As investors buy long-dated Treasuries after a historic slide that saw the price of some issues fall by half, some traders are using esoteric “bond math” to justify big contrarian bets.

Their reasoning goes like this: At current yields, rather than holding a 10- or 30-year Treasury note to maturity, traders who want to profit from fluctuations in the price of underlying bonds can theoretically stand to gain more from a rally than to lose if it does prices continue to fall.

Asymmetric returns

In a post following a Bloomberg News report earlier this week, Rich Falk-Wallace, CEO and founder of Arcana and former portfolio manager at Citadel, explained how the relationship between bond yields and bond prices leads to the prospect of “asymmetric” returns.

This means that investors benefit more from a 50 basis point decline in yields than they would lose from a 50 basis point increase. Bond yields move in the opposite direction to prices.

In a spreadsheet shared with MarketWatch, Falk-Wallace calculated what those theoretical returns could be for a 30-year bond with a 5% coupon.

According to his calculations, a 50 basis point drop in the yield on such a government bond would result in a total return of 13%, whereas investors would face a loss of 2.6% if the reverse were to happen.


According to FactSet, the most recently issued 30-year Treasury bond, known as the “on the run” Treasury bond because it typically trades more heavily than older issues, has a coupon rate of 4.125%.

Of course, charts like Falk-Wallace’s have sparked debate on social media platforms like X, formerly known as Twitter, where some have argued that calculating returns in this way doesn’t tell the whole story.

Andy Constan, founder of Damped Spring Advisors and a veteran of hedge funds including Bridgewater Associates, said returns appear less attractive when you consider the “opportunity cost” of holding a one-year Treasury bill with a 5.4% yield.

Adjust for the fact that bond investors can earn a 5.4% return over a 12-month period while being protected from price fluctuations – since they theoretically plan to hold the bond until maturity – and the asymmetry disappears.

Constan did not respond to a request for comment from MarketWatch.

Falk-Wallace acknowledged that Costan has a valid point. But for traders betting on bonds with an exchange-traded fund like the iShares 20+ Year Treasury Bond ETF TLT (or perhaps even using leverage via options or Treasury futures), the absolute return in dollar terms is likely more important.

Of course, such a bond market theory has little influence on where prices ultimately go. Many other factors, including inflation expectations, underlying U.S. economic data, concerns about rising U.S. debt and signs that investors are demanding a higher term premium, are having a much larger impact on prices, analysts say. And just because something looks cheap doesn’t mean it can’t get cheaper.

“This has nothing to do with the price of a bond,” Falk-Wallace said. “That is the question for those making a directional bet. Rather, it is a description of possible outcomes.”

Two key concepts to keep in mind

The calculation of these potential returns is based on two concepts that investors use to quantify and describe the relationship between a bond’s return and price. This is where things start to get complicated.

The first of these concepts is known as duration and can be described as the change in a bond’s price for every one percentage point change in yield. The concept of duration can be used to approximate the change in bond prices quite accurately.

However, this does not take into account that a bond’s price sensitivity also changes as yields rise and fall. This is where the concept of convexity comes into play. It recognizes that the distribution of potential returns is curved rather than linear, opening up the prospect of asymmetric returns. Falk-Wallace illustrated this concept in the following table.


Treasury yields have been rising for months, causing prices to fall. But recently there have been signs that the selloff may soon be over. For example, according to FactSet data, TLT saw inflows of more than $900 million in September – the largest monthly inflow of the entire year.

A recent Bank of America fund manager survey found that 56% of respondents expected bond yields to be lower a year from now.

Strategists at UBS Group and Goldman Sachs Group recently said they expect government bond yields to be either near or at their cycle highs and to fall soon.

“…[W]With risk asset valuations broadly in line with this macroeconomic view and interest rates having risen to cyclical highs, we believe near-term risks to sector diversification and bond yields are tilted to the downside, particularly given the possibility that incoming economic data will fall short of expectations or appear completely weak,” a team of fixed income strategists at Goldman Sachs Asset Management said in a recent note detailing their outlook for the fourth quarter.

On the other hand, investors have recently shown some reluctance to bond auctions, which some analysts described as a potentially worrying development. On Thursday, Treasury traders bought an above-average amount of $20 billion in 30-year Treasury bonds, triggering a selloff in Treasurys that also helped drive down stock prices.

Treasury yields were back near their highest level in 16 years on Tuesday, as the selloff continued after a brief respite last week. The 10-year yield BX:TMUBMUSD10Y rose 14.5 basis points to 4.853%, while the 30-year bond yield BX:TMUBMUSD30Y rose 8.6 basis points to 4.949%.

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