Long-Term Stock Forecasting
Magnus Pedersen (Hvass Laboratories)
December 17, 2020
When plotting the relation between valuation ratios and long-term returns on individual stocks or entire stock-indices, we often see a particular pattern in the plot, where higher valuation ratios are strongly correlated with lower long-term stock-returns, and vice versa. Moreover the plots often show a particular curvature for this relation between valuation ratio and long-term stock-returns. The explanation turns out to be quite simple and follows directly from the mathematical definition of the annualized return. Furthermore, we can decompose the change in share-price into the change in valuation ratio such as the P/E or P/Sales ratio, and the change in the Earnings or Sales Per Share. This is intuitively obvious because the share-price simply equals the valuation ratio e.g. P/Sales multiplied by the Sales Per Share. Using this with the formula for annualized return, we get a fairly simple formula for estimating the future stock-returns, based on the current valuation ratio and our best guess for the future valuation ratio, and the future growth in e.g. Earnings or Sales Per Share, and the future Dividend Yield. This is the basis of the long-term forecasting model, for estimating the mean and standard deviation of future stock-returns. Although the forecasting model is “embarrassingly” obvious in hindsight, it has apparently never been formalized in any previous publications, which have merely studied the empirical relation between valuation ratios and long-term stock-returns, without giving a formal explanation why this relation exists, and how to use it properly for long-term forecasting. That is done in this paper and we will also show when and why the forecasting model does not work, using real-world data for both individual stocks as well as entire stock-indices such as the S&P 500, 400 and 600 for U.S. stocks, and various Exchange Traded Funds (ETF) for international stock-indices.
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