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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.

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CFOs Project the Equity Risk Premium

How do the corporate experts most responsible for assessing the cost of equity currently feel about future U.S stock market returns? In their March 2018 paper entitled “The Equity Risk Premium in 2018”, John Graham and Campbell Harvey update their continuing study of the views of U.S. Chief Financial Officers (CFOs) and equivalent corporate officers on the prospective U.S. equity risk premium (ERP) relative to the 10-year U.S. Treasury note (T-note) yield, assuming a 10-year investment horizon. Based on 71 quarterly surveys over the period June 2000 through December 2017 (an average 351 responses per survey), they find that: Keep Reading

Federal Funds Rate-Stock Market Interactions

A subscriber wondered whether U.S. stock market movements predict Federal Funds Rate (FFR) actions taken by the Federal Reserve open market operations committee. To investigate and evaluate usefulness of findings, we relate three series:

  1. FFR actions per the above source, along with recent and historical committee meeting dates.
  2. S&P 500 Index returns.
  3. Changes in yield for the 10-Year U.S. Constant Maturity Treasury note (T-note).

In constructing the first series, for Federal Reserve open market operations committee meeting dates which do not produce FFR changes, we quantify committee actions as 0%. We ignore committee conference calls that result in no changes in FFR. We calculate the second and third series between committee meeting dates because that irregular interval represents new information to the committee and potential exploitation points for investors. Using data for the three series during January 1990 through March 2018, we find that:

Keep Reading

Best Equity Risk Premium

What are the different ways of estimating the equity risk premium, and which one is best? In his March 2018 paper entitled “Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2018 Edition”, Aswath Damodaran updates a comprehensive overview of equity risk premium estimation and application. He examines why different approaches to estimating the premium disagree and how to choose among them. Using data from multiple countries (but focusing on the U.S.) over long periods through the end of 2017, he concludes that: Keep Reading

Exploitability of Stock Anomalies Worldwide

Are published stock return anomalies exploitable worldwide? In their January 2018 paper entitled “Does it Pay to Follow Anomalies Research? International Evidence”, Ondrej Tobek and Martin Hronec investigate out-of-sample and post-publication performances of 153 cross-sectional stock return anomalies documented in the academic literature, mostly in the top three finance and top three accounting journals. Of the 153 anomalies, 93 involve firm fundamentals, 11 involve firm earnings estimates and 49 involve market frictions. They calculate returns for each anomaly via a hedge portfolio that is long (short) the value-weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for that anomaly. To ensure capacity, they focus on the universe of stocks in the top 90% of NYSE capitalizations. They first examine out-of-sample (after the sample used for discovery but before publication) and post-publication performances of anomalies among U.S. stocks for evidence of performance decay. They then look at anomaly performance outside the U.S. They further test whether strategies that work most widely should be of greatest interest to investors. Finally, they consider a multi-anomaly strategy that each year invests equally in all anomalies that are significant in the U.S. through June, starting in July 1990 for developed country markets and July 2000 for emerging country markets. Using required firm/stock data since July 1963 for the U.S., since January 1987 for Europe, Japan and developed Asia-Pacific and since January 2000 for China and emerging Asia-Pacific, all through December 2016, they find that: Keep Reading

Stock Market Performance Perspectives

How different are stock market performance metrics for:

  • Capital gains only, capital gains plus dividends accrued as cash (spent or saved), and capital gains plus dividends reinvested in the stock market?
  • Nominal versus real returns?
  • Simple return-to-risk calculations versus Sharpe ratio?

Using quarterly S&P 500 Index levels and dividends, quarterly U.S. Consumer Price Index (CPI) data (all items) and monthly 3-month U.S. Treasury bill (T-bill) yield as the risk-free rate/return on cash during the first quarter of 1988 through the fourth quarter of 2017, we find that: Keep Reading

Will the November 2016-December 2017 Run-up in U.S. Stocks Stick?

Is the strong gain in the U.S. stock market following the November 2016 national election rational or irrational? In their February 2018 paper “Why Has the Stock Market Risen So Much Since the US Presidential Election?”, flagged by a subscriber, Olivier Blanchard, Christopher Collins, Mohammad Jahan-Parvar, Thomas Pellet and Beth Anne Wilson examine sources of the 25% U.S. stock market advance during November 2016 through December 2017. They consider four sources: (1) increases in actual and expected dividends; (2) perceived probability and the fact of a reduction in the corporate tax rate; (3) decrease in the U.S. equity risk premium; and, (4) an irrational price bubble. For the impact of the tax rate reduction on corporate income, they use estimates from the Joint Congressional Committee on Taxation. For the relationship between dividends and the equity risk premium, they assume the difference between dividend-price ratio and risk-free rate equals equity risk premium minus expected dividend growth rate. They also consider the effect of U.S. and European economic policy uncertainty on the U.S. equity risk premium. Using the specified data during November 2016 (and earlier for validation) through December 2017, they find that: Keep Reading

Rise and Fall of the Fed Model?

What is the historical relationship between U.S. stock market earnings yield (E/P) and U.S. government bond yield (Y)? In their February 2018 paper entitled “Stock Earnings and Bond Yields in the US 1871 – 2016: The Story of a Changing Relationship”, Valeriy Zakamulin and Arngrim Hunnes examine the relationship between E/P Y over the long run, with focus on structural breaks, causes of breaks and direction of causality. They employ a vector error correction model that allows multiple structural breaks. In assessing causes of breaks, they consider inflation, income taxes and Federal Reserve Bank monetary policy. Using quarterly S&P Composite Index level, index earnings, long-term government bond yield and inflation data during 1871 through 2016, along with contemporaneous income tax rates and Federal Reserve monetary actions, they find that:

Keep Reading

T-note Yield Divergence from Trend and Future Stock Market Return

A subscriber requested review of a finding that deviation of 10-year constant maturity U.S. Treasury note (T-note) yield from an intermediate-term linear trend predicts U.S. stock market return. Specifically, when weekly yield is more than one standard deviation of weekly trend divergences below (above) a weekly 70-week linear extrapolation, next-week S&P 500 Index return is on average unusually high (low). To confirm and test usefulness of this finding, we each week:

  1. Perform a linear extrapolation of past T-note yields to forecast next-week T-note yield, but using a 52-week rolling window rather than a 70-week window. A 52-week lookback aligns with an annual inflation cycle, while a 70-week lookback seems arbitrary and may be snooped.
  2. Calculate the difference between next-week actual and forecasted T-note yields.
  3. Calculate the standard deviation of these differences over the 52-week rolling window.

We then segment weekly actual minus forecasted T-note yield differences into: those more than one standard deviation below forecasted yield (Below Lower); those between one standard deviation below and above forecasted yield (Between); and, those more than one standard deviation above forecasted yield (Above Upper). Next, we calculate next-week S&P 500 Index returns for these three segments. Limited by availability of weekly T-note yield data, return calculations commence January 1964. To check robustness of results, we also consider a recent subsample commencing January 2008. To test economic value of findings, we examine a Dynamic Weighted strategy that modifies a benchmark 60% allocation to SPDR S&P 500 (SPY) and 40% allocation to iShares Barclays 7-10 Year Treasuries (IEF), rebalanced weekly, to 80% SPY when T-note condition the prior week is Below Lower and 40% SPY when Above Upper. The strategy backtest commences with inception of IEF at the end of July 2002 and focuses on weekly return statistics, compound annual growth rate (CAGR) and maximum drawdown (MaxDD), ignoring rebalancing/reallocation frictions. Using weekly T-note yields (average of daily values measured on Friday) and contemporaneous S&P 500 Index levels since January 1962, and weekly dividend-adjusted levels of SPY and IEF since July 2002, all through January 2018, we find that: Keep Reading

Technical Trading of Equity Factor Premiums

Do technical trend trading/intrinsic momentum strategies work for widely used equity factors such as size (small minus big market capitalizations), value (high minus low book-to-market ratios), profitability (robust minus weak), investment (conservative minus aggressive) and momentum (winners minus losers)? In their January 2018 paper entitled “What Goes up Must Not Come Down – Time Series Momentum in Factor Risk Premiums”, Maximilian Renz investigates time variation and trend-based predictability of these five factors and the market factor. He first constructs price series for the six long-short factor portfolios. He then considers seven rules based on a short simple moving average (SMA) crossing above (bullish) or below (bearish) a long SMA measured in trading days: SMA(1, 20), SMA(1, 40), SMA(1, 120), SMA(1, 180), SMA(1, 240), SMA(20, 180) and SMA(20, 240). He also considers two intrinsic (absolute or time series) momentum rules based on change in price over the past 180 or 240 trading days (positive bullish and negative bearish). Motivated by prior research by others, he focuses on SMA(1, 180), daily price crossing its 180-day SMA. He measures trend-based statistical predictability of factor premiums and investigates economic value via a strategy that levers factor exposures between 0 and 1.5 using trend-based signals. Finally, he examines whether incorporating trend information improves accuracies of 1-factor (market), 3-factor (adding size and value) and 5-factor (further adding profitability and investment) models of stock returns. Using daily returns for the six selected U.S. stock market equity factors and for 30 industries during July 1963 through December 2015, he finds that: Keep Reading

Equity Risk Premium and Investment Horizon

How should an investor’s view of the equity risk premium vary with investment horizon? In the December 2017 update of their paper entitled “Volatility Lessons”, Eugene Fama and Kenneth French examine how the U.S. equity risk premium (difference in returns between the expected equity market return over some horizon and return on U.S. Treasury instrument of matched duration) varies across investment horizons ranging from one month to 30 years. To generate distributions of equity risk premiums for horizons longer than one month, they employ bootstrap simulations. Specifically, for each matched horizon/duration, they randomly draw 100,000 pairs of stock market and U.S. Treasury instrument returns with replacement from a base sample of monthly data, without or with an adjustment for uncertainty in associated equity premiums. They repeat analyses on three value portfolios (Market Value, Big Value and Small Value) and on a Small stock portfolio with no value tilt, defining size and value as follows: (1) big (small) stocks are U.S. listed stocks with market capitalizations above (below) the NYSE median; and, (2) value stocks are U.S. listed stocks with book-to-market ratios above the 70th percentile of those for NYSE stocks. All style portfolios are capitalization-weighted and rebalanced annually at the end of June. Using monthly U.S. stock returns and and U.S. Treasury instrument yields across durations during July 1963 through December 2016 (642 months), they find that: Keep Reading

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