It is well-known that there is a strong correlation between valuation ratios and long-term returns on certain stock-market indices such as the S&P 500. Scatter-plots of valuation ratios versus long-term stock-returns often show a characteristic downwards slope, where higher valuation ratios correspond to lower future stock-market returns, and vice versa. But a formal explanation of this phenomenon has never been given until now. In this paper we show how to properly decompose stock-returns into three components: Dividend yield, change in valuation ratio such as the P/E or P/Sales ratio, and the change in Earnings or Sales Per Share. Together with the basic formula for calculating annualized returns, this explains the characteristic curves we often see in scatter-plots of long-term stock-returns. We also derive formulas that let us forecast the mean and standard deviation for the future stock-returns from these three components. This is demonstrated on real-world data for both individual stocks as well as entire stock-market indices such as the S&P 500, 400 and 600 for U.S. stocks, and various Exchange Traded Funds (ETF) for international stock-market indices.