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We have been seeing negative bond yields in Switzerland and Germany. Which is very odd if you ask me. The question begs to be asked: "How low can negative yields go?".

To give an answer to this you need to have an understanding of the price-yield curve of bonds. You can gain money if yields go lower (bond price rises), but you will lose money because you need to pay interest on the negative yield. So there should be an equilibrium point and as a scientist I very much want to find that equilibrium point.

There is a very nice online tool for the price-yield curve here.

Inputs for this tool are:

  1. Years to maturity (if you buy a new 2 year bond it has 2 years to maturity)

  2. Annual Coupon payment (the amount of cash you get per annum)

  3. Yield (the annual percentage cash you get on the principal)

Let's analyze the Swiss government bonds: (Click to enlarge)

Chart 1: 2 year Swiss Government Bonds

Let's say you buy a 2 year Swiss government bond right now with a value of 100 Swiss francs.

Let's take a look at the incurred losses. You will have to pay 0.43% annually, because the yield is -0.43% (Chart 1). So annually you need to pay 0.43 Swiss franc. After 2 years, you will have paid 0.86 Swiss franc, which is a loss of 0.86% on your investment.

Next, let's take a look at the possible gains. Chart 2 gives the price yield curve for 2 year Swiss government bonds at -0.43% yield as calculated by the price-yield equation on the Wolfram site. (Click to enlarge)

Chart 2: Price - Yield curve: 2 year Swiss Government Bonds (-0.43% yield)

Chart 3: Price-Yield curve: 2 year Swiss Government Bonds (-0.43% yield)

Let's extrapolate this curve and add some numbers to the axis (Chart 3).

You can see that our 100 Swiss franc is located on the -0.43% yield on the X-axis (Chart 3: Star pattern). If yields were to go to -0,92% in the short-term, then you would gain 1% on your bonds. The price of your bond would be 101 Swiss franc. So after 2 years you would have gained 1% in bond price, but you lost 1% on interest payments. Basically, if the bond yield goes lower than -0.92%, you win money (if you sell the bond soon enough). Of course, everything depends on when you sell your bond into the market, this is just an approximate calculation to give an idea of the valuation of the bond.

Conclusion:

2 year Swiss government bonds can be bought with a profit, if yields were to go below -0.92% in the near-term. I think there could be a chance that Swiss government bonds will go below -0.92%, so investors can try buying the 2 year Swiss government bonds. If the yield doesn't go below -0.92%, you are bound to lose money in the Swiss franc.

The same calculation can be made for all other bonds.

Source: How Low Can Negative Yields On 2 Year Swiss Government Bonds Go?