There are perhaps few financial instruments more fundamental than bonds. Everyone from corporations to treasuries to municipal governments issues bonds. Those same organizations, along with other participants like central banks, also buy bonds, using those purchases to do everything from propping up flagging economies to balancing out an investment portfolio. Even individuals buy bonds—treasuries, savings bonds, municipal bonds, and so on. The entire modern economy hinges on the smooth transfer of capital from lenders to borrowers, and bonds play a critical role in that.

The smoothness of that process depends largely on whether investors think the rate of return appropriately reflects the bond’s underlying risk. Bonds may be relatively stable assets compared to more volatile ones like stocks—and tend to earn lower returns as a result—but they still face a measure of uncertainty. Understanding that uncertainty is important for a smoothly functioning bond market. Academics have been studying bond yield volatility for decades, and they have developed a widely accepted benchmark that can be directly linked to the cross-section of yields—an economist would say “the volatility is spanned by the yields.” But it turns out that may not be correct, calling into question our understanding of risk in a very important part of our financial markets.

“There are nearly $37 trillion worth of fixed income securities out there that are directly linked to treasury bonds and closely related assets,” says Torben Andersen, a professor of finance at the Kellogg School of Management. Andersen and his colleague Luca Benzoni, a senior economist at the Federal Reserve Bank of Chicago, recently used a trove of high-frequency bond trading data to determine if the long-standing academic model could adequately describe the risk seen in many bonds. It could not.

“When we looked at the structure of the volatilities we extracted from the high-frequency data, they were clearly not spanned or linked to the underlying bond yields in the prescribed fashion,” Andersen says. “They were behaving fundamentally differently.”

A Straightforward Question
Andersen and Benzoni tested the old model by taking asking a very straightforward question: Did the model actually do as it purports to? Can a cross-section of bonds actually span volatility? Though straightforward, the question is not a simple one to answer. In fact, previously, it was thought to be unanswerable. “The reason it hadn’t been tested seriously before is that people were mostly thinking of these volatilities as unobservable,” Andersen says. “How do you test things that are not directly observable?”

Fortunately, Andersen had developed a technique a few years ago for measuring yield volatilities in high-frequency data, something that had been very difficult to do. By applying that metric to a very detailed data set—GovPX, which contains intraday yields and trade data from nearly every major Treasury securities broker—he and Benzoni were able to see that volatility was not, in fact, spanned by yields.

“The way the standard model is actually set up, it’s a relatively linear mapping between the expected returns and certain risks,” Andersen says. “After the volatilities have moved, the yield should also have moved.” And, he adds, yields also should have moved in a consistent manner. “What we find is, to be honest, that this property is badly violated,” Andersen says. “We don’t have to put too much structure on to find out that this doesn’t quite work.”

“There’s this unspanned stochastic volatility feature that turns out to be important for the bond markets, we think.”

With the standard academic model potentially badly broken, Andersen recommends a fix. His advice is to look outside yield cross-sections for information that might better characterize volatility. One such promising area is macroeconomic data that are not already represented in bond yields. These might include inflation not accounted for in yield curves, expectations about monetary policy, or even some knowledge about the global business cycle.

While the standard model is promising, Andersen does not think there is a bulletproof remedy for its problems. “There are some recent papers that purport to do some of this, but I wouldn’t declare success yet,” he notes.

Advice for Portfolio Managers
Though practitioners do not directly use the standard academic model tested in this study, Andersen points out that it serves as a foundation for algorithms that are used by traders. That poses a problem. In a perfect world, practitioners would be able to quickly sell an asset that is dragging down their portfolio, but that is not always possible. Many traders in charge of large holdings, Andersen says, “are going to have a trillion dollars worth of nominal bonds with various maturities. It’s not that easy to get rid of a third of the portfolio.”

To compensate for that lack of agility, traders assess their risk exposure using some variant of the standard academic model and then construct a hedging strategy based on the model’s results. Yet if the algorithms that help traders gauge risk are flawed—as Andersen and Benzoni’s research suggests—then many hedges may not adequately cover a portfolio’s risks.

Until existing models are overhauled to become less reliant on yield spans and incorporate more of the macroeconomic data that Andersen suggests would be useful, traders should be cautious when building a balanced portfolio. Based on his research, Andersen says, “I would warn against using what the model would tell you would be a decent hedge.”


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