Objective research to aid investing decisions
Value Allocations for Feb 2019 (Final)
Cash TLT LQD SPY
Momentum Allocations for Feb 2019 (Final)
1st ETF 2nd ETF 3rd ETF
CXO Advisory

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.

Interpreting Inverted Yield Curves as Economic Indigestion

Is there a straightforward way to interpret the state of the yield curve as a manifestation of how efficiently the economy is processing information? In his March 2017 paper entitled “Simple New Method to Predict Bear Markets (The Entropic Linkage between Equity and Bond Market Dynamics)”, Edgar Parker Jr. presents and tests a way to understand interaction between bond and equity markets based on arrival and consumption of economic information. He employs Shannon entropy to model the economy’s implied information processing ratio (R/C), with interpretations as follows:

  1. R/C ≈ 1: healthy continuously upward-sloping yield curve when information arrival and consumption rates are approximately equal.
  2. R/C >> 1: low end of the yield curve inverts when information is arriving much faster than it can be consumed.
  3. R/C << 1: high end of the yield curve inverts when information is arriving much slower than it can be consumed.

Under the latter two conditions, massive information loss (entropy growth) occurs, and firms cannot confidently plan. These conditions delay/depress economic growth and produce equity bear markets. He tests this approach by matching actual yield curve data with standardized (normal) R and C distributions that both have zero mean and standard deviation one (such that standardized R and C may be negative). Using daily yields for U.S. Treasuries across durations and daily S&P 500 Index levels during 1990 through 2016, he finds that: Keep Reading

True Iliquidity and Future Stock Returns

Does disentangling measures of stock illiquidity and market capitalization (size) support belief in an illiquidity premium (a reward for holding illiquid assets)? In the December 2016 version of their paper entitled “The Value of True Liquidity”, Robin Borcherding and Michael Stein investigate this question by controlling the most widely used stock illiquidity metric for size. Specifically they define and calculate true stock liquidities by:

  • Calculating for each stock the conventional Amihud monthly measure of illiquidity (average absolute price impact of dollar trading volume during a month).
  • Capture unexplained residuals from a regression that controls for the linear relationship (negative correlation) between this conventional illiquidity metric and size.
  • Sorting stocks by size and capturing more detail regression residuals within size ranges to control for the non-linear relationship between conventional illiquidity and size.

They then form double-sorted portfolios to compare interactions of conventional and true liquidity with stock volatility and size. Using daily returns, trading data and characteristics for 4,739 U.S. common stocks during January 1990 through September 2015, they find that: Keep Reading

Testing Stock Anomalies in Practical Context

How do widely studied anomalies relate to representative stocks-bonds portfolio returns (rather than the risk-free rate)? In his March 2017 paper entitled “Understanding Anomalies”, Filip Bekjarovski proposes an approach to asset pricing wherein a representative portfolio of stocks and bonds is the benchmark and stock anomalies are a set of investment opportunities that may enhance the benchmark. He therefore employs benchmark-adjusted returns, rather than excess returns, to determine anomaly significance. Specifically, his benchmark portfolio captures the equity, term and default premiums. He considers 10 potentially enhancing anomalies: size, value, profitability, investment, momentum, idiosyncratic volatility, quality, betting against beta, accruals and net share issuance. He estimates each anomaly premium as returns to a portfolio that is each month long (short) the value-weighted tenth, or decile, of stocks with the highest (lowest) expected returns for that anomaly. He assesses the potential of each anomaly in three ways: (1) alphas from time series regressions that control for equity, term and default premiums; (2) performances during economic recessions; and, (3) crash proneness. He measures the attractiveness of adding anomaly premiums to the benchmark portfolio by comparing Sharpe ratios, Sortino ratios and performances during recessions of five portfolios: (1) a traditional portfolio (TP) that equally weights equity, term and default premiums; (2) an equal weighting of size, value and momentum premiums (SVM) as a basic anomaly portfolio; (3) a factor portfolio (FP) that equally weights all 10 anomaly premiums; (4) a mixed portfolio (MP) that equally weights all 13 premiums; and, (5) a balanced portfolio (BP) that equally weights TP and FP. Using monthly returns for the 13 premiums specified above from a broad sample of U.S. stocks and NBER recession dates during July 1963 through December 2014, he finds that: Keep Reading

Early Retirement Safe Withdrawal Rate

What is a safe portfolio withdrawal rate for early retirees who expect more than 30 years of retirement? In their February 2017 paper entitled “Safe Withdrawal Rates: A Guide for Early Retirees”ERN tests effects of several variables on retirement portfolio success:

  • Retirement horizons of 30, 40, 50 and 60 years.
  • Annual inflation-adjusted withdrawal rates of 3% to 5% in increments of 0.25%.
  • Terminal values of 0% to 100% of initial portfolio value in increments of 25%.
  • Implications of different starting levels of Shiller’s Cyclically Adjusted Price-to-Earnings ratio (CAPE or P/E10).
  • Implications of Social Security payments coming into play after retirement.
  • Effects of reducing withdrawal rate over time (planning a gradual decline in consumption during retirement).

They assume 6.6% average real annual return for U.S. stocks with zero volatility. For 10-year U.S. Treasury notes (T-note), they assume 0% real return for the first 10 years and 2.6% thereafter (zero volatility except for one jump). They assume monthly withdrawal of one-twelfth the annual rate at the prior-month market close, with monthly portfolio rebalancing to target stocks and T-note allocations. They assume annual portfolio costs of 0.05% for low-cost mutual fund fees. Based on the stated assumptions, they find that: Keep Reading

Profitability and Investment Factor Premiums Sample-specific?

Are the profitability (Robust Minus Weak, RMW) and investment (Conservative Minus Aggressive, CMA) stock factor premiums observed post-1963 robust in earlier data? In the February 2017 version of his paper entitled “The Profitability and Investment Premium: Pre-1963 Evidence”, Sunil Wahal measures the profitability (revenue minus cost of goods sold, scaled by total assets) and investment (change in total assets) factor premiums using data hand-collected from Moody’s Manual that predates the sample commencing July 1963 used to discover these factors. He defines the premiums conventionally as returns to a portfolio that is each month long (short) stocks with relatively high (low) expected returns. Because of missing older data, inconsistent accounting methods and accounting data availability lag (at least six months between fiscal year end and returns), he starts his accounting data in 1938 and return data in July 1940. Using available firm accounting and monthly return data as specified through June 1963, he finds that: Keep Reading

Equity Factor Diversification Benefits

How diversifying are different equity factors within and across country stock markets? In his January 2016 paper entitled “The Power of Equity Factor Diversification”, Ulrich Carl analyzes diversification properties of six equity factors (market excess return, size, value, momentum, low-beta and quality) across 20 developed stock markets. He defines each factor conventionally as returns to a portfolio that is each month long (short) stocks with the highest (lowest) expected returns based on that factor. He considers: (1) cross-country correlations for each factor; (2) cross-factor correlations for each country; (3) cross-country, cross-factor correlations; (4) dynamics of cross-country correlations for each factor based on rolling 36-month windows of returns; and, (5) cross-country correlations for each factor for the 30% lowest and 30% highest market excess returns (tail events). He also applies principal component analysis as another way to evaluate how diverse the 120 country-factor return streams are. Finally, he constructs cross-factor and cross-country portfolios to assess economic value of diversification properties. Using monthly returns in U.S. dollars for the six factors in each of the 20 countries during January 1991 through April 2015, he finds that: Keep Reading

Long-run Predictive Power of Stock Market Dividend Yield

Do very long samples clarify the role of aggregate dividend yield as a stock market return predictor? In their January 2017 paper entitled “Four Centuries of Return Predictability”, Benjamin Golez and Peter Koudijs examine whether aggregate dividend yield (dividend-to-price ratio) predicts stock market return in a pieced sample spanning four centuries. They test predictability in the overall sample and the pieces separately, mostly based on real (inflation-adjusted) data. Using annual stock market price and dividend data and contemporaneous estimates of inflation and the risk-free rate for the Netherlands/UK during 1629-1812, for the UK alone during 1813-1870 and for the U.S. during 1871-2015, they find that: Keep Reading

Equity Factor Risk-return Predictability

Do factors widely used to model cross-sectional returns of U.S. stocks exhibit reward-for-risk behaviors? In other words, are expected factor returns higher (lower) when factor return volatility is high (low)? In their January 2017 paper entitled “The Risk-Return Tradeoff Among Equity Factors”, Pedro Barroso and Paulo Maio examine reward-for-risk behaviors of the size (small minus big market capitalizations), value (high minus low book-to-market ratios), momentum (winners minus losers from 12 months ago to one month ago), profitability (robust minus weak gross profit) and investment (conservative minus aggressive) risk factors. They compute risk as realized variance based on the last 21 daily factor returns and predict factor returns via regressions that relate monthly returns to respective factor variances. They test out-of-sample predictive power by comparing forecast errors from inception-to-date regressions (minimum 10 years of data) to those of the historical average. They test out-of-sample economic significance of findings via a strategy that each month holds a broad stock market index plus a 150% or 200% long (short) position in a factor portfolio when the regression-predicted factor risk premium is positive (negative). They compare the performance of this strategy to buying and holding the broad market index. They also consider a long-only factor exposure strategy. Finally, they perform an ancillary test of the ability of realized factor variances to predict the equity risk premium. Using daily and monthly factor returns for the U.S. equity market during January 1964 through December 2015, they find that: Keep Reading

Which Equity Factors Are Predictable?

Are the returns of factors widely used to predict the cross-section of stock returns themselves predictable? In the January 2016 draft of his paper entitled “Equity Factor Predictability”, Ulrich Carl analyzes predictability of market, size (market capitalization), value (book-to-market ratio), momentum (returns from 12 months ago to one month ago), low beta (betting against beta) and quality factor returns. All factor returns derive from hedge portfolios that are long (short) stocks with high (low) expected returns based on their factor values. He employs a broad range of economic and financial variables in four sets and multiple ways of testing predictability to ensure robustness of findings and limit model/data snooping bias. Predictability tests he applies include: combinations of simple forecasts (mean or median of single-variable regression forecasts); principal component analysis to distill forecasting variables into a few independent predictive factors; and, methods that adjust variable emphasis according to their respective past performances. He considers several predictability evaluation metrics, including: mean squared error compared to that of the historical average return; utility gain of timing based on predictability; and, information ratio (difference in return divided by difference in risk) relative to the historical average return. He mostly examines next-month forecasts with a one-month gap between predictive variable measurement and forecasted return over two test periods: 1975-2013 and 1950-2013. Using monthly returns for the six factors (start dates ranging from 1928 to 1958), a large set of financial variables since 1928 and a large set of economic variables since 1962, all through November 2013, he finds that: Keep Reading

When Potential Upside Is Bigger Than Potential Downside

How does the fact that many investments can go up more than they can go down interact with their optimal allocations? In their February 2017 paper entitled “What Our Market Return Forecasts Really Mean: Convexity in Equity Returns and its Implications for Investment Sizing”, Victor Haghani and James White examine how return convexity, return forecast and investment sizing tie together. They measure equity return convexity as arithmetic mean of returns over multiple intervals during a sample period minus geometric mean (compound annual growth rate) over the same sample period. They approximate its value generally as one-half the variance (square of standard deviation) of returns measured across the same multiple intervals. In the context of results from an early 2017 survey of 118 experienced finance professionals about expected U.S. stock market performance, they then consider implications of convexity return when applying the Merton rule for optimal allocation sizing (Sharpe ratio divided by the product of investor risk aversion and standard deviation of returns). Based on mathematical formulas and approximations, they conclude that: Keep Reading

Daily Email Updates
Login
Research Categories
Recent Research
Popular Posts
Popular Subscriber-Only Posts