### Predicting the future stock market returns

 It is futile to predict month-to-month stock price variations; however, the dividend discount model can be used to predict the long term (50+ years) stock market returns. Given the current dividend yield of Y~2% for SP500 and historical dividend growth rate of g = 5%, the total stock market return is expected to be around 2%+5%=7%. This return is from dividends only but it will take many years of dividend growth before the cash flow from investments becomes meaningful. As dividends have grown slower than earnings (historical annual earnings growth is ~6%) so it is possible that the future dividend growth rate is slightly higher than the historical average. This positive upside is balanced by the extremely long duration for the stock market: The low yield means that it will take about 25 years to realize just half of the value of the future dividends and even after 50 years, the investor has realized just 75% of the total value. Talk about long term investing! Given that there are some risks (war, run-away inflation, global warming, peak oil, soil depletion, water scarcity) involved with 50 investment, we stick to historical estimate and predict 7% total return for SP500 over the next 50 years. On a shorter time scale, the return is dominated stock price variations. If there were no price fluctuations, we would expect the future price after N to be The price fluctuations can be included in the analysis by including the dividend yield as variable and writing Equation (1) as If investors are optimistic, the stocks are expensive and yield is low. If investors are pessimistic, the stocks are cheap and yield is high. This is reflected in Equation (2) where future price is lower than today if yield today is higher than in future. Over 10 year investment horizon, the yield variations tend to be mean-reverting: over-priced stocks market will go down and vice versa. We thus predict the future stock price to be The annualized price appreciation from Equation (3) In addition to the price appreciation, the stock market returns rewards the investor with growing dividends. The annual return from dividends over next N years is approximately Thus, the total return from Equations (4) and (5) is Figure 1 and 2 show the predicted and realized 5 and 10 year annualized stock market returns for SP500. The fit is not perfect but correctly predicted the poor return in 1960s and 2000 and the good return in 1980s. With the current valuations, we can expect the annualized 5 year and 10 year return of 8%. These are higher than our 7% long term estimate reflecting the current slightly low stock valuations. Figure 1: Predicted and actual annualized 5 year stock market returns. Figure 2: Predicted and actual annualized 10 year stock market returns.