The normal yield curve is usually drawn concave. Why is this typically the case?
My current understanding is that long term bonds have higher interest rate risk because a higher percentage of its outflows come from coupon payments. For example, a 1 month bill price won't change much for a change in interest rates since its price is dominated by the par value which will be paid back in a month.
Applying the logic to convexity vs. concavity: as time to maturity increases, the percentage of a bond's price which comes from the final par value payout decreases slower and slower. Therefore, the risk premium should increase slower and slower creating a concave yield curve.
Is this logic correct or is there more to it?