Negative interest rates wreak havoc with finance textbooks

Prof. Jayanth R. Varma's Financial Markets Blog

By assuming non negative interest rates, finance textbooks arrive at many results that are false in a negative rates world. Finance theory does not rule out negative rates – theory requires only bond prices to be non negative, and this only prevents interest rates from dropping below −100%. In practice also, early 2015 saw interest rates go negative in many countries. The BIS 2015 Annual Report (Graph II.6, page 32) shows negative ten-year yields in Switzerland, and negative five year yields in Germany, France, Denmark and Sweden in April 2015.

Let us take a look at how many textbook results are no longer valid in this world:

  • The formula for the present value of a perpetuity PV=1/r yields the absurd result that the present value is negative when r is negative. In fact, the present value is infinite (the geometric series diverges for negative r).

  • Interestingly, the formula for…

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