# Equity Premium

Governments are largely insulated from market forces. Companies are not. Investments in stocks therefore carry substantial risk in comparison with holdings of government bonds, notes or bills. The marketplace presumably rewards risk with extra return. How much of a return premium should investors in equities expect? These blog entries examine the equity risk premium as a return benchmark for equity investors.

**March 31, 2021** - Equity Premium

How much does accounting for equity factor portfolio maintenance frictions affect usefulness of factor models of stock returns. In their March 2021 paper entitled “Model Selection with Transaction Costs”, Andrew Detzel, Robert Novy-Marx and Mihail Velikov examine effects of transaction costs on six leading models of stock returns:

- FF5 – Fama-French 5-factor model (market, size, book-to-market , investment and accruals-based profitability, reformed annually).
- FF6 – FF5 plus a momentum factor.
- HXZ4 – Hou, Xue, and Zhang 4-factor model (market, size, investment and profitability, all reformed monthly).
- BS6 – Barillas-Shanken 6-factor model (market, size, book-to-market reformed monthly, investment, return on equity and momentum).
- FF5
_{C} – FF5 with a cash flow-based profitability factor.
- FF6
_{C} – FF6 with a cash flow-based profitability factor.

They compare model effectiveness based on maximum squared Sharpe ratio (SR^{2}), which measures how closely a model approaches the in-sample efficient frontier for all test assets. They measure transaction costs using stock-level effective bid-ask spread. Using data to calculate all factors employed by the six models and effective spreads during January 1972 through December 2017, *they find that:* Keep Reading

**March 19, 2021** - Big Ideas, Equity Premium

Several recent papers find that most studies identifying factors that predict stock returns are not replicable or derive from snooping of many factors. Is there a good counter-argument? In their January 2021 paper entitled “Is There a Replication Crisis in Finance?”, Theis Ingerslev Jensen, Bryan Kelly and Lasse Pedersen apply a Bayesian model of factor replication to a set of 153 factors applied to stocks across 93 countries. For each factor in each country, they each month:

- Sort stocks into thirds (top/middle/bottom) with breakpoints based on non-micro stocks in that country.
- For each third, compute a “capped value weight” gross return (winsorizing market equity at the NYSE 80th percentile to ensure that tiny stocks have tiny weights no mega-stock dominates).
- Calculate the gross return for a hedge portfolio that is long (short) the third with the highest (lowest) expected return.
- Calculate the corresponding 1-factor gross alpha via simple regression versus the country portfolio.

They further propose a taxonomy that systematically assigns each of the 153 factors to one of 13 themes based on high within-theme return correlations and conceptual similarities. Using firm and stock data required to calculate the specified factors starting 1926 for U.S. stocks and 1986 for most developed countries (in U.S. dollars), and 1-month U.S. Treasury bill yields to compute excess returns, all through 2019, *they find that:* Keep Reading

**March 16, 2021** - Equity Premium, Individual Investing

Is following the lead of certain types of equity investors as effective as using widely accepted factor models of stock returns? In their March 2021 paper entitled “What Do the Portfolios of Individual Investors Reveal About the Cross-Section of Equity Returns?”, Sebastien Betermier, Laurent Calvet, Samuli Knüpfer and Jens Kvaerner construct a factor model of stocks returns based on demographics of the individual investors who own them. They construct investor factors by each year reforming portfolios that are long (short) the 30% of stocks with the highest (lowest) expected returns based on holdings-weighted investor demographics and then measuring returns of these hedge portfolios the following year. They compare these investor factors to conventional factors constructed from firm/stock characteristics. Using anonymized demographics and direct stock holdings of Norwegian investors (an average 365,000 per year), and associated firm/stock characteristics and returns (over 400 stocks listed on the Oslo Stock Exchange), during 1997 through 2018, *they find that:*

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**March 10, 2021** - Equity Premium, Individual Investing, Investing Expertise

How has the market environment changed with the introduction of zero-commission trading and associated interest in trading among many inexperienced users? In their January 2021 paper entitled “Zero-Commission Individual Investors, High Frequency Traders, and Stock Market Quality”, Gregory Eaton, Clifton Green, Brian Roseman and Yanbin Wu examine market implications of growth in trading by a new subclass of retail investors represented by Robinhood users, focusing on January 2020 through August 2020 when the number of Robinhood users becomes very large. They isolate Robinhood user impacts by comparing market behaviors during Robinhood outages (real-time complaints by at least 200 Robinhood users on DownDetector.com) to those during similar times of day the prior week. They rely on the Reddit WallStreetBets forum and lagged trading activity to identify which stocks Robinhood users would have traded during outages. Using hourly (normal market hours) breadth of stock ownership data for Robinhood users from Robintrack (stocks with minimum average ownership 500 and daily minimum owners 50) and associated stock trading data during July 2018 through August 2020 (when the RobinTrack dataset ends), *they find that:*

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**March 9, 2021** - Equity Premium, Individual Investing

How can the retail trader tail wag the market dog? In their February 2021 paper entitled “The Equity Market Implications of the Retail Investment Boom”, Philippe van der Beck and Coralie Jaunin quantify impacts of the Robinhood-catalyzed retail trading boom on the U.S. stock market. They focus on the early part of the COVID-19 pandemic, during which retail trading soars and institutional investors rebalance their portfolios. They approximate retail trading based on account holdings data from RobinTrack and institutional rebalancing based on SEC Form 13F filings. Using RobinTrack account U.S. common stock holdings data as available through the first half of 2020 (discontinued August 2020) and institutional common stock holdings as disclosed in 13F filings during January 2005 through June 2020, *they find that:* Keep Reading

**February 11, 2021** - Equity Premium, Value Premium

Why have so many quantitative funds performed poorly in recent years? In his January 2021 paper entitled “The Quant Crisis of 2018-2020: Cornered by Big Growth”, David Blitz examines in detail recent (June 2018 through August 2020) performance of stock portfolios constructed from five widely accepted long-short factors:

- Size – Small Minus Big (SMB) market capitalizations.
- Value – High Minus Low (HML) book-to-market ratios.
- Investment – Conservative Minus Aggressive (CMA).
- Profitability – Robust Minus Weak (RMW).
- Momentum – Winners Minus Losers (WML).

Using factor returns from the Kenneth French data library and additional firm/stock data for developed and U.S. markets to construct alternative factor performance tests from various start dates through August 2020, *he finds that:* Keep Reading

**February 3, 2021** - Equity Premium, Fundamental Valuation

What performance should investors expect from the S&P 500 Index based on price-to-earnings (P/E) and Cyclically-Adjusted Price-to-Earnings (CAPE, or P/E10)? In their November 2020 paper entitled “Extreme Valuations and Future Returns of the S&P 500”, Shaun Rowles and Andrew Mitchell take a layered “regression upon a regression” approach to predict S&P 500 Index returns and level. First, to estimate future returns, they run a linear regression on P/E, P/E10, S&P 500 dividend yield, inflation, 10-year U.S. Treasury note yield, historical 1-year, 3-year, 5-year and 10-year S&P 500 Index returns and percentiles of many of these variables within their respective historical distributions. Then, they run separate linear regressions to predict 1-year, 3-year, 5-year and 10-year future annualized returns. Finally, they run a linear regression to model current S&P 500 Index level for comparison to actual current level. Using Robert Shiller’s U.S. stock market and economic data spanning January 1871 through June 2020, *they find that:* Keep Reading

**January 14, 2021** - Bonds, Calendar Effects, Equity Premium

A subscriber requested evaluation of three retirement investment alternatives, assuming a constant increment invested at the end of each month, as follows:

- 50-50: allocate each increment via fixed percentages to stocks and bonds (for comparability, we use 50% to each).
- Seasonal 1: during April through September (October through March), allocate 100% of each increment to stocks (bonds).
- Seasonal 2: during April through September (October through March), allocate 100% of each increment to bonds (stocks).

The hypothesis is that seasonal variation in asset class allocations could improve overall long-term investment performance. We conduct a short-term test using SPDR S&P 500 ETF Trust (SPY) as a proxy for stocks and iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD) as a proxy for bonds. We then conduct a long-term test using Vanguard 500 Index Fund Investor Shares (VFINX) as a proxy for stocks and Vanguard Long-Term Investment-Grade Fund Investor Shares (VWESX) as a proxy for bonds. Based on the setup, we focus on terminal value as the essential performance metric. Using total (dividend-adjusted) returns for SPY and LQD since July 2002 and for VFINX and VWESX since January 1980, all through December 2020, *we find that:* Keep Reading

**December 23, 2020** - Bonds, Equity Premium, Strategic Allocation

“Simple Asset Class ETF Value Strategy” (SACEVS) finds that investors may be able to exploit relative valuation of the term risk premium, the credit (default) risk premium and the equity risk premium via exchange-traded funds (ETF). However, the backtesting period is limited by available histories for ETFs and for series used to estimate risk premiums. To construct a longer test, we make the following substitutions for potential holdings (selected for length of available samples):

To enable estimation of risk premiums over a longer history, we also substitute:

As with ETFs, we consider two alternatives for exploiting premium undervaluation: Best Value, which picks the most undervalued premium; and, Weighted, which weights all undervalued premiums according to degree of undervaluation. Based on the assets considered, the principal benchmark is a monthly rebalanced portfolio of 60% VFINX and 40% VFIIX. Using monthly risk premium calculation data during March 1934 through November 2020 (limited by availability of T-bill data), and monthly dividend-adjusted closing prices for the three asset class mutual funds during June 1980 through November 2020 (40+ years, limited by VFIIX), *we find that:*

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**December 21, 2020** - Bonds, Equity Premium, Strategic Allocation

Is there a better way than the Fed model to measure relative attractiveness of equities and bonds. In his October 2020 paper entitled “Towards a Better Fed Model”, Raymond Micaletti examines seven Fed Model alternatives, each comparing a 10-year forward annualized estimate of equity returns to the yield of 10-year constant maturity U.S. Treasury notes (T-note). The seven estimates of future equity returns are based on autocorrelation-corrected quarterly regressions using 10 years of past quarterly data for one of: (1) Aggregate Investor Allocation to Equities (AIAE); (2) Cyclically-Adjusted Price-to-Earnings Ratio (CAPE); (3) Tobin’s Q (QRATIO); (4) Market Capitalization-to-Nominal GDP (MC/GDP); (5) Market Capitalization-to-Adjusted Gross Value Added (MC/AGVANF); (6) Market Capitalization-to-Household and Non-Profit Total Assets (MC/HHNPTA); and, (7) Household and Non-Profit Equity Allocation-to-Nominal GDP (HHNPEQ/GDP). He calculates AIAE as total market value of equities divided by the sum of total market value of equities and total par value of bonds, approximated by adding the liabilities of five categories of borrowers. He then tests for each alternative a tactical asset allocation (TAA) strategy that each month weights equities and bonds based on a modified z-score of the forecasted 10-year equity risk premium (equity return minus T-note yield) computed by subtracting the median and dividing by the standard deviation of actual monthly premiums over the past 10 years. If modified z-score is greater than 1 (less than -1), the strategy is 100% in equities (0% in equities). In between those thresholds, weights are based on linear interpolation. Using quarterly data from the Archival Federal Reserve Economic Database (ALFRED) and Robert Shiller’s data library and daily U.S. equity market returns and U.S. Treasury bond/note roll-adjusted futures returns as available from the end of the fourth quarter of 1951 through the end of the third quarter of 2020, *he finds that:* Keep Reading