Fundamental Valuation

Do stock-by-stock return forecasts from deep learning produce an exploitable aggregate equity risk premium (ERP) forecast? In the January 2025 revision of their paper entitled “The Aggregated Equity Risk Premium”, Vitor Azevedo, Christoph Riedersberger and Mihail Velikov predict ERP by first applying deep learning to predict returns for individual U.S. stocks and then aggregating these returns at the market level. The firm-level forecasts come from combined outputs of several neural networks of varying complexity applied to 290 firm-level characteristics, 14 U.S. economic variables and 49 industry classification indicators. They iterate these forecasts annually using an expanding training window and a rolling six-year validation window. For comparison, they consider some conventional ERP forecasting approaches. They quantify the economic value of aggregate ERP forecasts via a stock market timing strategy that each month allocates to stocks or U.S. Treasury bills with a 50% leverage limit and conservative 0.5% portfolio rebalancing frictions. Using the specified inputs during March 1957 through December 2021 (with out-of-sample testing commencing January 2000), they find that:

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What do expectations for Bitcoin supply and demand imply for the future trajectory of its price? In the January 2025 revision of their paper entitled “A Supply and Demand Framework for Bitcoin Price Forecasting”, Murray Rudd and Dennis Porter construct a supply-and-demand model to forecast Bitcoin price trajectory. Their model combines a fixed, inelastic supply with demand drivers consisting of accumulation for strategic reserves, institutional adoption and other long-term holders. They consider a conservative scenario calibrated to April 2024 and December 2024 Bitcoin market snapshots and a bullish scenario with more aggressive institutional adoption. Based on an array of supply and demand assumptions and the market snapshots, they find that:

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Which price-to-earnings ratio is best for screening stocks? In the November 2024 first version of his paper entitled “Forward Price-Earnings Ratio”, Luca Conrads compares the practical abilities of seven price-to-earnings ratios to predict S&P 500 returns (see the chart below for four of these seven):

1. Conventional price-to-earnings (PE) – current price divided by prior-year actual earnings.
2. Cyclically Adjusted Price-to-Earnings (CAPE) – current price divided by average annual inflation-adjusted earnings over the last 10 years.
3. Cyclically Adjusted Price-to-Earnings (CAPE5) – current price divided by average annual inflation-adjusted earnings over the last five years.
4. Forward Price-to-Earnings Analysts (FPE^A) – current price divided by next-year annual earnings as forecasted by analyst consensus.
5. Average Forward Price-to-Earnings Analysts (AFPE^A) – current price divided by average annual earnings over the next five years as forecasted by analyst consensus.
6. Forward Price-to-Earnings Mechanical (FPE^M) – current price divided by next-year annual earnings as mechanically forecasted via ordinary least squares (OLS).
7. Average Forward Price-to-Earnings Mechanical (AFPE^M) – current price divided by average annual earnings over the next five years as mechanically forecasted via OLS.

He each quarter for each ratio ranks all S&P 500 stocks with positive ratios into equal-weighted fifths (quintiles) and applies four separate portfolio strategies:

1.  Assign weights of 30%, 20%, 20% 20% and 10% to quintiles 1, 2, 3, 4 and 5, respectively.
2. Invest only in quintile 1.
3. Modify Strategy 1 by taking a 130% position in quintile 1 and a -30% (short) position in quintile 5.
4. Modify Strategy 1 by taking a 200% position in quintile 1 and a -100% in quintile 5.

He then estimates and deducts quarterly portfolio reformation transaction costs for each ratio-strategy combination. His benchmark is the equal-weighted portfolio of all S&P 500 stocks. Using a broad sample of all listed U.S. stocks and firm fundamentals to evaluate earnings forecasts and a narrower sample of S&P 500 data for strategy tests during 1981 through 2023 (with tests commencing in 1991), he finds that:

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“Predicting Stock Market Return with Stocks-TIPS Yield Delta” summarizes results of a study finding that deviations of the S&P 500 earnings yield from the real government bond yield, as measured by the 10-year Treasury Inflation-Protected Securities (TIPS) coupon yield, has statistical power to predict future stock market returns. To corroborate this finding from an investing perspective, we:

• Reuse monthly estimates of the S&P 500 operating earnings yield from the Simple Asset Class ETF Value Strategy (SACEVS).
• Obtain the monthly series of market yields on 10-year constant maturity TIPS.
• Relate monthly differences between these two series to future monthly S&P 500 Index (SP500) returns via linear lead-lag regressions and ranked sorting.

Using monthly data as specified during January 2003 (limited by the TIPS series) through November 2024, we find that: Keep Reading

Do deviations of the aggregate stock market earnings yield from the real government bond yield, as measured by the 10-year Treasury Inflation-Protected Securities (TIPS) coupon yield, predict future stock market returns? In the December 2024 draft of their paper entitled “An Investigation into the Causes of Stock Market Return Deviations from Real Earnings Yields”, flagged by a subscriber, Austin Murphy, Zeina Alsalman and Ioannis Souropanis examine the ability of the difference between current S&P 500 earnings yield and 10-year TIPS real (coupon) yield to predict S&P 500 Index excess returns (relative to 1-year U.S. Treasury notes) at horizons of 1, 5 and 10 years. They also investigate whether any of 25 variables, including inflation rate, drive stock market earnings yield and TIPS real yield apart. Using monthly data for the specified variables during January 1997 (limited by TIPS data) through December 2022, they find that: Keep Reading

Is U.S. equity market valuation outrunning its productive value? For perspective, we compare the trajectories of S&P 500 (SP500) index, earnings and dividends over recent decades and look at some potential explanations for divergences. Using quarterly SP500 data and 10-year U.S. Treasury note (T-note) yield during March 1988 through September 2024 and Shiller data as available through October 2024, we find that: Keep Reading

What variables best explain increases and decreases in Cyclically Adjusted Price-to-Earnings ratio (CAPE or P/E10)? In their August 2024 paper entitled “Analyzing Changing ‘Investor Exuberance’: The Determinants of S&P Composite Index Total Return CAPE Changes”, C. Krishnan, Jiemin Yang and Xiyao Tan apply the following three techniques to investigate which of 42 potentially explanatory variables relate most strongly to changes in CAPE:

1. Linear regression with principal component analysis.
2. Least Absolute Shrinkage and Selection Operator (LASSO) regression analysis, which shrinks some regression coefficients to zero, thereby identifying the most important independent variables.
3. Elastic net, which combine approaches of LASSO and Ridge regression to distill the most important independent variables.

Using monthly values for CAPE and the 42  potentially explanatory variables during February 2000 through December 2019, they find that: Keep Reading

Does an elaborate firm valuation model outperform the blunt instrument of a simple ratio? In their July 2024 paper entitled “Intrinsic Value: A Solution to the Declining Performance of Value Strategies”, Derek Bergen, Francesco Franzoni, Daniel Obrycki and Rafael Resendes model the intrinsic value of a stock, defined as book value of equity plus the discounted sum of estimated future profits with a firm-specific discount rate. Their intrinsic value model includes for each firm:

• A profit forecast based on ultimate decay to zero, with the the path to zero guided by assumptions derived from the historical profit series for the firm, such as:
  • High profits may attract competitors that accelerate decay.
  • Low profits may persist.
  • Stable profits may persist due to a reliable competitive advantage.
  • Volatile profits have rapid decay potential.
  • Large firms have barriers to entry or economies of scale that support profitability.
• A forecast for reinvestment of firm operating cash flow after interest expense, dividends and replacement capital, assuming a consistent capital structure.
• A discount rate estimated by adjusting the median internal rate of return across all firms according to individual firm size and financial leverage.

They apply firm intrinsic value-to-market ratios (IVM) to forecast stock returns, comparing their accuracy to those of the conventional book-to-market ratios (BM). Using monthly inputs as specified for Russell 1000 and Russell 2000 stocks during July 1999 through December 2023, they find that:

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Is stock price-to-earnings ratio (P/E), in aggregate or by individual stock, truly predictive of returns? In their April 2024 paper entitled “Valuing Stocks With Earnings”, Sebastian Hillenbrand and Odhrain McCarthy examine relationships between P/E and future returns at both stock index and individual stock levels. They compare generally accepted accounting principles (GAAP) earnings and an alternative earnings used by Wall Street analysts and therefore designated “Street” earnings. Street earnings, constructed from Institutional Brokers’ Estimate System (I/B/E/S) data, are smoother than GAAP earnings and emphasize future fundamentals by excluding transitory items. They consider as potentially predictive metrics: GAAP P/E; GAAP P/E10 (or GAAP CAPE), based on a 10-year moving average of GAAP earnings; Street P/E; and, Street P/E3 (or Street CAPE), based on a 3-year moving average of Street earnings. They test whether: (1) aggregate GAAP and Street earnings metrics predict stock market returns; and, (2) stock-level GAAP and Street earnings yields (E/P) support profitable long-short hedge portfolios. Using quarterly GAAP and Street earnings data, S&P 500 Index levels and individual stock prices during 1988 through 2021, extended back to 1965 for some aggregate earnings tests and forward through 2023 for some portfolio tests, they find that:

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Do analysts systematically ignore the connection between future firm earnings and current economic conditions? In their July 2024 paper entitled “Predicting Analysts’ S&P 500 Earnings Forecast Errors and Stock Market Returns Using Macroeconomic Data and Nowcasts”, Steven Sharpe and Antonio Gil de Rubio Cruz examine the quality of bottom-up forecasts of near-term S&P 500 earnings aggregated from analyst forecasts across individual firms. Specifically, they:

• Model expected aggregate S&P 500 quarterly earnings growth as a function of GDP growth, output and wage inflation and change in dollar exchange rate. They also consider a simplified model based only on real GDP growth and change in the dollar exchange rate.
• Calculate the gap between modeled S&P 500 earnings growth and analyst-forecasted growth.
• Estimate how well this forecast gap predicts analyst forecast errors.
• Test the extent to which the forecast gap predicts S&P 500 Index total returns.

Using quarterly actual and forecasted S&P 500 earnings, S&P 500 Index total return and values for the specified economic variables during 1993 through 2023, they find that: Keep Reading