Previously a member of the Accounting faculty at Kellogg
Previously a Visiting Professor of Accounting at Kellogg
When it comes to investing, everyone—whether a novice e-trader or a billionaire professional like Warren Buffett—faces the same two-part problem: How do you identify which stocks are likely to increase in value, and how many of each should you buy? Together, these two questions are known as “the investor’s problem.”
Buffett’s knack for solving both parts of the investor’s problem has earned him the nickname “the Oracle of Omaha.” Economists, however, have struggled to develop a comprehensive model that reliably does the same.
A method called “fundamental analysis,” pioneered by Buffett’s business school mentor, uses accounting metrics to identify which stocks are likely to rise in value (part one of the investor’s problem). Another method, “portfolio optimization,” which won its creator the Nobel Prize for Economics in 1990, uses math to specify how investors can allocate money across a set of stocks to simultaneously minimize risk and maximize return (part two).
But with each tool only addressing half of the investor’s problem, this leaves investors without an end-to-end method for building their investment portfolios.
Kellogg’s Matthew Lyle, an associate professor of accounting, and Teri Yohn, a visiting professor of accounting, wanted to know if there was, in fact, a way to combine fundamental analysis and portfolio optimization. No investing method is perfect—but if a method could cover both parts of the investor’s problem, would that generate portfolios that outperform fundamental analysis or portfolio optimization alone?
A strategy that successfully brought the two processes together to improve investors’ returns would mark a significant breakthrough, says Lyle. “What we were proposing, and what we wanted to test, is whether you could build a single model that handles both steps of the investment process,” Lyle says.
The mathematical foundations of both fundamental analysis and portfolio theory, according to Lyle, are solid. The trouble lies in what each of them leaves out.
Fundamental analysis, sometimes called “value investing,” is the same technique that Warren Buffett uses to choose stocks, and it sounds simple enough: evaluate the so-called “fundamentals” of a business, and invest in companies with relatively low stock prices and sound fundamentals. (“Fundamentals” is a term that encompasses all of a firm’s financial nuts and bolts—its revenues and earnings, capital assets and liabilities, and profitability ratios.)
This method of assessing and ranking the intrinsic values of stocks is no secret. A large body of research shows that it can reliably predict a firm’s future financial performance.
“Fundamental analysis gives signals about which stocks we should hold and which stocks we should avoid,” Lyle says, “but then what do you do with this information?” For instance, an investor could simply invest everything she has in the top-ranked stock.
“In order for portfolio optimization to actually optimize something, it has to be able to take inputs that it understands.”
However, common sense suggests that it’s risky to put all of one’s eggs into one basket. “And so you say, ‘Well, maybe I’ll just pick the top two stocks. Or the top three,’” Lyle continues. “But the question is: Where do you stop? How do you actually allocate your money across a portfolio that makes sense for the amount of risk you’re willing to accept?”
Fundamental analysis offers no answers to this practical question. Portfolio optimization, on the other hand, does.
In modern portfolio optimization, an investor uses a mathematical program called “mean variance” to define a quantitative sweet spot between risk and expected return across all the stocks in her portfolio. This mean-variance optimization, in theory, tells her how much to invest in each stock in her portfolio in order to minimize risk and maximize return.
“It feels like it should work, because it’s very intuitive,” says Lyle of the Nobel Prize–winning theory.
Unfortunately, “theory” is as good as portfolio optimization gets. “Most of the empirical research shows that it generates poor results,” Lyle explains. The reason: portfolio optimization says nothing about what stocks to put into the portfolio in the first place.
“It turns out if you put garbage in, you get garbage out,” says Lyle.
In addressing the investor’s problem, fundamental analysis and portfolio optimization would seem like perfect companions. But mathematically speaking, combining these two tools has been like trying to put a square peg in a round hole.
“One of the reasons it has been hard to establish a link,” explains Lyle, “is that in order for portfolio optimization to actually optimize something, it has to be able to take inputs that it understands.” Unfortunately, fundamental analysis and portfolio optimization have not historically spoken the same mathematical language.
Lyle and Yohn, however, noticed that some recent technical innovations in fundamental analysis allowed it to generate values that portfolio optimization could understand as inputs. Now what was needed was someone to connect the two tools, and to run new empirical tests to see how well the hybrid technique actually worked—which Lyle and Yohn decided to do.
Lyle and Yohn tested the new, combined model on twenty years’ worth of stock-market data between 1996 and 2016.
“The idea was to mimic an investor who knew everything we knew and wanted to set up a portfolio,” Lyle says in explaining why they used historical data. “You basically go out and look at your fundamentals, press ‘run’ on the portfolio optimizer, and out would pop how much you should hold of each stock. We then ‘buy’ that amount of each stock, and we see how the portfolio does in the future.”
The timeframe was chosen because it occurred after much of the research on fundamental analysis had been published—meaning that, in theory, investors would have already been aware that it was useful to identify stocks based on their fundamentals. (By contrast, testing their model on stock market data from, say, the early 20th century—when prevalent investment strategies were far less well-known—would have felt like “cheating.”)
The researchers’ model yielded a portfolio that included an average of 174 shares per month, spread out over a small number of companies. (The exact number varied day to day, since they were constantly buying and selling according to what the model dictated.)
“The gains are actually there. So we need to think of them as not independent tools, but as a natural chain.”
To measure the portfolio’s performance, Lyle and Yohn used a handful of financial metrics and investment benchmarks, such as a Sharpe ratio, which quantifies risk versus return, and an information ratio, which captures how much better or worse a portfolio performs compared to the overall stock market.
By both of these metrics (and others) their investing model excelled. When Lyle and Yohn measured the performance of their portfolio over both a five- and a twenty-year timeframe, they found that combining fundamental analysis and portfolio optimization resulted in “significantly higher” Sharpe and Information ratios than using either strategy on its own.
In essence, the researchers’ model was successfully “solving” the entire investor’s problem.
The study breaks new ground by proving that these two investing methods, long seen as independent, can actually be combined—and that combining them indeed yields substantial returns.
“The gains are actually there,” says Lyle. “So we need to think of them as not independent tools, but as a natural chain.”
Lyle and Yohn are optimistic that their work could inspire other researchers to take a fresh look at the investor’s problem. “We’re kind of the first ones to do a large study on this,” says Lyle. “The fact that we do find improvement has a lot of potential for future research, because how to construct portfolios is a big and important question.”
The authors also suspect that major investors like hedge funds may want to begin experimenting with this combined technique, and that it could be adopted more widely down the road. “It might be a lofty hope, but I hope [our work] starts to make its way into more mainstream financial asset management,” says Lyle.