Bond yield

CFA Level I
#1

Government bonds are instruments that pay nominal amount money (100 euros) at a certain point in time in the future (the time to maturity). About these bonds the following is known:

  • A bond maturing one year from now costs today 95 euros.
  • A bond maturing two years from costs today 92 euros.
  • A bond maturing 3 years from now costs today 89 euros.

Based on these facts find the yield to maturity for each of the three bonds. (This quantity equals to the Internal Rate of Return of the bond on the yearly level). In performing calculations assume that the compounding is annual.

How would you solve that? I have calculated for each year separately the IRR: 1Y 100/95; 2Y IRR2 100/92; IIR3 100/89.

#2

You’re partway there.

FV = PV* (1+i)n

i = (FV/PV)1/n - 1

FV=100

#3

We’re assuming that these are zero coupon bonds, yes?

#4

Yes, Dad.

#5

So here I need to first calculate the interest rate: (100/95)1-1; (100/92)1/2-1;…

Then for each year 95*(1+i); 92*(1+i)2 and so on…

#6

Yes, you have calculated what are called spot rates (5.26%, 4.26%, 3.96%). If I invest at the given n-year spot rate for n years compounded, the purchase price accumulates to the FV of 100.