The purpose of holding a portion of one’s wealth in bonds, as opposed to money, is to make a positive return from the bond’s interest payments. Bondholders don’t simply want to break even—they want to gain something from making an investment. When investors purchase bonds, they are forgoing their ability to hold money in the present, which means that they’re unable to make purchases or engage in economic transactions. Breaking even implies that the bondholder would have been just as well off had they held their wealth in money—in fact, it implies that they may have been better off because they could have made purchases (as opposed to forgoing purchases). With that being said, it’s still important to understand—in mathematical terms—what it means for a bondholder to break even.
We begin with the concepts of risk and expected value. Because there is always a possibility of default, investors want to be compensated for this added risk—compensation that goes beyond the ordinary interest payments. We call this compensation the risk premium, and we denote it with the variable x. Furthermore, if ρ equals the probability of default, then 1- ρ equals the probability of not defaulting—i.e., the borrower pays back the entirety of the bond’s principal and interest payments. Therefore, the expected value of a bondholder breaking even is:
1+i=(1-p)(1+i+x)+p(0),
where (1 + i + x) is the bondholder’s outcome should the borrower not default. Because the outcome of a default is simply zero (the bondholder loses all their money), this equation simplifies to
1+i=(1-p)(1+i+x).
This equation implies that a bondholder is indifferent to holding a riskless bond (left-hand side) compared with a riskier bond but that includes a risk premium, x (right-hand side). Rearranging this equation, we arrive at the value of the risk premium of a break even situation:
x=(1+i)p/(1-p)
In recent news, Portugal’s 10-year bond yield fell below zero as of November 2020. More simply, the return (or face value) of Portugal’s 10-year bond is now less than the price paid for it. According to the Financial Times article (Stubbington 2020) the reason for Portugal’s negative bond yield are largely due to the Covid-19 Pandemic. Stubbington states, “[Portugal’s] expecting output to shrink 8.8 per cent in 2020,” and, “will raise Portuguese public debt to 136 per cent of output by the end of the year.” Portugal increased government borrowing to fund their pandemic response, like most countries did during these unprecedented times. In response the European Central Bank (ECB) expanded its €1.35 trillion emergency bond “buy-back” program.
What does it mean when bond yields fall negative? According to the “break-even” or “bond-return” equation, the premium paid on a bond (x) is inherently high due to a high probability of default;
x=(1+i)p/(1-p)
The probability of default (p) increases as the risk for holding the bond increases. This risk for holding the bond increases when the credit risk (risk of default associated with the borrower failing to make required payments) and liquidity risk (risk associated with the inability to exit your bond contract) increase. According to the peer-reviewed journal article (Li, Yang, Su, et. al 2021) unlike US-issued bonds, corporate bonds require Risk Compensation. Hence, the risk premium must reflect risk associated with holding a bond. According to the article, these two types of risk are interconnected, so there must be enough incentive (risk premium) to encourage more investment into that bond market. When Portugal increased their debt from borrowing to fund their pandemic protocols, the probability of default increased due to both credit and liquidity risk working together associated with that increased debt. With a higher risk premium (x) associated with a higher probability of default (p), the expected return on a risky asset (like Corporate Bonds) must exceed the known return on a “risk-free” bond (usually Government issued Bonds) in order to induce investors to hold the risky asset rather than the risk-free asset.
However, what the peer-reviewed journal article from JP Morgan (Dryden 2019) points out is how negative-yield bonds are financially and economically nonsensical. This is because a logical bond investor would not buy a bond with the expectation to lose money off their investment. A purchaser of a negative-yield bond would always guarantee themselves a loss. Negative-Yield bonds occur when bonds are issued with a zero (or just above zero) coupon payment, but their selling price is higher than face value (Dryden 2019).
So who would want to buy these kinds of bonds that yield a negative return on investment. Dryden explains how there are two types of consumers of these negative-yield bonds. There are the “Forced Buyers” who are profit agnostic (indifferent of a positive or negative profit when buying a bond) and hold these types of bonds for reasons other than making a profit. Central Banks are a common example of “Forced Buyers” because they buy negative-yield bonds to achieve asset purchase targets (Dryden 2019). Currently the ECB owns 21% of their own government debt. The other type of consumer is “Speculative Investors.” They hold negative-yield bonds hoping that yields will continue to fall further making them a small profit from price appreciation (Dryden 2019). In some scenarios, these speculative investors invest in negative-yield bonds as a means of protection from the government they are paying off (giving profit to), however, this is a very incremental portion of the negative-yield bond market.
Would US bond yields ever fall into the negatives? According to Dryden, it is unlikely for bond yields to fall into the negatives because unlike Japan and the EU, the US relies on their balance sheet to provide additional stimulus rather than cutting interest rates into the negatives and enacting aggressive asset purchasing schemes. However, Dryden stresses the fact that if the FED were to cut interest rates to its record low (0.25%) and restart its bond purchasing programs, bond yields would likely lower (Dryden 2019). He goes on to say, “combined with weak outlooks for the economy and inflation, the resulting forces may be enough to drive Treasury Yields negative.”
Works Cited
Dryden, A. (2019). Entering uncharted waters: Understanding negative bond yields. JP Morgan
Market Insights, 1-5. Retrieved March 25, 2021, from
https://am.jpmorgan.com/blob-gim/1383637630519/83456/MI-MB%20Negative%20Bond
%20Yields.pdf
Li, X., Yang, B., Su, Y., & An, Y. (2021). Pricing corporate bonds with credit risk, liquidity risk,
and their correlation. Discrete Dynamics in Nature and Society, 2021
doi:http://dx.doi.org.ezproxy.plu.edu/10.1155/2021/6681035
Stubbington, T. (2020, Nov 27). Portugal's 10-year bond yield drops below zero: Fixed
income. Financial Times Retrieved from https://ezproxy.plu.edu/login?url=https://www-proquest-com.ezproxy.plu.edu/newspapers/portugals-10-year-bond-yield-drops-below-zero/docview/2472941443/se-2?accountid=2130
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