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.     

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%.     

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.     

Estimating the Equity Risk Premium Using Accounting Fundamentals

This study uses recent developments in the theoretical modelling of the links between unrecorded accounting goodwill, accounting profitability and the cost of equity, together with Capital Asset Pricing Model (CAPM) betas, to estimate the ex-ante equity risk premium in the UK. The results suggest that, over our sample period from 1968 to 1995, the premium has been in the region of 5%. Our estimate lends support to the view that the ex-ante equity risk premium is substantially less than the historical average of the excess of equity returns over the risk-free rate, and is similar to the rates applied recently by UK competition regulators.     

Predicting the equity market with option-implied variables

We comprehensively analyze the predictive power of several option-implied variables for monthly S&P 500 excess returns and realized variance. The correlation risk premium (CRP) and the variance risk premium (VRP) emerge as strong predictors of both excess returns and realized variance. This is true both in- and out-of-sample. Our results also reveal that statistical evidence of predictability does not necessarily lead to economic gains. However, a timing strategy based on the CRP leads to utility gains of more than 5.03% per annum. Forecast combinations provide stable forecasts for both excess returns and realized variance, and add economic value.     

ESTIMATING THE EQUITY RISK PREMIUM AND EQUITY COSTS: NEW WAYS OF LOOKING AT OLD DATA

This article examines three alternative ways of estimating the expected return on the equity market in using the CAPM or some other risk premium model. The three techniques are (1) direct estimation of the average nominal equity return for use as a forecast nominal equity return; (2) estimation of the average real equity return, which can then be added to a forecast inflation rate; and (3) estimation of an average equity risk premium, which is then added to a current risk-free rate. Ibbotson and Sinquefeld's data on annual holding period returns are used to test the validity of their assumption that the equity risk premium follows a random walk and that the third of these approaches is thus the best method.
The paper reaches three major conclusions. First, each of these three techniques involves a "bias" of some kind. The use of average equity returns as a forecast is subject to "risk-free rate" and "inflation rate" biases, while the use of an average equity risk premium is subject to a "term premium" bias. As a result, only the data can tell us which approach is best. Second, from analyzing equity and bond return data and the trend in interest rates, the author concludes that the term premium bias when using average historic equity risk premium is by far the largest of the three sources of bias. Indeed, the popular practice of adding an historic average equity risk premium to the 30-year Treasury bond rate significantly overstates equity costs. Third, after examining equity rates of return back to 1871, the author concludes that the real equity return seems to follow a process that is close to a random walk and is thus the "best" of the three techniques to use as a "naive" forecast.     

Equity returns,bond returns,and the equity premium in the German capital market

This article reviews the empirical evidence for equity returns, bond returns, and the equity premium in the German capital market for the period from 1870 to 1995. Taken together, the studies reviewed provide convincing evidence that over longer investment periods, average equity returns have been higher than average bond returns. These excess returns, however, have been highly volatile and negative in many years, illustrating the higher risk of equity investments. Moreover, market timing had a major positive or negative impact on overall returns. Despite the historical evidence of a substantial equity premium there is still little equity investment by German households.     

Explaining the default risk anomaly by the two-beta model

This study attempts to explain the anomaly that firms with high-default risk earn low average realized returns. We measure default risk according to Ohlson's (1980) O-score and Campbell, Hilscher, and Szilagyi's (2008) failure probability and further implement Duffie, Saita, and Wang's (2007) doubly-stochastic intensity model to estimate default probabilities that incorporate the dynamics of the changes in covariates. We then employ Campbell and Vuolteenaho's (2004) two-beta model to estimate firms' cash-flow and discount-rate betas according to the default risk. The default risk anomaly persists when using Duffie el al.'s (2007) method. We show that cash-flow and discount-rate betas, respectively, earn a high and low premium and find that high-default firms tend to have relatively high discount-rate and low cash-flow betas. Hence, high-default firms deliver low expected returns. Importantly, 25.5% of the default risk anomaly can be explained by the two-beta model and that, on average, also accounts for 49.2% of the cross-sectional variation across the portfolios formed on default risk. This result implies that investors believe that high-default firms are unlikely to generate significantly extra cash flows when market-wide profitable opportunities improve.     

Credit default swap spreads and variance risk premia

We find that the firm-level variance risk premium has a prominent explanatory power for credit spreads in the presence of market- and firm-level control variables established in the existing literature. Such predictability complements that of the leading state variable—the leverage ratio—and strengthens significantly with a lower firm credit rating, longer credit contract maturity, and model-free implied variance. We provide further evidence that (1) the variance risk premium has a cleaner systematic component than implied variance or expected variance, (2) the cross-section of firms’ variance risk premia capture systematic variance risk in a stronger way than firms’ equity returns in capturing market return risk, and (3) a structural model with stochastic volatility can reproduce the predictability pattern of variance risk premia for credit spreads.     

An introduction to security returns

The equity premium - the difference between the return achievable from investment in the equity market (R_M ) and the risk-free rate of return (R_F )- plays an important part in corporate finance. The expression equity premium (sometimes referred to as the equity risk premium) is used to denote the ex ante expectation of investors. The term excess return refers to the ex post achievement of stock returns over and above the risk-free return. If we compare US and UK returns, we find that total returns, real returns and the value of (R_M - R_F ) are all marginally higher for the UK. Summarized evidence appears in Table 1 and Table 6. Such greater returns may be due to an increased risk premium related to increasing unexpected inflation. Particularly important in estimating the equity risk premium is whether excess returns are measured using a geometric or an arithmetic mean return. To a significant extent, this question revolves around mean reversion in stock returns. Evidence of mean reversion is substantial, although it cannot be proved unequivocally. Given the weight of evidence of mean reversion, there may be a strong case for the use of a geometric mean with an equity premium of between 3% and 5% - or even less.     

Consumption-based equity valuation

Using a CCAPM-based risk-adjustment model, we perform yearly valuations of a large sample of stocks listed on NYSE, AMEX, and NASDAQ over a 30-year period. The model differs from standard valuation models in the sense that it adjusts forecasted residual income for risk in the numerator rather than through a risk-adjusted cost of equity in the denominator. The risk adjustments are derived based on assumptions about the time-series properties of residual income returns and aggregate consumption rather than on historical stock returns. We compare the performance of the model with several implementations of standard valuation models, both in terms of median absolute valuation errors (MAVE) and in terms of excess returns on simple investment strategies based on the differences between model and market prices. The CCAPM-based valuation model yields a significantly lower MAVE than the best performing standard valuation model. Both types of models can identify investment strategies with subsequent excess returns. The CCAPM-based valuation model yields time-series of realized hedge returns with more and higher positive returns and fewer and less negative returns compared with the time-series of realized hedge returns based on the best performing standard valuation model for holding periods from 1 to 5 years. In a statistical test of 1-year-ahead excess return predictability based on the models’ implied pricing errors, the CCAPM-based valuation model is selected as the better model. Using the standard series of aggregate consumption and the nominal price index, a reasonable level of relative risk aversion, and calibrated growth rates in the continuing value at each valuation date, the CCAPM-based valuation model produces small risk adjustments to forecasted residual income and low continuing values. Compared with standard valuation models, it relies less on estimated parameters and speculative elements when aggregating residual earnings forecasts into a valuation.     

Can Operating Leverage Be the Cause of the Value Premium?

Recent theoretical models (Carlson, Fisher, and Giammarino, 2004) predict an association between the book-to-market equity ratio (BE/ME) and operating leverage in the cross-section. Consistent with these models, we find a positive association between BE/ME and the degree of operating leverage (DOL), between DOL and stock returns, and between DOL and systematic risk. Overall, our findings provide support for a risk-based explanation for the value premium that is consistent with existing theoretical models. The evolution of systematic risk associated with firm-level investment activity, rather than financial distress, seems to be the main determinant of the value premium.     

SYMMETRIC VERSUS ASYMMETRIC CONDITIONAL COVARIANCE FORECASTS: DOES IT PAY TO SWITCH?

Volatilities and correlations for equity markets rise more after negative returns shocks than after positive shocks. Allowing for these asymmetries in covariance forecasts decreases mean‐variance portfolio risk and improves investor welfare. We compute optimal weights for international equity portfolios using predictions from asymmetric covariance forecasting models and a spectrum of expected returns. Investors who are moderately risk averse, have longer rebalancing horizons, and hold U.S. equities benefit most and may be willing to pay around 100 basis points annually to switch from symmetric to asymmetric forecasts. Accounting for asymmetry in both variances and correlations significantly lowers realized portfolio risk.