Help - Fixed Income

If I am to hold a zero coupon, government bond for a year, which option has less interest rate risk? A 20 year bond or a 10 year?

I’ve tried modeling it out, and I am confident that the 10 year bond has less interest rate risk should one hold said bond for its entirety. I am less confident in which bond has less interest rate risk if solely holding for a year. I want to think it is still the 10 year, but an extremely large hypothetical fluctuation in said year makes me think the 20 year would experience less variance in price.

What am I missing? Am I overthinking this after an extremely long work week? Probably shouldn’t try to study for the CFA when gassed.

Thanks.

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