Hi
@filip313 that's interesting. To me the author's inaccuracy is to refer to the 2% and 5% as yields. Following Hull or Tuckman, we should call them spot rates or zero rates. It's true we see this {2% at 2 years, 5% at 5 years) called a yield curve, but it's really a spot rate curve. If the 2-year spot rate is 2.0%, then I agree with you that we discount a 2-year-forward cash flow--let's just say it is a $5.00 coupon to be received in 2.0 years--if the 2 year spot rate is 2.0% with annual compound frequency, to its present value with $5.0/(1+0.020)^2 = $4.806. It's similarly true that $1.00 today grows to $1.0 * (1 + 0.020)^2 = $1.0404 at the end of two years. Now, this is rarely discussed (and does not appear in the FRM) but the 1.0404 can be called a
future value factor which is the "cousin" of the more familiar discount factor; the discount factor is the reciprocal of this future value factor because the discount factor (df) = $1.00/(1+0.020)^2 or (1+0.020)^-2 and it represents the present value of $1.00 received at the end of two years if discounted at 2.0% per annum with annual compounding.
There is an old saying that "discount factors don't lie" and it could be said of future value factors, too. The article assume, really, a spot (or zero) rate curve of 2.0% @ 2 years and 5.0% @ 5.0 years, and it is helpful to understand why these are
stated or nominal
spot rates, they are stated because they don't specify the compound frequency. But the 2-year discount factor of 0.9612 (and its cousin the 1.0404 future value factor) improve on the spot rates by incorporating the compound frequency. So this spot rate curve could also be represented by a discount function (i.e., set of discount factors): 0.9612 at 2 years and 0.7835 at 5 years. Getting to your point (maybe?), it would be atypical, but it could also be represented by a future value function: 1.0404 at 2 years and 1.2763. I hope that helps!
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