Why do short term bonds have higher yield volatility but lower price volatility?

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Price volatility is related to duration. A 100 bp rise in interest rates can cause a 1-year bond’s price to fall 1%, while a 10-year bond’s price will fall 10% with that same interest rate change. Long-term rates tend to stay closer to long-term averages, since rates over long periods don’t typically change that much (beginning and end). The Fed raising rates 75 bps will typically add 75 bps to short-term bond yields, while a 30-year bond yield is likely to rise less. The short end of the yield curve is more sensitive to Fed interest rate changes.