Removing predictable analyst forecast errors to improve implied cost of equity estimates

Prior research documents a weak association between the implied cost of equity inferred from analyst forecasts and realized returns. It points to predictable errors in analyst forecasts as a possible cause. We show that removing predictable errors from analyst forecasts leads to a much stronger association between implied cost of equity estimates obtained from adjusted forecasts and realized returns after controlling for cash flow news and discount rate news. An estimate of implied risk premium based on the average of four commonly used methods after making adjustments for predictable errors exhibits strong correlations with future realized returns as well as the lowest measurement error. Overall, our results confirm the validity of implied cost of equity estimates as measures of expected returns. Future research using implied cost of equity should remove predictable errors from implied cost of capital estimates and then average across multiple metrics.     

Components of Market Risk and Return

This article proposes a flexible but parsimonious specificationof the joint dynamics of market risk and return to produce forecastsof a time-varying market equity premium. Our parsimonious volatilitymodel allows components to decay at different rates, generatesmean-reverting forecasts, and allows variance targeting. Thesefeatures contribute to realistic equity premium forecasts forthe U.S. market over the 1840–2006 period. For example,the premium forecast was low in the mid-1990s but has recentlyincreased. Although the market's total conditional variancehas a positive effect on returns, the smooth long-run componentof volatility is more important for capturing the dynamics ofthe premium. This result is robust to univariate specificationsthat condition on either levels or logs of past realized volatility(RV), as well as to a new bivariate model of returns and RV.     

Cyclicality in catastrophic and operational risk measurements

Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973–2003. We find evidence of cyclical components in both the catastrophic and operational risk measures obtained from the generalized Pareto distribution and the skewed generalized error distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions’ returns represent compensation for operational risk. However, depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events.     

Comoment risk and stock returns

We estimate investable comoment equity risk premiums for the US markets. The stock's contribution to the asymmetry and the fat tails of the market portfolio's payoff are priced into a coskewness premium and a cokurtosis premium. We construct zero-investment strategies that are long and short in coskewness and cokurtosis equity risks; we infer from the spread the returns attached to a unit exposure to US equity coskewness and cokurtosis. The coskewness and cokurtosis premiums present positive monthly average returns of 0.27% and 0.14% from January 1959 to December 2011. Comoment risks appear to be significantly priced within the US stock market and display significant explanatory power regarding the US size and book-to-market effects. The premiums do not subsume, but rather complement the empirical capital asset pricing model. Our analysis relies on data collected from CRSP (Chicago Research Center for Security Prices) over December 1955 to December 2011. To our knowledge, the paper is the first to propose investable higher-moment risk factors over such an extensive time period.     

Terminal valuations, growth rates and the implied cost of capital

We develop a model based on the notion that prices lead earnings, allowing for a simultaneous estimation of the implied growth rate and the cost of equity capital for US industrial sectors. The major difference between our approach and that in prior literature is that ours avoids the necessity to make assumptions about terminal values and consequently about future growth rates. In fact, growth rates are an endogenous variable, which is estimated simultaneously with the implied cost of equity capital. Since we require only 1-year-ahead forecasts of earnings and no assumptions about dividend payouts, our methodology allows us to estimate ex ante aggregate growth and risk premia over a larger sample of firms than has previously been possible. Our estimate of the risk premium being between 3.1 and 3.9 % is at the lower end of recent estimates, reflecting the inclusion of these short-lived companies. Our estimate of the long run growth is from 4.2 to 4.7 %.     

Implied cost of capital investment strategies: evidence from international stock markets

Investors can generate excess returns by implementing trading strategies based on publicly available equity analyst forecasts. This paper captures the information provided by analysts by the implied cost of capital (ICC), the internal rate of return that equates a firm’s share price to the present value of analysts’ earnings forecasts. We find that U.S. stocks with a high ICC outperform low ICC stocks on average by 6.0 % per year. This spread is significant when controlling the investment returns for their risk exposure as proxied by standard pricing models. Further analysis across the world’s largest equity markets validates these results.     

Estimating the Equity Risk Premium and Expected Equity Rates of Return: The Case of Canada

It is common to use the average excess return of equities over bonds estimated over long time periods as an expected equity risk premium on the grounds that going back far enough covers most possible economic scenarios. But although this data is useful in guiding the exercise of judgment, it cannot substitute for judgment. Adding more years of data to the near century of Canadian stock and bond returns that inform today's estimate of the equity risk premium will not produce a “random walk” for a simple reason: the historic bond series is the result of a specific historic monetary policy. This is particularly true of and important for the case of Canada, where today's very low current bond yields reflect the emergence of the Canadian dollar as a reserve currency as well as the impact of unconventional monetary policy elsewhere. After analyzing the historic record of the Canadian equity risk premium and noting the need for adjustments when this premium is applied to the current anomalously low Canadian long‐term bond yields, the author reaches the following conclusions:

• The historic Canadian equity risk premium is approximately 5.0% (based on arithmetic returns), which is slightly lower than the roughly 6.0% value for the U.S.
• The historic equity risk premium has not been constant because of obvious changes in the Canadian bond market. To some extent, the huge cycle in which bond yields began their increase from the 4.0% level starting in 1957, when markets were liberalized, and then fell back to the 4.0% level in 2007‐2008 completed an adjustment to changes in fiscal versus monetary policy. However, in 2016, average long Canada bond yields dropped to an anomalously low 1.8%, which is below the long‐term inflation target of the Bank of Canada, and have barely recovered since. It is difficult to view this as an equilibrium rate determined by private investors.
• Of the drop in bond yields, about 0.50% is unique to Government of Canada bonds as they became attractive to sovereign investors as a rare AAA‐rated issuer.
• Using an indicator variable for the post‐2010 years, a simple regression analysis indicates that current long Canada bond yields should be about 2.75% higher but for the recent changes. And for 2018, this means that the 2.35% average long Canada bond yield should have been about 5.0%. Apart from the impact of higher government deficits, this is consistent with average yields before the 2008 financial crisis.
• Adding an adjusted 5.0% long Canada bond yield to the historic equity risk premium in Canada of 4.50% gives 9.50% for the cost of the overall equity market or, given the Bank of Canada's target inflation rate of 2.0%, a real equity return of 7.5%, both slightly higher than the long‐run averages.

In sum, the conventional practice of adding a historic market risk premium to the current low Canada long bond yields would impart a sharp downward bias to current equity cost estimates; use of this method would not be appropriate until long Canada bond yields increase to at least the 4.0% level.     

Accuracy of Long-Range Actuarial Projections of Health Care Costs

The Office of the Actuary, mandated to provide projections of future medical spending for use by the U.S. Medicare and Medicaid programs, publishes forecasts that have been widely used by private firms and government budget officials as a baseline for expected long-run premium trends and to estimate liabilities for retiree health benefits. Although these projections have been made publicly available since 1986, they have not yet been subject to systematic evaluation by an external reviewer. This article develops a method for assessment of both short- and long-run accuracy and applies it to the 17 sets of projections made public over the last 25 years. The more recent set of projections (1998–2010) incorporating lagged macroeconomic effects appear to be more accurate than the older (1986–1995) projections that relied more heavily on demographic cost of illness trends. The average annualized error of the forecasts is approximately 0.5–1% per year, whether assessed over a span of one, two, or 10 years. Projecting “excess” growth in health spending (the rise in the share of wages or GDP) tends to be more accurate than forecasting nominal or real spending per capita.     

ESTIMATING EXPECTED EXCESS RETURNS USING HISTORICAL AND OPTION‐IMPLIED VOLATILITY

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward‐to‐risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option‐implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994–1998 subperiod. In the 1999–2003 subperiod, the option‐implied volatility risk measure yields a positive, but statistically insignificant, risk‐return relation. We attribute this performance difference to the fact that, in the 1994–1998 subperiod, return volatility was lower and the average return was much higher than in the 1999–2003 subperiod, thereby increasing the signal‐to‐noise ratio in the latter subperiod.     

Beyond Basis Basics: Liquidity Demand and Deviations from the Law of One Price

Deviations from the law of one price between futures and spot prices—the futures-cash basis—capture information about liquidity demand for equity market exposure in global markets. We show that the basis comoves with dealer and investor futures positions, is contemporaneously positively correlated with futures and spot market returns, and negatively predicts futures and spot returns. These findings are consistent with the futures-cash basis reflecting liquidity demand that is common to futures and cash equity markets. We find persistent supply-demand imbalances for equity index exposure reflected in the basis, giving rise to an annual premium of 5% to 6%.