Abstract
We present additional evidence on the risk and return of stocks in the USA and globally in the 1997–2009 period. We use a stock selection model incorporating fundamental data, momentum, and analysts’ expectations and create portfolios using fundamental and statistically based risk models. We find additional evidence to support the use of multifactor models for portfolio construction and risk control. We created portfolios for the January 1997 to December 2009 period. We report three conclusions: (1) a stock selection model incorporating reported fundamental data, such as earnings, book value, cash flow, and sales, and analysts’ earnings forecasts and revisions and momentum can identify mispriced securities; (2) statistically based risk models produce a more effective return-to-risk portfolio measures than fundamentally based risk models; and (3) the global portfolio returns of the multifactor risk-controlled portfolio returns dominate USA-only portfolios.
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Notes
- 1.
Chan et al. (1991) define cash as the sum of earnings and depreciation without explicit correction for other noncash revenue or expenses.
- 2.
One finds the Price/Earnings, Price/Book, Price/Sales listed among the accounting anomalies in Levy (1999), p. 434. Levy also discusses the dividend yield as a (positive) stock anomaly. Malkiel (1996) cites evidence in support of buying low P/E, low P/B, and high D/P (dividend yield) stocks for outperformance, provided the low P/E stocks have modest growth prospects (pp. 204–210). Malkiel speaks of a “double bonus”; that is, if growth occurs, earnings increase and the price-to-earnings multiple may increase, further driving up the price. Of course, should growth fail to occur, both earnings and the P/E multiple may fall.
- 3.
The use of nonfinancial stocks led to a customized index for the Markowitz Global Portfolio Research Group (GPRD) analysis. The Chan et al. and an initial Guerard presentation occurred in September 1991 at the Berkeley Program in Finance, Santa Barbara, on Fundamental Analysis. Bill Ziemba presented a very interesting study comparing US and Japanese fundamental strategies at the same Berkeley Program meeting. Markowitz refers to this meeting in his Nobel Prize lecture (1991). Ziemba and Schwartz (1993) used capitalization-weighted regressions. The Chan et al., Guerard, and Ziemba studies found statistical significance with expectation and reported fundamental data.
- 4.
Fifty-seven factors are used in the model. See Haugen and Baker(1996) for definitions.
- 5.
In Fama and French (2008) p. 1668, ad hoc cross-section regressions are used in an attempt to explain the cross-sectional structure of stock returns. They report t-statistics as large as −8.59, but no attempt is made to investigate the out-of-sample predictive power of their regressions. Fama and French further research book-to-price and momentum anomalies in their 1995 and 2008 studies.
- 6.
See, for example, Fama and French (1992).
- 7.
Haugen and Baker (2010) address the argument that these measures of cheapness in the regressions would make the methodology prone to multicolinearity. Significant problems associated with multicollinearity should result in instability in the estimated regression coefficients from month to month. However, Haugen and Baker (2010) point to their mean values for these variable coefficients are very large relative to their standard errors and argue that multicollinearity is clearly not a significant problem in their analysis.
- 8.
With unconstrained optimization, with 24 monthly observations and 1000 stocks, there is no unique solution. However, given the constraints provided above, unique solutions exist.
- 9.
Haugen and Baker (2010, p. 14)actually close their work with the following observations: “High-return stock deciles tend to be relatively large companies with low risk and they have positive market price momentum. The profitability of high-return stocks is good and getting better. The low-return counterparts to these stocks have the opposite profile. A rational investor would likely find the high-return profile very attractive and the low-return profile very scary. Given the evidence, and this evidence will be reproduced by others, the following conclusions are undeniable.
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The cross-sectional payoff to risk is highly negative.
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The longitudinal payoff to risk is highly positive.
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The most attractive stock portfolios have the highest expected returns.
-
The scariest stock portfolios have the lowest expected returns.
The stock market is inefficient. “Case closed.”
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- 10.
Guerard (2012) decomposed the MQ variable into (1) price momentum, (2) the consensus analysts’ forecasts efficiency variable, CIBF, which itself is composed of forecasted earnings yield, EP, revisions, EREV, and direction of revisions, EB, identified as breadth, Wheeler (1994), and (3) the stock standard deviation, identified as a variable with predictive power regarding the stock price-earnings multiple. Guerard reported that the consensus analysts’ forecast variable dominated analysts’ forecasted earnings yield, as measured by I/B/E/S 1-year-ahead forecasted earnings yield, FEP, revisions, and breadth. Guerard reported domestic (US) evidence that the predicted earnings yield is incorporated into the stock price through the earnings yield risk index. Moreover, CIBF dominates the historic low price-to-earnings effect, or high earnings-to-price, PE.
- 11.
Cragg and Malkiel (1968) created a database of five forecasters of long-term earnings forecasts for 185 companies in 1962 and 1963. These five forecast firms included two New York City banks (trust departments), an investment banker, a mutual fund manager, and the final firm was a broker and an investment advisor. The Cragg and Malkiel (1968) forecasts were 5-year average annual growth rates. The earnings forecasts were highly correlated with one another, the highest paired correlation was 0.889 (in 1962) and the lowest paired correlation was 0.450 (in 1963) with most correlations exceeding 0.7. They calculated used the Thiel Inequality Coefficient (1966) to measure the efficiency of the financial forecasts and found that the correlations of predicted and realized earnings growth were low, although most were statistically greater than zero. The TICs were large, according to Cragg and Malkiel (1968), although they were less than 1.0 (showing better than no-change forecasting). The TICS were lower (better) within sectors; the forecasts in electronics and electric utility firms were best and foods and oils were the worst firms to forecast earnings growth. Elton and Gruber (1972) built upon the Cragg and Malkiel study and found similar results. That is, a simple exponentially weighted moving average was a better forecasting model of annual earnings than additive or multiplicative exponential smoothing models with trend or regression models using time as an independent variable. Indeed, a very good model was a naïve model, which assumed a no-change in annual earnings per shares with the exceptional of the prior change had occurred in earnings. One can clearly see the random walk with drift concept of earnings in the Elton and Gruber (1972). Elton and Gruber compared the naïve and time series forecasts to three financial service firms, and found for their 180 firm sample that two of the three firms were better forecasters than the naïve models. Elton, Gruber, and Gultekin (1981) build upon the Cragg and Malkiel (1968) and Elton and Gruber (1972) results and create an earnings forecasting database that evolves to include over 16,000 companies, the Institutional Brokerage Estimation Services, Inc. (I/B/E/S). Elton et al. (1981) find than earnings revisions, more than the earnings forecasts, determine the securities that will outperform the market.Found the I/B/E/S consensus forecasts were not statistically different than random walk with drift time series forecasts for 648 firms during the 1982–1985 period. Lim (2001), using the I/B/E/S Detailed database from 1984 to December 1996, found forecast bias was associated with small and more volatile stocks, experienced poor past stock returns, and had prior negative earnings surprises. Moreover, Lim (2001) found that relative bias was negative associated with the size of the number of analysts in the brokerage firm. That is, smaller firms with fewer analysts, often with more stale data, produced more optimistic forecasts. Keane and Runkle (1998) found during the 1983–1991 period that analysts’ forecasts were rational, once discretionary special charges are removed. The Keane and Runkle (1998) study is one of the very few studies finding rationality of analysts’ forecasts; most find analysts are optimistic. Further work by Wheeler (1994) will find that firms where analysts agree with the direction of earnings revisions, denoted breadth, will outperform stocks with lesser agreement of earnings revisions. Guerard et al. (1997) combined the work of Elton et al. (1981) and Wheeler (1994) to create a better earnings forecasting model, CTEF, which we use in this analysis. The CTEF variable continues to produce statistically significant excess return in backtest and in identifying real-time security mispricing, see Guerard (2012). See Brown (1999, 2008) and Ramnath,Rock, and Shane (2008) for an extensive review of financial analysts’ forecasting efficiences.
- 12.
The ICs on the analysts’ forecast variable, CTEF, and price momentum variable, PM, were lower than in the US universe, reported in Guerard et al. (2012).
- 13.
See Markowitz (1959), Chapter 9.
- 14.
Harry Markowitz reminds readers that he discussed the possibility of looking at security returns relative to index returns in Chapter 4, footnote 1, page 100, of Portfolio Selection (1959).
- 15.
See Chapter 2 of Guerard (2010) for a history of multi-index and multifactor risk models.
- 16.
Note that when symbols are assigned their proper meaning the first equation below simply states ρ = ρ.
- 17.
Although not perhaps in the Treynor spirit a more useful index might be δ = (r p (i) − r 0)/ (a + b r m*), the ratio of excess to market returns, in lieu of the original form TI = (r p (i) − r 0)/b.
- 18.
In Sharpe (1966) it is somewhat incorrectly stated that the Sharpe ratio is equivalent to the Treynor ratio. As is seen from the discussion above noting in particular the modification in footnote 17, this is not true; the Treynor ratio as modified in that footnote is merely the ratio of excess returns divided by market returns, not the standard deviation.
- 19.
The authors are indebted to Vishhu Anand, of Axioma, who ran the Axioma attribution analysis based on the Axioma Fundamental Risk Model.
- 20.
Readers may question the use of a 12-year backtesting period. The USER model was tested with the Barra USE3 Model for the 1980–2009 period and asset selection of 449 basis points, annualized, is reported. The t-value on the USER variable is 4.60, which is highly statistically significant. Stone and Guerard (2010b) found good stock selection returns in the USA and Japan, 1980–2005, using similar models.
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Dhrymes, P.J., Guerard, J.B. (2017). Returns, Risk, Portfolio Selection, and Evaluation. In: Guerard, Jr., J. (eds) Portfolio Construction, Measurement, and Efficiency. Springer, Cham. https://doi.org/10.1007/978-3-319-33976-4_4
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