# Is return required by a bond investor a function of base interest rate and credit worthiness of the issuer?

The price of a non-zero coupon bond (with dicrete discounting) is found using $$B = \frac{C}{r}\Bigg(1-\frac{1}{(1+r)^n}\Bigg) + \frac{P}{(1+r)^{n}}$$ or for a continuously dicounted version: $$B = C\cdot e^{-r}\Bigg(\frac{1-e^{-r \cdot n}}{1-e^{-r}}\Bigg) + P\cdot e^{-r \cdot n}$$ where $C$ -- coupon payment, $P$ -- face value, $n$ -- number of compounding periods.

Now $r$ depending on the context is called yield to maturity, the return required by investor or base interest rate.

It seems that often an implicit suggestion is made that: $$return \; required \; by \; investor \; = base \; interest \; rate$$

My question is as follows: is above equality true or is yield (or return required by investor) more like $$r (i, c)$$ a function of base interest rate $i$ and credit worthiness $c$?

Yes, in the US, the yield on a bond equals the yield on a US Treasury bond with a similar maturity plus a credit spread reflecting the creditworthiness of the issuer. If the issuer is high quality the spread might be a low number (say 0.50%), and if the issuer is low quality it could be much higher say 2%).

• What if we are pricing the US Treasury bond itself? – A.L. Verminburger Oct 24 '17 at 9:41
• Credit spreads are relative to something. In US market the US Treasury is considered the highest quality issuer, so its spread is 0 by definition. – noob2 Oct 24 '17 at 12:38
• @noob2 I was more interested in the interest rate. If you are pricing a short maturity US treasury bond you can't really use it for the interest rate as well. I would imagine one would use the base rate of the currency (which as I have seen is not always the same as say 1 month treasury yield)? – A.L. Verminburger Oct 24 '17 at 16:44