# Why are the yields on short-term bonds more volatile than those of long-term bonds?

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

I believe because of what we call duration prices of long terms bonds are more volatile. But what does yield volatility mean here?

I believe "yield volatility" here means the realized variance in the interest rate. Generally speaking, we think that the price of a bond will be the NPV of its cash flows: $$p = \sum_{\tau = 0} ^ {T} \frac{C}{\Pi_{s = 0} ^ {\tau} (1+r_s)} + \frac{FaceAmount}{\Pi_{s = 0} ^ {T} (1+r_s)}$$ If we can assume that interest rates are constant, then this simplifies: $$p = \sum_{\tau = 0} ^ {T} \frac{C}{(1+r)^\tau} + \frac{FaceAmount}{(1+r)^T}$$
For a long term bond, T will be large and the discount factor of the later cashflows will be something like $$(1+r)^10$$ or $$(1+r)^30$$ That means that a small difference in r will be amplified many many times by the exponentiation, leading to the price being very sensitive to $$r$$, especially compared to a short-term bond where we might have the largest terms of $$(1+r)^{1/12}$$, $$(1+r)^{1/4}$$, or $$(1+r)^{1/2}$$. The math is more complex if interest rates change, but the idea is similar.