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An employee assembles a model with Lego toy bricks in a rest area during the opening of the Robert Bosch Internet of Things campus in Berlin on Jan. 18, 2018.

A lot of fancy things can be built with Lego sets nowadays. Such as a diversifying portfolio that loads on the Fama-French size factor.

Collecting Lego — yes, the plastic toys made of interlocking bricks that become cars and castles and robots — returned more than large stocks, bonds and gold in the three decades ending in 2015, says a study by Victoria Dobrynskaya, an assistant professor at Russia's Higher School of Economics. Aspects of the performance even align with returns sought by owners of smart-beta ETFs.

While the premise sounds goofy, it's serious enough for the academy, especially in a world where intrepid investors will go practically anywhere for uncorrelated returns. You might not know this, but older Lego sets are often resold online for many times their original price. In one extreme case, a kit for Star Wars Darth Revan that retailed in 2014 for $3.99 went for $28.46 on eBay a year later — a 613 percent premium.

And while quantitative investment firms spend hundreds of hours studying whether factors like size and momentum translate beyond the equity market, for Dobrynskaya, who wrote the paper with student Julia Kishilova, the inspiration was less theoretical.

"My son likes playing with Lego and I have a lot of it at home. At one point I thought: maybe I have a ready-made investment portfolio?" she said. "I know that Lego has nothing to do with multifactor models I spend my time focusing on. It doesn't mean the performance of Lego sets has absolutely nothing to do with factor investing. You'll be surprised to know that it does."

In a paper titled "Lego — The Toy of Smart Investors," Dobrynskaya analyzed 2,300 sets sold from 1987 to 2015 to measure their price-return over time. She found that collections used for Hogwarts Castles and Jedi star fighters beat U.S. large-cap stocks and bonds, yielding 11 percent a year. Smaller kits rose more than medium-sized ones, similar to the size effect in the Fama-French model (though the relation isn't exact).

"The beta of the size factor is statistically significant and the dynamics of the Lego index we created for our research is similar to that of the size factor," Dobrynskaya said by phone from Moscow. "Lego sets don't show a significant correlation to the financial crises and can be seen as an attractive investment with a diversification potential."

Guess what? Not everyone loves the science. Trying to shoehorn Legos into model of factor returns strikes some people as a little silly and creates the potential for human judgment to distort findings. First among the hazards is the possibility that everything is explained by happenstance — a criticism that looms over many factor models.

"If you think about all the academics in the world, there are a lot of them, and all of them are looking for something interesting to say and it's always going to be related to the Fama-French factor," said Roberto Croce, Managing Director, senior portfolio manager at BNY Mellon. "Someone is going to find something that is correlated. Purely by randomness that's going to happen. I'd take it with a grain of salt."

To determine the average yearly Lego return, Dobrynskaya gathered the initial price of 2,000 toys released between 1981 and 2014 and their cost in the secondary market in 2015. She analyzed price trends for links to risk factors like value, volatility and size in the models developed by theorists Eugene Fama and Kenneth French. While the first three weren't significant, returns did loosely resemble those attributed to the size factor. The Fama-French's "small-firm effect" that holds smaller-cap companies often outperform during sustained rallies.

The data showed that sets with a relatively few pieces, up to 113, returned 22 percent per year, almost 16 percentage points more than the group with about 860 bricks in each. The relation wasn't perfectly linear. Small sets yield the most, but those with 2,000 pieces do better than medium-sized ones. The large group contains less than 100 Lego sets compared with 1,600 in the small camp and can be potentially seen as an outlier, Dobrynskaya said.

"Smaller Lego sets could be more rare than larger sets produced en masse, though it's hard to know for sure," Dobrynskaya said.

Dobrynskaya, a 37-year-old London School of Economics PhD who spent years writing papers on carry trades and momentum investing, first looked at Lego as a topic for research after her son's hobby steered her to a community of investors discussing how to profit from buying and selling the toy.

Lego sets that focus on Super Heroes, Batman and Indiana Jones are among the ones that do best over time. The Simpsons is the only Lego theme that has lost value, falling by 3.5 percent on average. Newer sets have higher returns than older ones, though this can be due to a growing popularity of investments in Lego, Dobrynskaya said.

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