**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.*

**Towards a Better Fed Model**

Raymond Micaletti

**October 4, 2020**

*We present an alternative to the widely known and much-maligned “Fed model.” The proposed alternative makes a coherent comparison between equities and bonds that eliminates the theoretical and empirical flaws of the original (as well as any need for ad hoc asset-class volatility adjustments). The output of the model is a time-series value factor, which is then used to develop a tactical asset allocation strategy. Historical simulations suggest the resulting strategy is superior not only to the original Fed model, but to tactical strategies based on other popular time-series value factors as well. Beyond its forecasting and tactical allocation performance, the proposed model also provides significant insight into equity market dynamics–insight that has been validated by recent historical events.*

**The Probability of Recession: A Critique of a New Forecasting Technique**

Noah Weisberger and Vishv Jeet (PGIM)

**June 2020**

*A recent research publication develops a new business cycle forecasting technique using a metric called “Mahalanobis distance.” This measure is intuitive, is based on a straightforward set of computations, is able to identify post-war US recessions with few false positives, and, as claimed by the authors, has a reasonable forward hit rate. In late 2019, according to this new measure, the estimated probability that the US was in a recession had climbed to about 75%, a prediction that was at odds with many other models. However, by early 2020 and still prior to the pandemic, the measure’s probability of recession had retreated, falling below 3%, and remaining subdued through March. The measure’s volatility prompted a closer technical look into its strengths and weaknesses and its potential as a market timing tool.*

**Geo-Economics Chapter 5: My Rules of Forecasting**

Joachim Klement (Fidante Partners)

**January 5, 2021**

*Chapter 5 of Geo-Economics: The Interplay between Geopolitics, Economics, and Investments opens the second part of this book, in which I focus on geopolitical trends that might become important in the coming decade. To set the scene, Chapter 5 introduces my 10 rules of forecasting. Developed over years of practical application, these 10 rules have served me well in predicting both financial and political developments and can easily be adopted by every investor. They will also serve as the guiding principles in the discussion of the important geopolitical trends of our time.*

**Extreme Valuations and Future Returns of the S&P 500**

Shaun Rowles and Andrew Mitchell

**November 1, 2020**

*Higher than average Price-to-Earnings (P/E) ratios and Cyclically-Adjusted Price-to-Earnings (CAPE) ratios have been tolerated by investors recently on the basis of low interest and inflation rates. This white paper analyzes what level of returns can reasonably be expected going forward from today’s elevated valuation multiples.*

**Combining Forecasts: Can Machines Beat the Average?**

Tyler Pike and Francisco Vazquez-Grande (Federal Reserve)

**September 11, 2020**

*This paper documents benefits of combining forecasts using weights that depend non-linearly of past forecast errors. We propose combining out of sample forecasts from simple models using weights, computed using machine learning algorithms trained on the models’ past forecast errors. These nonlinear weights produce more accurate forecasts than conventional approaches based on equal-weighed forecasts, breaking the so-called “forecast combination puzzle”.*

**Time-Frequency Forecast of the Equity Premium**

Gonçalo Faria (Catholic University of Portugal and Fabio Verona (Bank of Finland)

**April 27, 2020**

*Any time series can be decomposed into cyclical components fluctuating at different frequencies. Accordingly, in this paper we propose a method to forecast the stock market’s equity premium which exploits the frequency relationship between the equity premium and several predictor variables. We evaluate a large set of models and find that, by selecting the relevant frequencies for equity premium forecasting, this method significantly improves in both statistical and economic sense upon standard time series forecasting methods. This improvement is robust regardless of the predictor used, the out-of-sample period considered, and the frequency of the data used.*

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