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I tried to search for this specific question, although I didn’t found a conclusive answer. I have a dataset containing the yields of several T-Bills and T-Notes that were downloaded from a Bloomberg Terminal using the function px_last. In order to achieve the actual prices of such securities how I should set up the formula?

  1. $P=\frac{FV}{\left(1 + \frac{px_{last}}{100}\right)^{\frac{m}{12}}}$
  2. $P=FV \times \left(1 - \left(\frac{px_{last}}{100} \right)^{\frac{m}{12}}\right)$

where $m$ are the months up to maturity.

Then if I need to calculate daily returns, I would kindly ask you if it is correct to use a formula:

$$ \begin{aligned} R =& \left(1+\frac{px_{last}.shift(1)}{100}\right)^{\frac{1}{365}} - 1 \times \frac{\partial P}{\partial px_{last}} \times \frac{px_{last} - px_{last}.shift(1)}{100} \\ &+ 0.5 \times \frac{\partial^2 P}{\partial px_{last}^2} \times \left( \frac{px_{last} - px_{last}.shift(1)}{100} \right)^2 \end{aligned} $$

or simply

$$R=\frac{P_{t+1}-P_t}{P_t}$$

where: $P$ represent the price formula, $px_{last}.shift(1)$ is intended as the yield of the previous day

Thank you in advance,

A

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    $\begingroup$ (1) Bloomberg can give you the price directly, no need for you to calculate. (2) Your formulas don't comply with industry standards for T-bill calculations. $\endgroup$ – Alex C Dec 19 '19 at 15:04
  • $\begingroup$ (3) The formula $R=(P_{t+1}-P_t)/P_t$ is the best way to calculate return. The other is (a) an approximation (b) requires additional complicated calculations to find the two derivatives, Duration and Convexity. $\endgroup$ – Alex C Dec 19 '19 at 16:39

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