Talk:Discounting/Archives/2016

Assessment comment
Substituted at 13:29, 29 April 2016 (UTC)

Discount factor
Can anybody give a citation (source) for what is written in section "Discount Factor"? The statement that if the interest rates are taken from a yield curve, the discount factor is $${1 / (1 + rT)}$$ contradicts to what is written in the article on the Yield curve:

"More generally, returns (1+ yield) on a long-term instrument are assumed to equal the geometric mean of the expected returns on a series of short-term instruments: $${\displaystyle (1+i_{lt})^{n}=(1+i_{st}^{{\text{year }}1})(1+i_{st}^{{\text{year }}2})\cdots (1+i_{st}^{{\text{year }}n}),} (1 + i_{lt})^n=(1 + i_{st}^{\text{year }1})(1 + i_{st}^{\text{year }2}) \cdots (1 + i_{st}^{\text{year }n})$$, where ist and ilt are the expected short-term and actual long-term interest rates."

Example: If the yield curve is flat at 2%, shouldn't the market value of any risk-free bond paying a yearly coupon of 2% p.a. whose time-to-maturity is an integer multiple of entire years equal its face value? Now, if future payments were discounted by the discount factor $${1 / (1 + T*0.02)}$$, as stated in the text, this would not be true, as one can easily check.

If $$r$$ is the spot rate p.a. for a $$T$$-year investment, then the $$T$$-year discount factor is, by definition of a spot rate, $$1 / (1+r)^T$$. No? 46.126.111.69 (talk) 21:14, 24 October 2016 (UTC)