Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market 3, size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in 3 that is unrelated to size, the relation between market /3 and average return is flat, even when 3 is the only explanatory variable. THE ASSET-PRICING MODEL OF Sharpe (1964), Lintner (1965), and Black (1972) has long shaped the way academics and practitioners think about average returns and risk. The central prediction of the model is that the market portfolio of invested wealth is mean-variance efficient in the sense of Markowitz (1959). The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market O3s (the slope in the regression of a security's return on the market's return), and (b) market O3s suffice to describe the cross-section of expected returns. There are several empirical contradictions of the Sharpe-Lintner-Black (SLB) model. The most prominent is the size effect of Banz (1981). He finds that market equity, ME (a stock's price times shares outstanding), adds to the explanation of the cross-section of average returns provided by market Os. Average returns on small (low ME) stocks are too high given their f estimates, and average returns on large stocks are too low. Another contradiction of the SLB model is the positive relation between leverage and average return documented by Bhandari (1988). It is plausible that leverage is associated with risk and expected return, but in the SLB model, leverage risk should be captured by market S. Bhandari finds, howev er, that leverage helps explain the cross-section of average stock returns in tests that include size (ME) as well as A. Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) find that average returns on U.S. stocks are positively related to the ratio of a firm's book value of common equity, BE, to its market value, ME. Chan, Hamao, and Lakonishok (1991) find that book-to-market equity, BE/ME, also has a strong role in explaining the cross-section of average returns on Japanese stocks.

http://www.business.unr.edu/faculty/liuc/files/badm742/fama_french_1992.pdf

The Cross‐Section of Expected Stock Returns

Using daily stock returns: The case of event studies

This paper studies the cross-sectional properties of return forecasts derived from Fama-MacBeth regressions. These forecasts mimic how an investor could, in real time, combine many firm characteristics to obtain a composite estimate of a stockâs expected return. Empirically, the forecasts vary substantially across stocks and have strong predictive power for actual returns. For example, using ten-year rolling estimates of Fama- MacBeth slopes and a cross-sectional model with 15 firm characteristics (all based on low-frequency data), the expected-return estimates have a cross-sectional standard deviation of 0.87% monthly and a predictive slope for future monthly returns of 0.74, with a standard error of 0.07.

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The Cross-section of Expected Stock Returns

The underpricing of initial public offerings (IPOs) that has been widely documented appears to be a short-run phenomenon. Issuing firms during 1975-84 substantially underperformed a sample of matching firms from the closing price on the first day of public trading to their three-year anniversaries. There is substantial variation in the underperformance year-to-year and across industries, with companies that went public in high-volume years faring the worst. The patterns are consistent with an IPO market in which (1) investors are periodically overoptimistic about the earnings potential of young growth companies, and (2) firms take advantage of these "windows of opportunity." NUMEROUS STUDIES HAVE DOCUMENTED two anomalies in the pricing of initial public offerings (IPOs) of common stock: (1) the (short-run) underpricing phenomenon, and (2) the "hot issue" market phenomenon. Measured from the offering price to the market price at the end of the first day of trading, IPOs produce an average initial return that has been estimated at 16.4%.1 Furthermore, the extent of this underpricing is highly cyclical, with some periods, lasting many months at a time, in which the average initial return is much higher.2 In this paper, I document a third anomaly: in the long-run, initial public offerings appear to be overpriced. Using a sample of 1,526 IPOs that went public in the U.S. in the 1975-84 period, I find that in the 3 years after going public these firms significantly underperformed a set of comparable firms matched by size and industry.

https://www.jstor.org/stable/pdfplus/2328687.pdf

The Long‐Run Performance of initial Public Offerings

A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex-post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex-post interdaily volatility measurements based on high-frequency intradaily data are also discussed.

https://faculty.washington.edu/ezivot/econ589//////AndersenBollerslevIER1998.pdf

Answering the skeptics: yes, standard volatility models do provide accurate forecasts*

Risk measurement when shares are subject to infrequent trading

Investors have too often extrapolated from recent experience. In the 1950s, who but the most rampant optimist would have dreamt that over the next fifty years the real return on equities would be 9% per year? Yet this is what happened in the U.S. stock market. The optimists triumphed. However, as Don Marquis observed, an optimist is someone who never had much experience. The authors of this book extend our experience across regions and across time. They present a comprehensive and consistent analysis of investment returns for equities, bonds, bills, currencies and inflation, spanning sixteen countries, from the end of the nineteenth century to the beginning of the twenty-first. This is achieved in a clear and simple way, with over 130 color diagrams that make comparison easy.Crucially, the authors analyze total returns, including reinvested income. They show that some historical indexes overstate long-term performance because they are contaminated by survivorship bias and that long-term stock returns are in most countries seriously overestimated, due to a focus on periods that with hindsight are known to have been successful.The book also provides the first comprehensive evidence on the long-term equity risk premium--the reward for bearing the risk of common stocks. The authors reveal whether the United States and United Kingdom have had unusually high stock market returns compared to other countries. The book covers the U.S., the U.K., Japan, France, Germany, Canada, Italy, Spain, Switzerland, Australia, the Netherlands, Sweden, Belgium, Ireland, Denmark, and South Africa.Triumph of the Optimists is required reading for investment professionals, financial economists, and investors. It will be the definitive reference in the field and consulted for years to come.

Triumph of the Optimists: 101 Years of Global Investment Returns

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Triumph of the Optimists

Event study methodologies and the size effect

We use a new database of long-run stock, bond, bill, inflation, and currency returns to estimate the equity risk premium for 17 countries and a world index over a 106-year interval. Taking U.S. Treasury bills (government bonds) as the risk-free asset, the annualised equity premium for the world index was 4.7% (4.0%). We report the historical equity premium for each market in local currency and US dollars, and decompose the premium into dividend growth, multiple expansion, the dividend yield, and changes in the real exchange rate. We infer that investors expect a premium on the world index of around 3-3 1/2% on a geometric mean basis, or approximately 4 1/2-5% on an arithmetic basis.

/pdf/the-worldwide-equity-premium-a-smaller-puzzle-2i1wq9nv30.pdf

Elroy Dimson

Papers

Risk measurement when shares are subject to infrequent trading

Triumph of the Optimists: 101 Years of Global Investment Returns

Triumph of the Optimists

Event study methodologies and the size effect

The Worldwide Equity Premium: A Smaller Puzzle