Warren believes that investments compete against each other for investors' dollars. He also believes that a business is worth what it can earn for investors during the time that it is owned. The comparison of available investment returns between various investments will determine the selling price for a given company.
The value of a company's earnings is dependent on interest rates. If interest rates drop, investors generally have more choice of stocks with superior earnings potential to that of bonds (all other things equal). For this reason, when interest rates decline, stocks prices generally rise and when interest rates rise, stock prices decline.
One situation where interest rate movements may not have much affect on stock prices is during a bubble situation where the market has succumbed to momentum trading. In these situations, the market may need to see a slowing down of the economy before it makes any stock price adjustments, which at that time can be very dramatic.