected returns. This behaviour exemplifies the low volatility anomaly.
Andrea Frazzini and Lasse Heje Pedersen in 2014 discovered that this behaviour exists because institutional investors, i.e. big investors with billions of dollars, prefer risky stocks to a certain extent. These investors include mutual funds, pension funds, and government funds. Many big investors are regulated, so they are not allowed to borrow additional money to scale up their return. To earn high returns, they have no choice but to invest in risky stocks, hoping that risky stocks will swing past their investment goals one day. One of the most successful mutual funds, T. Rowe Price New Horizons Fund, offers a 20% return each year on average in the past ten years. This is remarkable considering the total stock market grew by only 13% each year during the same period. However, T. Rowe Price New Horizons Fund primarily invests in riskier, smaller companies, which goes against the assumption that investors prefer safe stocks.
On the other hand, retail investors (i.e. individual investors like us) also prefer risky stocks only to some extent. In 2011, Turan Bali, Nusret Cakici, and Robert F. Whitelaw found that retail investors irrationally prefer stocks that exhibited extremely positive returns in the past, which are usually risky, hoping these stocks can replicate the same extremely high returns again in the future. For example, investors swarmed into investing in Bitcoin after seeing its price doubled every few months in late 2017. Rationally, we understand that it will only be more difficult for the Bitcoin price to double again. But many irrational investors nevertheless were attracted to Bitcoin, hoping it can replicate the doubling up again. Investing in Bitcoin in late 2017 was risky, but many investors irrationally preferred such a risky investment, which also goes against the assumption that investors prefer safe stocks.
Therefore, in some cases, investors can prefer the Risky Game over the Safe Game, which leads to the Risky Game, or risky stocks, being more expensive now, and in turn, exhibiting lower returns in the future.
Although investing in “hot” and risky stocks can potentially offer us high returns and excitement, investing in “boring” or “grandma” stocks such as utility or telecommunications might not be a bad idea after all. Safe stocks can offer roughly the same returns on average over a long horizon. Rather than chasing Bitcoin, Tesla, or other trending stocks, perhaps it might be beneficial also to consider safe stocks in your investment portfolio.
Po-Yu Liu is a financial researcher with an engineering spirit. He is a Taiwanese pursuing a PhD in finance after completing a bachelor’s degree in electronic engineering, both at HKU. He is experienced in finance, data science, and machine learning.
