Since nominal yields going out 6 years or more are currently negative in several developed markets in Europe, many investors have been asking if investing in bonds with negative yields means they are “locking in” a loss. It is a very good question, and our response may be surprising to some. The simple answer is no. Why? Because we can’t forget to add currency into the equation.

Let me expand on this. Comparing U.S. Treasury yields to, say, German Bund yields is like comparing apples to oranges—both are a round fruit, but there are important differences between the two. A yield on a foreign bond always carries with it the currency effects accruing to the home-based investor. This is where we need to bring in the financial math: The currency effect should offset the yield differential between the domestic and the international bond. This is why in the chart below the U.S. yield-maturity curve (purple line) lies virtually on top of the German curve with the expected currency return (green line) over the life of the bond.

Where does this currency return come from? Basically, from the currency hedging. Technically, the hedge return arises from the current and expected short-term interest rates (1- or 3-month yields, depending on the hedge contract). When you add these hedge returns to each Bund yield, the resulting expected return is almost exactly equal to the corresponding U.S. Treasury yield.

Davis_Neg_Yield_042015

While expected currency returns depend on what markets are pricing in ex ante, that relationship may not hold ex post since currency and bond markets fluctuate and no one can predict exactly how they may drift from the ex ante equilibrium. These duration and currency risks should be similar for both domestic and international bonds, and they could go either way, positive or negative, which is why I believe that global diversification in an investor’s bond portfolio is important.

Keep in mind that, in this scenario, German investors would be locking in a loss because the negative yield is in their local market. Even if they try to avoid the local negative yield by investing in U.S. Treasuries, for example, the currency effect, or hedge return, would pull them back to parity with the local bonds.

In either situation, the logic holds. Regardless of negative yields, when doing the right financial math, an investor should be indifferent between local and foreign bonds. Don’t just compare yields, and keep in mind that the hedge return will bring you back to parity.

I’d like to thank Matthew Christopher Tufano of Vanguard Investment Strategy Group for his invaluable contributions to this blog.