What 3 Month US Treasury Data to use when graphing a risk vs reward scatter plot over 5 years?

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What 3 Month US Treasury Data to use when graphing a risk vs reward scatter plot over 5 years?

edited

Visualization Risk Model

I am making a risk/return scatter plot (seen here from this site).

What data must be used for bonds (e.g. 3 month or 10 year US bonds)? I thought you would use this data, but if you take the years 2013-2018, then the price rose from $0.01 to $2.29, or a 229x growth. This is clearly incorrect for a 3 month bond, seeing as that it is basically the equivalent of cash. My understanding says that the 3 month bond should be at the bottom left of a scatter plot (low risk and low return). If this is the case, what data should be used for the 90 day treasury return?

Edit: this site verifies that the "US Treasury Short" should be at the lower left.

3 responses

You cannot compute returns directly on interest rates, that's not logical. 90-day US rate is the underlying rate of a 90-day bill. Thus the risk associated with such a rate is the relative price evolution of the fixed income instrument, i.e. you have to use the duration of the instrument to approximate its price change. Given a 3 month bill:

deltaP = -D*detaY

For example if the yield increased from 0.01 to 2.29%, let say the duration is 0.25 and the initial price $100, the price change would be approximately:

-0.25 * 2.28% = -0.0057

However, this is an approximation because with this approach, you linearise the yield-price relationship of FI securities, while it is quadratic in reality. If you want to properly compute deltaP, you need to use convexity.

for further explanations:
https://analystprep.com/cfa-level-1-exam/fixed-income/percentage-price-change-bond-duration-convexity/

This makes sense. Thank you.

Get yield data from the St Louis Fed and construct your time series from that. ```
St Louis Fed

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.

In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.