A buy and hold portfolio has a linear relationship with its value since the value of the portfolio increases or decreases with price linearly. The liquidity provider has a near linear relationship with price moves around the initial price only. When the price drops to zero the portfolio value drops sharply to zero, since the liquidity provider is buying more and more of the asset losing its value until the price is exactly zero and all of the other liquidity asset has dropped to zero. When the price increases the liquidity provider loses more and more of the upside gains since he is selling more and more of the appreciating asset as the price increases. This is the reason why the liquidity provider is losing money in both directions...