We endorse the decisive evidence that markets and economies are complex, dynamic systems which are not reducible to linear cause-effect analysis over short or intermediate time frames. However, we are willing to acknowledge the likelihood that the future is likely to rhyme with the past. Thus, we believe there is substantial value in applying simple statistical models to discover average estimates of what the future may hold over meaningful investment horizons (10+ years), while acknowledging the wide range of possibilities that exist around these averages.

To be crystal clear, the commentary below makes no assertions about whether markets will carry on higher from current levels. Expensive markets can get much more expensive in the intermediate term, and investors need look no further back than the late 2000s for just such an example. However, the *historical implications* of investing in expensive markets is that, at some point in the future, perhaps years from now, the market has a very high probability of trading back below current prices; perhaps far below. More importantly, investors must recognize that buying stocks at very expensive valuations will necessarily lead to future returns over the subsequent 10 – 20 years that are far below average.

- People who are approaching retirement need to estimate probable returns in order to budget how much they need to save.
- A retiree’s level of sustainable income is largely dictated by expected returns over the early years of retirement.
- Investors of all types must make informed decisions about how best to allocate their capital among various investment opportunities.

*inflation-adjusted*stock returns including reinvested dividends over subsequent multi-year periods. Our analysis provides compelling evidence that future returns will be lower when starting valuations are high, and that returns will be higher in periods where starting valuations are low.

“Rich valuation is strongly associated with weak subsequent returns, but only reliably so over periods of 7-10 years. In contrast, the present syndrome of overvalued, overbought, overbullish, rising-yield conditions is typically associated with abrupt and often steep losses, but is more commonly resolved over a period of months rather than years.” (Hussman, Jul. 2013).

*meaningful*historical precedents, markets are currently expensive and overbought by all three measures, indicating a strong likelihood of low inflation-adjusted returns going forward over periods as long as 20 years.

The profit margin picture is critically important. Jeremy Grantham recently stated, “Profit margins are probably the most mean-reverting series in finance, and if profit margins do not mean-revert, then something has gone badly wrong with capitalism. If high profits do not attract competition, there is something wrong with the system and it is not functioning properly.” On this basis, we can expect profit margins to begin to revert to more normalized ratios over coming months. If so, stocks may face a future where multiples to corporate earnings are contracting at the same time that the growth in earnings is also contracting. This double feedback mechanism may partially explain why our statistical model predicts such low real returns in coming years. Caveat Emptor.

### Modeling Across Many Horizons

**Table 1. Factor Based Return Forecasts Over Important Investment Horizons**

### Process

**Matrix 1. Explanatory power of valuation/future returns relationships**

### Forecasting Expected Returns

**Matrix 2. Slope of regression line for each valuation factor/time horizon pair.**

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

**Matrix 3. Intercept of regression line for each valuation factor/time horizon pair.**

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

**Matrix 4. Modeled forecast future returns using current valuations.**

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

**note that the best forecast for future real equity returns integrating all available valuation metrics is less than 1% per year over horizons covering the next 5 to 20 years**. We also provided the R-squared for each multiple regression underneath each forecast; you can see that at the 15-year forecast horizon, our regression explains 80% of total returns to stocks.

**Chart 2. 15-Year Forecast Returns vs. 15-Year Actual Future Returns**

### Putting the Forecasts to the Test

**Table 2. Comparing Long-term average forecasts with model forecasts**

*350% more error*than estimations from our multi-factor regression model over 15-year forecast horizons (1.16% annualized return error from our model vs 5.55% using the long-term average). Clearly the model offers substantially more insight into future return expectations than simple long-term averages, especially near valuation extremes.