How to calculate daily log return of T-bill, using treasury yield curve rates?

Question

I am trying to calculate daily log return of T-bill and T-note (3-month, 5-year, and 10-year) in excel. At first, I thought that just by dividing a treasury yield curve rate at time t by that at time t-1 would lead to the answer, but after seeing its standard deviation higher than other assets, I figured out that something is wrong. I googled a solution to it and one says unlike stock return, use ln(1 + r) and this is the solution. I am not sure if this is correct or not. It would be great if you could clarify this. Thank you.

Answer 1

Hi Makoto,

Calculating Daily Log Returns for Treasury Securities

This document provides a guide on how to calculate the daily logarithmic (log) returns for

Treasury bills (T-bills) and Treasury notes (T-notes) using treasury yield curve rates. The

method involves using the natural logarithm to account for the continuous compounding of

returns.

Instructions

Step 1: Input Data

Ensure that you have the daily yield data for the respective Treasury securities (such as 3-

month, 5-year, and 10-year T-bills and T-notes) ready for use in Excel.

Step 2: Calculate Daily Log Return

For each day, use the following formula to calculate the daily log return:

Daily Log Return ≈ ln(1 + Yield at t) - ln(1 + Yield at t-1)

In Excel, if today's yield is in cell B2 and yesterday's yield is in cell B1, the formula will be:

=LN(1 + B2) - LN(1 + B1)

Step 3: Drag Formula

Drag the formula down across all your data points to compute the daily log returns for the

entire data series.

Further Analysis

Once you have calculated the daily log returns, you can perform further statistical analysis,

such as calculating the standard deviation, to understand the volatility and other

characteristics of these Treasury securities.