Hedge fund manager reluctantly challenged — then collaborated with — Harry Markowitz

When Sander Gerber of Hudson Bay Capital set out to create a portfolio management system, he had no intention of challenging Harry Markowitz.

Yet, after developing a new statistic to understand how two stocks move relative to each other – known as co-movement – that’s exactly what he ended up doing. Gerber’s goal was to better understand how diversified his portfolio was after discovering that historical covariance, the measure used by Markowitz supporters, was not enough.

To Gerber’s surprise, the father of modern portfolio theory, which laid out a framework for the now ubiquitous investment management strategy, was receptive. The two eventually collaborated to research whether this measurement, now known as Gerber’s statistic, held water.

It made. The research, published in the February 2022 issue of Portfolio Management Journalshows that using the Gerber statistic instead of historical covariance – a metric used by most investors – leads to outperformance in terms of cumulative return, geometric mean return, and Sharpe ratio.

The Gerber statistic assesses the level of risk and diversification in a portfolio by determining whether stocks move in tandem, in opposition to each other, or have no relationship. The statistic uses certain thresholds to filter out noisy data that may signal that relationships exist, even when, in fact, they do not.

Without the Gerber statistic, investors might end up building portfolios that aren’t as diverse as they think.

Blindly relying on models is a mistake

The development of the statistic has its roots in Gerber’s own background as a stock options market maker on the floor of the U.S. Stock Exchange, where he said he learned from a “guttural perspective” how markets worked. Between the shouting, hand signals and paper orders, Gerber said he saw with his own eyes that there was a “crescendo and diminuendo in the markets” that may indicate human error. For Gerber, it was a perfect illustration of behavioral economics.

“I’ve seen how models break down,” Gerber said, commenting on how his time on the floor made him think about the limitations of all models, including MPT. He added: “I’m not saying all models are bad. Blindly relying on the model is a common failure. It happens again and again and again. People don’t understand the risk they run.

After gaining experience on the stock market, Gerber decided to start a business to trade his own capital. Originally called Gerber Asset Management, the company became Hudson Bay Capital, a multi-strategy hedge fund that now manages $13.6 billion in assets. In 2021, the fund returned 13.5% net of fees.

“I had several risk takers trading my money and I didn’t want to lose any money,” Gerber said. “I wanted to give them the freedom to trade and exercise their talent and liveliness.”

To do this, he developed a portfolio management system that eventually included the Gerber statistic. Gerber, who studied both philosophy and finance in college, was used to thinking in frameworks and found them helpful in managing money. But in Gerber’s view, the widely used MPT framework has been fueled by data that misrepresents portfolio diversification.

For example, let’s say the S&P 500 moves 10 basis points. Although this move may coincide with a 10 basis point move in another index used in a portfolio, an investor may deem the move too small to show a true relationship between the two. Using historical covariance, this relationship would appear as co-movement.

The Gerber statistic allows investors to filter out these small moves. Unlike historical covariance, it does not calculate the degree of movement, only trying to measure whether or not the movement indicates a significant relationship.

Gerber has used the statistic for years within Hudson Bay’s Deal Code System, a portfolio management framework for a high-conviction strategy that is uncorrelated with broader markets and with set thresholds to limit losses. .

But Gerber thought his idea could use input from a heavyweight academic.

Is there another way to express Markowitz’s ideas?

After an email exchange with Markowitz, Gerber flew to San Diego, where Markowitz is based, so the two could discuss the idea in person.

Walking on the beach, with the wind whipping loudly, Gerber told the legendary economist that he believed the way MPT was applied was based on a faulty assumption.

In 1952, Markowitz laid out the principles of MPT, which emphasized the benefits of a comprehensive portfolio of investments, including its risks, the benefits of diversification, and the correlations between securities. Markowitz, along with William Sharpe and Merton Miller, shared the 1990 Nobel Prize. Their work changed the way people invest and remains the backbone of the asset management industry.

Also called mean variance, the practical application of MPT relies on entering a covariance matrix, which shows the relationships between two data points – in this case, titles. In the decades since MPT was developed, industry practitioners began calculating covariance using historical data, Gerber said. They still use this practice today.

“That’s not what Harry wanted to do,” Gerber said. “He wanted it to be based on human judgment of forward-looking assumptions, not calculations from the past. The Gerber stat solved something he was looking for.

In the early 2000s, researchers found a way to exclude some market noise from appearing in the model using an approach called the shrinkage estimator. The shrinkage model, however, is still based on the historical covariance matrix.

According to Gerber, historical correlation is not as useful as forward-looking assumptions. That was the purpose of the beach meeting – to explain to Markowitz that there might be another way to express his ideas.

“I thought it might be insulting, so I tried to be gentle with it,” Gerber said. But Markowitz agreed. At first, Gerber thought he had heard him wrong. After all, it was noisy along the beach. Gerber asked Markowitz to repeat himself.

“He said, ‘I don’t think [historical correlation is] helpful,” Gerber recalls. “It was from that moment that we decided to collaborate.”

After more conversation, they began working with Philip Ernst, a tenured associate professor of statistics at Rice University. “It’s great to latch on to a new idea that works really well,” Ernst said of the research. Other co-authors included Yinsen Miao, Babak Javid and Paul Sargen.

In a mathematical sense, Gerber’s statistic is a generalization of a statistic called Kendall’s Tau, which shows motion relationships between pairs. The Gerber statistic also superimposes thresholds for co-movements in the measurement.

“We want to cut through the noise and focus on meaningful relationships,” Gerber said.

It worked. Research has shown that in each risk scenario, the Gerber statistic offered a more favorable risk-reward profile than the historical correlation model. In all but the most conservative risk targets, it also outperforms the shrinkage estimator.

Diversification is still the only free lunch

“You don’t have to seize the past,” Ernst said of the advantages of the Gerber statistic over these two other models. “You can decide what is a significant co-movement and what is not.”

Hudson Bay uses the statistics as part of an internal risk monitoring system to make investment decisions.

As an example, the risk model showed a relationship between a Chinese stock index and certain US stocks. After doing some research, the team realized that these US companies, especially when grouped together in a portfolio, had significant exposure to China.

“When China wasn’t moving a lot, you didn’t see it,” Gerber said. Aggregate, he did. The company opted to layer on a Chinese hedge to mitigate some of that risk, a decision based on the Gerber statistic.

The hedge fund manager pointed out that the model does not make decisions for Hudson’s Bay. Instead, it helps the company decide where and how to diversify.

And that goes back to Markowitz’s original work.

“There’s only one free lunch in the markets,” Gerber said. “The free lunch is diversification because if you can achieve it, you can reduce risk and get the same stream of returns.”

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