Why Is the Actual Execution Price for a Large Trade Slightly Worse than the Instantaneous Price Ratio?

The actual execution price for a large trade is worse due to slippage. The instantaneous price is based on the current ratio of reserves (x/y).

A large trade significantly alters the reserves, moving the pool along the bonding curve and changing the price as the trade is executed. The average price paid across the entire trade is thus worse than the starting price.

This is an inherent characteristic of the constant product formula.