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.

This makes sense. Thank you.

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