Practical analysis for investment professionals
11 June 2012

Negative Nominal Debt Yields: How Low Can Yields Go?

Posted In: Fixed Income

Fixed-income markets are awash in news of the increasing number of sovereign debt issues coming to market with negative nominal yields. The question is how low can yields go?

In order to help answer the question we created a spreadsheet that helps to demonstrate and evaluate the strategy behind purchasing a negative nominal yield debt instrument. (Feel free to download and play with the spreadsheet. Please see the instructions for use in the postscript.) Take the recently priced two-year maturity −0.12% German Schatz. On the surface, purchasing this instrument seems very peculiar and raises the question, “Why would anyone purchase a negative nominal yield bond?” After all, to purchase such a bond effectively means that you are paying the issuer to safeguard your capital until maturity. Why not just convert your money to cash and stash it in a safe-deposit box instead?

Yet when we look at the spreadsheet, we can see that a compelling argument, not unique to the fixed-income world (see below), can be made for purchasing negative nominal yield securities. This is due to the possibility of interest rates going even lower/capital gains rising even higher. Obviously, this is a greater fool/musical chairs game. The game nears its end with the relentless march toward maturity when the music finally stops. But, up until the very last trading day prior to maturity, there is still the possibility of making money in a negative nominal yield bond if the change in market yields (i.e., they still go negative further) compensates you for your cost of capital.

Of course, what this means is that the income component of investing in sovereign fixed income is now almost meaningless; what really matters is the gamble on the shape of the future yield curve and the credit quality of the issuer. If you can accurately forecast the future yield curve — and in the United States, the Federal Reserve now telegraphs its intentions — you can still make money in a negative nominal yield world. You just have to hope that the rates keep getting lower after you have purchased your bond.

While this is a whole new world in the fixed-income space, effectively this strategy is no different than U.S. equity investors who from September 1965 to December 2007, on average, purchased stocks with negative equity risk premiums (−0.91%; source: CFA Institute). Put another way, earnings yields (the inverse of the P/E ratio) relative to sovereign debt yields were persistently negative. Interpretation: Earnings yields didn’t matter; what mattered were capital gains. Sound familiar? That is, equity investors’ only hope for outperforming sovereign debt was if prices would be higher, net of transaction costs, at some point after they bought their stocks. As we know that assumption persisted intermittently for more than 42 years. Could the bond market stay in a negative yield situation for 42 years? Who knows, but these are indeed strange times.

One final point about the risk of investing in a negative nominal yield security: In the equity arena maturities are perpetual, but in the fixed-income space maturities are certain and fixed. This makes “investing” in negative nominal debt yields a potentially more dangerous activity, because the music will play for only so long.

Using the Spreadsheet

Bonds: How Capital Gains Change with Interest Rate Changes, GP (Click to download)

Click here to download the spreadsheet: Bonds: How Capital Gains Change with Interest Rate Changes, GP

Instructions for using spreadsheet:

  • Cells shaded in yellow are for inputting data.
  • Inputs are in two sections: upper section, or bond details; and lower section, or scenario details.
  • For the bond details section you will need to provide the:
    • Par value of the debt instrument
    • Nominal interest rate
    • Number of payments per year
    • Maturity in years
  • For the scenario details section you will need to provide the:
    • Number of periods into the future you want to examine
    • Your interest rate assumption for that future period

Note: the graph clearly demonstrates the duration and convexity of a bond issue given changes in both time to maturity and interest rates. This feature of the spreadsheet alone is instructive.

Robert Gowen, CFA, Dave Larrabee, CFA, and Ron Rimkus, CFA, contributed to this article.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

Business chart illustration from Shutterstock.


About the Author(s)
Jason Voss, CFA

Jason Voss, CFA, tirelessly focuses on improving the ability of investors to better serve end clients. He is the author of the Foreword Reviews Business Book of the Year Finalist, The Intuitive Investor and the CEO of Active Investment Management (AIM) Consulting. Voss also sub-contracts for the well known firm, Focus Consulting Group. Previously, he was a portfolio manager at Davis Selected Advisers, L.P., where he co-managed the Davis Appreciation and Income Fund to noteworthy returns. Voss holds a BA in economics and an MBA in finance and accounting from the University of Colorado.

Ethics Statement

My statement of ethics is very simple, really: I treat others as I would like to be treated. In my opinion, all systems of ethics distill to this simple statement. If you believe I have deviated from this standard, I would love to hear from you: [email protected]

15 thoughts on “Negative Nominal Debt Yields: How Low Can Yields Go?”

  1. Amit M Kadam says:


  2. Tim Richmond says:

    Thanks for the spreadsheet and the instructions on how to use it.

  3. Shiv Desai, CFA says:


    You are right to point out that the bond with negative yield will earn capital gains if the interest rate decreases further (required yield turning more negative). But isn’t it that the capital gains (present value of the cash of $1000 to be spent after two years) from holding the cash will always outperform investment into negative return yielding bonds?

    My view also matches with macroeconomics view that the central banks runs out of tools in deflation as it can’t lower nominal rates less than 0%.

    According to my working*, outperformance of holding cash rather than investing in bond yielding -0.12% ranges from $0.57 to $2.73 depending upon after how many periods, the interest changes. I have expected the future changes in interest rates to be -10% and +10% (range mentioned in the original worksheet).

    So, I think that ignoring the future capital gains from appreciated exchange rate, the bonds will not have negative yield. Currently, investors expect that Germany’s currency will appreciate significantly in the event Euro Zone falling apart. This may be the reason that investors are willing to purchase negative yielding bonds issued by Germany.

    Please help me with this and provide me your email id so that I can share my working with you.

    * I am assuming no cost of holding cash for two years and I have calculated the present value of $1000 using required yield. No intermediate cash-flow is considered.

    1. Hi Shiv,

      Current levels of negative market yields seem to suggest that you are correct in your belief that the difference between negative returns and positive returns are differences in currencies. In fact, a well known market commentator has said that the negative yields are the cost of a call option on an appreciating currency after a breakup in the Euro.

      My own opinion is that whatever the cause of the negative nominal yields, there are rational reasons to buy the instruments having nothing to do with collecting the coupon. For each investors there is probably a unique story.

      With smiles,

      Jason A. Voss, CFA

  4. Shiv Desai, CFA says:


    In order to profit from the cash as mentioned in the alternative I provided to investing in negative yielding bond, we need to borrow at the prevailing interest rate for the same maturity as of the bond. In this case, if we are willing to pay a bullet payment of $1000, at the end of inital 2 years then, we will be able to borrow more money then the capital gain earned on investing in mentioned bonds.

  5. Volunter says:

    Can you please explain (using PV=, PMT=, i= etc.), how did you get $1025.03?

    1. Hello Volunter,

      From where did I get the $1,025.03 figure?

      It is the sum of the par value of the bond, 1,000, plus the capital gains achieved when interest rates fall to -5.0%, or 25.03. The calculation makes use of Microsoft Excel’s “PV” function. Here are the inputs:

      * rate = annual interest rate (-5.0%) divided by number of payments per year (2)

      * nper = number of total payments for the life of the bond (4) – how many periods in the future you wish to run your scenario (3)

      * pmt = the value of one payment for the bond (-0.60)

      * fv = the par value of the bond (1,000)

      * type = 0 (interest payments are made at the end of the period, not at the beginning

      I hope that helps.

      With smiles,


  6. Tong Foo Cheong says:

    If the only reason for buying negative nominal yield securities is the possibility of capital gains i.e. interest rate play, it may be better to buy Bunds which offer positive nominal yields, sovereign credit risk and better liquidity.

    1. Hello Foo Cheong,

      Thank you for your comment and for reading The Enterprising Investor. I think the other reason for investing in sovereign debt securities (beside the possibility of capital gains) is preservation of capital. It is my opinion, however, that this is a dangerous gamble.

      With smiles!


  7. Nathan Evans says:

    A far more relevant effect than speculation on future rate moves is the very real securities lending return to High Quality Liquid Assets. All the 2yr Schatz out there are NOT held by those speculating rates will go lower. All the insurances, pension funds, etc that need to hold these assets as part of a diversified portfolio have lending programs. Especially the CTDs deliverable into the 2, 5 and 10yr futures contracts have “repo value”. Buy, hold, lend on a fully collateralised basis and I can that negatively yielding 2yr paper then has a positive total return even in a non-changing interest rate environment.

    1. Hi Nathan,

      Thank you for pointing out that wrinkle/nuance – much appreciated to help contextualize the dialogue best.

      Yours, in service,


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