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

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