00. Calculations

Annualising

Annualised Equivalent Yield

Let $r_n$ be the holding period return over an $n$-day period, i.e.

$$r_n=\frac{P_{\text{end}}-P_{\text{begin}}}{P_{\text{begin}}}$$

The equivalent annual yield (EAY) is the annually compounded rate that produces the same return:

$$\text{EAY}={\left(1+r_n\right)}^{365/n}-1$$

The exponent $365/n$ counts how many $n$-day periods fit in a year, so compounding $r_n$ that many times gives the annualised figure.

Example: A Treasury bill with face value \100{,}000$and182-daymaturitytradesat$$98{,}000$. Then

$$r_{182}=\frac{100,000-98,000}{98,000}=\frac{2}{98}\approx 2.0408\%$$ $$\text{EAY}={\left(1+\frac{2}{98}\right)}^{365/182}-1={\left(\frac{100}{98}\right)}^{365/182}-1\approx 4.16\%$$

Return

For something bought at $P_0$ and sold for $P_1$, the return is $=\frac{P_1}{P_0}$