Equity premium estimates from economic fundamentals under structural breaks

This article compares three estimates of the conditional equity premium using dividend and earnings growth rates to measure the expected rate of capital gain. The premia are estimated using a theory-informed Bayesian model that admits structural breaks. The equity premium fell from 8.16% in 1951 to 1.15% in 1985. Approximately half of this decline was reversion of a high conditional premium to the long run mean and the remainder resulted from a decline in the expected stock return. The decline in the expected stock return was largely driven by the Fed Accord (1951) and the Fed's ‘monetarist policy experiment’ (1979–1982).     

The expected value premium

Fama and French [2002. The equity premium. Journal of Finance 57, 637–659] estimate the equity premium using dividend growth rates to measure expected rates of capital gain. We apply their method to study the value premium. From 1945 to 2005, the expected value premium is on average 6.1% per annum, consisting of an expected dividend growth component of 4.4% and an expected dividend price ratio component of 1.7%. Unlike the equity premium, the value premium has been largely stable over the last half century.     

The Equity Premium: Consistent with GDP Growth and Portfolio Insurance

We find that the long‐term equity premium is consistent with both GDP growth and portfolio insurance. We use a supply‐side growth model and demonstrate that the arithmetic average stock market return and the returns on corporate assets and debt depend on GDP per capita growth. The implied equity premium matches the U.S. historical average over 1926–2001. Separately, we find that the equity premium tracks the value of a put option on the S&P 500. Our theory predicts a smaller equity premium in the future, assuming that the recent regime shifts in dividend policies, interest rates, and tax rates are permanent.     

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.     

What Cost of Capital Should You Use? The Market Has an Answer

The most widely used means of estimating a company's cost of equity capital is the Capital Asset Pricing Model (CAPM). But as a growing number of academics and practitioners have suggested, use of the CAPM produces estimates that often fail to reflect the risks of the companies as perceived by current and potential investors. The authors' work, together with other research, also suggests that the cost of equity produced by the CAPM is often too high. To the extent this is so, companies are discounting investment projects at rates of return that may be leading them to pass up value‐adding opportunities. The authors advocate the use of a simple and practical alternative to the CAPM that does not use either an assumed market risk premium or a beta. It uses instead an equity premium that is implied by the current market price of a company's stock and, as such, is implicitly derived from investors' assessments of the firm's risk that are reflected in that price. More specifically, the alternative approach solves for the internal rate of return that equates the present value of expected future cash flows to the current market price. In support of this approach, studies have shown that such market‐implied measures are better predictors than CAPM‐based estimates of future stock returns, both at the individual‐firm and aggregate market levels.     

The Cost of Equity Capital—a Comment

An algebraic relationship is developed linking the expected long-term yield to an investor with the company's expected internal rate of return on its equity assets. Assuming that the market normally ranks shares by expected yield, allowing where necessary for a risk premium, it is shown that the cost of equity capital must be the company's expected internal rate of return.     

The Risk‐Return Relation in International Stock Markets

We investigate the risk‐return relation in international stock markets using realized variance constructed from MSCI (Morgan Stanley Capital International) daily stock price indices. In contrast with the capital asset pricing model, realized variance by itself provides negligible information about future excess stock market returns; however, we uncover a positive and significant risk‐return tradeoff in many countries after controlling for the (U.S.) consumption‐wealth ratio. U.S. realized variance is also significantly related to future international stock market returns; more importantly, it always subsumes the information content of its local counterparts. Our results indicate that stock market variance is an important determinant of the equity premium.     

Using Forecasts of Earnings to Simultaneously Estimate Growth and the Rate of Return on Equity Investment

We develop a method for simultaneously estimating the cost of equity capital and the growth in residual earnings that are implied by current stock prices, current book value of equity, and short-term forecasts of accounting earnings. We demonstrate the use of our method by calculating the expected equity risk premium. Our estimate is higher than estimates in extant studies that are based on the same earnings forecast data. The main difference between our study and these papers is that while they provide arguments supporting an assumed rate of growth beyond the forecast horizon, we estimate this rate.     

What determines the stock market's reaction to monetary policy statements?

We find that information communicated through monetary policy statements has important business cycle dependent implications for stock prices. For example, during periods of economic expansion, stocks tend to respond negatively to announcements of higher rates ahead. In recessions, however, we find a strong positive reaction of stocks to seemingly similar signals of future monetary tightening. We provide evidence that the state dependence in the stock market's response is explained by information about the expected equity premium and future corporate cash flows contained in monetary policy statements. We also show state dependence in the average stock returns on days of scheduled FOMC meetings and in the impact of monetary policy statements on stock and bond return volatility.     

Survival

Empirical analysis of rates of return in finance implicitly condition on the security surviving into the sample. We investigate the implications of such conditioning on the time series of rates of return. In general this conditioning induces a spurious relationship between observed return and total risk for those securities that survive to be included in the sample. This result has immediate implications for the equity premium puzzle. We show how these results apply to other outstanding problems of empirical finance. Long-term autocorrelation studies focus on the statistical relation between successive holding period returns, where the holding period is of possibly extensive duration. If the equity market survives, then we find that average return in the beginning is higher than average return near the end of the time period. For this reason, statistical measures of long-term dependence are typically biased towards the rejection of a random walk. The result also has implications for event studies. There is a strong association between the magnitude of an earnings announcement and the postannouncement performance of the equity. This might be explained in part as an artefact of the stock price performance of firms in financial distress that survive an earnings announcement. The final example considers stock split studies. In this analysis we implicitly exclude securities whose price on announcement is less than the prior average stock price. We apply our results to this case, and find that the condition that the security forms part of our positive stock split sample suffices to explain the upward trend in event-related cumulated excess return in the preannouncement period.     

Equity Carve-Outs and Managerial Discretion

This study proposes a managerial discretion hypothesis of equity carve-outs in which managers value control over assets and are reluctant to carve out subsidiaries. Thus, managers undertake carve-outs only when the firm is capital constrained. Consistent with this hypothesis, firms that carve out subsidiaries exhibit poor operating performance and high leverage prior to carve-outs. Also consistent with this hypothesis, in carve-outs wherein funds raised are used to pay down debt, the average excess stock return of + 6.63 percent is significantly greater than the average excess stock return of −0.01 percent for carve-outs wherein funds are retained for investment purposes.     

Characteristics, Covariances, and Average Returns: 1929 to 1997

The value premium in U.S. stock returns is robust. The positive relation between average return and book-to-market equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers. A three-factor risk model explains the value premium better than the hypothesis that the book-to-market characteristic is compensated irrespective of risk loadings.     

The Presidential Puzzle: Political Cycles and the Stock Market

The excess return in the stock market is higher under Democratic than Republican presidencies: 9 percent for the value‐weighted and 16 percent for the equal‐weighted portfolio. The difference comes from higher real stock returns and lower real interest rates, is statistically significant, and is robust in subsamples. The difference in returns is not explained by business‐cycle variables related to expected returns, and is not concentrated around election dates. There is no difference in the riskiness of the stock market across presidencies that could justify a risk premium. The difference in returns through the political cycle is therefore a puzzle.     

Effect of Analysts' Optimism on Estimates of the Expected Rate of Return Implied by Earnings Forecasts

Recent literature has used analysts' earnings forecasts, which are known to be optimistic, to estimate implied expected rates of return, yielding upwardly biased estimates. We estimate that the bias, computed as the difference between the estimates of the implied expected rate of return based on analysts' earnings forecasts and estimates based on current earnings realizations, is 2.84%. The importance of this bias is illustrated by the fact that several extant studies estimate an equity premium in the vicinity of 3%, which would be eliminated by the removal of the bias. We illustrate the point that cross‐sample differences in the bias may lead to the erroneous conclusion that cost of capital differs across these samples by showing that analysts' optimism, and hence, bias in the implied estimates of the expected rate of return, differs with firm size and with analysts' recommendation. As an important aside, we show that the bias in a value‐weighted estimate of the implied equity premium is 1.60% and that the unbiased value‐weighted estimate of this premium is 4.43%.     

Detecting news in aggregate accounting earnings: implications for stock market valuation

How much news is there in aggregate accounting earnings? I provide evidence that earnings changes at the stock market level are correlated with new information about not only expected future cash flows but also discount rates. A comprehensive investigation of the link to discount rates reveals that aggregate earnings changes are tied to news about all components of the expected future stock market return, i.e., the real riskless rate, expected inflation, and the expected equity risk premium. Over the sample period studied, cash flow news and discount rate news in aggregate earnings changes covary positively and have offsetting impacts on stock market prices. As a result, stock market prices appear to be insensitive to aggregate earnings changes. The findings highlight the importance of separating cash flow news from discount rate news when evaluating the information content of accounting earnings at the stock market level. Overall, my study sheds new light on the informativeness and relevance of accounting earnings for valuation at the stock market level.     

Financial reporting for employee stock options: liabilities or equity?

This study seeks to determine whether employee stock options share key characteristics of liabilities or equity. Consistent with warrant pricing theory, we find that common equity risk and expected return are negatively associated with the extent to which a firm has outstanding employee stock options, which is opposite to the association for liabilities. We also find the following. (1) The association is positive for firms that reprice options and less negative for firms that have options with longer remaining terms to maturity, which indicates that some employee stock options have characteristics that make them more similar to liabilities. (2) Leverage measured based on treating options as equity has a stronger positive relation with common equity risk than leverage measured based on treating options as liabilities. (3) The sensitivity of employee stock option value to changes in asset value mirrors that of common equity value and is opposite to that of liability value. Also, we find that, unlike liabilities, employee stock options have substantially higher risk and expected return than common equity. Our findings are not consistent with classifying employee stock options as liabilities for financial reporting if classification were based on the directional association of a claim with common equity risk and expected return. Rather, our findings suggest the options act more like another type of equity.     

Conditional Skewness in Asset Pricing Tests

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.     

Isolating the disaster risk premium with equity options

The US equity risk premium is approximated with a mean unhedged equity return. I utilize out-of-the-money put options to obtain a hedged equity return, which allows me to quantify the disaster risk premium as the difference between the means of unhedged and hedged equity returns. I demonstrate that a substantial fraction of the U.S. equity risk premium over the period from 1996 to 2016 is attributed to disasters defined as stock price depreciations below a pre-specified strike price. Employing alternative hedging schemes increases the contribution of disasters to the equity risk premium.     

The UK Equity Premium: 1901–2004

Abstract:  This paper examines the UK equity premium over more than a century using dividend growth to estimate expectations of capital gains employing the approach of Fama and French (2002) . Over recent decades estimated equity premia implied by dividend growth have been much lower than that produced by average stock returns for the UK market as a whole; a finding corroborated by all economic sub-sectors. The empirical analysis suggests this is primarily due to a declining discount rate, during the latter part of the 20th century, which would rationally stimulate unanticipated equity price rises during this period. Thus, I conclude that historical stock returns over recent decades have been above investors' expectations.     

Pricing assets with stochastic cash-flow growth

We model the time series behavior of dividend growth rates, as well as the profitability rate, with a variety of autoregressive moving-average processes, and use the capital asset pricing model (CAPM) to derive the appropriate discount rate. One of the most important implications of this research is that the rate of return beta changes with the time to maturity of the expected cash flow, and the degree of mean reversion displayed by the growth rate. We explore the consequences of this observation for three different strands of the literature. The first is for the value premium anomaly, the second for stock valuation and learning about long-run profitability, and the third is for the St. Petersburg paradox. One of the most surprising results is that the CAPM implies a higher rate of return beta for value stocks than growth stocks. Therefore, value stocks must have higher expected returns, and this is what is required theoretically in order to explain the well-known value premium anomaly.