# Bloomberg Treasuries PX_Last and daily returns

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

• (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. – Alex C Dec 19 '19 at 16:39